1,0,0,0,0.426624," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((C*sec(d*x + c)^4 + A*sec(d*x + c)^2)*(b*sec(d*x + c))^(1/3), x)","F",0
2,0,0,0,0.447514," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((C*sec(d*x + c)^3 + A*sec(d*x + c))*(b*sec(d*x + c))^(1/3), x)","F",0
3,0,0,0,0.422989," ","integrate((b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3), x)","F",0
4,0,0,0,0.431163," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((C*cos(d*x + c)*sec(d*x + c)^2 + A*cos(d*x + c))*(b*sec(d*x + c))^(1/3), x)","F",0
5,0,0,0,0.438058," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2*sec(d*x + c)^2 + A*cos(d*x + c)^2)*(b*sec(d*x + c))^(1/3), x)","F",0
6,0,0,0,0.575035," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{5} + 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((C*b*sec(d*x + c)^5 + A*b*sec(d*x + c)^3)*(b*sec(d*x + c))^(1/3), x)","F",0
7,0,0,0,0.428748," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{4} + 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((C*b*sec(d*x + c)^4 + A*b*sec(d*x + c)^2)*(b*sec(d*x + c))^(1/3), x)","F",0
8,0,0,0,0.460693," ","integrate((b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{3} + 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((C*b*sec(d*x + c)^3 + A*b*sec(d*x + c))*(b*sec(d*x + c))^(1/3), x)","F",0
9,0,0,0,0.455367," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + 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((C*b*cos(d*x + c)*sec(d*x + c)^3 + A*b*cos(d*x + c)*sec(d*x + c))*(b*sec(d*x + c))^(1/3), x)","F",0
10,0,0,0,0.472390," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + 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((C*b*cos(d*x + c)^2*sec(d*x + c)^3 + A*b*cos(d*x + c)^2*sec(d*x + c))*(b*sec(d*x + c))^(1/3), x)","F",0
11,0,0,0,0.424412," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b}, x\right)"," ",0,"integral((C*sec(d*x + c)^3 + A*sec(d*x + c))*(b*sec(d*x + c))^(2/3)/b, x)","F",0
12,0,0,0,0.426481," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(2/3)/b, x)","F",0
13,0,0,0,0.488792," ","integrate((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(2/3)/(b*sec(d*x + c)), x)","F",0
14,0,0,0,0.421645," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)*sec(d*x + c)^2 + A*cos(d*x + c))*(b*sec(d*x + c))^(2/3)/(b*sec(d*x + c)), x)","F",0
15,0,0,0,0.442981," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2*sec(d*x + c)^2 + A*cos(d*x + c)^2)*(b*sec(d*x + c))^(2/3)/(b*sec(d*x + c)), x)","F",0
16,0,0,0,0.417047," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(2/3)/b^2, x)","F",0
17,0,0,0,0.454393," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(2/3)/(b^2*sec(d*x + c)), x)","F",0
18,0,0,0,0.445338," ","integrate((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(2/3)/(b^2*sec(d*x + c)^2), x)","F",0
19,0,0,0,0.468551," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\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((C*cos(d*x + c)*sec(d*x + c)^2 + A*cos(d*x + c))*(b*sec(d*x + c))^(2/3)/(b^2*sec(d*x + c)^2), x)","F",0
20,0,0,0,0.492405," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{2}\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((C*cos(d*x + c)^2*sec(d*x + c)^2 + A*cos(d*x + c)^2)*(b*sec(d*x + c))^(2/3)/(b^2*sec(d*x + c)^2), x)","F",0
21,0,0,0,0.471630," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{3} + 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((C*b*sec(d*x + c)^3 + A*b*sec(d*x + c))*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
22,0,0,0,0.437973," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m, x)","F",0
23,0,0,0,0.446127," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
24,0,0,0,0.456120," ","integrate(sec(d*x+c)^m*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m/(b*sec(d*x + c)), x)","F",0
25,0,0,0,0.465027," ","integrate(sec(d*x+c)^m*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m/(b*sec(d*x + c)), x)","F",0
26,0,0,0,0.440304," ","integrate(sec(d*x+c)^m*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}}{b^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m/(b^2*sec(d*x + c)^2), x)","F",0
27,0,0,0,0.442571," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
28,0,0,0,0.430159," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((C*sec(d*x + c)^4 + A*sec(d*x + c)^2)*(b*sec(d*x + c))^n, x)","F",0
29,0,0,0,0.596213," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((C*sec(d*x + c)^3 + A*sec(d*x + c))*(b*sec(d*x + c))^n, x)","F",0
30,0,0,0,0.432997," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n, x)","F",0
31,0,0,0,0.440040," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((C*cos(d*x + c)*sec(d*x + c)^2 + A*cos(d*x + c))*(b*sec(d*x + c))^n, x)","F",0
32,0,0,0,0.448790," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((C*cos(d*x + c)^2*sec(d*x + c)^2 + A*cos(d*x + c)^2)*(b*sec(d*x + c))^n, x)","F",0
33,0,0,0,0.446636," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{3}\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((C*cos(d*x + c)^3*sec(d*x + c)^2 + A*cos(d*x + c)^3)*(b*sec(d*x + c))^n, x)","F",0
34,0,0,0,0.472375," ","integrate(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{2}\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^4 + A*sec(d*x + c)^2)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
35,0,0,0,0.461689," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + A*sec(d*x + c))*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
36,0,0,0,0.442045," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
37,0,0,0,0.469382," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n/sqrt(sec(d*x + c)), x)","F",0
38,0,0,0,0.450219," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(3/2), x)","F",0
39,0,0,0,0.455313," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(5/2), x)","F",0
40,0,0,0,0.458974," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
41,0,0,0,0.446222," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*(b*sec(d*x + c))^(2/3), x)","F",0
42,0,0,0,0.475168," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + B*sec(d*x + c)^2 + A*sec(d*x + c))*(b*sec(d*x + c))^(2/3), x)","F",0
43,0,0,0,0.436335," ","integrate((b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3), x)","F",0
44,0,0,0,0.469405," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*(b*sec(d*x + c))^(2/3), x)","F",0
45,0,0,0,0.455457," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
46,0,0,0,0.459239," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{3}\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((C*cos(d*x + c)^3*sec(d*x + c)^2 + B*cos(d*x + c)^3*sec(d*x + c) + A*cos(d*x + c)^3)*(b*sec(d*x + c))^(2/3), x)","F",0
47,0,0,0,0.429392," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{5} + 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((C*b*sec(d*x + c)^5 + B*b*sec(d*x + c)^4 + A*b*sec(d*x + c)^3)*(b*sec(d*x + c))^(1/3), x)","F",0
48,0,0,0,0.456344," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{4} + 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((C*b*sec(d*x + c)^4 + B*b*sec(d*x + c)^3 + A*b*sec(d*x + c)^2)*(b*sec(d*x + c))^(1/3), x)","F",0
49,0,0,0,0.463908," ","integrate((b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{3} + 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((C*b*sec(d*x + c)^3 + B*b*sec(d*x + c)^2 + A*b*sec(d*x + c))*(b*sec(d*x + c))^(1/3), x)","F",0
50,0,0,0,0.469415," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + 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((C*b*cos(d*x + c)*sec(d*x + c)^3 + 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
51,0,0,0,0.447942," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + 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((C*b*cos(d*x + c)^2*sec(d*x + c)^3 + 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
52,0,0,0,0.436479," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + B b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3*sec(d*x + c)^3 + B*b*cos(d*x + c)^3*sec(d*x + c)^2 + A*b*cos(d*x + c)^3*sec(d*x + c))*(b*sec(d*x + c))^(1/3), x)","F",0
53,0,0,0,0.421943," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + B*sec(d*x + c)^2 + A*sec(d*x + c))*(b*sec(d*x + c))^(1/3)/b, x)","F",0
54,0,0,0,0.456409," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{b}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)/b, x)","F",0
55,0,0,0,0.471474," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)/(b*sec(d*x + c)), x)","F",0
56,0,0,0,0.433369," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{b}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)/b, x)","F",0
57,0,0,0,0.423236," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + B*sec(d*x + c)^2 + A*sec(d*x + c))*(b*sec(d*x + c))^(1/3)/b, x)","F",0
58,0,0,0,0.424737," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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{1}{3}}}{b}, x\right)"," ",0,"integral((C*sec(d*x + c)^4 + B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*(b*sec(d*x + c))^(1/3)/b, x)","F",0
59,0,0,0,0.451811," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)/b^2, x)","F",0
60,0,0,0,0.459945," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2} \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)/(b^2*sec(d*x + c)), x)","F",0
61,0,0,0,0.468589," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)/(b^2*sec(d*x + c)^2), x)","F",0
62,0,0,0,0.483716," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2} \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)/(b^2*sec(d*x + c)), x)","F",0
63,0,0,0,0.447114," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)/b^2, x)","F",0
64,0,0,0,0.438663," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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}}}{b^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^3 + B*sec(d*x + c)^2 + A*sec(d*x + c))*(b*sec(d*x + c))^(2/3)/b^2, x)","F",0
65,0,0,0,0.432562," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{3} + 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((C*b*sec(d*x + c)^3 + 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
66,0,0,0,0.479359," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m, x)","F",0
67,0,0,0,0.442155," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
68,0,0,0,0.439415," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
69,0,0,0,0.444320," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}}{b \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
70,0,0,0,0.473116," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}}{b^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
71,0,0,0,0.440950," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
72,0,0,0,0.462590," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*(b*sec(d*x + c))^n, x)","F",0
73,0,0,0,0.471408," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + B*sec(d*x + c)^2 + A*sec(d*x + c))*(b*sec(d*x + c))^n, x)","F",0
74,0,0,0,0.435604," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n, x)","F",0
75,0,0,0,0.433481," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*(b*sec(d*x + c))^n, x)","F",0
76,0,0,0,0.467319," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
77,0,0,0,0.448032," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{3}\right)} \left(b \sec\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((C*cos(d*x + c)^3*sec(d*x + c)^2 + B*cos(d*x + c)^3*sec(d*x + c) + A*cos(d*x + c)^3)*(b*sec(d*x + c))^n, x)","F",0
78,0,0,0,0.460255," ","integrate(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{4} + 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} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^4 + B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
79,0,0,0,0.437451," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + 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
80,0,0,0,0.434443," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
81,0,0,0,0.466355," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sqrt(sec(d*x + c)), x)","F",0
82,0,0,0,0.446365," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(3/2), x)","F",0
83,0,0,0,0.436949," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(5/2), x)","F",0
84,1,147,0,0.482689," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, C\right)} a \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, A + 3 \, C\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 \, C\right)} a \cos\left(d x + c\right)^{4} + 15 \, {\left(4 \, A + 3 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 4 \, C\right)} a \cos\left(d x + c\right)^{2} + 30 \, C a \cos\left(d x + c\right) + 24 \, C a\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(4*A + 3*C)*a*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*A + 3*C)*a*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(5*A + 4*C)*a*cos(d*x + c)^4 + 15*(4*A + 3*C)*a*cos(d*x + c)^3 + 8*(5*A + 4*C)*a*cos(d*x + c)^2 + 30*C*a*cos(d*x + c) + 24*C*a)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
85,1,129,0,0.452617," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A + 3 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, A + 3 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(3 \, A + 2 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 3 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, C a \cos\left(d x + c\right) + 6 \, C a\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(4*A + 3*C)*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*A + 3*C)*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(3*A + 2*C)*a*cos(d*x + c)^3 + 3*(4*A + 3*C)*a*cos(d*x + c)^2 + 8*C*a*cos(d*x + c) + 6*C*a)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
86,1,107,0,0.448179," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + C\right)} a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A + C\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 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, C a \cos\left(d x + c\right) + 2 \, C a\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(2*A + C)*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*A + C)*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(3*A + 2*C)*a*cos(d*x + c)^2 + 3*C*a*cos(d*x + c) + 2*C*a)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
87,1,101,0,0.490923," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, A a d x \cos\left(d x + c\right)^{2} + {\left(2 \, A + C\right)} a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, A + C\right)} a \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a \cos\left(d x + c\right) + C a\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*A*a*d*x*cos(d*x + c)^2 + (2*A + C)*a*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*A + C)*a*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*a*cos(d*x + c) + C*a)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
88,1,86,0,0.491158," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, A a d x \cos\left(d x + c\right) + C a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - C a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a \cos\left(d x + c\right) + C a\right)} \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) + C*a*cos(d*x + c)*log(sin(d*x + c) + 1) - C*a*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(A*a*cos(d*x + c) + C*a)*sin(d*x + c))/(d*cos(d*x + c))","B",0
89,1,63,0,0.449390," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(A + 2 \, C\right)} a d x + C a \log\left(\sin\left(d x + c\right) + 1\right) - C a \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(A a \cos\left(d x + c\right) + 2 \, A a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((A + 2*C)*a*d*x + C*a*log(sin(d*x + c) + 1) - C*a*log(-sin(d*x + c) + 1) + (A*a*cos(d*x + c) + 2*A*a)*sin(d*x + c))/d","A",0
90,1,56,0,0.431061," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(A + 2 \, C\right)} a d x + {\left(2 \, A a \cos\left(d x + c\right)^{2} + 3 \, A a \cos\left(d x + c\right) + 2 \, {\left(2 \, A + 3 \, C\right)} a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(A + 2*C)*a*d*x + (2*A*a*cos(d*x + c)^2 + 3*A*a*cos(d*x + c) + 2*(2*A + 3*C)*a)*sin(d*x + c))/d","A",0
91,1,76,0,0.442572," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 4 \, C\right)} a d x + {\left(6 \, A a \cos\left(d x + c\right)^{3} + 8 \, A a \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 4 \, C\right)} a \cos\left(d x + c\right) + 8 \, {\left(2 \, A + 3 \, C\right)} a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*A + 4*C)*a*d*x + (6*A*a*cos(d*x + c)^3 + 8*A*a*cos(d*x + c)^2 + 3*(3*A + 4*C)*a*cos(d*x + c) + 8*(2*A + 3*C)*a)*sin(d*x + c))/d","A",0
92,1,94,0,0.444814," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, A + 4 \, C\right)} a d x + {\left(24 \, A a \cos\left(d x + c\right)^{4} + 30 \, A a \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, A + 5 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, A + 4 \, C\right)} a \cos\left(d x + c\right) + 16 \, {\left(4 \, A + 5 \, C\right)} a\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(3*A + 4*C)*a*d*x + (24*A*a*cos(d*x + c)^4 + 30*A*a*cos(d*x + c)^3 + 8*(4*A + 5*C)*a*cos(d*x + c)^2 + 15*(3*A + 4*C)*a*cos(d*x + c) + 16*(4*A + 5*C)*a)*sin(d*x + c))/d","A",0
93,1,161,0,0.436347," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, A + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, {\left(25 \, A + 18 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 15 \, {\left(4 \, A + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 4 \, {\left(5 \, A + 9 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 30 \, C a^{2} \cos\left(d x + c\right) + 12 \, C a^{2}\right)} \sin\left(d x + c\right)}{120 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/120*(15*(4*A + 3*C)*a^2*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*A + 3*C)*a^2*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(4*(25*A + 18*C)*a^2*cos(d*x + c)^4 + 15*(4*A + 3*C)*a^2*cos(d*x + c)^3 + 4*(5*A + 9*C)*a^2*cos(d*x + c)^2 + 30*C*a^2*cos(d*x + c) + 12*C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
94,1,141,0,0.442865," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(12 \, A + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(12 \, A + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(3 \, A + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 16 \, C a^{2} \cos\left(d x + c\right) + 6 \, C a^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(12*A + 7*C)*a^2*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(12*A + 7*C)*a^2*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(3*A + 2*C)*a^2*cos(d*x + c)^3 + 3*(4*A + 7*C)*a^2*cos(d*x + c)^2 + 16*C*a^2*cos(d*x + c) + 6*C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
95,1,131,0,0.459667," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{6 \, A a^{2} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A + C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A + C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(3 \, A + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, C a^{2} \cos\left(d x + c\right) + C a^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(6*A*a^2*d*x*cos(d*x + c)^3 + 3*(2*A + C)*a^2*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*A + C)*a^2*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*((3*A + 5*C)*a^2*cos(d*x + c)^2 + 3*C*a^2*cos(d*x + c) + C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
96,1,129,0,0.460321," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{8 \, A a^{2} d x \cos\left(d x + c\right)^{2} + {\left(2 \, A + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, A + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + 4 \, C a^{2} \cos\left(d x + c\right) + C a^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(8*A*a^2*d*x*cos(d*x + c)^2 + (2*A + 3*C)*a^2*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*A + 3*C)*a^2*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a^2*cos(d*x + c)^2 + 4*C*a^2*cos(d*x + c) + C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
97,1,116,0,0.455488," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(3 \, A + 2 \, C\right)} a^{2} d x \cos\left(d x + c\right) + 2 \, C a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, C a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(A a^{2} \cos\left(d x + c\right)^{2} + 4 \, A a^{2} \cos\left(d x + c\right) + 2 \, C a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((3*A + 2*C)*a^2*d*x*cos(d*x + c) + 2*C*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) - 2*C*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + (A*a^2*cos(d*x + c)^2 + 4*A*a^2*cos(d*x + c) + 2*C*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
98,1,95,0,0.465201," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{6 \, {\left(A + 2 \, C\right)} a^{2} d x + 3 \, C a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, C a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{2} \cos\left(d x + c\right)^{2} + 3 \, A a^{2} \cos\left(d x + c\right) + {\left(5 \, A + 3 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(6*(A + 2*C)*a^2*d*x + 3*C*a^2*log(sin(d*x + c) + 1) - 3*C*a^2*log(-sin(d*x + c) + 1) + 2*(A*a^2*cos(d*x + c)^2 + 3*A*a^2*cos(d*x + c) + (5*A + 3*C)*a^2)*sin(d*x + c))/d","A",0
99,1,86,0,0.443768," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A + 12 \, C\right)} a^{2} d x + {\left(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 16 \, A a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A + 4 \, C\right)} a^{2} \cos\left(d x + c\right) + 16 \, {\left(2 \, A + 3 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(7*A + 12*C)*a^2*d*x + (6*A*a^2*cos(d*x + c)^3 + 16*A*a^2*cos(d*x + c)^2 + 3*(7*A + 4*C)*a^2*cos(d*x + c) + 16*(2*A + 3*C)*a^2)*sin(d*x + c))/d","A",0
100,1,106,0,0.428341," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, A + 4 \, C\right)} a^{2} d x + {\left(12 \, A a^{2} \cos\left(d x + c\right)^{4} + 30 \, A a^{2} \cos\left(d x + c\right)^{3} + 4 \, {\left(9 \, A + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, A + 4 \, C\right)} a^{2} \cos\left(d x + c\right) + 4 \, {\left(18 \, A + 25 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(15*(3*A + 4*C)*a^2*d*x + (12*A*a^2*cos(d*x + c)^4 + 30*A*a^2*cos(d*x + c)^3 + 4*(9*A + 5*C)*a^2*cos(d*x + c)^2 + 15*(3*A + 4*C)*a^2*cos(d*x + c) + 4*(18*A + 25*C)*a^2)*sin(d*x + c))/d","A",0
101,1,126,0,0.437521," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(11 \, A + 14 \, C\right)} a^{2} d x + {\left(40 \, A a^{2} \cos\left(d x + c\right)^{5} + 96 \, A a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(11 \, A + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 32 \, {\left(4 \, A + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(11 \, A + 14 \, C\right)} a^{2} \cos\left(d x + c\right) + 64 \, {\left(4 \, A + 5 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(11*A + 14*C)*a^2*d*x + (40*A*a^2*cos(d*x + c)^5 + 96*A*a^2*cos(d*x + c)^4 + 10*(11*A + 6*C)*a^2*cos(d*x + c)^3 + 32*(4*A + 5*C)*a^2*cos(d*x + c)^2 + 15*(11*A + 14*C)*a^2*cos(d*x + c) + 64*(4*A + 5*C)*a^2)*sin(d*x + c))/d","A",0
102,1,181,0,0.457721," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(30 \, A + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(30 \, A + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(45 \, A + 34 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} + 15 \, {\left(30 \, A + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 16 \, {\left(15 \, A + 17 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 10 \, {\left(6 \, A + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 144 \, C a^{3} \cos\left(d x + c\right) + 40 \, C a^{3}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(30*A + 23*C)*a^3*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(30*A + 23*C)*a^3*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(45*A + 34*C)*a^3*cos(d*x + c)^5 + 15*(30*A + 23*C)*a^3*cos(d*x + c)^4 + 16*(15*A + 17*C)*a^3*cos(d*x + c)^3 + 10*(6*A + 23*C)*a^3*cos(d*x + c)^2 + 144*C*a^3*cos(d*x + c) + 40*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
103,1,161,0,0.424239," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(20 \, A + 13 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(20 \, A + 13 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(55 \, A + 38 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 15 \, {\left(12 \, A + 13 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 19 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 90 \, C a^{3} \cos\left(d x + c\right) + 24 \, C a^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(20*A + 13*C)*a^3*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(20*A + 13*C)*a^3*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(55*A + 38*C)*a^3*cos(d*x + c)^4 + 15*(12*A + 13*C)*a^3*cos(d*x + c)^3 + 8*(5*A + 19*C)*a^3*cos(d*x + c)^2 + 90*C*a^3*cos(d*x + c) + 24*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
104,1,151,0,0.867965," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{16 \, A a^{3} d x \cos\left(d x + c\right)^{4} + {\left(28 \, A + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(28 \, A + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, {\left(A + C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(4 \, A + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 8 \, C a^{3} \cos\left(d x + c\right) + 2 \, C a^{3}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*A*a^3*d*x*cos(d*x + c)^4 + (28*A + 15*C)*a^3*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (28*A + 15*C)*a^3*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*(A + C)*a^3*cos(d*x + c)^3 + (4*A + 15*C)*a^3*cos(d*x + c)^2 + 8*C*a^3*cos(d*x + c) + 2*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
105,1,151,0,0.463618," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{36 \, A a^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(6 \, A + 5 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(6 \, A + 5 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, A a^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A + 11 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 9 \, C a^{3} \cos\left(d x + c\right) + 2 \, C a^{3}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(36*A*a^3*d*x*cos(d*x + c)^3 + 3*(6*A + 5*C)*a^3*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(6*A + 5*C)*a^3*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*A*a^3*cos(d*x + c)^3 + 2*(3*A + 11*C)*a^3*cos(d*x + c)^2 + 9*C*a^3*cos(d*x + c) + 2*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
106,1,148,0,0.460482," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, A + 2 \, C\right)} a^{3} d x \cos\left(d x + c\right)^{2} + {\left(2 \, A + 7 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, A + 7 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{3} \cos\left(d x + c\right)^{3} + 6 \, A a^{3} \cos\left(d x + c\right)^{2} + 6 \, C a^{3} \cos\left(d x + c\right) + C a^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*(7*A + 2*C)*a^3*d*x*cos(d*x + c)^2 + (2*A + 7*C)*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*A + 7*C)*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a^3*cos(d*x + c)^3 + 6*A*a^3*cos(d*x + c)^2 + 6*C*a^3*cos(d*x + c) + C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
107,1,138,0,0.452333," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, A + 6 \, C\right)} a^{3} d x \cos\left(d x + c\right) + 9 \, C a^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, C a^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, A a^{3} \cos\left(d x + c\right)^{3} + 9 \, A a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 6 \, C a^{3}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(3*(5*A + 6*C)*a^3*d*x*cos(d*x + c) + 9*C*a^3*cos(d*x + c)*log(sin(d*x + c) + 1) - 9*C*a^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*A*a^3*cos(d*x + c)^3 + 9*A*a^3*cos(d*x + c)^2 + 2*(11*A + 3*C)*a^3*cos(d*x + c) + 6*C*a^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
108,1,112,0,0.476960," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(15 \, A + 28 \, C\right)} a^{3} d x + 4 \, C a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 4 \, C a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, A a^{3} \cos\left(d x + c\right)^{3} + 8 \, A a^{3} \cos\left(d x + c\right)^{2} + {\left(15 \, A + 4 \, C\right)} a^{3} \cos\left(d x + c\right) + 24 \, {\left(A + C\right)} a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*((15*A + 28*C)*a^3*d*x + 4*C*a^3*log(sin(d*x + c) + 1) - 4*C*a^3*log(-sin(d*x + c) + 1) + (2*A*a^3*cos(d*x + c)^3 + 8*A*a^3*cos(d*x + c)^2 + (15*A + 4*C)*a^3*cos(d*x + c) + 24*(A + C)*a^3)*sin(d*x + c))/d","A",0
109,1,106,0,0.429691," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, A + 20 \, C\right)} a^{3} d x + {\left(24 \, A a^{3} \cos\left(d x + c\right)^{4} + 90 \, A a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(19 \, A + 5 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(13 \, A + 12 \, C\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(38 \, A + 55 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(13*A + 20*C)*a^3*d*x + (24*A*a^3*cos(d*x + c)^4 + 90*A*a^3*cos(d*x + c)^3 + 8*(19*A + 5*C)*a^3*cos(d*x + c)^2 + 15*(13*A + 12*C)*a^3*cos(d*x + c) + 8*(38*A + 55*C)*a^3)*sin(d*x + c))/d","A",0
110,1,126,0,0.432829," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(23 \, A + 30 \, C\right)} a^{3} d x + {\left(40 \, A a^{3} \cos\left(d x + c\right)^{5} + 144 \, A a^{3} \cos\left(d x + c\right)^{4} + 10 \, {\left(23 \, A + 6 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(17 \, A + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(23 \, A + 30 \, C\right)} a^{3} \cos\left(d x + c\right) + 16 \, {\left(34 \, A + 45 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(23*A + 30*C)*a^3*d*x + (40*A*a^3*cos(d*x + c)^5 + 144*A*a^3*cos(d*x + c)^4 + 10*(23*A + 6*C)*a^3*cos(d*x + c)^3 + 16*(17*A + 15*C)*a^3*cos(d*x + c)^2 + 15*(23*A + 30*C)*a^3*cos(d*x + c) + 16*(34*A + 45*C)*a^3)*sin(d*x + c))/d","A",0
111,1,201,0,0.449058," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(14 \, A + 11 \, C\right)} a^{4} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(14 \, A + 11 \, C\right)} a^{4} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, {\left(581 \, A + 454 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} + 105 \, {\left(14 \, A + 11 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 4 \, {\left(238 \, A + 227 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(6 \, A + 11 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 12 \, {\left(7 \, A + 48 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 280 \, C a^{4} \cos\left(d x + c\right) + 60 \, C a^{4}\right)} \sin\left(d x + c\right)}{840 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/840*(105*(14*A + 11*C)*a^4*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(14*A + 11*C)*a^4*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 2*(4*(581*A + 454*C)*a^4*cos(d*x + c)^6 + 105*(14*A + 11*C)*a^4*cos(d*x + c)^5 + 4*(238*A + 227*C)*a^4*cos(d*x + c)^4 + 70*(6*A + 11*C)*a^4*cos(d*x + c)^3 + 12*(7*A + 48*C)*a^4*cos(d*x + c)^2 + 280*C*a^4*cos(d*x + c) + 60*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
112,1,181,0,0.453795," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(10 \, A + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(10 \, A + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(64 \, {\left(25 \, A + 18 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 15 \, {\left(54 \, A + 49 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 64 \, {\left(5 \, A + 9 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 10 \, {\left(6 \, A + 41 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 192 \, C a^{4} \cos\left(d x + c\right) + 40 \, C a^{4}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(105*(10*A + 7*C)*a^4*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 105*(10*A + 7*C)*a^4*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(64*(25*A + 18*C)*a^4*cos(d*x + c)^5 + 15*(54*A + 49*C)*a^4*cos(d*x + c)^4 + 64*(5*A + 9*C)*a^4*cos(d*x + c)^3 + 10*(6*A + 41*C)*a^4*cos(d*x + c)^2 + 192*C*a^4*cos(d*x + c) + 40*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
113,1,177,0,0.453119," ","integrate((a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{60 \, A a^{4} d x \cos\left(d x + c\right)^{5} + 15 \, {\left(12 \, A + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(12 \, A + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(100 \, A + 83 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 15 \, {\left(4 \, A + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, A + 34 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 30 \, C a^{4} \cos\left(d x + c\right) + 6 \, C a^{4}\right)} \sin\left(d x + c\right)}{60 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/60*(60*A*a^4*d*x*cos(d*x + c)^5 + 15*(12*A + 7*C)*a^4*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(12*A + 7*C)*a^4*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(2*(100*A + 83*C)*a^4*cos(d*x + c)^4 + 15*(4*A + 7*C)*a^4*cos(d*x + c)^3 + 2*(5*A + 34*C)*a^4*cos(d*x + c)^2 + 30*C*a^4*cos(d*x + c) + 6*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
114,1,171,0,0.470193," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{192 \, A a^{4} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(52 \, A + 35 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(52 \, A + 35 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, A a^{4} \cos\left(d x + c\right)^{4} + 32 \, {\left(3 \, A + 5 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 27 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 32 \, C a^{4} \cos\left(d x + c\right) + 6 \, C a^{4}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(192*A*a^4*d*x*cos(d*x + c)^4 + 3*(52*A + 35*C)*a^4*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(52*A + 35*C)*a^4*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*A*a^4*cos(d*x + c)^4 + 32*(3*A + 5*C)*a^4*cos(d*x + c)^3 + 3*(4*A + 27*C)*a^4*cos(d*x + c)^2 + 32*C*a^4*cos(d*x + c) + 6*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
115,1,170,0,0.456769," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(13 \, A + 2 \, C\right)} a^{4} d x \cos\left(d x + c\right)^{3} + 6 \, {\left(2 \, A + 3 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left(2 \, A + 3 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(3 \, A a^{4} \cos\left(d x + c\right)^{4} + 24 \, A a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A + 20 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 12 \, C a^{4} \cos\left(d x + c\right) + 2 \, C a^{4}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(3*(13*A + 2*C)*a^4*d*x*cos(d*x + c)^3 + 6*(2*A + 3*C)*a^4*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 6*(2*A + 3*C)*a^4*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + (3*A*a^4*cos(d*x + c)^4 + 24*A*a^4*cos(d*x + c)^3 + 2*(3*A + 20*C)*a^4*cos(d*x + c)^2 + 12*C*a^4*cos(d*x + c) + 2*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
116,1,171,0,0.474597," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{24 \, {\left(3 \, A + 2 \, C\right)} a^{4} d x \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A + 13 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A + 13 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{4} \cos\left(d x + c\right)^{4} + 12 \, A a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(20 \, A + 3 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 24 \, C a^{4} \cos\left(d x + c\right) + 3 \, C a^{4}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(24*(3*A + 2*C)*a^4*d*x*cos(d*x + c)^2 + 3*(2*A + 13*C)*a^4*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*(2*A + 13*C)*a^4*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a^4*cos(d*x + c)^4 + 12*A*a^4*cos(d*x + c)^3 + 2*(20*A + 3*C)*a^4*cos(d*x + c)^2 + 24*C*a^4*cos(d*x + c) + 3*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
117,1,158,0,0.453000," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(35 \, A + 52 \, C\right)} a^{4} d x \cos\left(d x + c\right) + 48 \, C a^{4} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 48 \, C a^{4} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, A a^{4} \cos\left(d x + c\right)^{4} + 32 \, A a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(27 \, A + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 32 \, {\left(5 \, A + 3 \, C\right)} a^{4} \cos\left(d x + c\right) + 24 \, C a^{4}\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}"," ",0,"1/24*(3*(35*A + 52*C)*a^4*d*x*cos(d*x + c) + 48*C*a^4*cos(d*x + c)*log(sin(d*x + c) + 1) - 48*C*a^4*cos(d*x + c)*log(-sin(d*x + c) + 1) + (6*A*a^4*cos(d*x + c)^4 + 32*A*a^4*cos(d*x + c)^3 + 3*(27*A + 4*C)*a^4*cos(d*x + c)^2 + 32*(5*A + 3*C)*a^4*cos(d*x + c) + 24*C*a^4)*sin(d*x + c))/(d*cos(d*x + c))","A",0
118,1,138,0,0.463082," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(7 \, A + 12 \, C\right)} a^{4} d x + 15 \, C a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, C a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, A a^{4} \cos\left(d x + c\right)^{4} + 30 \, A a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(34 \, A + 5 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 15 \, {\left(7 \, A + 4 \, C\right)} a^{4} \cos\left(d x + c\right) + 2 \, {\left(83 \, A + 100 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(15*(7*A + 12*C)*a^4*d*x + 15*C*a^4*log(sin(d*x + c) + 1) - 15*C*a^4*log(-sin(d*x + c) + 1) + (6*A*a^4*cos(d*x + c)^4 + 30*A*a^4*cos(d*x + c)^3 + 2*(34*A + 5*C)*a^4*cos(d*x + c)^2 + 15*(7*A + 4*C)*a^4*cos(d*x + c) + 2*(83*A + 100*C)*a^4)*sin(d*x + c))/d","A",0
119,1,126,0,0.433640," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(7 \, A + 10 \, C\right)} a^{4} d x + {\left(40 \, A a^{4} \cos\left(d x + c\right)^{5} + 192 \, A a^{4} \cos\left(d x + c\right)^{4} + 10 \, {\left(41 \, A + 6 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 64 \, {\left(9 \, A + 5 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 15 \, {\left(49 \, A + 54 \, C\right)} a^{4} \cos\left(d x + c\right) + 64 \, {\left(18 \, A + 25 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(105*(7*A + 10*C)*a^4*d*x + (40*A*a^4*cos(d*x + c)^5 + 192*A*a^4*cos(d*x + c)^4 + 10*(41*A + 6*C)*a^4*cos(d*x + c)^3 + 64*(9*A + 5*C)*a^4*cos(d*x + c)^2 + 15*(49*A + 54*C)*a^4*cos(d*x + c) + 64*(18*A + 25*C)*a^4)*sin(d*x + c))/d","A",0
120,1,146,0,0.449111," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(11 \, A + 14 \, C\right)} a^{4} d x + {\left(60 \, A a^{4} \cos\left(d x + c\right)^{6} + 280 \, A a^{4} \cos\left(d x + c\right)^{5} + 12 \, {\left(48 \, A + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(11 \, A + 6 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 4 \, {\left(227 \, A + 238 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(11 \, A + 14 \, C\right)} a^{4} \cos\left(d x + c\right) + 4 \, {\left(454 \, A + 581 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{420 \, d}"," ",0,"1/420*(105*(11*A + 14*C)*a^4*d*x + (60*A*a^4*cos(d*x + c)^6 + 280*A*a^4*cos(d*x + c)^5 + 12*(48*A + 7*C)*a^4*cos(d*x + c)^4 + 70*(11*A + 6*C)*a^4*cos(d*x + c)^3 + 4*(227*A + 238*C)*a^4*cos(d*x + c)^2 + 105*(11*A + 14*C)*a^4*cos(d*x + c) + 4*(454*A + 581*C)*a^4)*sin(d*x + c))/d","A",0
121,1,189,0,0.483484," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left({\left(4 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(4 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, {\left({\left(4 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(4 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(3 \, A + 4 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(12 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(12 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) - 6 \, C\right)} \sin\left(d x + c\right)}{48 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/48*(9*((4*A + 5*C)*cos(d*x + c)^5 + (4*A + 5*C)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) - 9*((4*A + 5*C)*cos(d*x + c)^5 + (4*A + 5*C)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) - 2*(16*(3*A + 4*C)*cos(d*x + c)^4 + (12*A + 19*C)*cos(d*x + c)^3 - (12*A + 13*C)*cos(d*x + c)^2 + 2*C*cos(d*x + c) - 6*C)*sin(d*x + c))/(a*d*cos(d*x + c)^5 + a*d*cos(d*x + c)^4)","A",0
122,1,172,0,0.430850," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(2 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(2 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, A + 3 \, C\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 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} - C \cos\left(d x + c\right) + 2 \, C\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*(3*((2*A + 3*C)*cos(d*x + c)^4 + (2*A + 3*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((2*A + 3*C)*cos(d*x + c)^4 + (2*A + 3*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(4*(3*A + 4*C)*cos(d*x + c)^3 + (6*A + 7*C)*cos(d*x + c)^2 - C*cos(d*x + c) + 2*C)*sin(d*x + c))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
123,1,152,0,0.457137," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(2 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(2 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(A + 2 \, C\right)} \cos\left(d x + c\right)^{2} + C \cos\left(d x + c\right) - C\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*C)*cos(d*x + c)^3 + (2*A + 3*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((2*A + 3*C)*cos(d*x + c)^3 + (2*A + 3*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(2*(A + 2*C)*cos(d*x + c)^2 + C*cos(d*x + c) - C)*sin(d*x + c))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
124,1,109,0,0.459761," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(C \cos\left(d x + c\right)^{2} + C \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C \cos\left(d x + c\right)^{2} + C \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(A + 2 \, C\right)} \cos\left(d x + c\right) + C\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*((C*cos(d*x + c)^2 + C*cos(d*x + c))*log(sin(d*x + c) + 1) - (C*cos(d*x + c)^2 + C*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*((A + 2*C)*cos(d*x + c) + C)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
125,1,88,0,0.443972," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, A d x \cos\left(d x + c\right) + 2 \, A d x + {\left(C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A + C\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*(2*A*d*x*cos(d*x + c) + 2*A*d*x + (C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - (C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) - 2*(A + C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
126,1,53,0,0.453638," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{A d x \cos\left(d x + c\right) + A d x - {\left(A \cos\left(d x + c\right) + 2 \, A + C\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*cos(d*x + c) + 2*A + C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
127,1,77,0,0.452502," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, A + 2 \, C\right)} d x \cos\left(d x + c\right) + {\left(3 \, A + 2 \, C\right)} d x + {\left(A \cos\left(d x + c\right)^{2} - A \cos\left(d x + c\right) - 4 \, A - 2 \, C\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*C)*d*x*cos(d*x + c) + (3*A + 2*C)*d*x + (A*cos(d*x + c)^2 - A*cos(d*x + c) - 4*A - 2*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
128,1,97,0,0.419327," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(3 \, A + 2 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(3 \, A + 2 \, C\right)} d x - {\left(2 \, A \cos\left(d x + c\right)^{3} - A \cos\left(d x + c\right)^{2} + {\left(7 \, A + 6 \, C\right)} \cos\left(d x + c\right) + 16 \, A + 12 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/6*(3*(3*A + 2*C)*d*x*cos(d*x + c) + 3*(3*A + 2*C)*d*x - (2*A*cos(d*x + c)^3 - A*cos(d*x + c)^2 + (7*A + 6*C)*cos(d*x + c) + 16*A + 12*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
129,1,113,0,0.444759," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left(5 \, A + 4 \, C\right)} d x \cos\left(d x + c\right) + 9 \, {\left(5 \, A + 4 \, C\right)} d x + {\left(6 \, A \cos\left(d x + c\right)^{4} - 2 \, A \cos\left(d x + c\right)^{3} + {\left(13 \, A + 12 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(19 \, A + 12 \, C\right)} \cos\left(d x + c\right) - 64 \, A - 48 \, C\right)} \sin\left(d x + c\right)}{24 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/24*(9*(5*A + 4*C)*d*x*cos(d*x + c) + 9*(5*A + 4*C)*d*x + (6*A*cos(d*x + c)^4 - 2*A*cos(d*x + c)^3 + (13*A + 12*C)*cos(d*x + c)^2 - (19*A + 12*C)*cos(d*x + c) - 64*A - 48*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
130,1,237,0,0.470001," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(2 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(2 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(2 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(2 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(5 \, A + 12 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(14 \, A + 33 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + 2 \, C\right)} \cos\left(d x + c\right)^{2} - C \cos\left(d x + c\right) + C\right)} \sin\left(d x + c\right)}{6 \, {\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,"-1/6*(3*((2*A + 5*C)*cos(d*x + c)^5 + 2*(2*A + 5*C)*cos(d*x + c)^4 + (2*A + 5*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((2*A + 5*C)*cos(d*x + c)^5 + 2*(2*A + 5*C)*cos(d*x + c)^4 + (2*A + 5*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(2*(5*A + 12*C)*cos(d*x + c)^4 + (14*A + 33*C)*cos(d*x + c)^3 + 3*(A + 2*C)*cos(d*x + c)^2 - C*cos(d*x + c) + C)*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
131,1,222,0,0.477656," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(2 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(2 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(8 \, {\left(A + 4 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(10 \, A + 43 \, C\right)} \cos\left(d x + c\right)^{2} + 6 \, C \cos\left(d x + c\right) - 3 \, C\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*((2*A + 7*C)*cos(d*x + c)^4 + 2*(2*A + 7*C)*cos(d*x + c)^3 + (2*A + 7*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*((2*A + 7*C)*cos(d*x + c)^4 + 2*(2*A + 7*C)*cos(d*x + c)^3 + (2*A + 7*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(8*(A + 4*C)*cos(d*x + c)^3 + (10*A + 43*C)*cos(d*x + c)^2 + 6*C*cos(d*x + c) - 3*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
132,1,167,0,0.452761," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(C \cos\left(d x + c\right)^{3} + 2 \, C \cos\left(d x + c\right)^{2} + C \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(C \cos\left(d x + c\right)^{3} + 2 \, C \cos\left(d x + c\right)^{2} + C \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left({\left(A + 10 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 7 \, C\right)} \cos\left(d x + c\right) + 3 \, C\right)} \sin\left(d x + c\right)}{3 \, {\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,"-1/3*(3*(C*cos(d*x + c)^3 + 2*C*cos(d*x + c)^2 + C*cos(d*x + c))*log(sin(d*x + c) + 1) - 3*(C*cos(d*x + c)^3 + 2*C*cos(d*x + c)^2 + C*cos(d*x + c))*log(-sin(d*x + c) + 1) - ((A + 10*C)*cos(d*x + c)^2 + 2*(A + 7*C)*cos(d*x + c) + 3*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
133,1,128,0,0.433311," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(A - 2 \, C\right)} \cos\left(d x + c\right) + A - 5 \, C\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*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - 3*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) + 2*(2*(A - 2*C)*cos(d*x + c) + A - 5*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
134,1,94,0,0.411987," ","integrate((A+C*sec(d*x+c)^2)/(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 - C\right)} \cos\left(d x + c\right) + 4 \, A - 2 \, C\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 - C)*cos(d*x + c) + 4*A - 2*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
135,1,102,0,0.443997," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, A d x \cos\left(d x + c\right)^{2} + 12 \, A d x \cos\left(d x + c\right) + 6 \, A d x - {\left(3 \, A \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A + C\right)} \cos\left(d x + c\right) + 10 \, A + C\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*(6*A*d*x*cos(d*x + c)^2 + 12*A*d*x*cos(d*x + c) + 6*A*d*x - (3*A*cos(d*x + c)^2 + 2*(7*A + C)*cos(d*x + c) + 10*A + 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
136,1,134,0,0.430053," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A + 2 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(7 \, A + 2 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(7 \, A + 2 \, C\right)} d x + {\left(3 \, A \cos\left(d x + c\right)^{3} - 6 \, A \cos\left(d x + c\right)^{2} - {\left(43 \, A + 10 \, C\right)} \cos\left(d x + c\right) - 32 \, A - 8 \, C\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 + 2*C)*d*x*cos(d*x + c)^2 + 6*(7*A + 2*C)*d*x*cos(d*x + c) + 3*(7*A + 2*C)*d*x + (3*A*cos(d*x + c)^3 - 6*A*cos(d*x + c)^2 - (43*A + 10*C)*cos(d*x + c) - 32*A - 8*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
137,1,148,0,0.436204," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(5 \, A + 2 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(5 \, A + 2 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(5 \, A + 2 \, C\right)} d x - {\left(A \cos\left(d x + c\right)^{4} - A \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A + C\right)} \cos\left(d x + c\right)^{2} + {\left(33 \, A + 14 \, C\right)} \cos\left(d x + c\right) + 24 \, A + 10 \, C\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*(5*A + 2*C)*d*x*cos(d*x + c)^2 + 6*(5*A + 2*C)*d*x*cos(d*x + c) + 3*(5*A + 2*C)*d*x - (A*cos(d*x + c)^4 - A*cos(d*x + c)^3 + 3*(2*A + C)*cos(d*x + c)^2 + (33*A + 14*C)*cos(d*x + c) + 24*A + 10*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
138,1,289,0,0.450292," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(2 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(2 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(2 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(2 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(11 \, A + 76 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(34 \, A + 239 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(64 \, A + 479 \, C\right)} \cos\left(d x + c\right)^{2} + 45 \, C \cos\left(d x + c\right) - 15 \, C\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*((2*A + 13*C)*cos(d*x + c)^5 + 3*(2*A + 13*C)*cos(d*x + c)^4 + 3*(2*A + 13*C)*cos(d*x + c)^3 + (2*A + 13*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 15*((2*A + 13*C)*cos(d*x + c)^5 + 3*(2*A + 13*C)*cos(d*x + c)^4 + 3*(2*A + 13*C)*cos(d*x + c)^3 + (2*A + 13*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(11*A + 76*C)*cos(d*x + c)^4 + 3*(34*A + 239*C)*cos(d*x + c)^3 + (64*A + 479*C)*cos(d*x + c)^2 + 45*C*cos(d*x + c) - 15*C)*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
139,1,222,0,0.445995," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{45 \, {\left(C \cos\left(d x + c\right)^{4} + 3 \, C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + C \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 45 \, {\left(C \cos\left(d x + c\right)^{4} + 3 \, C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + C \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(A + 36 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A + 57 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A + 117 \, C\right)} \cos\left(d x + c\right) + 15 \, C\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*(45*(C*cos(d*x + c)^4 + 3*C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + C*cos(d*x + c))*log(sin(d*x + c) + 1) - 45*(C*cos(d*x + c)^4 + 3*C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + C*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*(A + 36*C)*cos(d*x + c)^3 + 3*(2*A + 57*C)*cos(d*x + c)^2 + (7*A + 117*C)*cos(d*x + c) + 15*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
140,1,184,0,0.463144," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(3 \, A - 22 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 17 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 32 \, C\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*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - 15*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) + 2*((3*A - 22*C)*cos(d*x + c)^2 + 3*(3*A - 17*C)*cos(d*x + c) + 3*A - 32*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
141,1,89,0,0.410143," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(7 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(A + C\right)} \cos\left(d x + c\right) + 2 \, A + 7 \, C\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 + 2*C)*cos(d*x + c)^2 + 6*(A + C)*cos(d*x + c) + 2*A + 7*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
142,1,138,0,0.432976," ","integrate((A+C*sec(d*x+c)^2)/(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 - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(17 \, A - 3 \, C\right)} \cos\left(d x + c\right) + 22 \, A - 3 \, C\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 - 3*C)*cos(d*x + c)^2 + 3*(17*A - 3*C)*cos(d*x + c) + 22*A - 3*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
143,1,149,0,0.502222," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{45 \, A d x \cos\left(d x + c\right)^{3} + 135 \, A d x \cos\left(d x + c\right)^{2} + 135 \, A d x \cos\left(d x + c\right) + 45 \, A d x - {\left(15 \, A \cos\left(d x + c\right)^{3} + {\left(117 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(57 \, A + 2 \, C\right)} \cos\left(d x + c\right) + 72 \, A + 2 \, C\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*(45*A*d*x*cos(d*x + c)^3 + 135*A*d*x*cos(d*x + c)^2 + 135*A*d*x*cos(d*x + c) + 45*A*d*x - (15*A*cos(d*x + c)^3 + (117*A + 7*C)*cos(d*x + c)^2 + 3*(57*A + 2*C)*cos(d*x + c) + 72*A + 2*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
144,1,184,0,0.420978," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, A + 2 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(13 \, A + 2 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(13 \, A + 2 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(13 \, A + 2 \, C\right)} d x + {\left(15 \, A \cos\left(d x + c\right)^{4} - 45 \, A \cos\left(d x + c\right)^{3} - {\left(479 \, A + 64 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(239 \, A + 34 \, C\right)} \cos\left(d x + c\right) - 304 \, A - 44 \, C\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 + 2*C)*d*x*cos(d*x + c)^3 + 45*(13*A + 2*C)*d*x*cos(d*x + c)^2 + 45*(13*A + 2*C)*d*x*cos(d*x + c) + 15*(13*A + 2*C)*d*x + (15*A*cos(d*x + c)^4 - 45*A*cos(d*x + c)^3 - (479*A + 64*C)*cos(d*x + c)^2 - 3*(239*A + 34*C)*cos(d*x + c) - 304*A - 44*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
145,1,201,0,0.481438," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(23 \, A + 6 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(23 \, A + 6 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(23 \, A + 6 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(23 \, A + 6 \, C\right)} d x - {\left(10 \, A \cos\left(d x + c\right)^{5} - 15 \, A \cos\left(d x + c\right)^{4} + 5 \, {\left(19 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(869 \, A + 234 \, C\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(143 \, A + 38 \, C\right)} \cos\left(d x + c\right) + 544 \, A + 144 \, C\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 + 6*C)*d*x*cos(d*x + c)^3 + 45*(23*A + 6*C)*d*x*cos(d*x + c)^2 + 45*(23*A + 6*C)*d*x*cos(d*x + c) + 15*(23*A + 6*C)*d*x - (10*A*cos(d*x + c)^5 - 15*A*cos(d*x + c)^4 + 5*(19*A + 6*C)*cos(d*x + c)^3 + (869*A + 234*C)*cos(d*x + c)^2 + 9*(143*A + 38*C)*cos(d*x + c) + 544*A + 144*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
146,1,354,0,0.449122," ","integrate(sec(d*x+c)^5*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left({\left(2 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(2 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(2 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(2 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(2 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(2 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(2 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(2 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(64 \, {\left(5 \, A + 54 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(1070 \, A + 11619 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(310 \, A + 3411 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(130 \, A + 1509 \, C\right)} \cos\left(d x + c\right)^{2} + 420 \, C \cos\left(d x + c\right) - 105 \, C\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*((2*A + 21*C)*cos(d*x + c)^6 + 4*(2*A + 21*C)*cos(d*x + c)^5 + 6*(2*A + 21*C)*cos(d*x + c)^4 + 4*(2*A + 21*C)*cos(d*x + c)^3 + (2*A + 21*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 105*((2*A + 21*C)*cos(d*x + c)^6 + 4*(2*A + 21*C)*cos(d*x + c)^5 + 6*(2*A + 21*C)*cos(d*x + c)^4 + 4*(2*A + 21*C)*cos(d*x + c)^3 + (2*A + 21*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(64*(5*A + 54*C)*cos(d*x + c)^5 + (1070*A + 11619*C)*cos(d*x + c)^4 + 4*(310*A + 3411*C)*cos(d*x + c)^3 + 4*(130*A + 1509*C)*cos(d*x + c)^2 + 420*C*cos(d*x + c) - 105*C)*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
147,1,277,0,0.466761," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","-\frac{210 \, {\left(C \cos\left(d x + c\right)^{5} + 4 \, C \cos\left(d x + c\right)^{4} + 6 \, C \cos\left(d x + c\right)^{3} + 4 \, C \cos\left(d x + c\right)^{2} + C \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 210 \, {\left(C \cos\left(d x + c\right)^{5} + 4 \, C \cos\left(d x + c\right)^{4} + 6 \, C \cos\left(d x + c\right)^{3} + 4 \, C \cos\left(d x + c\right)^{2} + C \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(2 \, {\left(3 \, A + 332 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(6 \, A + 559 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A + 2636 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(9 \, A + 296 \, C\right)} \cos\left(d x + c\right) + 105 \, C\right)} \sin\left(d x + c\right)}{105 \, {\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,"-1/105*(210*(C*cos(d*x + c)^5 + 4*C*cos(d*x + c)^4 + 6*C*cos(d*x + c)^3 + 4*C*cos(d*x + c)^2 + C*cos(d*x + c))*log(sin(d*x + c) + 1) - 210*(C*cos(d*x + c)^5 + 4*C*cos(d*x + c)^4 + 6*C*cos(d*x + c)^3 + 4*C*cos(d*x + c)^2 + C*cos(d*x + c))*log(-sin(d*x + c) + 1) - (2*(3*A + 332*C)*cos(d*x + c)^4 + 4*(6*A + 559*C)*cos(d*x + c)^3 + (39*A + 2636*C)*cos(d*x + c)^2 + 4*(9*A + 296*C)*cos(d*x + c) + 105*C)*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
148,1,235,0,0.441041," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(C \cos\left(d x + c\right)^{4} + 4 \, C \cos\left(d x + c\right)^{3} + 6 \, C \cos\left(d x + c\right)^{2} + 4 \, C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(C \cos\left(d x + c\right)^{4} + 4 \, C \cos\left(d x + c\right)^{3} + 6 \, C \cos\left(d x + c\right)^{2} + 4 \, C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(A - 20 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(32 \, A - 535 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(13 \, A - 155 \, C\right)} \cos\left(d x + c\right) + 13 \, A - 260 \, C\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*(C*cos(d*x + c)^4 + 4*C*cos(d*x + c)^3 + 6*C*cos(d*x + c)^2 + 4*C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - 105*(C*cos(d*x + c)^4 + 4*C*cos(d*x + c)^3 + 6*C*cos(d*x + c)^2 + 4*C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) + 2*(8*(A - 20*C)*cos(d*x + c)^3 + (32*A - 535*C)*cos(d*x + c)^2 + 4*(13*A - 155*C)*cos(d*x + c) + 13*A - 260*C)*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
149,1,123,0,0.416326," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(13 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(13 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(32 \, A + 39 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 36 \, C\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 + 6*C)*cos(d*x + c)^3 + 4*(13*A + 6*C)*cos(d*x + c)^2 + (32*A + 39*C)*cos(d*x + c) + 8*A + 36*C)*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
150,1,124,0,0.402812," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(9 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A + 32 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(6 \, A + 13 \, C\right)} \cos\left(d x + c\right) + 6 \, A + 13 \, C\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*(4*(9*A + 2*C)*cos(d*x + c)^3 + (39*A + 32*C)*cos(d*x + c)^2 + 4*(6*A + 13*C)*cos(d*x + c) + 6*A + 13*C)*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
151,1,182,0,0.425881," ","integrate((A+C*sec(d*x+c)^2)/(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(13 \, {\left(20 \, A - C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(155 \, A - 13 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(535 \, A - 32 \, C\right)} \cos\left(d x + c\right) + 160 \, A - 8 \, C\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 - (13*(20*A - C)*cos(d*x + c)^3 + 4*(155*A - 13*C)*cos(d*x + c)^2 + (535*A - 32*C)*cos(d*x + c) + 160*A - 8*C)*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
152,1,193,0,0.453746," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","-\frac{420 \, A d x \cos\left(d x + c\right)^{4} + 1680 \, A d x \cos\left(d x + c\right)^{3} + 2520 \, A d x \cos\left(d x + c\right)^{2} + 1680 \, A d x \cos\left(d x + c\right) + 420 \, A d x - {\left(105 \, A \cos\left(d x + c\right)^{4} + 4 \, {\left(296 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2636 \, A + 39 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(559 \, A + 6 \, C\right)} \cos\left(d x + c\right) + 664 \, A + 6 \, C\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*(420*A*d*x*cos(d*x + c)^4 + 1680*A*d*x*cos(d*x + c)^3 + 2520*A*d*x*cos(d*x + c)^2 + 1680*A*d*x*cos(d*x + c) + 420*A*d*x - (105*A*cos(d*x + c)^4 + 4*(296*A + 9*C)*cos(d*x + c)^3 + (2636*A + 39*C)*cos(d*x + c)^2 + 4*(559*A + 6*C)*cos(d*x + c) + 664*A + 6*C)*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
153,1,234,0,0.442816," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(21 \, A + 2 \, C\right)} d x \cos\left(d x + c\right)^{4} + 420 \, {\left(21 \, A + 2 \, C\right)} d x \cos\left(d x + c\right)^{3} + 630 \, {\left(21 \, A + 2 \, C\right)} d x \cos\left(d x + c\right)^{2} + 420 \, {\left(21 \, A + 2 \, C\right)} d x \cos\left(d x + c\right) + 105 \, {\left(21 \, A + 2 \, C\right)} d x + {\left(105 \, A \cos\left(d x + c\right)^{5} - 420 \, A \cos\left(d x + c\right)^{4} - 4 \, {\left(1509 \, A + 130 \, C\right)} \cos\left(d x + c\right)^{3} - 4 \, {\left(3411 \, A + 310 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(11619 \, A + 1070 \, C\right)} \cos\left(d x + c\right) - 3456 \, A - 320 \, C\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 + 2*C)*d*x*cos(d*x + c)^4 + 420*(21*A + 2*C)*d*x*cos(d*x + c)^3 + 630*(21*A + 2*C)*d*x*cos(d*x + c)^2 + 420*(21*A + 2*C)*d*x*cos(d*x + c) + 105*(21*A + 2*C)*d*x + (105*A*cos(d*x + c)^5 - 420*A*cos(d*x + c)^4 - 4*(1509*A + 130*C)*cos(d*x + c)^3 - 4*(3411*A + 310*C)*cos(d*x + c)^2 - (11619*A + 1070*C)*cos(d*x + c) - 3456*A - 320*C)*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
154,1,252,0,0.443158," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","-\frac{210 \, {\left(11 \, A + 2 \, C\right)} d x \cos\left(d x + c\right)^{4} + 840 \, {\left(11 \, A + 2 \, C\right)} d x \cos\left(d x + c\right)^{3} + 1260 \, {\left(11 \, A + 2 \, C\right)} d x \cos\left(d x + c\right)^{2} + 840 \, {\left(11 \, A + 2 \, C\right)} d x \cos\left(d x + c\right) + 210 \, {\left(11 \, A + 2 \, C\right)} d x - {\left(35 \, A \cos\left(d x + c\right)^{6} - 70 \, A \cos\left(d x + c\right)^{5} + 35 \, {\left(14 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(799 \, A + 148 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(3592 \, A + 659 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6109 \, A + 1118 \, C\right)} \cos\left(d x + c\right) + 3632 \, A + 664 \, C\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*(210*(11*A + 2*C)*d*x*cos(d*x + c)^4 + 840*(11*A + 2*C)*d*x*cos(d*x + c)^3 + 1260*(11*A + 2*C)*d*x*cos(d*x + c)^2 + 840*(11*A + 2*C)*d*x*cos(d*x + c) + 210*(11*A + 2*C)*d*x - (35*A*cos(d*x + c)^6 - 70*A*cos(d*x + c)^5 + 35*(14*A + 3*C)*cos(d*x + c)^4 + 8*(799*A + 148*C)*cos(d*x + c)^3 + 4*(3592*A + 659*C)*cos(d*x + c)^2 + 2*(6109*A + 1118*C)*cos(d*x + c) + 3632*A + 664*C)*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
155,1,133,0,0.417246," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, {\left(99 \, A + 80 \, C\right)} \cos\left(d x + c\right)^{5} + 8 \, {\left(99 \, A + 80 \, C\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(99 \, A + 80 \, C\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(99 \, A + 80 \, C\right)} \cos\left(d x + c\right)^{2} + 350 \, C \cos\left(d x + c\right) + 315 \, C\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*(16*(99*A + 80*C)*cos(d*x + c)^5 + 8*(99*A + 80*C)*cos(d*x + c)^4 + 6*(99*A + 80*C)*cos(d*x + c)^3 + 5*(99*A + 80*C)*cos(d*x + c)^2 + 350*C*cos(d*x + c) + 315*C)*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
156,1,116,0,0.438538," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(21 \, A + 16 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(21 \, A + 16 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 16 \, C\right)} \cos\left(d x + c\right)^{2} + 40 \, C \cos\left(d x + c\right) + 35 \, C\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*(21*A + 16*C)*cos(d*x + c)^4 + 4*(21*A + 16*C)*cos(d*x + c)^3 + 3*(21*A + 16*C)*cos(d*x + c)^2 + 40*C*cos(d*x + c) + 35*C)*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
157,1,98,0,0.463794," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(35 \, A + 24 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(35 \, A + 24 \, C\right)} \cos\left(d x + c\right)^{2} + 18 \, C \cos\left(d x + c\right) + 15 \, C\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*(35*A + 24*C)*cos(d*x + c)^3 + (35*A + 24*C)*cos(d*x + c)^2 + 18*C*cos(d*x + c) + 15*C)*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
158,1,81,0,0.440960," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(15 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, C \cos\left(d x + c\right) + 3 \, C\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*((15*A + 8*C)*cos(d*x + c)^2 + 4*C*cos(d*x + c) + 3*C)*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
159,1,294,0,0.470604," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A \cos\left(d x + c\right)^{2} + 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(2 \, C \cos\left(d x + c\right) + C\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 \cos\left(d x + c\right)^{2} + 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(2 \, C \cos\left(d x + c\right) + C\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*cos(d*x + c)^2 + 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*(2*C*cos(d*x + c) + C)*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*cos(d*x + c)^2 + 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))) - (2*C*cos(d*x + c) + C)*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
160,1,258,0,0.484296," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),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 \, {\left(A \cos\left(d x + c\right) + 2 \, C\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(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) - {\left(A \cos\left(d x + c\right) + 2 \, C\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*((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*(A*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -((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*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
161,1,298,0,0.521245," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, A + 8 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 8 \, C\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} + 3 \, 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(3 \, A + 8 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 8 \, C\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} + 3 \, 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*(((3*A + 8*C)*cos(d*x + c) + 3*A + 8*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*(2*A*cos(d*x + c)^2 + 3*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*(((3*A + 8*C)*cos(d*x + c) + 3*A + 8*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))) - (2*A*cos(d*x + c)^2 + 3*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
162,1,334,0,0.531695," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, A + 8 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 8 \, C\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} + 10 \, A \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 8 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 8 \, C\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} + 10 \, A \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 8 \, C\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 + 8*C)*cos(d*x + c) + 5*A + 8*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*(8*A*cos(d*x + c)^3 + 10*A*cos(d*x + c)^2 + 3*(5*A + 8*C)*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 + 8*C)*cos(d*x + c) + 5*A + 8*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))) - (8*A*cos(d*x + c)^3 + 10*A*cos(d*x + c)^2 + 3*(5*A + 8*C)*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
163,1,368,0,0.545204," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(35 \, A + 48 \, C\right)} \cos\left(d x + c\right) + 35 \, A + 48 \, C\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} + 56 \, A \cos\left(d x + c\right)^{3} + 2 \, {\left(35 \, A + 48 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(35 \, A + 48 \, C\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{3 \, {\left({\left(35 \, A + 48 \, C\right)} \cos\left(d x + c\right) + 35 \, A + 48 \, C\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} + 56 \, A \cos\left(d x + c\right)^{3} + 2 \, {\left(35 \, A + 48 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(35 \, A + 48 \, C\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*(3*((35*A + 48*C)*cos(d*x + c) + 35*A + 48*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*(48*A*cos(d*x + c)^4 + 56*A*cos(d*x + c)^3 + 2*(35*A + 48*C)*cos(d*x + c)^2 + 3*(35*A + 48*C)*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*((35*A + 48*C)*cos(d*x + c) + 35*A + 48*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))) - (48*A*cos(d*x + c)^4 + 56*A*cos(d*x + c)^3 + 2*(35*A + 48*C)*cos(d*x + c)^2 + 3*(35*A + 48*C)*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
164,1,139,0,0.428701," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(143 \, A + 112 \, C\right)} a \cos\left(d x + c\right)^{5} + 4 \, {\left(143 \, A + 112 \, C\right)} a \cos\left(d x + c\right)^{4} + 3 \, {\left(143 \, A + 112 \, C\right)} a \cos\left(d x + c\right)^{3} + 5 \, {\left(33 \, A + 56 \, C\right)} a \cos\left(d x + c\right)^{2} + 245 \, C a \cos\left(d x + c\right) + 105 \, C a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{1155 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"2/1155*(8*(143*A + 112*C)*a*cos(d*x + c)^5 + 4*(143*A + 112*C)*a*cos(d*x + c)^4 + 3*(143*A + 112*C)*a*cos(d*x + c)^3 + 5*(33*A + 56*C)*a*cos(d*x + c)^2 + 245*C*a*cos(d*x + c) + 105*C*a)*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
165,1,120,0,0.467784," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(189 \, A + 136 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(189 \, A + 136 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 34 \, C\right)} a \cos\left(d x + c\right)^{2} + 85 \, C a \cos\left(d x + c\right) + 35 \, C 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*(2*(189*A + 136*C)*a*cos(d*x + c)^4 + (189*A + 136*C)*a*cos(d*x + c)^3 + 3*(21*A + 34*C)*a*cos(d*x + c)^2 + 85*C*a*cos(d*x + c) + 35*C*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
166,1,101,0,0.434338," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(175 \, A + 104 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(35 \, A + 52 \, C\right)} a \cos\left(d x + c\right)^{2} + 39 \, C a \cos\left(d x + c\right) + 15 \, C 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*((175*A + 104*C)*a*cos(d*x + c)^3 + (35*A + 52*C)*a*cos(d*x + c)^2 + 39*C*a*cos(d*x + c) + 15*C*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
167,1,346,0,0.471820," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(A a \cos\left(d x + c\right)^{3} + A a \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(5 \, A + 6 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, C a \cos\left(d x + c\right) + C a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{5 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, -\frac{2 \, {\left(5 \, {\left(A a \cos\left(d x + c\right)^{3} + A a \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(5 \, A + 6 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, C a \cos\left(d x + c\right) + C 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)}}{5 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/5*(5*(A*a*cos(d*x + c)^3 + A*a*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*((5*A + 6*C)*a*cos(d*x + c)^2 + 3*C*a*cos(d*x + c) + C*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), -2/5*(5*(A*a*cos(d*x + c)^3 + A*a*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))) - ((5*A + 6*C)*a*cos(d*x + c)^2 + 3*C*a*cos(d*x + c) + C*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
168,1,330,0,0.485529," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{9 \, {\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(3 \, A a \cos\left(d x + c\right)^{2} + 10 \, C a \cos\left(d x + c\right) + 2 \, C a\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{9 \, {\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(3 \, A a \cos\left(d x + c\right)^{2} + 10 \, C a \cos\left(d x + c\right) + 2 \, C 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)}}\right]"," ",0,"[1/6*(9*(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*a*cos(d*x + c)^2 + 10*C*a*cos(d*x + c) + 2*C*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)), -1/3*(9*(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*a*cos(d*x + c)^2 + 10*C*a*cos(d*x + c) + 2*C*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
169,1,318,0,0.517343," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(7 \, A + 8 \, C\right)} a \cos\left(d x + c\right) + {\left(7 \, A + 8 \, 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 \, {\left(2 \, A a \cos\left(d x + c\right)^{2} + 7 \, A a \cos\left(d x + c\right) + 8 \, C a\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 + 8 \, C\right)} a \cos\left(d x + c\right) + {\left(7 \, A + 8 \, 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) - {\left(2 \, A a \cos\left(d x + c\right)^{2} + 7 \, A a \cos\left(d x + c\right) + 8 \, C a\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 + 8*C)*a*cos(d*x + c) + (7*A + 8*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*(2*A*a*cos(d*x + c)^2 + 7*A*a*cos(d*x + c) + 8*C*a)*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 + 8*C)*a*cos(d*x + c) + (7*A + 8*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*A*a*cos(d*x + c)^2 + 7*A*a*cos(d*x + c) + 8*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
170,1,348,0,0.510922," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(11 \, A + 24 \, C\right)} a \cos\left(d x + c\right) + {\left(11 \, A + 24 \, 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 \, {\left(8 \, A a \cos\left(d x + c\right)^{3} + 22 \, A a \cos\left(d x + c\right)^{2} + 3 \, {\left(11 \, A + 8 \, C\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 + 24 \, C\right)} a \cos\left(d x + c\right) + {\left(11 \, A + 24 \, 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) - {\left(8 \, A a \cos\left(d x + c\right)^{3} + 22 \, A a \cos\left(d x + c\right)^{2} + 3 \, {\left(11 \, A + 8 \, C\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 + 24*C)*a*cos(d*x + c) + (11*A + 24*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*(8*A*a*cos(d*x + c)^3 + 22*A*a*cos(d*x + c)^2 + 3*(11*A + 8*C)*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 + 24*C)*a*cos(d*x + c) + (11*A + 24*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))) - (8*A*a*cos(d*x + c)^3 + 22*A*a*cos(d*x + c)^2 + 3*(11*A + 8*C)*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
171,1,380,0,0.542376," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(75 \, A + 112 \, C\right)} a \cos\left(d x + c\right) + {\left(75 \, A + 112 \, 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 \, {\left(16 \, A a \cos\left(d x + c\right)^{4} + 40 \, A a \cos\left(d x + c\right)^{3} + 2 \, {\left(25 \, A + 16 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(75 \, A + 112 \, C\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)}{128 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{{\left({\left(75 \, A + 112 \, C\right)} a \cos\left(d x + c\right) + {\left(75 \, A + 112 \, 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) - {\left(16 \, A a \cos\left(d x + c\right)^{4} + 40 \, A a \cos\left(d x + c\right)^{3} + 2 \, {\left(25 \, A + 16 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(75 \, A + 112 \, C\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)}{64 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/128*(((75*A + 112*C)*a*cos(d*x + c) + (75*A + 112*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*(16*A*a*cos(d*x + c)^4 + 40*A*a*cos(d*x + c)^3 + 2*(25*A + 16*C)*a*cos(d*x + c)^2 + (75*A + 112*C)*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), -1/64*(((75*A + 112*C)*a*cos(d*x + c) + (75*A + 112*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))) - (16*A*a*cos(d*x + c)^4 + 40*A*a*cos(d*x + c)^3 + 2*(25*A + 16*C)*a*cos(d*x + c)^2 + (75*A + 112*C)*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
172,1,420,0,0.557458," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(133 \, A + 176 \, C\right)} a \cos\left(d x + c\right) + {\left(133 \, A + 176 \, 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 \, {\left(384 \, A a \cos\left(d x + c\right)^{5} + 912 \, A a \cos\left(d x + c\right)^{4} + 8 \, {\left(133 \, A + 80 \, C\right)} a \cos\left(d x + c\right)^{3} + 10 \, {\left(133 \, A + 176 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(133 \, A + 176 \, C\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)}{3840 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{15 \, {\left({\left(133 \, A + 176 \, C\right)} a \cos\left(d x + c\right) + {\left(133 \, A + 176 \, 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) - {\left(384 \, A a \cos\left(d x + c\right)^{5} + 912 \, A a \cos\left(d x + c\right)^{4} + 8 \, {\left(133 \, A + 80 \, C\right)} a \cos\left(d x + c\right)^{3} + 10 \, {\left(133 \, A + 176 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(133 \, A + 176 \, C\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)}{1920 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/3840*(15*((133*A + 176*C)*a*cos(d*x + c) + (133*A + 176*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*(384*A*a*cos(d*x + c)^5 + 912*A*a*cos(d*x + c)^4 + 8*(133*A + 80*C)*a*cos(d*x + c)^3 + 10*(133*A + 176*C)*a*cos(d*x + c)^2 + 15*(133*A + 176*C)*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), -1/1920*(15*((133*A + 176*C)*a*cos(d*x + c) + (133*A + 176*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))) - (384*A*a*cos(d*x + c)^5 + 912*A*a*cos(d*x + c)^4 + 8*(133*A + 80*C)*a*cos(d*x + c)^3 + 10*(133*A + 176*C)*a*cos(d*x + c)^2 + 15*(133*A + 176*C)*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
173,1,171,0,0.441676," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(10439 \, A + 8368 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + 4 \, {\left(10439 \, A + 8368 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 3 \, {\left(10439 \, A + 8368 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(1859 \, A + 2092 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 35 \, {\left(143 \, A + 523 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 11970 \, C a^{2} \cos\left(d x + c\right) + 3465 \, C 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)}{45045 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"2/45045*(8*(10439*A + 8368*C)*a^2*cos(d*x + c)^6 + 4*(10439*A + 8368*C)*a^2*cos(d*x + c)^5 + 3*(10439*A + 8368*C)*a^2*cos(d*x + c)^4 + 10*(1859*A + 2092*C)*a^2*cos(d*x + c)^3 + 35*(143*A + 523*C)*a^2*cos(d*x + c)^2 + 11970*C*a^2*cos(d*x + c) + 3465*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^7 + d*cos(d*x + c)^6)","A",0
174,1,149,0,0.441401," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(759 \, A + 568 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(759 \, A + 568 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 6 \, {\left(66 \, A + 71 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(99 \, A + 355 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 224 \, C a^{2} \cos\left(d x + c\right) + 63 \, C 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)}{693 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"2/693*(2*(759*A + 568*C)*a^2*cos(d*x + c)^5 + (759*A + 568*C)*a^2*cos(d*x + c)^4 + 6*(66*A + 71*C)*a^2*cos(d*x + c)^3 + (99*A + 355*C)*a^2*cos(d*x + c)^2 + 224*C*a^2*cos(d*x + c) + 63*C*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
175,1,130,0,0.437011," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(903 \, A + 584 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 2 \, {\left(147 \, A + 146 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 73 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 130 \, C a^{2} \cos\left(d x + c\right) + 35 \, C 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*((903*A + 584*C)*a^2*cos(d*x + c)^4 + 2*(147*A + 146*C)*a^2*cos(d*x + c)^3 + 3*(21*A + 73*C)*a^2*cos(d*x + c)^2 + 130*C*a^2*cos(d*x + c) + 35*C*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
176,1,408,0,0.490659," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{21 \, {\left(A a^{2} \cos\left(d x + c\right)^{4} + A a^{2} \cos\left(d x + c\right)^{3}\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 \, {\left(28 \, A + 23 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(7 \, A + 23 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 12 \, C a^{2} \cos\left(d x + c\right) + 3 \, C 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)}{21 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}, -\frac{2 \, {\left(21 \, {\left(A a^{2} \cos\left(d x + c\right)^{4} + A a^{2} \cos\left(d x + c\right)^{3}\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 \, {\left(28 \, A + 23 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(7 \, A + 23 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 12 \, C a^{2} \cos\left(d x + c\right) + 3 \, C 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)}}{21 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/21*(21*(A*a^2*cos(d*x + c)^4 + A*a^2*cos(d*x + c)^3)*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*(28*A + 23*C)*a^2*cos(d*x + c)^3 + (7*A + 23*C)*a^2*cos(d*x + c)^2 + 12*C*a^2*cos(d*x + c) + 3*C*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), -2/21*(21*(A*a^2*cos(d*x + c)^4 + A*a^2*cos(d*x + c)^3)*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*(28*A + 23*C)*a^2*cos(d*x + c)^3 + (7*A + 23*C)*a^2*cos(d*x + c)^2 + 12*C*a^2*cos(d*x + c) + 3*C*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
177,1,398,0,0.472210," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{75 \, {\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(15 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(15 \, A + 43 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 28 \, C a^{2} \cos\left(d x + c\right) + 6 \, C 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)}{30 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, -\frac{75 \, {\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(15 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(15 \, A + 43 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 28 \, C a^{2} \cos\left(d x + c\right) + 6 \, C 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)}}\right]"," ",0,"[1/30*(75*(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*(15*A*a^2*cos(d*x + c)^3 + 2*(15*A + 43*C)*a^2*cos(d*x + c)^2 + 28*C*a^2*cos(d*x + c) + 6*C*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), -1/15*(75*(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))) - (15*A*a^2*cos(d*x + c)^3 + 2*(15*A + 43*C)*a^2*cos(d*x + c)^2 + 28*C*a^2*cos(d*x + c) + 6*C*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
178,1,402,0,0.510237," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(19 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(19 \, A + 8 \, C\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(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 33 \, A a^{2} \cos\left(d x + c\right)^{2} + 64 \, C a^{2} \cos\left(d x + c\right) + 8 \, C 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)}{24 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, -\frac{3 \, {\left({\left(19 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(19 \, A + 8 \, C\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(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 33 \, A a^{2} \cos\left(d x + c\right)^{2} + 64 \, C a^{2} \cos\left(d x + c\right) + 8 \, C 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)}{12 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/24*(3*((19*A + 8*C)*a^2*cos(d*x + c)^2 + (19*A + 8*C)*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*(6*A*a^2*cos(d*x + c)^3 + 33*A*a^2*cos(d*x + c)^2 + 64*C*a^2*cos(d*x + c) + 8*C*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)), -1/12*(3*((19*A + 8*C)*a^2*cos(d*x + c)^2 + (19*A + 8*C)*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))) - (6*A*a^2*cos(d*x + c)^3 + 33*A*a^2*cos(d*x + c)^2 + 64*C*a^2*cos(d*x + c) + 8*C*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
179,1,380,0,0.508257," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(5 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(5 \, A + 8 \, C\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} + 34 \, A a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(25 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + 48 \, C 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)}{48 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{15 \, {\left({\left(5 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(5 \, A + 8 \, C\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} + 34 \, A a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(25 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + 48 \, C 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)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/48*(15*((5*A + 8*C)*a^2*cos(d*x + c) + (5*A + 8*C)*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 + 34*A*a^2*cos(d*x + c)^2 + 3*(25*A + 8*C)*a^2*cos(d*x + c) + 48*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/24*(15*((5*A + 8*C)*a^2*cos(d*x + c) + (5*A + 8*C)*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 + 34*A*a^2*cos(d*x + c)^2 + 3*(25*A + 8*C)*a^2*cos(d*x + c) + 48*C*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
180,1,408,0,0.557720," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(163 \, A + 304 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(163 \, A + 304 \, C\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} + 184 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(163 \, A + 48 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A + 176 \, C\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 + 304 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(163 \, A + 304 \, C\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} + 184 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(163 \, A + 48 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A + 176 \, C\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 + 304*C)*a^2*cos(d*x + c) + (163*A + 304*C)*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 + 184*A*a^2*cos(d*x + c)^3 + 2*(163*A + 48*C)*a^2*cos(d*x + c)^2 + 3*(163*A + 176*C)*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 + 304*C)*a^2*cos(d*x + c) + (163*A + 304*C)*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 + 184*A*a^2*cos(d*x + c)^3 + 2*(163*A + 48*C)*a^2*cos(d*x + c)^2 + 3*(163*A + 176*C)*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
181,1,448,0,0.548194," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(283 \, A + 400 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(283 \, A + 400 \, C\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} + 1392 \, A a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(283 \, A + 80 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(283 \, A + 272 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(283 \, A + 400 \, C\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 + 400 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(283 \, A + 400 \, C\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} + 1392 \, A a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(283 \, A + 80 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(283 \, A + 272 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(283 \, A + 400 \, C\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 + 400*C)*a^2*cos(d*x + c) + (283*A + 400*C)*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 + 1392*A*a^2*cos(d*x + c)^4 + 8*(283*A + 80*C)*a^2*cos(d*x + c)^3 + 10*(283*A + 272*C)*a^2*cos(d*x + c)^2 + 15*(283*A + 400*C)*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 + 400*C)*a^2*cos(d*x + c) + (283*A + 400*C)*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 + 1392*A*a^2*cos(d*x + c)^4 + 8*(283*A + 80*C)*a^2*cos(d*x + c)^3 + 10*(283*A + 272*C)*a^2*cos(d*x + c)^2 + 15*(283*A + 400*C)*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
182,1,488,0,0.555354," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(1015 \, A + 1304 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(1015 \, A + 1304 \, C\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(256 \, A a^{2} \cos\left(d x + c\right)^{6} + 896 \, A a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(29 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(203 \, A + 184 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(1015 \, A + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(1015 \, A + 1304 \, C\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)}{3072 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{3 \, {\left({\left(1015 \, A + 1304 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(1015 \, A + 1304 \, C\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(256 \, A a^{2} \cos\left(d x + c\right)^{6} + 896 \, A a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(29 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(203 \, A + 184 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(1015 \, A + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(1015 \, A + 1304 \, C\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)}{1536 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/3072*(3*((1015*A + 1304*C)*a^2*cos(d*x + c) + (1015*A + 1304*C)*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*(256*A*a^2*cos(d*x + c)^6 + 896*A*a^2*cos(d*x + c)^5 + 48*(29*A + 8*C)*a^2*cos(d*x + c)^4 + 8*(203*A + 184*C)*a^2*cos(d*x + c)^3 + 2*(1015*A + 1304*C)*a^2*cos(d*x + c)^2 + 3*(1015*A + 1304*C)*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), -1/1536*(3*((1015*A + 1304*C)*a^2*cos(d*x + c) + (1015*A + 1304*C)*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))) - (256*A*a^2*cos(d*x + c)^6 + 896*A*a^2*cos(d*x + c)^5 + 48*(29*A + 8*C)*a^2*cos(d*x + c)^4 + 8*(203*A + 184*C)*a^2*cos(d*x + c)^3 + 2*(1015*A + 1304*C)*a^2*cos(d*x + c)^2 + 3*(1015*A + 1304*C)*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
183,1,445,0,0.503225," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{315 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{5} + {\left(A + C\right)} a \cos\left(d x + c\right)^{4}\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(273 \, A + 257 \, C\right)} \cos\left(d x + c\right)^{4} - {\left(21 \, A + 29 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} - 5 \, C \cos\left(d x + c\right) + 35 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{630 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}, \frac{2 \, {\left({\left(273 \, A + 257 \, C\right)} \cos\left(d x + c\right)^{4} - {\left(21 \, A + 29 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} - 5 \, C \cos\left(d x + c\right) + 35 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) + \frac{315 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{5} + {\left(A + C\right)} a \cos\left(d x + c\right)^{4}\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}}}{315 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/630*(315*sqrt(2)*((A + C)*a*cos(d*x + c)^5 + (A + C)*a*cos(d*x + c)^4)*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*((273*A + 257*C)*cos(d*x + c)^4 - (21*A + 29*C)*cos(d*x + c)^3 + 3*(21*A + 19*C)*cos(d*x + c)^2 - 5*C*cos(d*x + c) + 35*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c)^5 + a*d*cos(d*x + c)^4), 1/315*(2*((273*A + 257*C)*cos(d*x + c)^4 - (21*A + 29*C)*cos(d*x + c)^3 + 3*(21*A + 19*C)*cos(d*x + c)^2 - 5*C*cos(d*x + c) + 35*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 315*sqrt(2)*((A + C)*a*cos(d*x + c)^5 + (A + C)*a*cos(d*x + c)^4)*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)^5 + a*d*cos(d*x + c)^4)]","A",0
184,1,412,0,0.502278," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A + C\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(35 \, A + 43 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(35 \, A + 31 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) - 15 \, C\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(35 \, A + 43 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(35 \, A + 31 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) - 15 \, C\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 + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A + C\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 + C)*a*cos(d*x + c)^4 + (A + C)*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*((35*A + 43*C)*cos(d*x + c)^3 - (35*A + 31*C)*cos(d*x + c)^2 + 3*C*cos(d*x + c) - 15*C)*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*((35*A + 43*C)*cos(d*x + c)^3 - (35*A + 31*C)*cos(d*x + c)^2 + 3*C*cos(d*x + c) - 15*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 105*sqrt(2)*((A + C)*a*cos(d*x + c)^4 + (A + C)*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
185,1,377,0,0.488869," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A + C\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(15 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{2} - C \cos\left(d x + c\right) + 3 \, C\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(15 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{2} - C \cos\left(d x + c\right) + 3 \, C\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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A + C\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 + C)*a*cos(d*x + c)^3 + (A + C)*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*((15*A + 13*C)*cos(d*x + c)^2 - C*cos(d*x + c) + 3*C)*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*((15*A + 13*C)*cos(d*x + c)^2 - C*cos(d*x + c) + 3*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 15*sqrt(2)*((A + C)*a*cos(d*x + c)^3 + (A + C)*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
186,1,336,0,0.501385," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A + C\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(C \cos\left(d x + c\right) - C\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(C \cos\left(d x + c\right) - C\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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A + C\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 + C)*a*cos(d*x + c)^2 + (A + C)*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*(C*cos(d*x + c) - C)*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*(C*cos(d*x + c) - C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 3*sqrt(2)*((A + C)*a*cos(d*x + c)^2 + (A + C)*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
187,1,427,0,1.241703," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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) - 2 \, {\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) + 4 \, C \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 \, {\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) - 2 \, C \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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + C)*a*cos(d*x + c) + (A + C)*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*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*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*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))) - 2*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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
188,1,437,0,1.250306," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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(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 \, {\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(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) - \frac{\sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + C)*a*cos(d*x + c) + (A + C)*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*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*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*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))) - sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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
189,1,489,0,2.401243," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + 8 \, C\right)} \cos\left(d x + c\right) + 7 \, A + 8 \, C\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} - 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(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{{\left({\left(7 \, A + 8 \, C\right)} \cos\left(d x + c\right) + 7 \, A + 8 \, C\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} - 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) - \frac{4 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + C)*a*cos(d*x + c) + (A + C)*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 + 8*C)*cos(d*x + c) + 7*A + 8*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*(2*A*cos(d*x + c)^2 - A*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 + 8*C)*cos(d*x + c) + 7*A + 8*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))) - (2*A*cos(d*x + c)^2 - A*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 4*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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
190,1,524,0,2.427733," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{24 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + 8 \, C\right)} \cos\left(d x + c\right) + 9 \, A + 8 \, C\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 \, A \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A + 8 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right) + 9 \, A + 8 \, C\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 \, A \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A + 8 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + C)*a*cos(d*x + c) + (A + C)*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 + 8*C)*cos(d*x + c) + 9*A + 8*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*(8*A*cos(d*x + c)^3 - 2*A*cos(d*x + c)^2 + 3*(7*A + 8*C)*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 + 8*C)*cos(d*x + c) + 9*A + 8*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))) + (8*A*cos(d*x + c)^3 - 2*A*cos(d*x + c)^2 + 3*(7*A + 8*C)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 24*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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
191,1,558,0,3.407634," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{192 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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(107 \, A + 112 \, C\right)} \cos\left(d x + c\right) + 107 \, A + 112 \, C\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 \, A \cos\left(d x + c\right)^{3} + 2 \, {\left(43 \, A + 48 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(21 \, A + 16 \, C\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(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{3 \, {\left({\left(107 \, A + 112 \, C\right)} \cos\left(d x + c\right) + 107 \, A + 112 \, C\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 \, A \cos\left(d x + c\right)^{3} + 2 \, {\left(43 \, A + 48 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(21 \, A + 16 \, C\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{192 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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}}}{192 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/384*(192*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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*((107*A + 112*C)*cos(d*x + c) + 107*A + 112*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*(48*A*cos(d*x + c)^4 - 8*A*cos(d*x + c)^3 + 2*(43*A + 48*C)*cos(d*x + c)^2 - 3*(21*A + 16*C)*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), -1/192*(3*((107*A + 112*C)*cos(d*x + c) + 107*A + 112*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))) - (48*A*cos(d*x + c)^4 - 8*A*cos(d*x + c)^3 + 2*(43*A + 48*C)*cos(d*x + c)^2 - 3*(21*A + 16*C)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 192*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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
192,1,527,0,0.499693," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, \sqrt{2} {\left({\left(11 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(11 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(11 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3}\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(665 \, A + 1201 \, C\right)} \cos\left(d x + c\right)^{4} + 12 \, {\left(35 \, A + 67 \, C\right)} \cos\left(d x + c\right)^{3} - 28 \, {\left(5 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 36 \, C \cos\left(d x + c\right) - 60 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{840 \, {\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)}}, -\frac{105 \, \sqrt{2} {\left({\left(11 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(11 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(11 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3}\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(665 \, A + 1201 \, C\right)} \cos\left(d x + c\right)^{4} + 12 \, {\left(35 \, A + 67 \, C\right)} \cos\left(d x + c\right)^{3} - 28 \, {\left(5 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 36 \, C \cos\left(d x + c\right) - 60 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{420 \, {\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)}}\right]"," ",0,"[-1/840*(105*sqrt(2)*((11*A + 19*C)*cos(d*x + c)^5 + 2*(11*A + 19*C)*cos(d*x + c)^4 + (11*A + 19*C)*cos(d*x + c)^3)*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*((665*A + 1201*C)*cos(d*x + c)^4 + 12*(35*A + 67*C)*cos(d*x + c)^3 - 28*(5*A + 7*C)*cos(d*x + c)^2 + 36*C*cos(d*x + c) - 60*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), -1/420*(105*sqrt(2)*((11*A + 19*C)*cos(d*x + c)^5 + 2*(11*A + 19*C)*cos(d*x + c)^4 + (11*A + 19*C)*cos(d*x + c)^3)*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*((665*A + 1201*C)*cos(d*x + c)^4 + 12*(35*A + 67*C)*cos(d*x + c)^3 - 28*(5*A + 7*C)*cos(d*x + c)^2 + 36*C*cos(d*x + c) - 60*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
193,1,492,0,0.527225," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{5 \, \sqrt{2} {\left({\left(7 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A + 15 \, C\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(25 \, A + 49 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(5 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{2} - 4 \, C \cos\left(d x + c\right) + 4 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{40 \, {\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{5 \, \sqrt{2} {\left({\left(7 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A + 15 \, C\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(25 \, A + 49 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(5 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{2} - 4 \, C \cos\left(d x + c\right) + 4 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{20 \, {\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,"[-1/40*(5*sqrt(2)*((7*A + 15*C)*cos(d*x + c)^4 + 2*(7*A + 15*C)*cos(d*x + c)^3 + (7*A + 15*C)*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*((25*A + 49*C)*cos(d*x + c)^3 + 4*(5*A + 9*C)*cos(d*x + c)^2 - 4*C*cos(d*x + c) + 4*C)*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), 1/20*(5*sqrt(2)*((7*A + 15*C)*cos(d*x + c)^4 + 2*(7*A + 15*C)*cos(d*x + c)^3 + (7*A + 15*C)*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*((25*A + 49*C)*cos(d*x + c)^3 + 4*(5*A + 9*C)*cos(d*x + c)^2 - 4*C*cos(d*x + c) + 4*C)*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
194,1,451,0,0.514422," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(3 \, A + 11 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A + 11 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A + 11 \, C\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(3 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 12 \, C \cos\left(d x + c\right) - 4 \, C\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(3 \, A + 11 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A + 11 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A + 11 \, C\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(3 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 12 \, C \cos\left(d x + c\right) - 4 \, C\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)*((3*A + 11*C)*cos(d*x + c)^3 + 2*(3*A + 11*C)*cos(d*x + c)^2 + (3*A + 11*C)*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*((3*A + 19*C)*cos(d*x + c)^2 + 12*C*cos(d*x + c) - 4*C)*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)*((3*A + 11*C)*cos(d*x + c)^3 + 2*(3*A + 11*C)*cos(d*x + c)^2 + (3*A + 11*C)*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*((3*A + 19*C)*cos(d*x + c)^2 + 12*C*cos(d*x + c) - 4*C)*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
195,1,374,0,0.501309," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(A - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 7 \, C\right)} \cos\left(d x + c\right) + A - 7 \, C\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 \, C\right)} \cos\left(d x + c\right) + 4 \, C\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(A - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 7 \, C\right)} \cos\left(d x + c\right) + A - 7 \, C\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 \, C\right)} \cos\left(d x + c\right) + 4 \, C\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)*((A - 7*C)*cos(d*x + c)^2 + 2*(A - 7*C)*cos(d*x + c) + A - 7*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*((A + 5*C)*cos(d*x + c) + 4*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)*((A - 7*C)*cos(d*x + c)^2 + 2*(A - 7*C)*cos(d*x + c) + A - 7*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*((A + 5*C)*cos(d*x + c) + 4*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
196,1,544,0,3.163257," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(A + C\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 - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - 3 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 3 \, C\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 + C\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 - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - 3 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 3 \, C\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 + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((5*A - 3*C)*cos(d*x + c)^2 + 2*(5*A - 3*C)*cos(d*x + c) + 5*A - 3*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)) + 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 + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((5*A - 3*C)*cos(d*x + c)^2 + 2*(5*A - 3*C)*cos(d*x + c) + 5*A - 3*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))) + 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
197,1,560,0,3.165631," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(9 \, A + C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(9 \, A + C\right)} \cos\left(d x + c\right) + 9 \, A + C\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) + 12 \, {\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) - 4 \, {\left(2 \, A \cos\left(d x + c\right)^{2} + {\left(3 \, A + C\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 + C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(9 \, A + C\right)} \cos\left(d x + c\right) + 9 \, A + C\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) - 12 \, {\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) - 2 \, {\left(2 \, A \cos\left(d x + c\right)^{2} + {\left(3 \, A + C\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 + C)*cos(d*x + c)^2 + 2*(9*A + C)*cos(d*x + c) + 9*A + 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)) + 12*(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)) - 4*(2*A*cos(d*x + c)^2 + (3*A + C)*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 + C)*cos(d*x + c)^2 + 2*(9*A + C)*cos(d*x + c) + 9*A + 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))) - 12*(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))) - 2*(2*A*cos(d*x + c)^2 + (3*A + C)*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
198,1,631,0,5.794735," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(13 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(13 \, A + 5 \, C\right)} \cos\left(d x + c\right) + 13 \, A + 5 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(19 \, A + 8 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 8 \, C\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} - 3 \, A \cos\left(d x + c\right)^{2} - {\left(7 \, A + 2 \, C\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 + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(13 \, A + 5 \, C\right)} \cos\left(d x + c\right) + 13 \, A + 5 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(19 \, A + 8 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 8 \, C\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} - 3 \, A \cos\left(d x + c\right)^{2} - {\left(7 \, A + 2 \, C\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 + 5*C)*cos(d*x + c)^2 + 2*(13*A + 5*C)*cos(d*x + c) + 13*A + 5*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)) + ((19*A + 8*C)*cos(d*x + c)^2 + 2*(19*A + 8*C)*cos(d*x + c) + 19*A + 8*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*(2*A*cos(d*x + c)^3 - 3*A*cos(d*x + c)^2 - (7*A + 2*C)*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 + 5*C)*cos(d*x + c)^2 + 2*(13*A + 5*C)*cos(d*x + c) + 13*A + 5*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))) - ((19*A + 8*C)*cos(d*x + c)^2 + 2*(19*A + 8*C)*cos(d*x + c) + 19*A + 8*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))) + (2*A*cos(d*x + c)^3 - 3*A*cos(d*x + c)^2 - (7*A + 2*C)*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
199,1,668,0,5.796963," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{6 \, \sqrt{2} {\left({\left(17 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(17 \, A + 9 \, C\right)} \cos\left(d x + c\right) + 17 \, A + 9 \, C\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 + 24 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(47 \, A + 24 \, C\right)} \cos\left(d x + c\right) + 47 \, A + 24 \, C\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 \, A \cos\left(d x + c\right)^{3} + {\left(37 \, A + 24 \, C\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(7 \, A + 4 \, C\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 + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(17 \, A + 9 \, C\right)} \cos\left(d x + c\right) + 17 \, A + 9 \, C\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 + 24 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(47 \, A + 24 \, C\right)} \cos\left(d x + c\right) + 47 \, A + 24 \, C\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 \, A \cos\left(d x + c\right)^{3} + {\left(37 \, A + 24 \, C\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(7 \, A + 4 \, C\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 + 9*C)*cos(d*x + c)^2 + 2*(17*A + 9*C)*cos(d*x + c) + 17*A + 9*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)) + 3*((47*A + 24*C)*cos(d*x + c)^2 + 2*(47*A + 24*C)*cos(d*x + c) + 47*A + 24*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*(8*A*cos(d*x + c)^4 - 6*A*cos(d*x + c)^3 + (37*A + 24*C)*cos(d*x + c)^2 + 9*(7*A + 4*C)*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 + 9*C)*cos(d*x + c)^2 + 2*(17*A + 9*C)*cos(d*x + c) + 17*A + 9*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))) - 3*((47*A + 24*C)*cos(d*x + c)^2 + 2*(47*A + 24*C)*cos(d*x + c) + 47*A + 24*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))) - (8*A*cos(d*x + c)^4 - 6*A*cos(d*x + c)^3 + (37*A + 24*C)*cos(d*x + c)^2 + 9*(7*A + 4*C)*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
200,1,588,0,0.510205," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left({\left(75 \, A + 283 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(75 \, A + 283 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(75 \, A + 283 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(75 \, A + 283 \, C\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(735 \, A + 2671 \, C\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(255 \, A + 911 \, C\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(15 \, A + 49 \, C\right)} \cos\left(d x + c\right)^{2} - 160 \, C \cos\left(d x + c\right) + 96 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{960 \, {\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)}}, \frac{15 \, \sqrt{2} {\left({\left(75 \, A + 283 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(75 \, A + 283 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(75 \, A + 283 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(75 \, A + 283 \, C\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(735 \, A + 2671 \, C\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(255 \, A + 911 \, C\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(15 \, A + 49 \, C\right)} \cos\left(d x + c\right)^{2} - 160 \, C \cos\left(d x + c\right) + 96 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{480 \, {\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)}}\right]"," ",0,"[-1/960*(15*sqrt(2)*((75*A + 283*C)*cos(d*x + c)^5 + 3*(75*A + 283*C)*cos(d*x + c)^4 + 3*(75*A + 283*C)*cos(d*x + c)^3 + (75*A + 283*C)*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*((735*A + 2671*C)*cos(d*x + c)^4 + 5*(255*A + 911*C)*cos(d*x + c)^3 + 32*(15*A + 49*C)*cos(d*x + c)^2 - 160*C*cos(d*x + c) + 96*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), 1/480*(15*sqrt(2)*((75*A + 283*C)*cos(d*x + c)^5 + 3*(75*A + 283*C)*cos(d*x + c)^4 + 3*(75*A + 283*C)*cos(d*x + c)^3 + (75*A + 283*C)*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*((735*A + 2671*C)*cos(d*x + c)^4 + 5*(255*A + 911*C)*cos(d*x + c)^3 + 32*(15*A + 49*C)*cos(d*x + c)^2 - 160*C*cos(d*x + c) + 96*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
201,1,545,0,0.529011," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(19 \, A + 163 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(19 \, A + 163 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 163 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(19 \, A + 163 \, C\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(27 \, A + 299 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A + 503 \, C\right)} \cos\left(d x + c\right)^{2} + 160 \, C \cos\left(d x + c\right) - 32 \, C\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(19 \, A + 163 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(19 \, A + 163 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 163 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(19 \, A + 163 \, C\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(27 \, A + 299 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A + 503 \, C\right)} \cos\left(d x + c\right)^{2} + 160 \, C \cos\left(d x + c\right) - 32 \, C\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)*((19*A + 163*C)*cos(d*x + c)^4 + 3*(19*A + 163*C)*cos(d*x + c)^3 + 3*(19*A + 163*C)*cos(d*x + c)^2 + (19*A + 163*C)*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*((27*A + 299*C)*cos(d*x + c)^3 + (39*A + 503*C)*cos(d*x + c)^2 + 160*C*cos(d*x + c) - 32*C)*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)*((19*A + 163*C)*cos(d*x + c)^4 + 3*(19*A + 163*C)*cos(d*x + c)^3 + 3*(19*A + 163*C)*cos(d*x + c)^2 + (19*A + 163*C)*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*((27*A + 299*C)*cos(d*x + c)^3 + (39*A + 503*C)*cos(d*x + c)^2 + 160*C*cos(d*x + c) - 32*C)*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
202,1,464,0,0.517759," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{5 \, \sqrt{2} {\left({\left(A - 15 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A - 15 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A - 15 \, C\right)} \cos\left(d x + c\right) + A - 15 \, C\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 + 49 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(A + 17 \, C\right)} \cos\left(d x + c\right) + 32 \, C\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{5 \, \sqrt{2} {\left({\left(A - 15 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A - 15 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A - 15 \, C\right)} \cos\left(d x + c\right) + A - 15 \, C\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 + 49 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(A + 17 \, C\right)} \cos\left(d x + c\right) + 32 \, C\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*(5*sqrt(2)*((A - 15*C)*cos(d*x + c)^3 + 3*(A - 15*C)*cos(d*x + c)^2 + 3*(A - 15*C)*cos(d*x + c) + A - 15*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*((A + 49*C)*cos(d*x + c)^2 + 5*(A + 17*C)*cos(d*x + c) + 32*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*(5*sqrt(2)*((A - 15*C)*cos(d*x + c)^3 + 3*(A - 15*C)*cos(d*x + c)^2 + 3*(A - 15*C)*cos(d*x + c) + A - 15*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*((A + 49*C)*cos(d*x + c)^2 + 5*(A + 17*C)*cos(d*x + c) + 32*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
203,1,479,0,0.491990," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(3 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 19 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 19 \, C\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 - 9 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - 13 \, C\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 + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 19 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 19 \, C\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 - 9 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - 13 \, C\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 + 19*C)*cos(d*x + c)^3 + 3*(3*A + 19*C)*cos(d*x + c)^2 + 3*(3*A + 19*C)*cos(d*x + c) + 3*A + 19*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*((7*A - 9*C)*cos(d*x + c)^2 + (3*A - 13*C)*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 + 19*C)*cos(d*x + c)^3 + 3*(3*A + 19*C)*cos(d*x + c)^2 + 3*(3*A + 19*C)*cos(d*x + c) + 3*A + 19*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*((7*A - 9*C)*cos(d*x + c)^2 + (3*A - 13*C)*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
204,1,670,0,6.376578," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(43 \, A - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 5 \, C\right)} \cos\left(d x + c\right) + 43 \, A - 5 \, C\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 - C\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, A - 5 \, C\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 - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 5 \, C\right)} \cos\left(d x + c\right) + 43 \, A - 5 \, C\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 - C\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, A - 5 \, C\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 - 5*C)*cos(d*x + c)^3 + 3*(43*A - 5*C)*cos(d*x + c)^2 + 3*(43*A - 5*C)*cos(d*x + c) + 43*A - 5*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)) - 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 - C)*cos(d*x + c)^2 + (11*A - 5*C)*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 - 5*C)*cos(d*x + c)^3 + 3*(43*A - 5*C)*cos(d*x + c)^2 + 3*(43*A - 5*C)*cos(d*x + c) + 43*A - 5*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))) - 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 - C)*cos(d*x + c)^2 + (11*A - 5*C)*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
205,1,692,0,6.333185," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(115 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(115 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 115 \, A + 3 \, C\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) + 160 \, {\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(16 \, A \cos\left(d x + c\right)^{3} + {\left(55 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(35 \, A + 3 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(115 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 115 \, A + 3 \, C\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) - 160 \, {\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(16 \, A \cos\left(d x + c\right)^{3} + {\left(55 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(35 \, A + 3 \, C\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 + 3*C)*cos(d*x + c)^3 + 3*(115*A + 3*C)*cos(d*x + c)^2 + 3*(115*A + 3*C)*cos(d*x + c) + 115*A + 3*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)) + 160*(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*(16*A*cos(d*x + c)^3 + (55*A + 7*C)*cos(d*x + c)^2 + (35*A + 3*C)*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 + 3*C)*cos(d*x + c)^3 + 3*(115*A + 3*C)*cos(d*x + c)^2 + 3*(115*A + 3*C)*cos(d*x + c) + 115*A + 3*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))) - 160*(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*(16*A*cos(d*x + c)^3 + (55*A + 7*C)*cos(d*x + c)^2 + (35*A + 3*C)*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
206,1,763,0,10.840128," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(219 \, A + 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(219 \, A + 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(219 \, A + 43 \, C\right)} \cos\left(d x + c\right) + 219 \, A + 43 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(39 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(39 \, A + 8 \, C\right)} \cos\left(d x + c\right) + 39 \, A + 8 \, C\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} - 20 \, A \cos\left(d x + c\right)^{3} - 5 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(63 \, A + 11 \, C\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 + 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(219 \, A + 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(219 \, A + 43 \, C\right)} \cos\left(d x + c\right) + 219 \, A + 43 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(39 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(39 \, A + 8 \, C\right)} \cos\left(d x + c\right) + 39 \, A + 8 \, C\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} - 20 \, A \cos\left(d x + c\right)^{3} - 5 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(63 \, A + 11 \, C\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 + 43*C)*cos(d*x + c)^3 + 3*(219*A + 43*C)*cos(d*x + c)^2 + 3*(219*A + 43*C)*cos(d*x + c) + 219*A + 43*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)) + 8*((39*A + 8*C)*cos(d*x + c)^3 + 3*(39*A + 8*C)*cos(d*x + c)^2 + 3*(39*A + 8*C)*cos(d*x + c) + 39*A + 8*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)) - 4*(8*A*cos(d*x + c)^4 - 20*A*cos(d*x + c)^3 - 5*(19*A + 3*C)*cos(d*x + c)^2 - (63*A + 11*C)*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 + 43*C)*cos(d*x + c)^3 + 3*(219*A + 43*C)*cos(d*x + c)^2 + 3*(219*A + 43*C)*cos(d*x + c) + 219*A + 43*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))) - 8*((39*A + 8*C)*cos(d*x + c)^3 + 3*(39*A + 8*C)*cos(d*x + c)^2 + 3*(39*A + 8*C)*cos(d*x + c) + 39*A + 8*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))) + 2*(8*A*cos(d*x + c)^4 - 20*A*cos(d*x + c)^3 - 5*(19*A + 3*C)*cos(d*x + c)^2 - (63*A + 11*C)*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
207,0,0,0,0.434569," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \sec\left(d x + c\right)^{4} + C a \sec\left(d x + c\right)^{3} + A 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((C*a*sec(d*x + c)^4 + C*a*sec(d*x + c)^3 + A*a*sec(d*x + c)^2 + A*a*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
208,0,0,0,0.438107," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \sec\left(d x + c\right)^{3} + C a \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right) + A a\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*a*sec(d*x + c)^3 + C*a*sec(d*x + c)^2 + A*a*sec(d*x + c) + A*a)*sqrt(sec(d*x + c)), x)","F",0
209,0,0,0,0.451467," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + C a \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right) + A a}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a*sec(d*x + c)^3 + C*a*sec(d*x + c)^2 + A*a*sec(d*x + c) + A*a)/sqrt(sec(d*x + c)), x)","F",0
210,0,0,0,0.439574," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + C a \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right) + A a}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a*sec(d*x + c)^3 + C*a*sec(d*x + c)^2 + A*a*sec(d*x + c) + A*a)/sec(d*x + c)^(3/2), x)","F",0
211,0,0,0,0.458987," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + C a \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right) + A a}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*a*sec(d*x + c)^3 + C*a*sec(d*x + c)^2 + A*a*sec(d*x + c) + A*a)/sec(d*x + c)^(5/2), x)","F",0
212,0,0,0,0.443612," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + C a \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right) + A a}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*a*sec(d*x + c)^3 + C*a*sec(d*x + c)^2 + A*a*sec(d*x + c) + A*a)/sec(d*x + c)^(7/2), x)","F",0
213,0,0,0,0.449367," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + C a \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right) + A a}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*a*sec(d*x + c)^3 + C*a*sec(d*x + c)^2 + A*a*sec(d*x + c) + A*a)/sec(d*x + c)^(9/2), x)","F",0
214,0,0,0,0.438716," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \sec\left(d x + c\right)^{5} + 2 \, C a^{2} \sec\left(d x + c\right)^{4} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{3} + 2 \, A 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((C*a^2*sec(d*x + c)^5 + 2*C*a^2*sec(d*x + c)^4 + (A + C)*a^2*sec(d*x + c)^3 + 2*A*a^2*sec(d*x + c)^2 + A*a^2*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
215,0,0,0,0.462804," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \sec\left(d x + c\right) + A a^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + 2*C*a^2*sec(d*x + c)^3 + (A + C)*a^2*sec(d*x + c)^2 + 2*A*a^2*sec(d*x + c) + A*a^2)*sqrt(sec(d*x + c)), x)","F",0
216,0,0,0,0.445165," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \sec\left(d x + c\right) + A a^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + 2*C*a^2*sec(d*x + c)^3 + (A + C)*a^2*sec(d*x + c)^2 + 2*A*a^2*sec(d*x + c) + A*a^2)/sqrt(sec(d*x + c)), x)","F",0
217,0,0,0,0.479431," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \sec\left(d x + c\right) + A a^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + 2*C*a^2*sec(d*x + c)^3 + (A + C)*a^2*sec(d*x + c)^2 + 2*A*a^2*sec(d*x + c) + A*a^2)/sec(d*x + c)^(3/2), x)","F",0
218,0,0,0,0.455883," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \sec\left(d x + c\right) + A a^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + 2*C*a^2*sec(d*x + c)^3 + (A + C)*a^2*sec(d*x + c)^2 + 2*A*a^2*sec(d*x + c) + A*a^2)/sec(d*x + c)^(5/2), x)","F",0
219,0,0,0,0.457738," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \sec\left(d x + c\right) + A a^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + 2*C*a^2*sec(d*x + c)^3 + (A + C)*a^2*sec(d*x + c)^2 + 2*A*a^2*sec(d*x + c) + A*a^2)/sec(d*x + c)^(7/2), x)","F",0
220,0,0,0,0.442331," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \sec\left(d x + c\right) + A a^{2}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + 2*C*a^2*sec(d*x + c)^3 + (A + C)*a^2*sec(d*x + c)^2 + 2*A*a^2*sec(d*x + c) + A*a^2)/sec(d*x + c)^(9/2), x)","F",0
221,0,0,0,0.490597," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \sec\left(d x + c\right) + A a^{2}}{\sec\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + 2*C*a^2*sec(d*x + c)^3 + (A + C)*a^2*sec(d*x + c)^2 + 2*A*a^2*sec(d*x + c) + A*a^2)/sec(d*x + c)^(11/2), x)","F",0
222,0,0,0,0.449864," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \sec\left(d x + c\right)^{6} + 3 \, C a^{3} \sec\left(d x + c\right)^{5} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{3} + 3 \, A 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((C*a^3*sec(d*x + c)^6 + 3*C*a^3*sec(d*x + c)^5 + (A + 3*C)*a^3*sec(d*x + c)^4 + (3*A + C)*a^3*sec(d*x + c)^3 + 3*A*a^3*sec(d*x + c)^2 + A*a^3*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
223,0,0,0,0.480865," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)*sqrt(sec(d*x + c)), x)","F",0
224,0,0,0,0.493073," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)/sqrt(sec(d*x + c)), x)","F",0
225,0,0,0,0.481806," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(3/2), x)","F",0
226,0,0,0,0.458153," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(5/2), x)","F",0
227,0,0,0,0.456013," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(7/2), x)","F",0
228,0,0,0,0.493598," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(9/2), x)","F",0
229,0,0,0,0.461246," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(11/2), x)","F",0
230,0,0,0,0.488016," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{13}{2}}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(13/2), x)","F",0
231,0,0,0,0.463051," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + A*sec(d*x + c)^2)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
232,0,0,0,0.452161," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + A*sec(d*x + c))*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
233,0,0,0,0.437381," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
234,0,0,0,0.469785," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c)^2 + a*sec(d*x + c)), x)","F",0
235,0,0,0,0.461050," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c)^3 + a*sec(d*x + c)^2), x)","F",0
236,0,0,0,0.474214," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c)^4 + a*sec(d*x + c)^3), x)","F",0
237,0,0,0,0.477445," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + 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
238,0,0,0,0.468105," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + 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
239,0,0,0,0.449762," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
240,0,0,0,0.457259," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
241,0,0,0,0.489418," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
242,0,0,0,0.466052," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
243,0,0,0,0.478821," ","integrate(sec(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{5} + 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((C*sec(d*x + c)^5 + 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
244,0,0,0,0.433145," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + 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
245,0,0,0,0.461468," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + 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
246,0,0,0,0.438036," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
247,0,0,0,0.473167," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
248,0,0,0,0.503339," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
249,0,0,0,0.489470," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
250,1,470,0,0.668049," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(48 \, A + 35 \, C\right)} \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(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 56 \, C \cos\left(d x + c\right) + 48 \, C\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(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(48 \, A + 35 \, C\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) + \frac{2 \, {\left(3 \, {\left(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 56 \, C \cos\left(d x + c\right) + 48 \, C\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*((48*A + 35*C)*cos(d*x + c)^4 + (48*A + 35*C)*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*(48*A + 35*C)*cos(d*x + c)^3 + 2*(48*A + 35*C)*cos(d*x + c)^2 + 56*C*cos(d*x + c) + 48*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)^4 + d*cos(d*x + c)^3), 1/384*(3*((48*A + 35*C)*cos(d*x + c)^4 + (48*A + 35*C)*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*(48*A + 35*C)*cos(d*x + c)^3 + 2*(48*A + 35*C)*cos(d*x + c)^2 + 56*C*cos(d*x + c) + 48*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)^4 + d*cos(d*x + c)^3)]","A",0
251,1,436,0,0.558069," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 5 \, C\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(8 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 10 \, C \cos\left(d x + c\right) + 8 \, C\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(8 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 5 \, C\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(8 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 10 \, C \cos\left(d x + c\right) + 8 \, C\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*((8*A + 5*C)*cos(d*x + c)^3 + (8*A + 5*C)*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*(8*A + 5*C)*cos(d*x + c)^2 + 10*C*cos(d*x + c) + 8*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)^3 + d*cos(d*x + c)^2), 1/48*(3*((8*A + 5*C)*cos(d*x + c)^3 + (8*A + 5*C)*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*(8*A + 5*C)*cos(d*x + c)^2 + 10*C*cos(d*x + c) + 8*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)^3 + d*cos(d*x + c)^2)]","A",0
252,1,392,0,0.548774," ","integrate(sec(d*x+c)^(1/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 3 \, C\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(3 \, C \cos\left(d x + c\right) + 2 \, C\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(8 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 3 \, C\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(3 \, C \cos\left(d x + c\right) + 2 \, C\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*(((8*A + 3*C)*cos(d*x + c)^2 + (8*A + 3*C)*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*(3*C*cos(d*x + c) + 2*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)^2 + d*cos(d*x + c)), 1/8*(((8*A + 3*C)*cos(d*x + c)^2 + (8*A + 3*C)*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*(3*C*cos(d*x + c) + 2*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)^2 + d*cos(d*x + c))]","A",0
253,1,328,0,0.480577," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(C \cos\left(d x + c\right) + C\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 \cos\left(d x + c\right) + C\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(C \cos\left(d x + c\right) + C\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 \cos\left(d x + c\right) + C\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*((C*cos(d*x + c) + 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*(2*A*cos(d*x + c) + 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), 1/2*((C*cos(d*x + c) + 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*(2*A*cos(d*x + c) + 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
254,1,348,0,0.488131," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(C \cos\left(d x + c\right) + C\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 \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)}} \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(C \cos\left(d x + c\right) + C\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 \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)}} \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*(C*cos(d*x + c) + 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*(A*cos(d*x + c)^2 + 2*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*(C*cos(d*x + c) + 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*(A*cos(d*x + c)^2 + 2*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
255,1,86,0,0.775657," ","integrate((A+C*sec(d*x+c)^2)*(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} + 4 \, A \cos\left(d x + c\right)^{2} + {\left(8 \, A + 15 \, C\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*cos(d*x + c)^2 + (8*A + 15*C)*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
256,1,103,0,0.438972," ","integrate((A+C*sec(d*x+c)^2)*(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} + 18 \, A \cos\left(d x + c\right)^{3} + {\left(24 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(24 \, A + 35 \, C\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 + 18*A*cos(d*x + c)^3 + (24*A + 35*C)*cos(d*x + c)^2 + 2*(24*A + 35*C)*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
257,1,121,0,0.429180," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A \cos\left(d x + c\right)^{5} + 40 \, A \cos\left(d x + c\right)^{4} + 3 \, {\left(16 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(16 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, A + 21 \, C\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)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/315*(35*A*cos(d*x + c)^5 + 40*A*cos(d*x + c)^4 + 3*(16*A + 21*C)*cos(d*x + c)^3 + 4*(16*A + 21*C)*cos(d*x + c)^2 + 8*(16*A + 21*C)*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
258,1,518,0,0.654986," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{5} + {\left(176 \, A + 133 \, C\right)} a \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(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{4} + 10 \, {\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 912 \, C a \cos\left(d x + c\right) + 384 \, C 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)}}}{7680 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}, \frac{15 \, {\left({\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{5} + {\left(176 \, A + 133 \, C\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) + \frac{2 \, {\left(15 \, {\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{4} + 10 \, {\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 912 \, C a \cos\left(d x + c\right) + 384 \, C 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)}}}{3840 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/7680*(15*((176*A + 133*C)*a*cos(d*x + c)^5 + (176*A + 133*C)*a*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*(176*A + 133*C)*a*cos(d*x + c)^4 + 10*(176*A + 133*C)*a*cos(d*x + c)^3 + 8*(80*A + 133*C)*a*cos(d*x + c)^2 + 912*C*a*cos(d*x + c) + 384*C*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)^5 + d*cos(d*x + c)^4), 1/3840*(15*((176*A + 133*C)*a*cos(d*x + c)^5 + (176*A + 133*C)*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)) + 2*(15*(176*A + 133*C)*a*cos(d*x + c)^4 + 10*(176*A + 133*C)*a*cos(d*x + c)^3 + 8*(80*A + 133*C)*a*cos(d*x + c)^2 + 912*C*a*cos(d*x + c) + 384*C*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)^5 + d*cos(d*x + c)^4)]","A",0
259,1,478,0,0.661480," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(112 \, A + 75 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(112 \, A + 75 \, C\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({\left(112 \, A + 75 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(16 \, A + 25 \, C\right)} a \cos\left(d x + c\right)^{2} + 40 \, C a \cos\left(d x + c\right) + 16 \, C 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)}}}{256 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}, \frac{{\left({\left(112 \, A + 75 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(112 \, A + 75 \, C\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({\left(112 \, A + 75 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(16 \, A + 25 \, C\right)} a \cos\left(d x + c\right)^{2} + 40 \, C a \cos\left(d x + c\right) + 16 \, C 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)}}}{128 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/256*(((112*A + 75*C)*a*cos(d*x + c)^4 + (112*A + 75*C)*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*((112*A + 75*C)*a*cos(d*x + c)^3 + 2*(16*A + 25*C)*a*cos(d*x + c)^2 + 40*C*a*cos(d*x + c) + 16*C*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), 1/128*(((112*A + 75*C)*a*cos(d*x + c)^4 + (112*A + 75*C)*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*((112*A + 75*C)*a*cos(d*x + c)^3 + 2*(16*A + 25*C)*a*cos(d*x + c)^2 + 40*C*a*cos(d*x + c) + 16*C*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
260,1,446,0,0.569342," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(24 \, A + 11 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(24 \, A + 11 \, C\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(8 \, A + 11 \, C\right)} a \cos\left(d x + c\right)^{2} + 22 \, C a \cos\left(d x + c\right) + 8 \, C 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(24 \, A + 11 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(24 \, A + 11 \, C\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(8 \, A + 11 \, C\right)} a \cos\left(d x + c\right)^{2} + 22 \, C a \cos\left(d x + c\right) + 8 \, C 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*((24*A + 11*C)*a*cos(d*x + c)^3 + (24*A + 11*C)*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*(8*A + 11*C)*a*cos(d*x + c)^2 + 22*C*a*cos(d*x + c) + 8*C*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*((24*A + 11*C)*a*cos(d*x + c)^3 + (24*A + 11*C)*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*(8*A + 11*C)*a*cos(d*x + c)^2 + 22*C*a*cos(d*x + c) + 8*C*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
261,1,424,0,0.593871," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, A + 7 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(8 \, A + 7 \, C\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(8 \, A a \cos\left(d x + c\right)^{2} + 7 \, C a \cos\left(d x + c\right) + 2 \, C 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(8 \, A + 7 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(8 \, A + 7 \, C\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(8 \, A a \cos\left(d x + c\right)^{2} + 7 \, C a \cos\left(d x + c\right) + 2 \, C 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*(((8*A + 7*C)*a*cos(d*x + c)^2 + (8*A + 7*C)*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*(8*A*a*cos(d*x + c)^2 + 7*C*a*cos(d*x + c) + 2*C*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*(((8*A + 7*C)*a*cos(d*x + c)^2 + (8*A + 7*C)*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*(8*A*a*cos(d*x + c)^2 + 7*C*a*cos(d*x + c) + 2*C*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
262,1,368,0,0.523721," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{9 \, {\left(C a \cos\left(d x + c\right) + C 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)^{2} + 10 \, A a \cos\left(d x + c\right) + 3 \, C 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)}}}{12 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{9 \, {\left(C a \cos\left(d x + c\right) + C 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)^{2} + 10 \, A a \cos\left(d x + c\right) + 3 \, C 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)}}}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/12*(9*(C*a*cos(d*x + c) + C*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)^2 + 10*A*a*cos(d*x + c) + 3*C*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), 1/6*(9*(C*a*cos(d*x + c) + C*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)^2 + 10*A*a*cos(d*x + c) + 3*C*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
263,1,392,0,0.538005," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(C a \cos\left(d x + c\right) + C 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)^{3} + 3 \, A a \cos\left(d x + c\right)^{2} + {\left(6 \, A + 5 \, C\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)}}}{10 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{5 \, {\left(C a \cos\left(d x + c\right) + C 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)^{3} + 3 \, A a \cos\left(d x + c\right)^{2} + {\left(6 \, A + 5 \, C\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)}}}{5 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/10*(5*(C*a*cos(d*x + c) + C*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)^3 + 3*A*a*cos(d*x + c)^2 + (6*A + 5*C)*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), 1/5*(5*(C*a*cos(d*x + c) + C*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)^3 + 3*A*a*cos(d*x + c)^2 + (6*A + 5*C)*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
264,1,106,0,0.425622," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, A a \cos\left(d x + c\right)^{4} + 39 \, A a \cos\left(d x + c\right)^{3} + {\left(52 \, A + 35 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(104 \, A + 175 \, C\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 + 39*A*a*cos(d*x + c)^3 + (52*A + 35*C)*a*cos(d*x + c)^2 + (104*A + 175*C)*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
265,1,125,0,0.414794," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A a \cos\left(d x + c\right)^{5} + 85 \, A a \cos\left(d x + c\right)^{4} + 3 \, {\left(34 \, A + 21 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(136 \, A + 189 \, C\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(136 \, A + 189 \, C\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 + 85*A*a*cos(d*x + c)^4 + 3*(34*A + 21*C)*a*cos(d*x + c)^3 + (136*A + 189*C)*a*cos(d*x + c)^2 + 2*(136*A + 189*C)*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
266,1,144,0,0.459923," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, A a \cos\left(d x + c\right)^{6} + 245 \, A a \cos\left(d x + c\right)^{5} + 5 \, {\left(56 \, A + 33 \, C\right)} a \cos\left(d x + c\right)^{4} + 3 \, {\left(112 \, A + 143 \, C\right)} a \cos\left(d x + c\right)^{3} + 4 \, {\left(112 \, A + 143 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(112 \, A + 143 \, C\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)}{1155 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/1155*(105*A*a*cos(d*x + c)^6 + 245*A*a*cos(d*x + c)^5 + 5*(56*A + 33*C)*a*cos(d*x + c)^4 + 3*(112*A + 143*C)*a*cos(d*x + c)^3 + 4*(112*A + 143*C)*a*cos(d*x + c)^2 + 8*(112*A + 143*C)*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
267,1,586,0,0.668235," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{5}\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(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 2 \, {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(184 \, A + 203 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 48 \, {\left(8 \, A + 29 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 896 \, C a^{2} \cos\left(d x + c\right) + 256 \, C 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)}}}{6144 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}, \frac{3 \, {\left({\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(1304 \, A + 1015 \, C\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) + \frac{2 \, {\left(3 \, {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 2 \, {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(184 \, A + 203 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 48 \, {\left(8 \, A + 29 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 896 \, C a^{2} \cos\left(d x + c\right) + 256 \, C 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)}}}{3072 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}\right]"," ",0,"[1/6144*(3*((1304*A + 1015*C)*a^2*cos(d*x + c)^6 + (1304*A + 1015*C)*a^2*cos(d*x + c)^5)*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*(1304*A + 1015*C)*a^2*cos(d*x + c)^5 + 2*(1304*A + 1015*C)*a^2*cos(d*x + c)^4 + 8*(184*A + 203*C)*a^2*cos(d*x + c)^3 + 48*(8*A + 29*C)*a^2*cos(d*x + c)^2 + 896*C*a^2*cos(d*x + c) + 256*C*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)^6 + d*cos(d*x + c)^5), 1/3072*(3*((1304*A + 1015*C)*a^2*cos(d*x + c)^6 + (1304*A + 1015*C)*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)) + 2*(3*(1304*A + 1015*C)*a^2*cos(d*x + c)^5 + 2*(1304*A + 1015*C)*a^2*cos(d*x + c)^4 + 8*(184*A + 203*C)*a^2*cos(d*x + c)^3 + 48*(8*A + 29*C)*a^2*cos(d*x + c)^2 + 896*C*a^2*cos(d*x + c) + 256*C*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)^6 + d*cos(d*x + c)^5)]","A",0
268,1,546,0,0.654056," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(400 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(400 \, A + 283 \, C\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(400 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(272 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 1392 \, C a^{2} \cos\left(d x + c\right) + 384 \, C 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(400 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(400 \, A + 283 \, C\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(400 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(272 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 1392 \, C a^{2} \cos\left(d x + c\right) + 384 \, C 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*((400*A + 283*C)*a^2*cos(d*x + c)^5 + (400*A + 283*C)*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*(400*A + 283*C)*a^2*cos(d*x + c)^4 + 10*(272*A + 283*C)*a^2*cos(d*x + c)^3 + 8*(80*A + 283*C)*a^2*cos(d*x + c)^2 + 1392*C*a^2*cos(d*x + c) + 384*C*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*((400*A + 283*C)*a^2*cos(d*x + c)^5 + (400*A + 283*C)*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*(400*A + 283*C)*a^2*cos(d*x + c)^4 + 10*(272*A + 283*C)*a^2*cos(d*x + c)^3 + 8*(80*A + 283*C)*a^2*cos(d*x + c)^2 + 1392*C*a^2*cos(d*x + c) + 384*C*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
269,1,506,0,0.655962," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(304 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(304 \, A + 163 \, C\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(176 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 184 \, C a^{2} \cos\left(d x + c\right) + 48 \, C 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(304 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(304 \, A + 163 \, C\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(176 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 184 \, C a^{2} \cos\left(d x + c\right) + 48 \, C 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*((304*A + 163*C)*a^2*cos(d*x + c)^4 + (304*A + 163*C)*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*(176*A + 163*C)*a^2*cos(d*x + c)^3 + 2*(48*A + 163*C)*a^2*cos(d*x + c)^2 + 184*C*a^2*cos(d*x + c) + 48*C*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*((304*A + 163*C)*a^2*cos(d*x + c)^4 + (304*A + 163*C)*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*(176*A + 163*C)*a^2*cos(d*x + c)^3 + 2*(48*A + 163*C)*a^2*cos(d*x + c)^2 + 184*C*a^2*cos(d*x + c) + 48*C*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
270,1,494,0,0.556360," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(8 \, A + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 5 \, C\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(48 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 34 \, C a^{2} \cos\left(d x + c\right) + 8 \, C 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{15 \, {\left({\left(8 \, A + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 5 \, C\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(48 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 34 \, C a^{2} \cos\left(d x + c\right) + 8 \, C 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*(15*((8*A + 5*C)*a^2*cos(d*x + c)^3 + (8*A + 5*C)*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*(48*A*a^2*cos(d*x + c)^3 + 3*(8*A + 25*C)*a^2*cos(d*x + c)^2 + 34*C*a^2*cos(d*x + c) + 8*C*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*(15*((8*A + 5*C)*a^2*cos(d*x + c)^3 + (8*A + 5*C)*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*(48*A*a^2*cos(d*x + c)^3 + 3*(8*A + 25*C)*a^2*cos(d*x + c)^2 + 34*C*a^2*cos(d*x + c) + 8*C*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
271,1,474,0,0.591704," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, A + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 19 \, C\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)^{3} + 64 \, A a^{2} \cos\left(d x + c\right)^{2} + 33 \, C a^{2} \cos\left(d x + c\right) + 6 \, C 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)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{3 \, {\left({\left(8 \, A + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 19 \, C\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)^{3} + 64 \, A a^{2} \cos\left(d x + c\right)^{2} + 33 \, C a^{2} \cos\left(d x + c\right) + 6 \, C 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)}}}{24 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/48*(3*((8*A + 19*C)*a^2*cos(d*x + c)^2 + (8*A + 19*C)*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)^3 + 64*A*a^2*cos(d*x + c)^2 + 33*C*a^2*cos(d*x + c) + 6*C*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)), 1/24*(3*((8*A + 19*C)*a^2*cos(d*x + c)^2 + (8*A + 19*C)*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)^3 + 64*A*a^2*cos(d*x + c)^2 + 33*C*a^2*cos(d*x + c) + 6*C*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
272,1,428,0,0.502556," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{75 \, {\left(C a^{2} \cos\left(d x + c\right) + C 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(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 28 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(43 \, A + 15 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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)}}}{60 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{75 \, {\left(C a^{2} \cos\left(d x + c\right) + C 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(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 28 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(43 \, A + 15 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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)}}}{30 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/60*(75*(C*a^2*cos(d*x + c) + C*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*(6*A*a^2*cos(d*x + c)^3 + 28*A*a^2*cos(d*x + c)^2 + 2*(43*A + 15*C)*a^2*cos(d*x + c) + 15*C*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), 1/30*(75*(C*a^2*cos(d*x + c) + C*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*(6*A*a^2*cos(d*x + c)^3 + 28*A*a^2*cos(d*x + c)^2 + 2*(43*A + 15*C)*a^2*cos(d*x + c) + 15*C*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
273,1,454,0,0.571950," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\left[\frac{21 \, {\left(C a^{2} \cos\left(d x + c\right) + C 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)^{4} + 12 \, A a^{2} \cos\left(d x + c\right)^{3} + {\left(23 \, A + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(23 \, A + 28 \, C\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)}}}{42 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{21 \, {\left(C a^{2} \cos\left(d x + c\right) + C 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)^{4} + 12 \, A a^{2} \cos\left(d x + c\right)^{3} + {\left(23 \, A + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(23 \, A + 28 \, C\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)}}}{21 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/42*(21*(C*a^2*cos(d*x + c) + C*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)^4 + 12*A*a^2*cos(d*x + c)^3 + (23*A + 7*C)*a^2*cos(d*x + c)^2 + 2*(23*A + 28*C)*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), 1/21*(21*(C*a^2*cos(d*x + c) + C*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)^4 + 12*A*a^2*cos(d*x + c)^3 + (23*A + 7*C)*a^2*cos(d*x + c)^2 + 2*(23*A + 28*C)*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
274,1,135,0,0.469801," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A a^{2} \cos\left(d x + c\right)^{5} + 130 \, A a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(73 \, A + 21 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(146 \, A + 147 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(584 \, A + 903 \, C\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 + 130*A*a^2*cos(d*x + c)^4 + 3*(73*A + 21*C)*a^2*cos(d*x + c)^3 + 2*(146*A + 147*C)*a^2*cos(d*x + c)^2 + (584*A + 903*C)*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
275,1,154,0,0.418953," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, A a^{2} \cos\left(d x + c\right)^{6} + 224 \, A a^{2} \cos\left(d x + c\right)^{5} + {\left(355 \, A + 99 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 6 \, {\left(71 \, A + 66 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(568 \, A + 759 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(568 \, A + 759 \, C\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)}{693 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/693*(63*A*a^2*cos(d*x + c)^6 + 224*A*a^2*cos(d*x + c)^5 + (355*A + 99*C)*a^2*cos(d*x + c)^4 + 6*(71*A + 66*C)*a^2*cos(d*x + c)^3 + (568*A + 759*C)*a^2*cos(d*x + c)^2 + 2*(568*A + 759*C)*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
276,1,176,0,0.429749," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, A a^{2} \cos\left(d x + c\right)^{7} + 11970 \, A a^{2} \cos\left(d x + c\right)^{6} + 35 \, {\left(523 \, A + 143 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 10 \, {\left(2092 \, A + 1859 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(8368 \, A + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 4 \, {\left(8368 \, A + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8368 \, A + 10439 \, C\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)}{45045 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/45045*(3465*A*a^2*cos(d*x + c)^7 + 11970*A*a^2*cos(d*x + c)^6 + 35*(523*A + 143*C)*a^2*cos(d*x + c)^5 + 10*(2092*A + 1859*C)*a^2*cos(d*x + c)^4 + 3*(8368*A + 10439*C)*a^2*cos(d*x + c)^3 + 4*(8368*A + 10439*C)*a^2*cos(d*x + c)^2 + 8*(8368*A + 10439*C)*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
277,1,647,0,0.589917," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 9 \, C\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{48 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A + C\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}} + \frac{4 \, {\left(3 \, {\left(8 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} - 2 \, C \cos\left(d x + c\right) + 8 \, C\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 d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}, -\frac{48 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A + C\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) + 3 \, {\left({\left(8 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 9 \, C\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(8 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} - 2 \, C \cos\left(d x + c\right) + 8 \, C\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(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/96*(3*((8*A + 9*C)*cos(d*x + c)^3 + (8*A + 9*C)*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)) + 48*sqrt(2)*((A + C)*a*cos(d*x + c)^3 + (A + C)*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) + 4*(3*(8*A + 7*C)*cos(d*x + c)^2 - 2*C*cos(d*x + c) + 8*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)^3 + a*d*cos(d*x + c)^2), -1/48*(48*sqrt(2)*((A + C)*a*cos(d*x + c)^3 + (A + C)*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)) + 3*((8*A + 9*C)*cos(d*x + c)^3 + (8*A + 9*C)*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*(8*A + 7*C)*cos(d*x + c)^2 - 2*C*cos(d*x + c) + 8*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)^3 + a*d*cos(d*x + c)^2)]","A",0
278,1,597,0,0.748861," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 7 \, C\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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A + C\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(C \cos\left(d x + c\right) - 2 \, C\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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A + C\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(8 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 7 \, C\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(C \cos\left(d x + c\right) - 2 \, C\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*(((8*A + 7*C)*cos(d*x + c)^2 + (8*A + 7*C)*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 + C)*a*cos(d*x + c)^2 + (A + C)*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*(C*cos(d*x + c) - 2*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)^2 + a*d*cos(d*x + c)), 1/8*(8*sqrt(2)*((A + C)*a*cos(d*x + c)^2 + (A + C)*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)) + ((8*A + 7*C)*cos(d*x + c)^2 + (8*A + 7*C)*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*(C*cos(d*x + c) - 2*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)^2 + a*d*cos(d*x + c))]","A",0
279,1,501,0,0.493738," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(C \cos\left(d x + c\right) + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 \, C \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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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(C \cos\left(d x + c\right) + C\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 \, C \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*((C*cos(d*x + c) + 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)) + 2*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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*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), -1/2*(2*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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)) + (C*cos(d*x + c) + 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*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
280,1,498,0,0.539583," ","integrate((A+C*sec(d*x+c)^2)/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) + {\left(C \cos\left(d x + c\right) + C\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{\sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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) + {\left(C \cos\left(d x + c\right) + C\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)}{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) + (C*cos(d*x + c) + 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)) + sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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 + C)*a*cos(d*x + c) + (A + C)*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) + (C*cos(d*x + c) + 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) + a*d)]","A",0
281,1,338,0,0.446516," ","integrate((A+C*sec(d*x+c)^2)/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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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} - 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(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{3 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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} - 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(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/6*(3*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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*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 + C)*a*cos(d*x + c) + (A + C)*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*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
282,1,372,0,0.486782," ","integrate((A+C*sec(d*x+c)^2)/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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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} - A \cos\left(d x + c\right)^{2} + {\left(13 \, A + 15 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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} - A \cos\left(d x + c\right)^{2} + {\left(13 \, A + 15 \, C\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 + C)*a*cos(d*x + c) + (A + C)*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*cos(d*x + c)^2 + (13*A + 15*C)*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 + C)*a*cos(d*x + c) + (A + C)*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*cos(d*x + c)^2 + (13*A + 15*C)*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
283,1,406,0,0.439326," ","integrate((A+C*sec(d*x+c)^2)/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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 \, A \cos\left(d x + c\right)^{3} + {\left(31 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(43 \, A + 35 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 \, A \cos\left(d x + c\right)^{3} + {\left(31 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(43 \, A + 35 \, C\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 + C)*a*cos(d*x + c) + (A + C)*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*cos(d*x + c)^3 + (31*A + 35*C)*cos(d*x + c)^2 - (43*A + 35*C)*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 + C)*a*cos(d*x + c) + (A + C)*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*cos(d*x + c)^3 + (31*A + 35*C)*cos(d*x + c)^2 - (43*A + 35*C)*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
284,1,623,0,0.526271," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(A + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 9 \, C\right)} \cos\left(d x + c\right) + A + 9 \, C\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) + 6 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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(A + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 9 \, C\right)} \cos\left(d x + c\right) + A + 9 \, C\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) + 6 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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)*((A + 9*C)*cos(d*x + c)^2 + 2*(A + 9*C)*cos(d*x + c) + A + 9*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)) + 6*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + 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*((A + 3*C)*cos(d*x + c) + 2*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)*((A + 9*C)*cos(d*x + c)^2 + 2*(A + 9*C)*cos(d*x + c) + A + 9*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))) + 6*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + 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*((A + 3*C)*cos(d*x + c) + 2*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
285,1,609,0,0.512043," ","integrate((A+C*sec(d*x+c)^2)*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 - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 5 \, C\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 + C\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(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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(3 \, A - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 5 \, C\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 + C\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(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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)*((3*A - 5*C)*cos(d*x + c)^2 + 2*(3*A - 5*C)*cos(d*x + c) + 3*A - 5*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 + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + 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)))/(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 - 5*C)*cos(d*x + c)^2 + 2*(3*A - 5*C)*cos(d*x + c) + 3*A - 5*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 + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + 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)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","B",0
286,1,426,0,0.460398," ","integrate((A+C*sec(d*x+c)^2)/(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 - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - C\right)} \cos\left(d x + c\right) + 7 \, A - C\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 + C\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 - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - C\right)} \cos\left(d x + c\right) + 7 \, A - C\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 + C\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 - C)*cos(d*x + c)^2 + 2*(7*A - C)*cos(d*x + c) + 7*A - 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*(4*A*cos(d*x + c)^2 + (5*A + C)*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 - C)*cos(d*x + c)^2 + 2*(7*A - C)*cos(d*x + c) + 7*A - 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*(4*A*cos(d*x + c)^2 + (5*A + C)*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
287,1,456,0,0.475813," ","integrate((A+C*sec(d*x+c)^2)/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 + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 11 \, A + 3 \, C\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 \, A \cos\left(d x + c\right)^{2} - {\left(19 \, A + 3 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 11 \, A + 3 \, C\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 \, A \cos\left(d x + c\right)^{2} - {\left(19 \, A + 3 \, C\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 + 3*C)*cos(d*x + c)^2 + 2*(11*A + 3*C)*cos(d*x + c) + 11*A + 3*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*(4*A*cos(d*x + c)^3 - 12*A*cos(d*x + c)^2 - (19*A + 3*C)*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 + 3*C)*cos(d*x + c)^2 + 2*(11*A + 3*C)*cos(d*x + c) + 11*A + 3*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*(4*A*cos(d*x + c)^3 - 12*A*cos(d*x + c)^2 - (19*A + 3*C)*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
288,1,488,0,0.482435," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{5 \, \sqrt{2} {\left({\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right) + 15 \, A + 7 \, C\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)^{4} - 4 \, A \cos\left(d x + c\right)^{3} + 4 \, {\left(9 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(49 \, A + 25 \, C\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)}}}{40 \, {\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{5 \, \sqrt{2} {\left({\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right) + 15 \, A + 7 \, C\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)^{4} - 4 \, A \cos\left(d x + c\right)^{3} + 4 \, {\left(9 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(49 \, A + 25 \, C\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)}}}{20 \, {\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,"[1/40*(5*sqrt(2)*((15*A + 7*C)*cos(d*x + c)^2 + 2*(15*A + 7*C)*cos(d*x + c) + 15*A + 7*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*(4*A*cos(d*x + c)^4 - 4*A*cos(d*x + c)^3 + 4*(9*A + 5*C)*cos(d*x + c)^2 + (49*A + 25*C)*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), 1/20*(5*sqrt(2)*((15*A + 7*C)*cos(d*x + c)^2 + 2*(15*A + 7*C)*cos(d*x + c) + 15*A + 7*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*(4*A*cos(d*x + c)^4 - 4*A*cos(d*x + c)^3 + 4*(9*A + 5*C)*cos(d*x + c)^2 + (49*A + 25*C)*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
289,1,755,0,0.559136," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 115 \, C\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) + 80 \, {\left(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\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 + 35 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A + 55 \, C\right)} \cos\left(d x + c\right) + 16 \, C\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 + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 115 \, C\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) + 80 \, {\left(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\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 + 35 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A + 55 \, C\right)} \cos\left(d x + c\right) + 16 \, C\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 + 115*C)*cos(d*x + c)^3 + 3*(3*A + 115*C)*cos(d*x + c)^2 + 3*(3*A + 115*C)*cos(d*x + c) + 3*A + 115*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)) + 80*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 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*((3*A + 35*C)*cos(d*x + c)^2 + (7*A + 55*C)*cos(d*x + c) + 16*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 + 115*C)*cos(d*x + c)^3 + 3*(3*A + 115*C)*cos(d*x + c)^2 + 3*(3*A + 115*C)*cos(d*x + c) + 3*A + 115*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))) + 80*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 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*((3*A + 35*C)*cos(d*x + c)^2 + (7*A + 55*C)*cos(d*x + c) + 16*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
290,1,745,0,0.568703," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 43 \, C\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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\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(5 \, A - 11 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(A - 15 \, C\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 - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 43 \, C\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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\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(5 \, A - 11 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(A - 15 \, C\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 - 43*C)*cos(d*x + c)^3 + 3*(5*A - 43*C)*cos(d*x + c)^2 + 3*(5*A - 43*C)*cos(d*x + c) + 5*A - 43*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)) - 32*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 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*((5*A - 11*C)*cos(d*x + c)^2 + (A - 15*C)*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 - 43*C)*cos(d*x + c)^3 + 3*(5*A - 43*C)*cos(d*x + c)^2 + 3*(5*A - 43*C)*cos(d*x + c) + 5*A - 43*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))) - 32*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 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*((5*A - 11*C)*cos(d*x + c)^2 + (A - 15*C)*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
291,1,502,0,0.484893," ","integrate((A+C*sec(d*x+c)^2)*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 + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 3 \, C\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 - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A - 7 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 3 \, C\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 - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A - 7 \, C\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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 3*C)*cos(d*x + c)^2 + 3*(19*A + 3*C)*cos(d*x + c) + 19*A + 3*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*((13*A - 3*C)*cos(d*x + c)^2 + (9*A - 7*C)*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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 3*C)*cos(d*x + c)^2 + 3*(19*A + 3*C)*cos(d*x + c) + 19*A + 3*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*((13*A - 3*C)*cos(d*x + c)^2 + (9*A - 7*C)*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
292,1,520,0,0.486842," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{5 \, \sqrt{2} {\left({\left(15 \, A - C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right) + 15 \, A - C\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} + 5 \, {\left(17 \, A + C\right)} \cos\left(d x + c\right)^{2} + {\left(49 \, A + C\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{5 \, \sqrt{2} {\left({\left(15 \, A - C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right) + 15 \, A - C\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} + 5 \, {\left(17 \, A + C\right)} \cos\left(d x + c\right)^{2} + {\left(49 \, A + C\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*(5*sqrt(2)*((15*A - C)*cos(d*x + c)^3 + 3*(15*A - C)*cos(d*x + c)^2 + 3*(15*A - C)*cos(d*x + c) + 15*A - 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*(32*A*cos(d*x + c)^3 + 5*(17*A + C)*cos(d*x + c)^2 + (49*A + C)*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*(5*sqrt(2)*((15*A - C)*cos(d*x + c)^3 + 3*(15*A - C)*cos(d*x + c)^2 + 3*(15*A - C)*cos(d*x + c) + 15*A - 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*(32*A*cos(d*x + c)^3 + 5*(17*A + C)*cos(d*x + c)^2 + (49*A + C)*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
293,1,552,0,0.480797," ","integrate((A+C*sec(d*x+c)^2)/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 + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right) + 163 \, A + 19 \, C\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} - 160 \, A \cos\left(d x + c\right)^{3} - {\left(503 \, A + 39 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(299 \, A + 27 \, C\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 + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right) + 163 \, A + 19 \, C\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} - 160 \, A \cos\left(d x + c\right)^{3} - {\left(503 \, A + 39 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(299 \, A + 27 \, C\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 + 19*C)*cos(d*x + c)^3 + 3*(163*A + 19*C)*cos(d*x + c)^2 + 3*(163*A + 19*C)*cos(d*x + c) + 163*A + 19*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*(32*A*cos(d*x + c)^4 - 160*A*cos(d*x + c)^3 - (503*A + 39*C)*cos(d*x + c)^2 - (299*A + 27*C)*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 + 19*C)*cos(d*x + c)^3 + 3*(163*A + 19*C)*cos(d*x + c)^2 + 3*(163*A + 19*C)*cos(d*x + c) + 163*A + 19*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*(32*A*cos(d*x + c)^4 - 160*A*cos(d*x + c)^3 - (503*A + 39*C)*cos(d*x + c)^2 - (299*A + 27*C)*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
294,1,584,0,0.503954," ","integrate((A+C*sec(d*x+c)^2)/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 + 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right) + 283 \, A + 75 \, C\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 \, A \cos\left(d x + c\right)^{4} + 32 \, {\left(49 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(911 \, A + 255 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(2671 \, A + 735 \, C\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 + 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right) + 283 \, A + 75 \, C\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 \, A \cos\left(d x + c\right)^{4} + 32 \, {\left(49 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(911 \, A + 255 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(2671 \, A + 735 \, C\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 + 75*C)*cos(d*x + c)^3 + 3*(283*A + 75*C)*cos(d*x + c)^2 + 3*(283*A + 75*C)*cos(d*x + c) + 283*A + 75*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*(96*A*cos(d*x + c)^5 - 160*A*cos(d*x + c)^4 + 32*(49*A + 15*C)*cos(d*x + c)^3 + 5*(911*A + 255*C)*cos(d*x + c)^2 + (2671*A + 735*C)*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 + 75*C)*cos(d*x + c)^3 + 3*(283*A + 75*C)*cos(d*x + c)^2 + 3*(283*A + 75*C)*cos(d*x + c) + 283*A + 75*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*(96*A*cos(d*x + c)^5 - 160*A*cos(d*x + c)^4 + 32*(49*A + 15*C)*cos(d*x + c)^3 + 5*(911*A + 255*C)*cos(d*x + c)^2 + (2671*A + 735*C)*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
295,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(7/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,0,0,0,0.880431," ","integrate(sec(d*x+c)^m*(a+a*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^m, x)","F",0
304,0,0,0,0.789959," ","integrate(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{-n - 1}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1), x)","F",0
305,1,58,0,1.102932," ","integrate((a+a*sec(d*x+c))^n*(-a*A*n-a*C*(1+n)*sec(d*x+c))/a/(1+n)/(sec(d*x+c)^n)+sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{A \left(\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}\right)^{n} \frac{1}{\cos\left(d x + c\right)}^{-n - 1} \sin\left(d x + c\right)}{{\left(d n + d\right)} \cos\left(d x + c\right)}"," ",0,"A*((a*cos(d*x + c) + a)/cos(d*x + c))^n*(1/cos(d*x + c))^(-n - 1)*sin(d*x + c)/((d*n + d)*cos(d*x + c))","A",0
306,1,127,0,0.482971," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 6 \, C a\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(4*B + 3*C)*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*B + 3*C)*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(B + C)*a*cos(d*x + c)^3 + 3*(4*B + 3*C)*a*cos(d*x + c)^2 + 8*(B + C)*a*cos(d*x + c) + 6*C*a)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
307,1,105,0,0.491749," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(3 \, B + 2 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 2 \, C a\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(B + C)*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B + C)*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(3*B + 2*C)*a*cos(d*x + c)^2 + 3*(B + C)*a*cos(d*x + c) + 2*C*a)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
308,1,89,0,0.465700," ","integrate((a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(2 \, B + C\right)} a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, B + C\right)} a \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(B + C\right)} a \cos\left(d x + c\right) + C a\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((2*B + C)*a*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*B + C)*a*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*(B + C)*a*cos(d*x + c) + C*a)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
309,1,79,0,0.465111," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, B a d x \cos\left(d x + c\right) + {\left(B + C\right)} a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B + C\right)} a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, C a \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*B*a*d*x*cos(d*x + c) + (B + C)*a*cos(d*x + c)*log(sin(d*x + c) + 1) - (B + C)*a*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*C*a*sin(d*x + c))/(d*cos(d*x + c))","B",0
310,1,51,0,0.492859," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(B + C\right)} a d x + C a \log\left(\sin\left(d x + c\right) + 1\right) - C a \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(B + C)*a*d*x + C*a*log(sin(d*x + c) + 1) - C*a*log(-sin(d*x + c) + 1) + 2*B*a*sin(d*x + c))/d","A",0
311,1,38,0,0.478654," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(B + 2 \, C\right)} a d x + {\left(B a \cos\left(d x + c\right) + 2 \, {\left(B + C\right)} a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((B + 2*C)*a*d*x + (B*a*cos(d*x + c) + 2*(B + C)*a)*sin(d*x + c))/d","A",0
312,1,56,0,0.485913," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(B + C\right)} a d x + {\left(2 \, B a \cos\left(d x + c\right)^{2} + 3 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 2 \, {\left(2 \, B + 3 \, C\right)} a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(B + C)*a*d*x + (2*B*a*cos(d*x + c)^2 + 3*(B + C)*a*cos(d*x + c) + 2*(2*B + 3*C)*a)*sin(d*x + c))/d","A",0
313,1,74,0,0.485070," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, B + 4 \, C\right)} a d x + {\left(6 \, B a \cos\left(d x + c\right)^{3} + 8 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, B + 4 \, C\right)} a \cos\left(d x + c\right) + 16 \, {\left(B + C\right)} a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*B + 4*C)*a*d*x + (6*B*a*cos(d*x + c)^3 + 8*(B + C)*a*cos(d*x + c)^2 + 3*(3*B + 4*C)*a*cos(d*x + c) + 16*(B + C)*a)*sin(d*x + c))/d","A",0
314,1,165,0,0.507843," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(7 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(7 \, B + 6 \, C\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 \, B + 9 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 15 \, {\left(7 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(10 \, B + 9 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 30 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + 24 \, C a^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(7*B + 6*C)*a^2*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(7*B + 6*C)*a^2*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(10*B + 9*C)*a^2*cos(d*x + c)^4 + 15*(7*B + 6*C)*a^2*cos(d*x + c)^3 + 8*(10*B + 9*C)*a^2*cos(d*x + c)^2 + 30*(B + 2*C)*a^2*cos(d*x + c) + 24*C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
315,1,145,0,0.517053," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, B + 7 \, C\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 \, B + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + 6 \, C a^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(8*B + 7*C)*a^2*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*B + 7*C)*a^2*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(5*B + 4*C)*a^2*cos(d*x + c)^3 + 3*(8*B + 7*C)*a^2*cos(d*x + c)^2 + 8*(B + 2*C)*a^2*cos(d*x + c) + 6*C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
316,1,125,0,0.500507," ","integrate((a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, B + 2 \, C\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 \, B + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, C a^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(3*B + 2*C)*a^2*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(3*B + 2*C)*a^2*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(6*B + 5*C)*a^2*cos(d*x + c)^2 + 3*(B + 2*C)*a^2*cos(d*x + c) + 2*C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
317,1,119,0,0.512225," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, B a^{2} d x \cos\left(d x + c\right)^{2} + {\left(4 \, B + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(4 \, B + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + C a^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*B*a^2*d*x*cos(d*x + c)^2 + (4*B + 3*C)*a^2*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (4*B + 3*C)*a^2*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*(B + 2*C)*a^2*cos(d*x + c) + C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
318,1,108,0,0.519481," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, B + C\right)} a^{2} d x \cos\left(d x + c\right) + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{2} \cos\left(d x + c\right) + C a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(2*B + C)*a^2*d*x*cos(d*x + c) + (B + 2*C)*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) - (B + 2*C)*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(B*a^2*cos(d*x + c) + C*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
319,1,79,0,0.490669," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(3 \, B + 4 \, C\right)} a^{2} d x + C a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - C a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(B a^{2} \cos\left(d x + c\right) + 2 \, {\left(2 \, B + C\right)} a^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((3*B + 4*C)*a^2*d*x + C*a^2*log(sin(d*x + c) + 1) - C*a^2*log(-sin(d*x + c) + 1) + (B*a^2*cos(d*x + c) + 2*(2*B + C)*a^2)*sin(d*x + c))/d","A",0
320,1,70,0,0.456020," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, B + 3 \, C\right)} a^{2} d x + {\left(2 \, B a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B + C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(5 \, B + 6 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*B + 3*C)*a^2*d*x + (2*B*a^2*cos(d*x + c)^2 + 3*(2*B + C)*a^2*cos(d*x + c) + 2*(5*B + 6*C)*a^2)*sin(d*x + c))/d","A",0
321,1,90,0,0.512026," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, B + 8 \, C\right)} a^{2} d x + {\left(6 \, B a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(2 \, B + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(4 \, B + 5 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(7*B + 8*C)*a^2*d*x + (6*B*a^2*cos(d*x + c)^3 + 8*(2*B + C)*a^2*cos(d*x + c)^2 + 3*(7*B + 8*C)*a^2*cos(d*x + c) + 8*(4*B + 5*C)*a^2)*sin(d*x + c))/d","A",0
322,1,110,0,0.472498," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, B + 7 \, C\right)} a^{2} d x + {\left(24 \, B a^{2} \cos\left(d x + c\right)^{4} + 30 \, {\left(2 \, B + C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(9 \, B + 10 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(6 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right) + 16 \, {\left(9 \, B + 10 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(6*B + 7*C)*a^2*d*x + (24*B*a^2*cos(d*x + c)^4 + 30*(2*B + C)*a^2*cos(d*x + c)^3 + 8*(9*B + 10*C)*a^2*cos(d*x + c)^2 + 15*(6*B + 7*C)*a^2*cos(d*x + c) + 16*(9*B + 10*C)*a^2)*sin(d*x + c))/d","A",0
323,1,165,0,0.493633," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(15 \, B + 13 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(15 \, B + 13 \, C\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 \, B + 38 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 15 \, {\left(15 \, B + 13 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, B + 19 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 30 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 24 \, C a^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(15*B + 13*C)*a^3*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(15*B + 13*C)*a^3*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(45*B + 38*C)*a^3*cos(d*x + c)^4 + 15*(15*B + 13*C)*a^3*cos(d*x + c)^3 + 8*(15*B + 19*C)*a^3*cos(d*x + c)^2 + 30*(B + 3*C)*a^3*cos(d*x + c) + 24*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
324,1,145,0,0.476098," ","integrate((a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, B + 3 \, C\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 \, B + 9 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 9 \, {\left(4 \, B + 5 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 8 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 6 \, C a^{3}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(15*(4*B + 3*C)*a^3*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 15*(4*B + 3*C)*a^3*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(11*B + 9*C)*a^3*cos(d*x + c)^3 + 9*(4*B + 5*C)*a^3*cos(d*x + c)^2 + 8*(B + 3*C)*a^3*cos(d*x + c) + 6*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
325,1,141,0,0.489879," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{12 \, B a^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, B + 5 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(7 \, B + 5 \, C\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 \, B + 11 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 2 \, C a^{3}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*B*a^3*d*x*cos(d*x + c)^3 + 3*(7*B + 5*C)*a^3*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(7*B + 5*C)*a^3*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(9*B + 11*C)*a^3*cos(d*x + c)^2 + 3*(B + 3*C)*a^3*cos(d*x + c) + 2*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
326,1,137,0,0.490636," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, B + C\right)} a^{3} d x \cos\left(d x + c\right)^{2} + {\left(6 \, B + 7 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(6 \, B + 7 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + C a^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*(3*B + C)*a^3*d*x*cos(d*x + c)^2 + (6*B + 7*C)*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (6*B + 7*C)*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*B*a^3*cos(d*x + c)^2 + 2*(B + 3*C)*a^3*cos(d*x + c) + C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
327,1,127,0,0.483052," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(7 \, B + 6 \, C\right)} a^{3} d x \cos\left(d x + c\right) + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(B a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right) + 2 \, C a^{3}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((7*B + 6*C)*a^3*d*x*cos(d*x + c) + (B + 3*C)*a^3*cos(d*x + c)*log(sin(d*x + c) + 1) - (B + 3*C)*a^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + (B*a^3*cos(d*x + c)^2 + 2*(3*B + C)*a^3*cos(d*x + c) + 2*C*a^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
328,1,102,0,0.476591," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, B + 7 \, C\right)} a^{3} d x + 3 \, C a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, C a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, B a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right) + 2 \, {\left(11 \, B + 9 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(5*B + 7*C)*a^3*d*x + 3*C*a^3*log(sin(d*x + c) + 1) - 3*C*a^3*log(-sin(d*x + c) + 1) + (2*B*a^3*cos(d*x + c)^2 + 3*(3*B + C)*a^3*cos(d*x + c) + 2*(11*B + 9*C)*a^3)*sin(d*x + c))/d","A",0
329,1,90,0,0.457336," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B + 4 \, C\right)} a^{3} d x + {\left(6 \, B a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 9 \, {\left(5 \, B + 4 \, C\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(9 \, B + 11 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(15*(3*B + 4*C)*a^3*d*x + (6*B*a^3*cos(d*x + c)^3 + 8*(3*B + C)*a^3*cos(d*x + c)^2 + 9*(5*B + 4*C)*a^3*cos(d*x + c) + 8*(9*B + 11*C)*a^3)*sin(d*x + c))/d","A",0
330,1,110,0,0.476806," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, B + 15 \, C\right)} a^{3} d x + {\left(24 \, B a^{3} \cos\left(d x + c\right)^{4} + 30 \, {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(19 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(13 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(38 \, B + 45 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(13*B + 15*C)*a^3*d*x + (24*B*a^3*cos(d*x + c)^4 + 30*(3*B + C)*a^3*cos(d*x + c)^3 + 8*(19*B + 15*C)*a^3*cos(d*x + c)^2 + 15*(13*B + 15*C)*a^3*cos(d*x + c) + 8*(38*B + 45*C)*a^3)*sin(d*x + c))/d","A",0
331,1,130,0,0.509079," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(23 \, B + 26 \, C\right)} a^{3} d x + {\left(40 \, B a^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right)^{4} + 10 \, {\left(23 \, B + 18 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(17 \, B + 19 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(23 \, B + 26 \, C\right)} a^{3} \cos\left(d x + c\right) + 32 \, {\left(17 \, B + 19 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(23*B + 26*C)*a^3*d*x + (40*B*a^3*cos(d*x + c)^5 + 48*(3*B + C)*a^3*cos(d*x + c)^4 + 10*(23*B + 18*C)*a^3*cos(d*x + c)^3 + 16*(17*B + 19*C)*a^3*cos(d*x + c)^2 + 15*(23*B + 26*C)*a^3*cos(d*x + c) + 32*(17*B + 19*C)*a^3)*sin(d*x + c))/d","A",0
332,1,170,0,0.492347," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left({\left(B - C\right)} \cos\left(d x + c\right)^{4} + {\left(B - C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, {\left({\left(B - C\right)} \cos\left(d x + c\right)^{4} + {\left(B - C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(3 \, B - 4 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, B - C\right)} \cos\left(d x + c\right) - 2 \, C\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*((B - C)*cos(d*x + c)^4 + (B - C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 9*((B - C)*cos(d*x + c)^4 + (B - C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(4*(3*B - 4*C)*cos(d*x + c)^3 + (3*B - 7*C)*cos(d*x + c)^2 - (3*B - C)*cos(d*x + c) - 2*C)*sin(d*x + c))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
333,1,156,0,0.478163," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left({\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(B - C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B - C\right)} \cos\left(d x + c\right) + C\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*B - 3*C)*cos(d*x + c)^3 + (2*B - 3*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((2*B - 3*C)*cos(d*x + c)^3 + (2*B - 3*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(B - C)*cos(d*x + c)^2 + (2*B - C)*cos(d*x + c) + C)*sin(d*x + c))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
334,1,127,0,0.482180," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(B - C\right)} \cos\left(d x + c\right)^{2} + {\left(B - C\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(B - C\right)} \cos\left(d x + c\right)^{2} + {\left(B - C\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(B - 2 \, C\right)} \cos\left(d x + c\right) - C\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*(((B - C)*cos(d*x + c)^2 + (B - C)*cos(d*x + c))*log(sin(d*x + c) + 1) - ((B - C)*cos(d*x + c)^2 + (B - C)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*((B - 2*C)*cos(d*x + c) - C)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","B",0
335,1,74,0,0.483180," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B - C\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*((C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - (C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) + 2*(B - C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
336,1,44,0,0.445051," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{B d x \cos\left(d x + c\right) + B d x - {\left(B - C\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"(B*d*x*cos(d*x + c) + B*d*x - (B - C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
337,1,63,0,0.455957," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(B - C\right)} d x \cos\left(d x + c\right) + {\left(B - C\right)} d x - {\left(B \cos\left(d x + c\right) + 2 \, B - C\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"-((B - C)*d*x*cos(d*x + c) + (B - C)*d*x - (B*cos(d*x + c) + 2*B - C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
338,1,81,0,0.477098," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, B - 2 \, C\right)} d x \cos\left(d x + c\right) + {\left(3 \, B - 2 \, C\right)} d x + {\left(B \cos\left(d x + c\right)^{2} - {\left(B - 2 \, C\right)} \cos\left(d x + c\right) - 4 \, B + 4 \, C\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*((3*B - 2*C)*d*x*cos(d*x + c) + (3*B - 2*C)*d*x + (B*cos(d*x + c)^2 - (B - 2*C)*cos(d*x + c) - 4*B + 4*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
339,1,97,0,0.610476," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{9 \, {\left(B - C\right)} d x \cos\left(d x + c\right) + 9 \, {\left(B - C\right)} d x - {\left(2 \, B \cos\left(d x + c\right)^{3} - {\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 16 \, B - 12 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/6*(9*(B - C)*d*x*cos(d*x + c) + 9*(B - C)*d*x - (2*B*cos(d*x + c)^3 - (B - 3*C)*cos(d*x + c)^2 + (7*B - 3*C)*cos(d*x + c) + 16*B - 12*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
340,1,228,0,0.508449," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(4 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(4 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(4 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(4 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(5 \, B - 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(28 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(B - C\right)} \cos\left(d x + c\right) + 3 \, C\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*B - 7*C)*cos(d*x + c)^4 + 2*(4*B - 7*C)*cos(d*x + c)^3 + (4*B - 7*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*((4*B - 7*C)*cos(d*x + c)^4 + 2*(4*B - 7*C)*cos(d*x + c)^3 + (4*B - 7*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(5*B - 8*C)*cos(d*x + c)^3 + (28*B - 43*C)*cos(d*x + c)^2 + 6*(B - C)*cos(d*x + c) + 3*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
341,1,195,0,0.467501," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(B - 2 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(B - 2 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 2 \, C\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(B - 2 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(B - 2 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 2 \, C\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, B - 14 \, C\right)} \cos\left(d x + c\right) - 3 \, C\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*((B - 2*C)*cos(d*x + c)^3 + 2*(B - 2*C)*cos(d*x + c)^2 + (B - 2*C)*cos(d*x + c))*log(sin(d*x + c) + 1) - 3*((B - 2*C)*cos(d*x + c)^3 + 2*(B - 2*C)*cos(d*x + c)^2 + (B - 2*C)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*(2*B - 5*C)*cos(d*x + c)^2 + (5*B - 14*C)*cos(d*x + c) - 3*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
342,1,129,0,0.489007," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(B - 4 \, C\right)} \cos\left(d x + c\right) + 2 \, B - 5 \, C\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*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - 3*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) + 2*((B - 4*C)*cos(d*x + c) + 2*B - 5*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
343,1,58,0,0.477189," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, B + C\right)} \cos\left(d x + c\right) + B + 2 \, C\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*B + C)*cos(d*x + c) + B + 2*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
344,1,94,0,0.486849," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, B d x \cos\left(d x + c\right)^{2} + 6 \, B d x \cos\left(d x + c\right) + 3 \, B d x - {\left({\left(5 \, B - 2 \, C\right)} \cos\left(d x + c\right) + 4 \, B - C\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*B*d*x*cos(d*x + c)^2 + 6*B*d*x*cos(d*x + c) + 3*B*d*x - ((5*B - 2*C)*cos(d*x + c) + 4*B - 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
345,1,123,0,0.491025," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(2 \, B - C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(2 \, B - C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(2 \, B - C\right)} d x - {\left(3 \, B \cos\left(d x + c\right)^{2} + {\left(14 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 10 \, B - 4 \, C\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*B - C)*d*x*cos(d*x + c)^2 + 6*(2*B - C)*d*x*cos(d*x + c) + 3*(2*B - C)*d*x - (3*B*cos(d*x + c)^2 + (14*B - 5*C)*cos(d*x + c) + 10*B - 4*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
346,1,138,0,0.498961," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, B - 4 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(7 \, B - 4 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(7 \, B - 4 \, C\right)} d x + {\left(3 \, B \cos\left(d x + c\right)^{3} - 6 \, {\left(B - C\right)} \cos\left(d x + c\right)^{2} - {\left(43 \, B - 28 \, C\right)} \cos\left(d x + c\right) - 32 \, B + 20 \, C\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*B - 4*C)*d*x*cos(d*x + c)^2 + 6*(7*B - 4*C)*d*x*cos(d*x + c) + 3*(7*B - 4*C)*d*x + (3*B*cos(d*x + c)^3 - 6*(B - C)*cos(d*x + c)^2 - (43*B - 28*C)*cos(d*x + c) - 32*B + 20*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
347,1,157,0,0.486129," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(10 \, B - 7 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(10 \, B - 7 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(10 \, B - 7 \, C\right)} d x - {\left(2 \, B \cos\left(d x + c\right)^{4} - {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(2 \, B - C\right)} \cos\left(d x + c\right)^{2} + {\left(66 \, B - 43 \, C\right)} \cos\left(d x + c\right) + 48 \, B - 32 \, C\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*B - 7*C)*d*x*cos(d*x + c)^2 + 6*(10*B - 7*C)*d*x*cos(d*x + c) + 3*(10*B - 7*C)*d*x - (2*B*cos(d*x + c)^4 - (2*B - 3*C)*cos(d*x + c)^3 + 6*(2*B - C)*cos(d*x + c)^2 + (66*B - 43*C)*cos(d*x + c) + 48*B - 32*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
348,1,295,0,0.487850," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(6 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(6 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(6 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(6 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(6 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(6 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(9 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(114 \, B - 239 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(234 \, B - 479 \, C\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 15 \, C\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*B - 13*C)*cos(d*x + c)^5 + 3*(6*B - 13*C)*cos(d*x + c)^4 + 3*(6*B - 13*C)*cos(d*x + c)^3 + (6*B - 13*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 15*((6*B - 13*C)*cos(d*x + c)^5 + 3*(6*B - 13*C)*cos(d*x + c)^4 + 3*(6*B - 13*C)*cos(d*x + c)^3 + (6*B - 13*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(16*(9*B - 19*C)*cos(d*x + c)^4 + 3*(114*B - 239*C)*cos(d*x + c)^3 + (234*B - 479*C)*cos(d*x + c)^2 + 15*(2*B - 3*C)*cos(d*x + c) + 15*C)*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
349,1,256,0,0.474227," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 3 \, C\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 3 \, C\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(11 \, B - 36 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(17 \, B - 57 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(32 \, B - 117 \, C\right)} \cos\left(d x + c\right) - 15 \, C\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*((B - 3*C)*cos(d*x + c)^4 + 3*(B - 3*C)*cos(d*x + c)^3 + 3*(B - 3*C)*cos(d*x + c)^2 + (B - 3*C)*cos(d*x + c))*log(sin(d*x + c) + 1) - 15*((B - 3*C)*cos(d*x + c)^4 + 3*(B - 3*C)*cos(d*x + c)^3 + 3*(B - 3*C)*cos(d*x + c)^2 + (B - 3*C)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*(11*B - 36*C)*cos(d*x + c)^3 + 3*(17*B - 57*C)*cos(d*x + c)^2 + (32*B - 117*C)*cos(d*x + c) - 15*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
350,1,183,0,0.495932," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(B - 11 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B - 17 \, C\right)} \cos\left(d x + c\right) + 7 \, B - 32 \, C\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*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - 15*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) + 2*(2*(B - 11*C)*cos(d*x + c)^2 + 3*(2*B - 17*C)*cos(d*x + c) + 7*B - 32*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
351,1,93,0,0.435946," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(3 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, B + 2 \, C\right)} \cos\left(d x + c\right) + 3 \, B + 7 \, C\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*B + 2*C)*cos(d*x + c)^2 + 3*(3*B + 2*C)*cos(d*x + c) + 3*B + 7*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
352,1,93,0,0.432789," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(7 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 2 \, B + 3 \, C\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*B + 3*C)*cos(d*x + c)^2 + 3*(2*B + 3*C)*cos(d*x + c) + 2*B + 3*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
353,1,138,0,0.486249," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, B d x \cos\left(d x + c\right)^{3} + 45 \, B d x \cos\left(d x + c\right)^{2} + 45 \, B d x \cos\left(d x + c\right) + 15 \, B d x - {\left({\left(32 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(17 \, B - 2 \, C\right)} \cos\left(d x + c\right) + 22 \, B - 2 \, C\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*B*d*x*cos(d*x + c)^3 + 45*B*d*x*cos(d*x + c)^2 + 45*B*d*x*cos(d*x + c) + 15*B*d*x - ((32*B - 7*C)*cos(d*x + c)^2 + 3*(17*B - 2*C)*cos(d*x + c) + 22*B - 2*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
354,1,173,0,0.452489," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(3 \, B - C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(3 \, B - C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(3 \, B - C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(3 \, B - C\right)} d x - {\left(15 \, B \cos\left(d x + c\right)^{3} + {\left(117 \, B - 32 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(57 \, B - 17 \, C\right)} \cos\left(d x + c\right) + 72 \, B - 22 \, C\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*B - C)*d*x*cos(d*x + c)^3 + 45*(3*B - C)*d*x*cos(d*x + c)^2 + 45*(3*B - C)*d*x*cos(d*x + c) + 15*(3*B - C)*d*x - (15*B*cos(d*x + c)^3 + (117*B - 32*C)*cos(d*x + c)^2 + 3*(57*B - 17*C)*cos(d*x + c) + 72*B - 22*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
355,1,190,0,0.483875," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, B - 6 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(13 \, B - 6 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(13 \, B - 6 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(13 \, B - 6 \, C\right)} d x + {\left(15 \, B \cos\left(d x + c\right)^{4} - 15 \, {\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(479 \, B - 234 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(239 \, B - 114 \, C\right)} \cos\left(d x + c\right) - 304 \, B + 144 \, C\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*B - 6*C)*d*x*cos(d*x + c)^3 + 45*(13*B - 6*C)*d*x*cos(d*x + c)^2 + 45*(13*B - 6*C)*d*x*cos(d*x + c) + 15*(13*B - 6*C)*d*x + (15*B*cos(d*x + c)^4 - 15*(3*B - 2*C)*cos(d*x + c)^3 - (479*B - 234*C)*cos(d*x + c)^2 - 3*(239*B - 114*C)*cos(d*x + c) - 304*B + 144*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
356,1,139,0,0.480908," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, {\left(11 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{5} + 64 \, {\left(11 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{4} + 48 \, {\left(11 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{3} + 40 \, {\left(11 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{2} + 35 \, {\left(11 \, B + 10 \, C\right)} \cos\left(d x + c\right) + 315 \, C\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*(128*(11*B + 10*C)*cos(d*x + c)^5 + 64*(11*B + 10*C)*cos(d*x + c)^4 + 48*(11*B + 10*C)*cos(d*x + c)^3 + 40*(11*B + 10*C)*cos(d*x + c)^2 + 35*(11*B + 10*C)*cos(d*x + c) + 315*C)*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
357,1,122,0,0.443957," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, {\left(9 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(9 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(9 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, B + 8 \, C\right)} \cos\left(d x + c\right) + 35 \, C\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*B + 8*C)*cos(d*x + c)^4 + 8*(9*B + 8*C)*cos(d*x + c)^3 + 6*(9*B + 8*C)*cos(d*x + c)^2 + 5*(9*B + 8*C)*cos(d*x + c) + 35*C)*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
358,1,105,0,0.464041," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(7 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(7 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B + 6 \, C\right)} \cos\left(d x + c\right) + 15 \, C\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*B + 6*C)*cos(d*x + c)^3 + 4*(7*B + 6*C)*cos(d*x + c)^2 + 3*(7*B + 6*C)*cos(d*x + c) + 15*C)*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
359,1,87,0,0.443658," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(5 \, B + 4 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, B + 4 \, C\right)} \cos\left(d x + c\right) + 3 \, C\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*B + 4*C)*cos(d*x + c)^2 + (5*B + 4*C)*cos(d*x + c) + 3*C)*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
360,1,66,0,0.473405," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(3 \, B + 2 \, C\right)} \cos\left(d x + c\right) + C\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*B + 2*C)*cos(d*x + c) + C)*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
361,1,235,0,0.492743," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(B \cos\left(d x + c\right) + 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 \, C \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(B \cos\left(d x + c\right) + 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) - C \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,"[((B*cos(d*x + c) + 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*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -2*((B*cos(d*x + c) + 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))) - C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
362,1,261,0,0.564443," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, B \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(B + 2 \, C\right)} \cos\left(d x + c\right) + B + 2 \, C\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{B \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(B + 2 \, C\right)} \cos\left(d x + c\right) + B + 2 \, C\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*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + ((B + 2*C)*cos(d*x + c) + B + 2*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)))/(d*cos(d*x + c) + d), (B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - ((B + 2*C)*cos(d*x + c) + B + 2*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))))/(d*cos(d*x + c) + d)]","A",0
363,1,308,0,0.545581," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, B + 4 \, C\right)} \cos\left(d x + c\right) + 3 \, B + 4 \, C\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 \, B \cos\left(d x + c\right)^{2} + {\left(3 \, B + 4 \, C\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 \, B + 4 \, C\right)} \cos\left(d x + c\right) + 3 \, B + 4 \, C\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 \, B \cos\left(d x + c\right)^{2} + {\left(3 \, B + 4 \, C\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*B + 4*C)*cos(d*x + c) + 3*B + 4*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*(2*B*cos(d*x + c)^2 + (3*B + 4*C)*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*B + 4*C)*cos(d*x + c) + 3*B + 4*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))) - (2*B*cos(d*x + c)^2 + (3*B + 4*C)*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
364,1,346,0,0.540251," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, B + 6 \, C\right)} \cos\left(d x + c\right) + 5 \, B + 6 \, C\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 \, B \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B + 6 \, C\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 \, B + 6 \, C\right)} \cos\left(d x + c\right) + 5 \, B + 6 \, C\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 \, B \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B + 6 \, C\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*B + 6*C)*cos(d*x + c) + 5*B + 6*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*(8*B*cos(d*x + c)^3 + 2*(5*B + 6*C)*cos(d*x + c)^2 + 3*(5*B + 6*C)*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*B + 6*C)*cos(d*x + c) + 5*B + 6*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))) - (8*B*cos(d*x + c)^3 + 2*(5*B + 6*C)*cos(d*x + c)^2 + 3*(5*B + 6*C)*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
365,1,145,0,0.454404," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, {\left(187 \, B + 168 \, C\right)} a \cos\left(d x + c\right)^{5} + 8 \, {\left(187 \, B + 168 \, C\right)} a \cos\left(d x + c\right)^{4} + 6 \, {\left(187 \, B + 168 \, C\right)} a \cos\left(d x + c\right)^{3} + 5 \, {\left(187 \, B + 168 \, C\right)} a \cos\left(d x + c\right)^{2} + 35 \, {\left(11 \, B + 21 \, C\right)} a \cos\left(d x + c\right) + 315 \, C a\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*(16*(187*B + 168*C)*a*cos(d*x + c)^5 + 8*(187*B + 168*C)*a*cos(d*x + c)^4 + 6*(187*B + 168*C)*a*cos(d*x + c)^3 + 5*(187*B + 168*C)*a*cos(d*x + c)^2 + 35*(11*B + 21*C)*a*cos(d*x + c) + 315*C*a)*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
366,1,127,0,0.454265," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(39 \, B + 34 \, C\right)} a \cos\left(d x + c\right)^{4} + 4 \, {\left(39 \, B + 34 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(39 \, B + 34 \, C\right)} a \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, B + 17 \, C\right)} a \cos\left(d x + c\right) + 35 \, C 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*B + 34*C)*a*cos(d*x + c)^4 + 4*(39*B + 34*C)*a*cos(d*x + c)^3 + 3*(39*B + 34*C)*a*cos(d*x + c)^2 + 5*(9*B + 17*C)*a*cos(d*x + c) + 35*C*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
367,1,108,0,0.453064," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(63 \, B + 52 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(63 \, B + 52 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B + 13 \, C\right)} a \cos\left(d x + c\right) + 15 \, C 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*B + 52*C)*a*cos(d*x + c)^3 + (63*B + 52*C)*a*cos(d*x + c)^2 + 3*(7*B + 13*C)*a*cos(d*x + c) + 15*C*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
368,1,89,0,0.448788," ","integrate((a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(25 \, B + 18 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(5 \, B + 9 \, C\right)} a \cos\left(d x + c\right) + 3 \, C 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*B + 18*C)*a*cos(d*x + c)^2 + (5*B + 9*C)*a*cos(d*x + c) + 3*C*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
369,1,314,0,0.501951," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a \cos\left(d x + c\right)^{2} + B 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 \, B + 5 \, C\right)} a \cos\left(d x + c\right) + C 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(B a \cos\left(d x + c\right)^{2} + B 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 \, B + 5 \, C\right)} a \cos\left(d x + c\right) + C 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*(B*a*cos(d*x + c)^2 + B*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*B + 5*C)*a*cos(d*x + c) + C*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*(B*a*cos(d*x + c)^2 + B*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*B + 5*C)*a*cos(d*x + c) + C*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
370,1,292,0,0.569279," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, B + 2 \, C\right)} a \cos\left(d x + c\right) + {\left(3 \, B + 2 \, 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 \, {\left(B a \cos\left(d x + c\right) + 2 \, C 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 \, B + 2 \, C\right)} a \cos\left(d x + c\right) + {\left(3 \, B + 2 \, 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) - {\left(B a \cos\left(d x + c\right) + 2 \, C 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*B + 2*C)*a*cos(d*x + c) + (3*B + 2*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*a*cos(d*x + c) + 2*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -(((3*B + 2*C)*a*cos(d*x + c) + (3*B + 2*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*a*cos(d*x + c) + 2*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
371,1,320,0,0.528048," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(7 \, B + 12 \, C\right)} a \cos\left(d x + c\right) + {\left(7 \, B + 12 \, 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 \, {\left(2 \, B a \cos\left(d x + c\right)^{2} + {\left(7 \, B + 4 \, C\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 \, B + 12 \, C\right)} a \cos\left(d x + c\right) + {\left(7 \, B + 12 \, 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) - {\left(2 \, B a \cos\left(d x + c\right)^{2} + {\left(7 \, B + 4 \, C\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*B + 12*C)*a*cos(d*x + c) + (7*B + 12*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*(2*B*a*cos(d*x + c)^2 + (7*B + 4*C)*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*B + 12*C)*a*cos(d*x + c) + (7*B + 12*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*B*a*cos(d*x + c)^2 + (7*B + 4*C)*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
372,1,360,0,0.526098," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(11 \, B + 14 \, C\right)} a \cos\left(d x + c\right) + {\left(11 \, B + 14 \, 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 \, {\left(8 \, B a \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, B + 6 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(11 \, B + 14 \, C\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 \, B + 14 \, C\right)} a \cos\left(d x + c\right) + {\left(11 \, B + 14 \, 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) - {\left(8 \, B a \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, B + 6 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(11 \, B + 14 \, C\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*B + 14*C)*a*cos(d*x + c) + (11*B + 14*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*(8*B*a*cos(d*x + c)^3 + 2*(11*B + 6*C)*a*cos(d*x + c)^2 + 3*(11*B + 14*C)*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*B + 14*C)*a*cos(d*x + c) + (11*B + 14*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))) - (8*B*a*cos(d*x + c)^3 + 2*(11*B + 6*C)*a*cos(d*x + c)^2 + 3*(11*B + 14*C)*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
373,1,396,0,0.567644," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(75 \, B + 88 \, C\right)} a \cos\left(d x + c\right) + {\left(75 \, B + 88 \, 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 \, {\left(48 \, B a \cos\left(d x + c\right)^{4} + 8 \, {\left(15 \, B + 8 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(75 \, B + 88 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, B + 88 \, C\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 \, B + 88 \, C\right)} a \cos\left(d x + c\right) + {\left(75 \, B + 88 \, 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) - {\left(48 \, B a \cos\left(d x + c\right)^{4} + 8 \, {\left(15 \, B + 8 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(75 \, B + 88 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, B + 88 \, C\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*B + 88*C)*a*cos(d*x + c) + (75*B + 88*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*(48*B*a*cos(d*x + c)^4 + 8*(15*B + 8*C)*a*cos(d*x + c)^3 + 2*(75*B + 88*C)*a*cos(d*x + c)^2 + 3*(75*B + 88*C)*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*B + 88*C)*a*cos(d*x + c) + (75*B + 88*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))) - (48*B*a*cos(d*x + c)^4 + 8*(15*B + 8*C)*a*cos(d*x + c)^3 + 2*(75*B + 88*C)*a*cos(d*x + c)^2 + 3*(75*B + 88*C)*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
374,1,177,0,0.503449," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, {\left(4615 \, B + 4184 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + 8 \, {\left(4615 \, B + 4184 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 6 \, {\left(4615 \, B + 4184 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(4615 \, B + 4184 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 35 \, {\left(416 \, B + 523 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 315 \, {\left(13 \, B + 38 \, C\right)} a^{2} \cos\left(d x + c\right) + 3465 \, C 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)}{45045 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"2/45045*(16*(4615*B + 4184*C)*a^2*cos(d*x + c)^6 + 8*(4615*B + 4184*C)*a^2*cos(d*x + c)^5 + 6*(4615*B + 4184*C)*a^2*cos(d*x + c)^4 + 5*(4615*B + 4184*C)*a^2*cos(d*x + c)^3 + 35*(416*B + 523*C)*a^2*cos(d*x + c)^2 + 315*(13*B + 38*C)*a^2*cos(d*x + c) + 3465*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^7 + d*cos(d*x + c)^6)","A",0
375,1,157,0,0.488747," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(803 \, B + 710 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 4 \, {\left(803 \, B + 710 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(803 \, B + 710 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 5 \, {\left(286 \, B + 355 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 35 \, {\left(11 \, B + 32 \, C\right)} a^{2} \cos\left(d x + c\right) + 315 \, C 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*B + 710*C)*a^2*cos(d*x + c)^5 + 4*(803*B + 710*C)*a^2*cos(d*x + c)^4 + 3*(803*B + 710*C)*a^2*cos(d*x + c)^3 + 5*(286*B + 355*C)*a^2*cos(d*x + c)^2 + 35*(11*B + 32*C)*a^2*cos(d*x + c) + 315*C*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
376,1,136,0,0.452807," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(345 \, B + 292 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(345 \, B + 292 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(60 \, B + 73 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, B + 26 \, C\right)} a^{2} \cos\left(d x + c\right) + 35 \, C 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*B + 292*C)*a^2*cos(d*x + c)^4 + (345*B + 292*C)*a^2*cos(d*x + c)^3 + 3*(60*B + 73*C)*a^2*cos(d*x + c)^2 + 5*(9*B + 26*C)*a^2*cos(d*x + c) + 35*C*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
377,1,115,0,0.457527," ","integrate((a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(301 \, B + 230 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(98 \, B + 115 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B + 20 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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*B + 230*C)*a^2*cos(d*x + c)^3 + (98*B + 115*C)*a^2*cos(d*x + c)^2 + 3*(7*B + 20*C)*a^2*cos(d*x + c) + 15*C*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
378,1,378,0,0.501852," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B a^{2} \cos\left(d x + c\right)^{3} + B 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 \, B + 43 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(5 \, B + 14 \, C\right)} a^{2} \cos\left(d x + c\right) + 3 \, C 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(B a^{2} \cos\left(d x + c\right)^{3} + B 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 \, B + 43 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(5 \, B + 14 \, C\right)} a^{2} \cos\left(d x + c\right) + 3 \, C 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*(B*a^2*cos(d*x + c)^3 + B*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*B + 43*C)*a^2*cos(d*x + c)^2 + (5*B + 14*C)*a^2*cos(d*x + c) + 3*C*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*(B*a^2*cos(d*x + c)^3 + B*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*B + 43*C)*a^2*cos(d*x + c)^2 + (5*B + 14*C)*a^2*cos(d*x + c) + 3*C*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
379,1,386,0,0.540774," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(5 \, B + 2 \, C\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 \, B a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, C 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 \, B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(5 \, B + 2 \, C\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 \, B a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, C 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*B + 2*C)*a^2*cos(d*x + c)^2 + (5*B + 2*C)*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*B*a^2*cos(d*x + c)^2 + 2*(3*B + 8*C)*a^2*cos(d*x + c) + 2*C*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*B + 2*C)*a^2*cos(d*x + c)^2 + (5*B + 2*C)*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*B*a^2*cos(d*x + c)^2 + 2*(3*B + 8*C)*a^2*cos(d*x + c) + 2*C*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
380,1,348,0,0.538062," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(19 \, B + 20 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(19 \, B + 20 \, C\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 \, B a^{2} \cos\left(d x + c\right)^{2} + {\left(11 \, B + 4 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, C 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 \, B + 20 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(19 \, B + 20 \, C\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 \, B a^{2} \cos\left(d x + c\right)^{2} + {\left(11 \, B + 4 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, C 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*B + 20*C)*a^2*cos(d*x + c) + (19*B + 20*C)*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*B*a^2*cos(d*x + c)^2 + (11*B + 4*C)*a^2*cos(d*x + c) + 8*C*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*B + 20*C)*a^2*cos(d*x + c) + (19*B + 20*C)*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*B*a^2*cos(d*x + c)^2 + (11*B + 4*C)*a^2*cos(d*x + c) + 8*C*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
381,1,380,0,0.574187," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(25 \, B + 38 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(25 \, B + 38 \, C\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 \, B a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(17 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(25 \, B + 22 \, C\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 \, B + 38 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(25 \, B + 38 \, C\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 \, B a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(17 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(25 \, B + 22 \, C\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*B + 38*C)*a^2*cos(d*x + c) + (25*B + 38*C)*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*B*a^2*cos(d*x + c)^3 + 2*(17*B + 6*C)*a^2*cos(d*x + c)^2 + 3*(25*B + 22*C)*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*B + 38*C)*a^2*cos(d*x + c) + (25*B + 38*C)*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*B*a^2*cos(d*x + c)^3 + 2*(17*B + 6*C)*a^2*cos(d*x + c)^2 + 3*(25*B + 22*C)*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
382,1,420,0,0.603385," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(163 \, B + 200 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(163 \, B + 200 \, C\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 \, B a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(23 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(163 \, B + 136 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, B + 200 \, C\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 \, B + 200 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(163 \, B + 200 \, C\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 \, B a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(23 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(163 \, B + 136 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, B + 200 \, C\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*B + 200*C)*a^2*cos(d*x + c) + (163*B + 200*C)*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*B*a^2*cos(d*x + c)^4 + 8*(23*B + 8*C)*a^2*cos(d*x + c)^3 + 2*(163*B + 136*C)*a^2*cos(d*x + c)^2 + 3*(163*B + 200*C)*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*B + 200*C)*a^2*cos(d*x + c) + (163*B + 200*C)*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*B*a^2*cos(d*x + c)^4 + 8*(23*B + 8*C)*a^2*cos(d*x + c)^3 + 2*(163*B + 136*C)*a^2*cos(d*x + c)^2 + 3*(163*B + 200*C)*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
383,1,460,0,0.630654," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(283 \, B + 326 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(283 \, B + 326 \, C\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 \, B a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(29 \, B + 10 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(283 \, B + 230 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(283 \, B + 326 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(283 \, B + 326 \, C\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 \, B + 326 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(283 \, B + 326 \, C\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 \, B a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(29 \, B + 10 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(283 \, B + 230 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(283 \, B + 326 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(283 \, B + 326 \, C\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*B + 326*C)*a^2*cos(d*x + c) + (283*B + 326*C)*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*B*a^2*cos(d*x + c)^5 + 48*(29*B + 10*C)*a^2*cos(d*x + c)^4 + 8*(283*B + 230*C)*a^2*cos(d*x + c)^3 + 10*(283*B + 326*C)*a^2*cos(d*x + c)^2 + 15*(283*B + 326*C)*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*B + 326*C)*a^2*cos(d*x + c) + (283*B + 326*C)*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*B*a^2*cos(d*x + c)^5 + 48*(29*B + 10*C)*a^2*cos(d*x + c)^4 + 8*(283*B + 230*C)*a^2*cos(d*x + c)^3 + 10*(283*B + 326*C)*a^2*cos(d*x + c)^2 + 15*(283*B + 326*C)*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
384,1,465,0,0.550203," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{315 \, \sqrt{2} {\left({\left(B - C\right)} a \cos\left(d x + c\right)^{5} + {\left(B - C\right)} a \cos\left(d x + c\right)^{4}\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(129 \, B - 257 \, C\right)} \cos\left(d x + c\right)^{4} - {\left(93 \, B - 29 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{2} - 5 \, {\left(9 \, B - C\right)} \cos\left(d x + c\right) - 35 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{630 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}, -\frac{2 \, {\left({\left(129 \, B - 257 \, C\right)} \cos\left(d x + c\right)^{4} - {\left(93 \, B - 29 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{2} - 5 \, {\left(9 \, B - C\right)} \cos\left(d x + c\right) - 35 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) + \frac{315 \, \sqrt{2} {\left({\left(B - C\right)} a \cos\left(d x + c\right)^{5} + {\left(B - C\right)} a \cos\left(d x + c\right)^{4}\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}}}{315 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[-1/630*(315*sqrt(2)*((B - C)*a*cos(d*x + c)^5 + (B - C)*a*cos(d*x + c)^4)*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*((129*B - 257*C)*cos(d*x + c)^4 - (93*B - 29*C)*cos(d*x + c)^3 + 3*(3*B - 19*C)*cos(d*x + c)^2 - 5*(9*B - C)*cos(d*x + c) - 35*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c)^5 + a*d*cos(d*x + c)^4), -1/315*(2*((129*B - 257*C)*cos(d*x + c)^4 - (93*B - 29*C)*cos(d*x + c)^3 + 3*(3*B - 19*C)*cos(d*x + c)^2 - 5*(9*B - C)*cos(d*x + c) - 35*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 315*sqrt(2)*((B - C)*a*cos(d*x + c)^5 + (B - C)*a*cos(d*x + c)^4)*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)^5 + a*d*cos(d*x + c)^4)]","A",0
385,1,432,0,0.537726," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, \sqrt{2} {\left({\left(B - C\right)} a \cos\left(d x + c\right)^{4} + {\left(B - C\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 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(7 \, B - 31 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B - C\right)} \cos\left(d x + c\right) + 15 \, C\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 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(7 \, B - 31 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B - C\right)} \cos\left(d x + c\right) + 15 \, C\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(B - C\right)} a \cos\left(d x + c\right)^{4} + {\left(B - C\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)*((B - C)*a*cos(d*x + c)^4 + (B - C)*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*B - 43*C)*cos(d*x + c)^3 - (7*B - 31*C)*cos(d*x + c)^2 + 3*(7*B - C)*cos(d*x + c) + 15*C)*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*B - 43*C)*cos(d*x + c)^3 - (7*B - 31*C)*cos(d*x + c)^2 + 3*(7*B - C)*cos(d*x + c) + 15*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 105*sqrt(2)*((B - C)*a*cos(d*x + c)^4 + (B - C)*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
386,1,397,0,0.513161," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left({\left(B - C\right)} a \cos\left(d x + c\right)^{3} + {\left(B - C\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 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(5 \, B - C\right)} \cos\left(d x + c\right) - 3 \, C\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 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(5 \, B - C\right)} \cos\left(d x + c\right) - 3 \, C\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(B - C\right)} a \cos\left(d x + c\right)^{3} + {\left(B - C\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)*((B - C)*a*cos(d*x + c)^3 + (B - C)*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*B - 13*C)*cos(d*x + c)^2 - (5*B - C)*cos(d*x + c) - 3*C)*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*B - 13*C)*cos(d*x + c)^2 - (5*B - C)*cos(d*x + c) - 3*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 15*sqrt(2)*((B - C)*a*cos(d*x + c)^3 + (B - C)*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
387,1,352,0,0.519218," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(B - C\right)} a \cos\left(d x + c\right)^{2} + {\left(B - C\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 \, B - C\right)} \cos\left(d x + c\right) + C\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 \, B - C\right)} \cos\left(d x + c\right) + C\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(B - C\right)} a \cos\left(d x + c\right)^{2} + {\left(B - C\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)*((B - C)*a*cos(d*x + c)^2 + (B - C)*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*B - C)*cos(d*x + c) + C)*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*B - C)*cos(d*x + c) + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 3*sqrt(2)*((B - C)*a*cos(d*x + c)^2 + (B - C)*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
388,1,287,0,0.531273," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(B - C\right)} a \cos\left(d x + c\right) + {\left(B - C\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 \, C \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 \, C \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(B - C\right)} a \cos\left(d x + c\right) + {\left(B - C\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)*((B - C)*a*cos(d*x + c) + (B - C)*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*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d), (2*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - sqrt(2)*((B - C)*a*cos(d*x + c) + (B - C)*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
389,1,307,0,1.253996," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(B - C\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 \, B \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(B - C\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 \, B \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)*(B - C)*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*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), (sqrt(2)*(B - 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*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))))/(a*d)]","A",0
390,1,458,0,1.553173," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, B \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(B - C\right)} a \cos\left(d x + c\right) + {\left(B - C\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(B - 2 \, C\right)} \cos\left(d x + c\right) + B - 2 \, C\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{B \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(B - 2 \, C\right)} \cos\left(d x + c\right) + B - 2 \, C\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(B - C\right)} a \cos\left(d x + c\right) + {\left(B - C\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*B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((B - C)*a*cos(d*x + c) + (B - C)*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)) + ((B - 2*C)*cos(d*x + c) + B - 2*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)))/(a*d*cos(d*x + c) + a*d), (B*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + ((B - 2*C)*cos(d*x + c) + B - 2*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))) - sqrt(2)*((B - C)*a*cos(d*x + c) + (B - C)*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
391,1,506,0,2.500604," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{2} {\left({\left(B - C\right)} a \cos\left(d x + c\right) + {\left(B - C\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 \, B - 4 \, C\right)} \cos\left(d x + c\right) + 7 \, B - 4 \, C\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 \, B \cos\left(d x + c\right)^{2} - {\left(B - 4 \, C\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 \, B - 4 \, C\right)} \cos\left(d x + c\right) + 7 \, B - 4 \, C\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 \, B \cos\left(d x + c\right)^{2} - {\left(B - 4 \, C\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(B - C\right)} a \cos\left(d x + c\right) + {\left(B - C\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)*((B - C)*a*cos(d*x + c) + (B - C)*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*B - 4*C)*cos(d*x + c) + 7*B - 4*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*(2*B*cos(d*x + c)^2 - (B - 4*C)*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*B - 4*C)*cos(d*x + c) + 7*B - 4*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))) - (2*B*cos(d*x + c)^2 - (B - 4*C)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 4*sqrt(2)*((B - C)*a*cos(d*x + c) + (B - C)*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
392,1,539,0,2.619763," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{24 \, \sqrt{2} {\left({\left(B - C\right)} a \cos\left(d x + c\right) + {\left(B - C\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 \, B - 14 \, C\right)} \cos\left(d x + c\right) + 9 \, B - 14 \, C\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 \, B \cos\left(d x + c\right)^{3} - 2 \, {\left(B - 6 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B - 2 \, C\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 \, B - 14 \, C\right)} \cos\left(d x + c\right) + 9 \, B - 14 \, C\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 \, B \cos\left(d x + c\right)^{3} - 2 \, {\left(B - 6 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B - 2 \, C\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(B - C\right)} a \cos\left(d x + c\right) + {\left(B - C\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)*((B - C)*a*cos(d*x + c) + (B - C)*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*B - 14*C)*cos(d*x + c) + 9*B - 14*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*(8*B*cos(d*x + c)^3 - 2*(B - 6*C)*cos(d*x + c)^2 + 3*(7*B - 2*C)*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*B - 14*C)*cos(d*x + c) + 9*B - 14*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))) + (8*B*cos(d*x + c)^3 - 2*(B - 6*C)*cos(d*x + c)^2 + 3*(7*B - 2*C)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 24*sqrt(2)*((B - C)*a*cos(d*x + c) + (B - C)*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
393,1,539,0,0.552697," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{2} {\left({\left(15 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(15 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(15 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{3}\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(1029 \, B - 1201 \, C\right)} \cos\left(d x + c\right)^{4} + 12 \, {\left(63 \, B - 67 \, C\right)} \cos\left(d x + c\right)^{3} - 28 \, {\left(3 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(7 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 60 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{840 \, {\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)}}, \frac{105 \, \sqrt{2} {\left({\left(15 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(15 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(15 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{3}\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(1029 \, B - 1201 \, C\right)} \cos\left(d x + c\right)^{4} + 12 \, {\left(63 \, B - 67 \, C\right)} \cos\left(d x + c\right)^{3} - 28 \, {\left(3 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(7 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 60 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{420 \, {\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)}}\right]"," ",0,"[1/840*(105*sqrt(2)*((15*B - 19*C)*cos(d*x + c)^5 + 2*(15*B - 19*C)*cos(d*x + c)^4 + (15*B - 19*C)*cos(d*x + c)^3)*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*((1029*B - 1201*C)*cos(d*x + c)^4 + 12*(63*B - 67*C)*cos(d*x + c)^3 - 28*(3*B - 7*C)*cos(d*x + c)^2 + 12*(7*B - 3*C)*cos(d*x + c) + 60*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), 1/420*(105*sqrt(2)*((15*B - 19*C)*cos(d*x + c)^5 + 2*(15*B - 19*C)*cos(d*x + c)^4 + (15*B - 19*C)*cos(d*x + c)^3)*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*((1029*B - 1201*C)*cos(d*x + c)^4 + 12*(63*B - 67*C)*cos(d*x + c)^3 - 28*(3*B - 7*C)*cos(d*x + c)^2 + 12*(7*B - 3*C)*cos(d*x + c) + 60*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
394,1,504,0,0.562825," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left({\left(11 \, B - 15 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(11 \, B - 15 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(11 \, B - 15 \, C\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 \, B - 147 \, C\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(5 \, B - 9 \, C\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(5 \, B - 3 \, C\right)} \cos\left(d x + c\right) - 12 \, C\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 \, B - 15 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(11 \, B - 15 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(11 \, B - 15 \, C\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 \, B - 147 \, C\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(5 \, B - 9 \, C\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(5 \, B - 3 \, C\right)} \cos\left(d x + c\right) - 12 \, C\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*B - 15*C)*cos(d*x + c)^4 + 2*(11*B - 15*C)*cos(d*x + c)^3 + (11*B - 15*C)*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*B - 147*C)*cos(d*x + c)^3 + 12*(5*B - 9*C)*cos(d*x + c)^2 - 4*(5*B - 3*C)*cos(d*x + c) - 12*C)*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*B - 15*C)*cos(d*x + c)^4 + 2*(11*B - 15*C)*cos(d*x + c)^3 + (11*B - 15*C)*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*B - 147*C)*cos(d*x + c)^3 + 12*(5*B - 9*C)*cos(d*x + c)^2 - 4*(5*B - 3*C)*cos(d*x + c) - 12*C)*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
395,1,459,0,0.528694," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(7 \, B - 11 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(7 \, B - 11 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, B - 11 \, C\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 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(B - C\right)} \cos\left(d x + c\right) + 4 \, C\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 \, B - 11 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(7 \, B - 11 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, B - 11 \, C\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 \, B - 19 \, C\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(B - C\right)} \cos\left(d x + c\right) + 4 \, C\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*B - 11*C)*cos(d*x + c)^3 + 2*(7*B - 11*C)*cos(d*x + c)^2 + (7*B - 11*C)*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*B - 19*C)*cos(d*x + c)^2 + 12*(B - C)*cos(d*x + c) + 4*C)*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*B - 11*C)*cos(d*x + c)^3 + 2*(7*B - 11*C)*cos(d*x + c)^2 + (7*B - 11*C)*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*B - 19*C)*cos(d*x + c)^2 + 12*(B - C)*cos(d*x + c) + 4*C)*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
396,1,386,0,0.508169," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(3 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B - 7 \, C\right)} \cos\left(d x + c\right) + 3 \, B - 7 \, C\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(B - 5 \, C\right)} \cos\left(d x + c\right) - 4 \, C\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 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B - 7 \, C\right)} \cos\left(d x + c\right) + 3 \, B - 7 \, C\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(B - 5 \, C\right)} \cos\left(d x + c\right) - 4 \, C\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*B - 7*C)*cos(d*x + c)^2 + 2*(3*B - 7*C)*cos(d*x + c) + 3*B - 7*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*((B - 5*C)*cos(d*x + c) - 4*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)*((3*B - 7*C)*cos(d*x + c)^2 + 2*(3*B - 7*C)*cos(d*x + c) + 3*B - 7*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*((B - 5*C)*cos(d*x + c) - 4*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
397,1,367,0,0.530443," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(B - C\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(B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B + 3 \, C\right)} \cos\left(d x + c\right) + B + 3 \, C\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(B - C\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(B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B + 3 \, C\right)} \cos\left(d x + c\right) + B + 3 \, C\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*(B - C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((B + 3*C)*cos(d*x + c)^2 + 2*(B + 3*C)*cos(d*x + c) + B + 3*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)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), 1/4*(2*(B - C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((B + 3*C)*cos(d*x + c)^2 + 2*(B + 3*C)*cos(d*x + c) + B + 3*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))))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","B",0
398,1,548,0,3.266523," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(B - C\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 \, B - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, B - C\right)} \cos\left(d x + c\right) + 5 \, B - C\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(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + 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)}{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(B - C\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 \, B - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, B - C\right)} \cos\left(d x + c\right) + 5 \, B - C\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(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + 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)}{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*(B - C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((5*B - C)*cos(d*x + c)^2 + 2*(5*B - C)*cos(d*x + c) + 5*B - 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)) + 8*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + 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^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/4*(2*(B - C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((5*B - C)*cos(d*x + c)^2 + 2*(5*B - C)*cos(d*x + c) + 5*B - 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))) + 8*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + 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))))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","B",0
399,1,609,0,4.136611," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(9 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(9 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 9 \, B - 5 \, C\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 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right) + 3 \, B - 2 \, C\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 \, B \cos\left(d x + c\right)^{2} + {\left(3 \, B - C\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 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(9 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 9 \, B - 5 \, C\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 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right) + 3 \, B - 2 \, C\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 \, B \cos\left(d x + c\right)^{2} + {\left(3 \, B - C\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*B - 5*C)*cos(d*x + c)^2 + 2*(9*B - 5*C)*cos(d*x + c) + 9*B - 5*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*((3*B - 2*C)*cos(d*x + c)^2 + 2*(3*B - 2*C)*cos(d*x + c) + 3*B - 2*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)) + 4*(2*B*cos(d*x + c)^2 + (3*B - C)*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*B - 5*C)*cos(d*x + c)^2 + 2*(9*B - 5*C)*cos(d*x + c) + 9*B - 5*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))) - 4*((3*B - 2*C)*cos(d*x + c)^2 + 2*(3*B - 2*C)*cos(d*x + c) + 3*B - 2*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))) - 2*(2*B*cos(d*x + c)^2 + (3*B - C)*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
400,1,644,0,5.909630," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(13 \, B - 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(13 \, B - 9 \, C\right)} \cos\left(d x + c\right) + 13 \, B - 9 \, C\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 \, B - 12 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(19 \, B - 12 \, C\right)} \cos\left(d x + c\right) + 19 \, B - 12 \, C\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 \, B \cos\left(d x + c\right)^{3} - {\left(3 \, B - 4 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(7 \, B - 6 \, C\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 \, B - 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(13 \, B - 9 \, C\right)} \cos\left(d x + c\right) + 13 \, B - 9 \, C\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 \, B - 12 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(19 \, B - 12 \, C\right)} \cos\left(d x + c\right) + 19 \, B - 12 \, C\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 \, B \cos\left(d x + c\right)^{3} - {\left(3 \, B - 4 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(7 \, B - 6 \, C\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*B - 9*C)*cos(d*x + c)^2 + 2*(13*B - 9*C)*cos(d*x + c) + 13*B - 9*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)) + ((19*B - 12*C)*cos(d*x + c)^2 + 2*(19*B - 12*C)*cos(d*x + c) + 19*B - 12*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*(2*B*cos(d*x + c)^3 - (3*B - 4*C)*cos(d*x + c)^2 - (7*B - 6*C)*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*B - 9*C)*cos(d*x + c)^2 + 2*(13*B - 9*C)*cos(d*x + c) + 13*B - 9*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))) - ((19*B - 12*C)*cos(d*x + c)^2 + 2*(19*B - 12*C)*cos(d*x + c) + 19*B - 12*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))) + (2*B*cos(d*x + c)^3 - (3*B - 4*C)*cos(d*x + c)^2 - (7*B - 6*C)*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
401,1,596,0,0.501755," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left({\left(163 \, B - 283 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(163 \, B - 283 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(163 \, B - 283 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(163 \, B - 283 \, C\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(1495 \, B - 2671 \, C\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(503 \, B - 911 \, C\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(25 \, B - 49 \, C\right)} \cos\left(d x + c\right)^{2} - 160 \, {\left(B - C\right)} \cos\left(d x + c\right) - 96 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{960 \, {\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)}}, -\frac{15 \, \sqrt{2} {\left({\left(163 \, B - 283 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(163 \, B - 283 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(163 \, B - 283 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(163 \, B - 283 \, C\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(1495 \, B - 2671 \, C\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(503 \, B - 911 \, C\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(25 \, B - 49 \, C\right)} \cos\left(d x + c\right)^{2} - 160 \, {\left(B - C\right)} \cos\left(d x + c\right) - 96 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{480 \, {\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)}}\right]"," ",0,"[1/960*(15*sqrt(2)*((163*B - 283*C)*cos(d*x + c)^5 + 3*(163*B - 283*C)*cos(d*x + c)^4 + 3*(163*B - 283*C)*cos(d*x + c)^3 + (163*B - 283*C)*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*((1495*B - 2671*C)*cos(d*x + c)^4 + 5*(503*B - 911*C)*cos(d*x + c)^3 + 32*(25*B - 49*C)*cos(d*x + c)^2 - 160*(B - C)*cos(d*x + c) - 96*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), -1/480*(15*sqrt(2)*((163*B - 283*C)*cos(d*x + c)^5 + 3*(163*B - 283*C)*cos(d*x + c)^4 + 3*(163*B - 283*C)*cos(d*x + c)^3 + (163*B - 283*C)*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*((1495*B - 2671*C)*cos(d*x + c)^4 + 5*(503*B - 911*C)*cos(d*x + c)^3 + 32*(25*B - 49*C)*cos(d*x + c)^2 - 160*(B - C)*cos(d*x + c) - 96*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
402,1,557,0,0.496579," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(75 \, B - 163 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(75 \, B - 163 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, B - 163 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(75 \, B - 163 \, C\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 \, B - 299 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(255 \, B - 503 \, C\right)} \cos\left(d x + c\right)^{2} + 32 \, {\left(3 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 32 \, C\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 \, B - 163 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(75 \, B - 163 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, B - 163 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(75 \, B - 163 \, C\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 \, B - 299 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(255 \, B - 503 \, C\right)} \cos\left(d x + c\right)^{2} + 32 \, {\left(3 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 32 \, C\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*B - 163*C)*cos(d*x + c)^4 + 3*(75*B - 163*C)*cos(d*x + c)^3 + 3*(75*B - 163*C)*cos(d*x + c)^2 + (75*B - 163*C)*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*B - 299*C)*cos(d*x + c)^3 + (255*B - 503*C)*cos(d*x + c)^2 + 32*(3*B - 5*C)*cos(d*x + c) + 32*C)*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*B - 163*C)*cos(d*x + c)^4 + 3*(75*B - 163*C)*cos(d*x + c)^3 + 3*(75*B - 163*C)*cos(d*x + c)^2 + (75*B - 163*C)*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*B - 299*C)*cos(d*x + c)^3 + (255*B - 503*C)*cos(d*x + c)^2 + 32*(3*B - 5*C)*cos(d*x + c) + 32*C)*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
403,1,484,0,0.524757," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(19 \, B - 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, B - 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, B - 75 \, C\right)} \cos\left(d x + c\right) + 19 \, B - 75 \, C\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 \, B - 49 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(13 \, B - 85 \, C\right)} \cos\left(d x + c\right) - 32 \, C\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 \, B - 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, B - 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, B - 75 \, C\right)} \cos\left(d x + c\right) + 19 \, B - 75 \, C\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 \, B - 49 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(13 \, B - 85 \, C\right)} \cos\left(d x + c\right) - 32 \, C\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*B - 75*C)*cos(d*x + c)^3 + 3*(19*B - 75*C)*cos(d*x + c)^2 + 3*(19*B - 75*C)*cos(d*x + c) + 19*B - 75*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*((9*B - 49*C)*cos(d*x + c)^2 + (13*B - 85*C)*cos(d*x + c) - 32*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)*((19*B - 75*C)*cos(d*x + c)^3 + 3*(19*B - 75*C)*cos(d*x + c)^2 + 3*(19*B - 75*C)*cos(d*x + c) + 19*B - 75*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*((9*B - 49*C)*cos(d*x + c)^2 + (13*B - 85*C)*cos(d*x + c) - 32*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
404,1,475,0,0.486632," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(5 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 5 \, B + 19 \, C\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(B - 9 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, B - 13 \, C\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 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 5 \, B + 19 \, C\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(B - 9 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, B - 13 \, C\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*B + 19*C)*cos(d*x + c)^3 + 3*(5*B + 19*C)*cos(d*x + c)^2 + 3*(5*B + 19*C)*cos(d*x + c) + 5*B + 19*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*((B - 9*C)*cos(d*x + c)^2 + (5*B - 13*C)*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*B + 19*C)*cos(d*x + c)^3 + 3*(5*B + 19*C)*cos(d*x + c)^2 + 3*(5*B + 19*C)*cos(d*x + c) + 5*B + 19*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*((B - 9*C)*cos(d*x + c)^2 + (5*B - 13*C)*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
405,1,475,0,0.540644," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(3 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 3 \, B + 5 \, C\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 \, B + C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B + 5 \, C\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 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 3 \, B + 5 \, C\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 \, B + C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B + 5 \, C\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*B + 5*C)*cos(d*x + c)^3 + 3*(3*B + 5*C)*cos(d*x + c)^2 + 3*(3*B + 5*C)*cos(d*x + c) + 3*B + 5*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*((7*B + C)*cos(d*x + c)^2 + (3*B + 5*C)*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*B + 5*C)*cos(d*x + c)^3 + 3*(3*B + 5*C)*cos(d*x + c)^2 + 3*(3*B + 5*C)*cos(d*x + c) + 3*B + 5*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*((7*B + C)*cos(d*x + c)^2 + (3*B + 5*C)*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
406,1,670,0,6.487961," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(43 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 43 \, B - 3 \, C\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(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{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 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, B - 3 \, C\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 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 43 \, B - 3 \, C\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(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{\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 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, B - 3 \, C\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*B - 3*C)*cos(d*x + c)^3 + 3*(43*B - 3*C)*cos(d*x + c)^2 + 3*(43*B - 3*C)*cos(d*x + c) + 43*B - 3*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)) - 64*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 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*((15*B - 7*C)*cos(d*x + c)^2 + (11*B - 3*C)*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*B - 3*C)*cos(d*x + c)^3 + 3*(43*B - 3*C)*cos(d*x + c)^2 + 3*(43*B - 3*C)*cos(d*x + c) + 43*B - 3*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))) - 64*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 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*((15*B - 7*C)*cos(d*x + c)^2 + (11*B - 3*C)*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
407,1,739,0,8.412919," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(115 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(115 \, B - 43 \, C\right)} \cos\left(d x + c\right) + 115 \, B - 43 \, C\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 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B - 2 \, C\right)} \cos\left(d x + c\right) + 5 \, B - 2 \, C\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 \, B \cos\left(d x + c\right)^{3} + 5 \, {\left(11 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(35 \, B - 11 \, C\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 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(115 \, B - 43 \, C\right)} \cos\left(d x + c\right) + 115 \, B - 43 \, C\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 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B - 2 \, C\right)} \cos\left(d x + c\right) + 5 \, B - 2 \, C\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 \, B \cos\left(d x + c\right)^{3} + 5 \, {\left(11 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(35 \, B - 11 \, C\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*B - 43*C)*cos(d*x + c)^3 + 3*(115*B - 43*C)*cos(d*x + c)^2 + 3*(115*B - 43*C)*cos(d*x + c) + 115*B - 43*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)) + 32*((5*B - 2*C)*cos(d*x + c)^3 + 3*(5*B - 2*C)*cos(d*x + c)^2 + 3*(5*B - 2*C)*cos(d*x + c) + 5*B - 2*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)) + 4*(16*B*cos(d*x + c)^3 + 5*(11*B - 3*C)*cos(d*x + c)^2 + (35*B - 11*C)*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*B - 43*C)*cos(d*x + c)^3 + 3*(115*B - 43*C)*cos(d*x + c)^2 + 3*(115*B - 43*C)*cos(d*x + c) + 115*B - 43*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))) - 32*((5*B - 2*C)*cos(d*x + c)^3 + 3*(5*B - 2*C)*cos(d*x + c)^2 + 3*(5*B - 2*C)*cos(d*x + c) + 5*B - 2*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))) - 2*(16*B*cos(d*x + c)^3 + 5*(11*B - 3*C)*cos(d*x + c)^2 + (35*B - 11*C)*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
408,1,164,0,0.439659," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, A + 3 \, B + 3 \, C\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 + 5 \, B + 4 \, C\right)} a \cos\left(d x + c\right)^{4} + 15 \, {\left(4 \, A + 3 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 5 \, B + 4 \, C\right)} a \cos\left(d x + c\right)^{2} + 30 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 24 \, C a\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(4*A + 3*B + 3*C)*a*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*A + 3*B + 3*C)*a*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(5*A + 5*B + 4*C)*a*cos(d*x + c)^4 + 15*(4*A + 3*B + 3*C)*a*cos(d*x + c)^3 + 8*(5*A + 5*B + 4*C)*a*cos(d*x + c)^2 + 30*(B + C)*a*cos(d*x + c) + 24*C*a)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
409,1,143,0,0.440376," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A + 4 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, A + 4 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(3 \, A + 2 \, B + 2 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 4 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 6 \, C a\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(4*A + 4*B + 3*C)*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*A + 4*B + 3*C)*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(3*A + 2*B + 2*C)*a*cos(d*x + c)^3 + 3*(4*A + 4*B + 3*C)*a*cos(d*x + c)^2 + 8*(B + C)*a*cos(d*x + c) + 6*C*a)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
410,1,114,0,0.507029," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + B + C\right)} a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A + B + C\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 + 3 \, B + 2 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 2 \, C a\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(2*A + B + C)*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*A + B + C)*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(3*A + 3*B + 2*C)*a*cos(d*x + c)^2 + 3*(B + C)*a*cos(d*x + c) + 2*C*a)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
411,1,109,0,0.450650," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, A a d x \cos\left(d x + c\right)^{2} + {\left(2 \, A + 2 \, B + C\right)} a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, A + 2 \, B + C\right)} a \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(B + C\right)} a \cos\left(d x + c\right) + C a\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*A*a*d*x*cos(d*x + c)^2 + (2*A + 2*B + C)*a*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*A + 2*B + C)*a*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*(B + C)*a*cos(d*x + c) + C*a)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
412,1,92,0,0.488816," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(A + B\right)} a d x \cos\left(d x + c\right) + {\left(B + C\right)} a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B + C\right)} a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a \cos\left(d x + c\right) + C a\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(A + B)*a*d*x*cos(d*x + c) + (B + C)*a*cos(d*x + c)*log(sin(d*x + c) + 1) - (B + C)*a*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(A*a*cos(d*x + c) + C*a)*sin(d*x + c))/(d*cos(d*x + c))","A",0
413,1,68,0,0.480966," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(A + 2 \, B + 2 \, C\right)} a d x + C a \log\left(\sin\left(d x + c\right) + 1\right) - C a \log\left(-\sin\left(d x + c\right) + 1\right) + {\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 + 2*C)*a*d*x + C*a*log(sin(d*x + c) + 1) - C*a*log(-sin(d*x + c) + 1) + (A*a*cos(d*x + c) + 2*(A + B)*a)*sin(d*x + c))/d","A",0
414,1,62,0,0.458722," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(A + B + 2 \, C\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 + 3 \, C\right)} a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(A + B + 2*C)*a*d*x + (2*A*a*cos(d*x + c)^2 + 3*(A + B)*a*cos(d*x + c) + 2*(2*A + 3*B + 3*C)*a)*sin(d*x + c))/d","A",0
415,1,87,0,0.441731," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 4 \, B + 4 \, C\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 + 4 \, C\right)} a \cos\left(d x + c\right) + 8 \, {\left(2 \, A + 2 \, B + 3 \, C\right)} a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*A + 4*B + 4*C)*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 + 4*C)*a*cos(d*x + c) + 8*(2*A + 2*B + 3*C)*a)*sin(d*x + c))/d","A",0
416,1,108,0,0.441232," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, A + 3 \, B + 4 \, C\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 + 5 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, A + 3 \, B + 4 \, C\right)} a \cos\left(d x + c\right) + 16 \, {\left(4 \, A + 5 \, B + 5 \, C\right)} a\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(3*A + 3*B + 4*C)*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 + 5*C)*a*cos(d*x + c)^2 + 15*(3*A + 3*B + 4*C)*a*cos(d*x + c) + 16*(4*A + 5*B + 5*C)*a)*sin(d*x + c))/d","A",0
417,1,203,0,0.555823," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(14 \, A + 12 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(14 \, A + 12 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(32 \, {\left(10 \, A + 9 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 15 \, {\left(14 \, A + 12 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 16 \, {\left(10 \, A + 9 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(6 \, A + 12 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 48 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + 40 \, C a^{2}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(14*A + 12*B + 11*C)*a^2*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(14*A + 12*B + 11*C)*a^2*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(32*(10*A + 9*B + 8*C)*a^2*cos(d*x + c)^5 + 15*(14*A + 12*B + 11*C)*a^2*cos(d*x + c)^4 + 16*(10*A + 9*B + 8*C)*a^2*cos(d*x + c)^3 + 10*(6*A + 12*B + 11*C)*a^2*cos(d*x + c)^2 + 48*(B + 2*C)*a^2*cos(d*x + c) + 40*C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
418,1,180,0,0.451432," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, A + 7 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, A + 7 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(25 \, A + 20 \, B + 18 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 15 \, {\left(8 \, A + 7 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 10 \, B + 9 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 30 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + 24 \, C a^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(8*A + 7*B + 6*C)*a^2*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(8*A + 7*B + 6*C)*a^2*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(25*A + 20*B + 18*C)*a^2*cos(d*x + c)^4 + 15*(8*A + 7*B + 6*C)*a^2*cos(d*x + c)^3 + 8*(5*A + 10*B + 9*C)*a^2*cos(d*x + c)^2 + 30*(B + 2*C)*a^2*cos(d*x + c) + 24*C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
419,1,157,0,0.476329," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(12 \, A + 8 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(12 \, A + 8 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(6 \, A + 5 \, B + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 8 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + 6 \, C a^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(12*A + 8*B + 7*C)*a^2*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(12*A + 8*B + 7*C)*a^2*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(6*A + 5*B + 4*C)*a^2*cos(d*x + c)^3 + 3*(4*A + 8*B + 7*C)*a^2*cos(d*x + c)^2 + 8*(B + 2*C)*a^2*cos(d*x + c) + 6*C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
420,1,150,0,0.455304," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{12 \, A a^{2} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 3 \, B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, A + 3 \, B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(3 \, A + 6 \, B + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, C a^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*A*a^2*d*x*cos(d*x + c)^3 + 3*(4*A + 3*B + 2*C)*a^2*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(4*A + 3*B + 2*C)*a^2*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(3*A + 6*B + 5*C)*a^2*cos(d*x + c)^2 + 3*(B + 2*C)*a^2*cos(d*x + c) + 2*C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
421,1,143,0,0.499462," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, {\left(2 \, A + B\right)} a^{2} d x \cos\left(d x + c\right)^{2} + {\left(2 \, A + 4 \, B + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, A + 4 \, B + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + C a^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*(2*A + B)*a^2*d*x*cos(d*x + c)^2 + (2*A + 4*B + 3*C)*a^2*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*A + 4*B + 3*C)*a^2*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a^2*cos(d*x + c)^2 + 2*(B + 2*C)*a^2*cos(d*x + c) + C*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
422,1,130,0,0.454025," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(3 \, A + 4 \, B + 2 \, C\right)} a^{2} d x \cos\left(d x + c\right) + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + 2 \, C a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((3*A + 4*B + 2*C)*a^2*d*x*cos(d*x + c) + (B + 2*C)*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) - (B + 2*C)*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + (A*a^2*cos(d*x + c)^2 + 2*(2*A + B)*a^2*cos(d*x + c) + 2*C*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
423,1,108,0,0.524881," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + 3 \, B + 4 \, C\right)} a^{2} d x + 3 \, C a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, C a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\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 + 3 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*A + 3*B + 4*C)*a^2*d*x + 3*C*a^2*log(sin(d*x + c) + 1) - 3*C*a^2*log(-sin(d*x + c) + 1) + (2*A*a^2*cos(d*x + c)^2 + 3*(2*A + B)*a^2*cos(d*x + c) + 2*(5*A + 6*B + 3*C)*a^2)*sin(d*x + c))/d","A",0
424,1,99,0,0.443074," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A + 8 \, B + 12 \, C\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 + 4 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(4 \, A + 5 \, B + 6 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(7*A + 8*B + 12*C)*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 + 4*C)*a^2*cos(d*x + c) + 8*(4*A + 5*B + 6*C)*a^2)*sin(d*x + c))/d","A",0
425,1,122,0,0.482306," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, A + 7 \, B + 8 \, C\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 + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(6 \, A + 7 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(18 \, A + 20 \, B + 25 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(6*A + 7*B + 8*C)*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 + 5*C)*a^2*cos(d*x + c)^2 + 15*(6*A + 7*B + 8*C)*a^2*cos(d*x + c) + 8*(18*A + 20*B + 25*C)*a^2)*sin(d*x + c))/d","A",0
426,1,145,0,0.449991," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(11 \, A + 12 \, B + 14 \, C\right)} a^{2} d x + {\left(40 \, A a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(11 \, A + 12 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 16 \, {\left(8 \, A + 9 \, B + 10 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(11 \, A + 12 \, B + 14 \, C\right)} a^{2} \cos\left(d x + c\right) + 32 \, {\left(8 \, A + 9 \, B + 10 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(11*A + 12*B + 14*C)*a^2*d*x + (40*A*a^2*cos(d*x + c)^5 + 48*(2*A + B)*a^2*cos(d*x + c)^4 + 10*(11*A + 12*B + 6*C)*a^2*cos(d*x + c)^3 + 16*(8*A + 9*B + 10*C)*a^2*cos(d*x + c)^2 + 15*(11*A + 12*B + 14*C)*a^2*cos(d*x + c) + 32*(8*A + 9*B + 10*C)*a^2)*sin(d*x + c))/d","A",0
427,1,226,0,0.478046," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(26 \, A + 23 \, B + 21 \, C\right)} a^{3} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(26 \, A + 23 \, B + 21 \, C\right)} a^{3} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(32 \, {\left(133 \, A + 119 \, B + 108 \, C\right)} a^{3} \cos\left(d x + c\right)^{6} + 105 \, {\left(26 \, A + 23 \, B + 21 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} + 16 \, {\left(133 \, A + 119 \, B + 108 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 70 \, {\left(18 \, A + 23 \, B + 21 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 48 \, {\left(7 \, A + 21 \, B + 27 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 280 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 240 \, C a^{3}\right)} \sin\left(d x + c\right)}{3360 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/3360*(105*(26*A + 23*B + 21*C)*a^3*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(26*A + 23*B + 21*C)*a^3*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 2*(32*(133*A + 119*B + 108*C)*a^3*cos(d*x + c)^6 + 105*(26*A + 23*B + 21*C)*a^3*cos(d*x + c)^5 + 16*(133*A + 119*B + 108*C)*a^3*cos(d*x + c)^4 + 70*(18*A + 23*B + 21*C)*a^3*cos(d*x + c)^3 + 48*(7*A + 21*B + 27*C)*a^3*cos(d*x + c)^2 + 280*(B + 3*C)*a^3*cos(d*x + c) + 240*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
428,1,203,0,0.466017," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(30 \, A + 26 \, B + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(30 \, A + 26 \, B + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(45 \, A + 38 \, B + 34 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} + 15 \, {\left(30 \, A + 26 \, B + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 16 \, {\left(15 \, A + 19 \, B + 17 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 10 \, {\left(6 \, A + 18 \, B + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 48 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 40 \, C a^{3}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(30*A + 26*B + 23*C)*a^3*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(30*A + 26*B + 23*C)*a^3*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(45*A + 38*B + 34*C)*a^3*cos(d*x + c)^5 + 15*(30*A + 26*B + 23*C)*a^3*cos(d*x + c)^4 + 16*(15*A + 19*B + 17*C)*a^3*cos(d*x + c)^3 + 10*(6*A + 18*B + 23*C)*a^3*cos(d*x + c)^2 + 48*(B + 3*C)*a^3*cos(d*x + c) + 40*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
429,1,180,0,0.466707," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(20 \, A + 15 \, B + 13 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(20 \, A + 15 \, B + 13 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(55 \, A + 45 \, B + 38 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 15 \, {\left(12 \, A + 15 \, B + 13 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 15 \, B + 19 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 30 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 24 \, C a^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(20*A + 15*B + 13*C)*a^3*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(20*A + 15*B + 13*C)*a^3*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(55*A + 45*B + 38*C)*a^3*cos(d*x + c)^4 + 15*(12*A + 15*B + 13*C)*a^3*cos(d*x + c)^3 + 8*(5*A + 15*B + 19*C)*a^3*cos(d*x + c)^2 + 30*(B + 3*C)*a^3*cos(d*x + c) + 24*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
430,1,173,0,0.468935," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{48 \, A a^{3} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(28 \, A + 20 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(28 \, A + 20 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(9 \, A + 11 \, B + 9 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 12 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 8 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 6 \, C a^{3}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(48*A*a^3*d*x*cos(d*x + c)^4 + 3*(28*A + 20*B + 15*C)*a^3*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(28*A + 20*B + 15*C)*a^3*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(9*A + 11*B + 9*C)*a^3*cos(d*x + c)^3 + 3*(4*A + 12*B + 15*C)*a^3*cos(d*x + c)^2 + 8*(B + 3*C)*a^3*cos(d*x + c) + 6*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
431,1,168,0,0.481526," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{12 \, {\left(3 \, A + B\right)} a^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(6 \, A + 7 \, B + 5 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(6 \, A + 7 \, B + 5 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, A a^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A + 9 \, B + 11 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 2 \, C a^{3}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*(3*A + B)*a^3*d*x*cos(d*x + c)^3 + 3*(6*A + 7*B + 5*C)*a^3*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(6*A + 7*B + 5*C)*a^3*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*A*a^3*cos(d*x + c)^3 + 2*(3*A + 9*B + 11*C)*a^3*cos(d*x + c)^2 + 3*(B + 3*C)*a^3*cos(d*x + c) + 2*C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
432,1,165,0,0.473899," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, A + 6 \, B + 2 \, C\right)} a^{3} d x \cos\left(d x + c\right)^{2} + {\left(2 \, A + 6 \, B + 7 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, A + 6 \, B + 7 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + C a^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*(7*A + 6*B + 2*C)*a^3*d*x*cos(d*x + c)^2 + (2*A + 6*B + 7*C)*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*A + 6*B + 7*C)*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a^3*cos(d*x + c)^3 + 2*(3*A + B)*a^3*cos(d*x + c)^2 + 2*(B + 3*C)*a^3*cos(d*x + c) + C*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
433,1,156,0,0.487496," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, A + 7 \, B + 6 \, C\right)} a^{3} d x \cos\left(d x + c\right) + 3 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, A a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A + 9 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 6 \, C a^{3}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(3*(5*A + 7*B + 6*C)*a^3*d*x*cos(d*x + c) + 3*(B + 3*C)*a^3*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*(B + 3*C)*a^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*A*a^3*cos(d*x + c)^3 + 3*(3*A + B)*a^3*cos(d*x + c)^2 + 2*(11*A + 9*B + 3*C)*a^3*cos(d*x + c) + 6*C*a^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
434,1,131,0,0.480777," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(15 \, A + 20 \, B + 28 \, C\right)} a^{3} d x + 12 \, C a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, C a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\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} + 3 \, {\left(15 \, A + 12 \, B + 4 \, C\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(9 \, A + 11 \, B + 9 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(15*A + 20*B + 28*C)*a^3*d*x + 12*C*a^3*log(sin(d*x + c) + 1) - 12*C*a^3*log(-sin(d*x + c) + 1) + (6*A*a^3*cos(d*x + c)^3 + 8*(3*A + B)*a^3*cos(d*x + c)^2 + 3*(15*A + 12*B + 4*C)*a^3*cos(d*x + c) + 8*(9*A + 11*B + 9*C)*a^3)*sin(d*x + c))/d","A",0
435,1,122,0,0.448364," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, A + 15 \, B + 20 \, C\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 + 5 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(13 \, A + 15 \, B + 12 \, C\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(38 \, A + 45 \, B + 55 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(13*A + 15*B + 20*C)*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 + 5*C)*a^3*cos(d*x + c)^2 + 15*(13*A + 15*B + 12*C)*a^3*cos(d*x + c) + 8*(38*A + 45*B + 55*C)*a^3)*sin(d*x + c))/d","A",0
436,1,145,0,0.445238," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(23 \, A + 26 \, B + 30 \, C\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 + 6 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(17 \, A + 19 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(23 \, A + 26 \, B + 30 \, C\right)} a^{3} \cos\left(d x + c\right) + 16 \, {\left(34 \, A + 38 \, B + 45 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(23*A + 26*B + 30*C)*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 + 6*C)*a^3*cos(d*x + c)^3 + 16*(17*A + 19*B + 15*C)*a^3*cos(d*x + c)^2 + 15*(23*A + 26*B + 30*C)*a^3*cos(d*x + c) + 16*(34*A + 38*B + 45*C)*a^3)*sin(d*x + c))/d","A",0
437,1,168,0,0.456854," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(21 \, A + 23 \, B + 26 \, C\right)} a^{3} d x + {\left(240 \, A a^{3} \cos\left(d x + c\right)^{6} + 280 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(27 \, A + 21 \, B + 7 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 70 \, {\left(21 \, A + 23 \, B + 18 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(108 \, A + 119 \, B + 133 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 105 \, {\left(21 \, A + 23 \, B + 26 \, C\right)} a^{3} \cos\left(d x + c\right) + 32 \, {\left(108 \, A + 119 \, B + 133 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(105*(21*A + 23*B + 26*C)*a^3*d*x + (240*A*a^3*cos(d*x + c)^6 + 280*(3*A + B)*a^3*cos(d*x + c)^5 + 48*(27*A + 21*B + 7*C)*a^3*cos(d*x + c)^4 + 70*(21*A + 23*B + 18*C)*a^3*cos(d*x + c)^3 + 16*(108*A + 119*B + 133*C)*a^3*cos(d*x + c)^2 + 105*(21*A + 23*B + 26*C)*a^3*cos(d*x + c) + 32*(108*A + 119*B + 133*C)*a^3)*sin(d*x + c))/d","A",0
438,1,226,0,0.472169," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(56 \, A + 49 \, B + 44 \, C\right)} a^{4} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(56 \, A + 49 \, B + 44 \, C\right)} a^{4} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(581 \, A + 504 \, B + 454 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} + 105 \, {\left(56 \, A + 49 \, B + 44 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 16 \, {\left(238 \, A + 252 \, B + 227 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(24 \, A + 41 \, B + 44 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 48 \, {\left(7 \, A + 28 \, B + 48 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 280 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right) + 240 \, C a^{4}\right)} \sin\left(d x + c\right)}{3360 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/3360*(105*(56*A + 49*B + 44*C)*a^4*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(56*A + 49*B + 44*C)*a^4*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 2*(16*(581*A + 504*B + 454*C)*a^4*cos(d*x + c)^6 + 105*(56*A + 49*B + 44*C)*a^4*cos(d*x + c)^5 + 16*(238*A + 252*B + 227*C)*a^4*cos(d*x + c)^4 + 70*(24*A + 41*B + 44*C)*a^4*cos(d*x + c)^3 + 48*(7*A + 28*B + 48*C)*a^4*cos(d*x + c)^2 + 280*(B + 4*C)*a^4*cos(d*x + c) + 240*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
439,1,203,0,0.506439," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(10 \, A + 8 \, B + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(10 \, A + 8 \, B + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(100 \, A + 83 \, B + 72 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 15 \, {\left(54 \, A + 56 \, B + 49 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 32 \, {\left(10 \, A + 17 \, B + 18 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 10 \, {\left(6 \, A + 24 \, B + 41 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 48 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right) + 40 \, C a^{4}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(105*(10*A + 8*B + 7*C)*a^4*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 105*(10*A + 8*B + 7*C)*a^4*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(100*A + 83*B + 72*C)*a^4*cos(d*x + c)^5 + 15*(54*A + 56*B + 49*C)*a^4*cos(d*x + c)^4 + 32*(10*A + 17*B + 18*C)*a^4*cos(d*x + c)^3 + 10*(6*A + 24*B + 41*C)*a^4*cos(d*x + c)^2 + 48*(B + 4*C)*a^4*cos(d*x + c) + 40*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
440,1,196,0,0.485810," ","integrate((a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{240 \, A a^{4} d x \cos\left(d x + c\right)^{5} + 15 \, {\left(48 \, A + 35 \, B + 28 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(48 \, A + 35 \, B + 28 \, C\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 + 100 \, B + 83 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 15 \, {\left(16 \, A + 27 \, B + 28 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 20 \, B + 34 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 30 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right) + 24 \, C a^{4}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(240*A*a^4*d*x*cos(d*x + c)^5 + 15*(48*A + 35*B + 28*C)*a^4*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(48*A + 35*B + 28*C)*a^4*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(100*A + 100*B + 83*C)*a^4*cos(d*x + c)^4 + 15*(16*A + 27*B + 28*C)*a^4*cos(d*x + c)^3 + 8*(5*A + 20*B + 34*C)*a^4*cos(d*x + c)^2 + 30*(B + 4*C)*a^4*cos(d*x + c) + 24*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
441,1,191,0,0.487240," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{48 \, {\left(4 \, A + B\right)} a^{4} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(52 \, A + 48 \, B + 35 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(52 \, A + 48 \, B + 35 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, A a^{4} \cos\left(d x + c\right)^{4} + 32 \, {\left(3 \, A + 5 \, B + 5 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 16 \, B + 27 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 8 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right) + 6 \, C a^{4}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(48*(4*A + B)*a^4*d*x*cos(d*x + c)^4 + 3*(52*A + 48*B + 35*C)*a^4*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(52*A + 48*B + 35*C)*a^4*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*A*a^4*cos(d*x + c)^4 + 32*(3*A + 5*B + 5*C)*a^4*cos(d*x + c)^3 + 3*(4*A + 16*B + 27*C)*a^4*cos(d*x + c)^2 + 8*(B + 4*C)*a^4*cos(d*x + c) + 6*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
442,1,191,0,0.467495," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{6 \, {\left(13 \, A + 8 \, B + 2 \, C\right)} a^{4} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 13 \, B + 12 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, A + 13 \, B + 12 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, A a^{4} \cos\left(d x + c\right)^{4} + 6 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A + 12 \, B + 20 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 3 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right) + 2 \, C a^{4}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(6*(13*A + 8*B + 2*C)*a^4*d*x*cos(d*x + c)^3 + 3*(8*A + 13*B + 12*C)*a^4*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(8*A + 13*B + 12*C)*a^4*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(3*A*a^4*cos(d*x + c)^4 + 6*(4*A + B)*a^4*cos(d*x + c)^3 + 2*(3*A + 12*B + 20*C)*a^4*cos(d*x + c)^2 + 3*(B + 4*C)*a^4*cos(d*x + c) + 2*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
443,1,191,0,0.479689," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{6 \, {\left(12 \, A + 13 \, B + 8 \, C\right)} a^{4} d x \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A + 8 \, B + 13 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A + 8 \, B + 13 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{4} \cos\left(d x + c\right)^{4} + 3 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(20 \, A + 12 \, B + 3 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 6 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right) + 3 \, C a^{4}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(6*(12*A + 13*B + 8*C)*a^4*d*x*cos(d*x + c)^2 + 3*(2*A + 8*B + 13*C)*a^4*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*(2*A + 8*B + 13*C)*a^4*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a^4*cos(d*x + c)^4 + 3*(4*A + B)*a^4*cos(d*x + c)^3 + 2*(20*A + 12*B + 3*C)*a^4*cos(d*x + c)^2 + 6*(B + 4*C)*a^4*cos(d*x + c) + 3*C*a^4)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
444,1,179,0,0.479243," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(35 \, A + 48 \, B + 52 \, C\right)} a^{4} d x \cos\left(d x + c\right) + 12 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, A a^{4} \cos\left(d x + c\right)^{4} + 8 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(27 \, A + 16 \, B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 32 \, {\left(5 \, A + 5 \, B + 3 \, C\right)} a^{4} \cos\left(d x + c\right) + 24 \, C a^{4}\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}"," ",0,"1/24*(3*(35*A + 48*B + 52*C)*a^4*d*x*cos(d*x + c) + 12*(B + 4*C)*a^4*cos(d*x + c)*log(sin(d*x + c) + 1) - 12*(B + 4*C)*a^4*cos(d*x + c)*log(-sin(d*x + c) + 1) + (6*A*a^4*cos(d*x + c)^4 + 8*(4*A + B)*a^4*cos(d*x + c)^3 + 3*(27*A + 16*B + 4*C)*a^4*cos(d*x + c)^2 + 32*(5*A + 5*B + 3*C)*a^4*cos(d*x + c) + 24*C*a^4)*sin(d*x + c))/(d*cos(d*x + c))","A",0
445,1,154,0,0.494563," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(28 \, A + 35 \, B + 48 \, C\right)} a^{4} d x + 60 \, C a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 60 \, C a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + {\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} + 8 \, {\left(34 \, A + 20 \, B + 5 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 15 \, {\left(28 \, A + 27 \, B + 16 \, C\right)} a^{4} \cos\left(d x + c\right) + 8 \, {\left(83 \, A + 100 \, B + 100 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(28*A + 35*B + 48*C)*a^4*d*x + 60*C*a^4*log(sin(d*x + c) + 1) - 60*C*a^4*log(-sin(d*x + c) + 1) + (24*A*a^4*cos(d*x + c)^4 + 30*(4*A + B)*a^4*cos(d*x + c)^3 + 8*(34*A + 20*B + 5*C)*a^4*cos(d*x + c)^2 + 15*(28*A + 27*B + 16*C)*a^4*cos(d*x + c) + 8*(83*A + 100*B + 100*C)*a^4)*sin(d*x + c))/d","A",0
446,1,145,0,0.459000," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(7 \, A + 8 \, B + 10 \, C\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 + 6 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 32 \, {\left(18 \, A + 17 \, B + 10 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 15 \, {\left(49 \, A + 56 \, B + 54 \, C\right)} a^{4} \cos\left(d x + c\right) + 16 \, {\left(72 \, A + 83 \, B + 100 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(105*(7*A + 8*B + 10*C)*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 + 6*C)*a^4*cos(d*x + c)^3 + 32*(18*A + 17*B + 10*C)*a^4*cos(d*x + c)^2 + 15*(49*A + 56*B + 54*C)*a^4*cos(d*x + c) + 16*(72*A + 83*B + 100*C)*a^4)*sin(d*x + c))/d","A",0
447,1,168,0,0.471996," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(44 \, A + 49 \, B + 56 \, C\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} + 48 \, {\left(48 \, A + 28 \, B + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(44 \, A + 41 \, B + 24 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 16 \, {\left(227 \, A + 252 \, B + 238 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(44 \, A + 49 \, B + 56 \, C\right)} a^{4} \cos\left(d x + c\right) + 16 \, {\left(454 \, A + 504 \, B + 581 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(105*(44*A + 49*B + 56*C)*a^4*d*x + (240*A*a^4*cos(d*x + c)^6 + 280*(4*A + B)*a^4*cos(d*x + c)^5 + 48*(48*A + 28*B + 7*C)*a^4*cos(d*x + c)^4 + 70*(44*A + 41*B + 24*C)*a^4*cos(d*x + c)^3 + 16*(227*A + 252*B + 238*C)*a^4*cos(d*x + c)^2 + 105*(44*A + 49*B + 56*C)*a^4*cos(d*x + c) + 16*(454*A + 504*B + 581*C)*a^4)*sin(d*x + c))/d","A",0
448,1,191,0,0.463367," ","integrate(cos(d*x+c)^8*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(323 \, A + 352 \, B + 392 \, C\right)} a^{4} d x + {\left(1680 \, A a^{4} \cos\left(d x + c\right)^{7} + 1920 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{6} + 280 \, {\left(55 \, A + 32 \, B + 8 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 1536 \, {\left(13 \, A + 12 \, B + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(323 \, A + 352 \, B + 328 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 128 \, {\left(208 \, A + 227 \, B + 252 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(323 \, A + 352 \, B + 392 \, C\right)} a^{4} \cos\left(d x + c\right) + 256 \, {\left(208 \, A + 227 \, B + 252 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{13440 \, d}"," ",0,"1/13440*(105*(323*A + 352*B + 392*C)*a^4*d*x + (1680*A*a^4*cos(d*x + c)^7 + 1920*(4*A + B)*a^4*cos(d*x + c)^6 + 280*(55*A + 32*B + 8*C)*a^4*cos(d*x + c)^5 + 1536*(13*A + 12*B + 7*C)*a^4*cos(d*x + c)^4 + 70*(323*A + 352*B + 328*C)*a^4*cos(d*x + c)^3 + 128*(208*A + 227*B + 252*C)*a^4*cos(d*x + c)^2 + 105*(323*A + 352*B + 392*C)*a^4*cos(d*x + c) + 256*(208*A + 227*B + 252*C)*a^4)*sin(d*x + c))/d","A",0
449,1,216,0,0.460718," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left({\left(4 \, A - 4 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(4 \, A - 4 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, {\left({\left(4 \, A - 4 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(4 \, A - 4 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(3 \, A - 4 \, B + 4 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(12 \, A - 28 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(12 \, A - 4 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(4 \, B - C\right)} \cos\left(d x + c\right) - 6 \, C\right)} \sin\left(d x + c\right)}{48 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/48*(9*((4*A - 4*B + 5*C)*cos(d*x + c)^5 + (4*A - 4*B + 5*C)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) - 9*((4*A - 4*B + 5*C)*cos(d*x + c)^5 + (4*A - 4*B + 5*C)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) - 2*(16*(3*A - 4*B + 4*C)*cos(d*x + c)^4 + (12*A - 28*B + 19*C)*cos(d*x + c)^3 - (12*A - 4*B + 13*C)*cos(d*x + c)^2 - 2*(4*B - C)*cos(d*x + c) - 6*C)*sin(d*x + c))/(a*d*cos(d*x + c)^5 + a*d*cos(d*x + c)^4)","A",0
450,1,195,0,0.449476," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(2 \, A - 3 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, A - 3 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(2 \, A - 3 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, A - 3 \, B + 3 \, C\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 - 3 \, B + 4 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, A - 3 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B - C\right)} \cos\left(d x + c\right) + 2 \, C\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*(3*((2*A - 3*B + 3*C)*cos(d*x + c)^4 + (2*A - 3*B + 3*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((2*A - 3*B + 3*C)*cos(d*x + c)^4 + (2*A - 3*B + 3*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(4*(3*A - 3*B + 4*C)*cos(d*x + c)^3 + (6*A - 3*B + 7*C)*cos(d*x + c)^2 + (3*B - C)*cos(d*x + c) + 2*C)*sin(d*x + c))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
451,1,174,0,0.451706," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(2 \, A - 2 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A - 2 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(2 \, A - 2 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A - 2 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(A - 2 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(2 \, B - C\right)} \cos\left(d x + c\right) - C\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 - 2*B + 3*C)*cos(d*x + c)^3 + (2*A - 2*B + 3*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((2*A - 2*B + 3*C)*cos(d*x + c)^3 + (2*A - 2*B + 3*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(2*(A - 2*B + 2*C)*cos(d*x + c)^2 - (2*B - C)*cos(d*x + c) - C)*sin(d*x + c))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
452,1,128,0,0.455165," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(B - C\right)} \cos\left(d x + c\right)^{2} + {\left(B - C\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(B - C\right)} \cos\left(d x + c\right)^{2} + {\left(B - C\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(A - B + 2 \, C\right)} \cos\left(d x + c\right) + C\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*(((B - C)*cos(d*x + c)^2 + (B - C)*cos(d*x + c))*log(sin(d*x + c) + 1) - ((B - C)*cos(d*x + c)^2 + (B - C)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*((A - B + 2*C)*cos(d*x + c) + C)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","B",0
453,1,91,0,0.457715," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, A d x \cos\left(d x + c\right) + 2 \, A d x + {\left(C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A - B + C\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*(2*A*d*x*cos(d*x + c) + 2*A*d*x + (C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - (C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) - 2*(A - B + C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
454,1,64,0,0.432099," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""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 + C\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 + C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
455,1,90,0,0.484715," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, A - 2 \, B + 2 \, C\right)} d x \cos\left(d x + c\right) + {\left(3 \, A - 2 \, B + 2 \, C\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 - 2 \, C\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 + 2*C)*d*x*cos(d*x + c) + (3*A - 2*B + 2*C)*d*x + (A*cos(d*x + c)^2 - (A - 2*B)*cos(d*x + c) - 4*A + 4*B - 2*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
456,1,113,0,0.475893," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(3 \, A - 3 \, B + 2 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(3 \, A - 3 \, B + 2 \, C\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 + 6 \, C\right)} \cos\left(d x + c\right) + 16 \, A - 12 \, B + 12 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/6*(3*(3*A - 3*B + 2*C)*d*x*cos(d*x + c) + 3*(3*A - 3*B + 2*C)*d*x - (2*A*cos(d*x + c)^3 - (A - 3*B)*cos(d*x + c)^2 + (7*A - 3*B + 6*C)*cos(d*x + c) + 16*A - 12*B + 12*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
457,1,132,0,0.450381," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left(5 \, A - 4 \, B + 4 \, C\right)} d x \cos\left(d x + c\right) + 9 \, {\left(5 \, A - 4 \, B + 4 \, C\right)} d x + {\left(6 \, A \cos\left(d x + c\right)^{4} - 2 \, {\left(A - 4 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, A - 4 \, B + 12 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(19 \, A - 28 \, B + 12 \, C\right)} \cos\left(d x + c\right) - 64 \, A + 64 \, B - 48 \, C\right)} \sin\left(d x + c\right)}{24 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/24*(9*(5*A - 4*B + 4*C)*d*x*cos(d*x + c) + 9*(5*A - 4*B + 4*C)*d*x + (6*A*cos(d*x + c)^4 - 2*(A - 4*B)*cos(d*x + c)^3 + (13*A - 4*B + 12*C)*cos(d*x + c)^2 - (19*A - 28*B + 12*C)*cos(d*x + c) - 64*A + 64*B - 48*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
458,1,271,0,0.475195," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(4 \, A - 7 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(4 \, A - 7 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, A - 7 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(4 \, A - 7 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(4 \, A - 7 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, A - 7 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(5 \, A - 8 \, B + 12 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(28 \, A - 43 \, B + 66 \, C\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(A - B + 2 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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*((4*A - 7*B + 10*C)*cos(d*x + c)^5 + 2*(4*A - 7*B + 10*C)*cos(d*x + c)^4 + (4*A - 7*B + 10*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((4*A - 7*B + 10*C)*cos(d*x + c)^5 + 2*(4*A - 7*B + 10*C)*cos(d*x + c)^4 + (4*A - 7*B + 10*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(4*(5*A - 8*B + 12*C)*cos(d*x + c)^4 + (28*A - 43*B + 66*C)*cos(d*x + c)^3 + 6*(A - B + 2*C)*cos(d*x + c)^2 + (3*B - 2*C)*cos(d*x + c) + 2*C)*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
459,1,252,0,0.456705," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(2 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(2 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(2 \, A - 5 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(10 \, A - 28 \, B + 43 \, C\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left(B - C\right)} \cos\left(d x + c\right) - 3 \, C\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*((2*A - 4*B + 7*C)*cos(d*x + c)^4 + 2*(2*A - 4*B + 7*C)*cos(d*x + c)^3 + (2*A - 4*B + 7*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*((2*A - 4*B + 7*C)*cos(d*x + c)^4 + 2*(2*A - 4*B + 7*C)*cos(d*x + c)^3 + (2*A - 4*B + 7*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(2*A - 5*B + 8*C)*cos(d*x + c)^3 + (10*A - 28*B + 43*C)*cos(d*x + c)^2 - 6*(B - C)*cos(d*x + c) - 3*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
460,1,198,0,0.471936," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(B - 2 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(B - 2 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 2 \, C\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(B - 2 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(B - 2 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 2 \, C\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(A - 4 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A - 5 \, B + 14 \, C\right)} \cos\left(d x + c\right) + 3 \, C\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*((B - 2*C)*cos(d*x + c)^3 + 2*(B - 2*C)*cos(d*x + c)^2 + (B - 2*C)*cos(d*x + c))*log(sin(d*x + c) + 1) - 3*((B - 2*C)*cos(d*x + c)^3 + 2*(B - 2*C)*cos(d*x + c)^2 + (B - 2*C)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*((A - 4*B + 10*C)*cos(d*x + c)^2 + (2*A - 5*B + 14*C)*cos(d*x + c) + 3*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
461,1,133,0,0.431808," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(2 \, A + B - 4 \, C\right)} \cos\left(d x + c\right) + A + 2 \, B - 5 \, C\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*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - 3*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) + 2*((2*A + B - 4*C)*cos(d*x + c) + A + 2*B - 5*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
462,1,100,0,0.432389," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(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 - C\right)} \cos\left(d x + c\right) + 4 \, A - B - 2 \, C\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 - C)*cos(d*x + c) + 4*A - B - 2*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
463,1,127,0,0.442926," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""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 + 2 \, C\right)} \cos\left(d x + c\right) + 10 \, A - 4 \, B + C\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 + 2*C)*cos(d*x + c) + 10*A - 4*B + 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
464,1,153,0,0.441568," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A - 4 \, B + 2 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(7 \, A - 4 \, B + 2 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(7 \, A - 4 \, B + 2 \, C\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 + 10 \, C\right)} \cos\left(d x + c\right) - 32 \, A + 20 \, B - 8 \, C\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 + 2*C)*d*x*cos(d*x + c)^2 + 6*(7*A - 4*B + 2*C)*d*x*cos(d*x + c) + 3*(7*A - 4*B + 2*C)*d*x + (3*A*cos(d*x + c)^3 - 6*(A - B)*cos(d*x + c)^2 - (43*A - 28*B + 10*C)*cos(d*x + c) - 32*A + 20*B - 8*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
465,1,173,0,0.442720," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(10 \, A - 7 \, B + 4 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(10 \, A - 7 \, B + 4 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(10 \, A - 7 \, B + 4 \, C\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 + C\right)} \cos\left(d x + c\right)^{2} + {\left(66 \, A - 43 \, B + 28 \, C\right)} \cos\left(d x + c\right) + 48 \, A - 32 \, B + 20 \, C\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 + 4*C)*d*x*cos(d*x + c)^2 + 6*(10*A - 7*B + 4*C)*d*x*cos(d*x + c) + 3*(10*A - 7*B + 4*C)*d*x - (2*A*cos(d*x + c)^4 - (2*A - 3*B)*cos(d*x + c)^3 + 6*(2*A - B + C)*cos(d*x + c)^2 + (66*A - 43*B + 28*C)*cos(d*x + c) + 48*A - 32*B + 20*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
466,1,328,0,0.477969," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(2 \, A - 6 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(2 \, A - 6 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, A - 6 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A - 6 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(2 \, A - 6 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(2 \, A - 6 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, A - 6 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A - 6 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(11 \, A - 36 \, B + 76 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(34 \, A - 114 \, B + 239 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(64 \, A - 234 \, B + 479 \, C\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right) - 15 \, C\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*((2*A - 6*B + 13*C)*cos(d*x + c)^5 + 3*(2*A - 6*B + 13*C)*cos(d*x + c)^4 + 3*(2*A - 6*B + 13*C)*cos(d*x + c)^3 + (2*A - 6*B + 13*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 15*((2*A - 6*B + 13*C)*cos(d*x + c)^5 + 3*(2*A - 6*B + 13*C)*cos(d*x + c)^4 + 3*(2*A - 6*B + 13*C)*cos(d*x + c)^3 + (2*A - 6*B + 13*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(11*A - 36*B + 76*C)*cos(d*x + c)^4 + 3*(34*A - 114*B + 239*C)*cos(d*x + c)^3 + (64*A - 234*B + 479*C)*cos(d*x + c)^2 - 15*(2*B - 3*C)*cos(d*x + c) - 15*C)*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
467,1,263,0,0.492698," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 3 \, C\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 3 \, C\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(A - 11 \, B + 36 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A - 17 \, B + 57 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 32 \, B + 117 \, C\right)} \cos\left(d x + c\right) + 15 \, C\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*((B - 3*C)*cos(d*x + c)^4 + 3*(B - 3*C)*cos(d*x + c)^3 + 3*(B - 3*C)*cos(d*x + c)^2 + (B - 3*C)*cos(d*x + c))*log(sin(d*x + c) + 1) - 15*((B - 3*C)*cos(d*x + c)^4 + 3*(B - 3*C)*cos(d*x + c)^3 + 3*(B - 3*C)*cos(d*x + c)^2 + (B - 3*C)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(2*(A - 11*B + 36*C)*cos(d*x + c)^3 + 3*(2*A - 17*B + 57*C)*cos(d*x + c)^2 + (7*A - 32*B + 117*C)*cos(d*x + c) + 15*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
468,1,193,0,0.451153," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(3 \, A + 2 \, B - 22 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 2 \, B - 17 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 7 \, B - 32 \, C\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*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - 15*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) + 2*((3*A + 2*B - 22*C)*cos(d*x + c)^2 + 3*(3*A + 2*B - 17*C)*cos(d*x + c) + 3*A + 7*B - 32*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
469,1,102,0,0.415625," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(7 \, A + 3 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A + 3 \, B + 2 \, C\right)} \cos\left(d x + c\right) + 2 \, A + 3 \, B + 7 \, C\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 + 2*C)*cos(d*x + c)^2 + 3*(2*A + 3*B + 2*C)*cos(d*x + c) + 2*A + 3*B + 7*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
470,1,147,0,0.439084," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(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 - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(17 \, A - 2 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 22 \, A - 2 \, B - 3 \, C\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 - 3*C)*cos(d*x + c)^2 + 3*(17*A - 2*B - 3*C)*cos(d*x + c) + 22*A - 2*B - 3*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
471,1,182,0,0.450132," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""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 + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(57 \, A - 17 \, B + 2 \, C\right)} \cos\left(d x + c\right) + 72 \, A - 22 \, B + 2 \, C\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 + 7*C)*cos(d*x + c)^2 + 3*(57*A - 17*B + 2*C)*cos(d*x + c) + 72*A - 22*B + 2*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
472,1,211,0,0.476193," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, A - 6 \, B + 2 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(13 \, A - 6 \, B + 2 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(13 \, A - 6 \, B + 2 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(13 \, A - 6 \, B + 2 \, C\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 + 64 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(239 \, A - 114 \, B + 34 \, C\right)} \cos\left(d x + c\right) - 304 \, A + 144 \, B - 44 \, C\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 + 2*C)*d*x*cos(d*x + c)^3 + 45*(13*A - 6*B + 2*C)*d*x*cos(d*x + c)^2 + 45*(13*A - 6*B + 2*C)*d*x*cos(d*x + c) + 15*(13*A - 6*B + 2*C)*d*x + (15*A*cos(d*x + c)^4 - 15*(3*A - 2*B)*cos(d*x + c)^3 - (479*A - 234*B + 64*C)*cos(d*x + c)^2 - 3*(239*A - 114*B + 34*C)*cos(d*x + c) - 304*A + 144*B - 44*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
473,1,229,0,0.446096," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(23 \, A - 13 \, B + 6 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(23 \, A - 13 \, B + 6 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(23 \, A - 13 \, B + 6 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(23 \, A - 13 \, B + 6 \, C\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 + 6 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(869 \, A - 479 \, B + 234 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(429 \, A - 239 \, B + 114 \, C\right)} \cos\left(d x + c\right) + 544 \, A - 304 \, B + 144 \, C\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 + 6*C)*d*x*cos(d*x + c)^3 + 45*(23*A - 13*B + 6*C)*d*x*cos(d*x + c)^2 + 45*(23*A - 13*B + 6*C)*d*x*cos(d*x + c) + 15*(23*A - 13*B + 6*C)*d*x - (10*A*cos(d*x + c)^5 - 15*(A - B)*cos(d*x + c)^4 + 5*(19*A - 9*B + 6*C)*cos(d*x + c)^3 + (869*A - 479*B + 234*C)*cos(d*x + c)^2 + 3*(429*A - 239*B + 114*C)*cos(d*x + c) + 544*A - 304*B + 144*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
474,1,400,0,0.524676," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left({\left(2 \, A - 8 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A - 8 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(2 \, A - 8 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, A - 8 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(20 \, A - 83 \, B + 216 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(1070 \, A - 4472 \, B + 11619 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(310 \, A - 1318 \, B + 3411 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(130 \, A - 592 \, B + 1509 \, C\right)} \cos\left(d x + c\right)^{2} - 210 \, {\left(B - 2 \, C\right)} \cos\left(d x + c\right) - 105 \, C\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*((2*A - 8*B + 21*C)*cos(d*x + c)^6 + 4*(2*A - 8*B + 21*C)*cos(d*x + c)^5 + 6*(2*A - 8*B + 21*C)*cos(d*x + c)^4 + 4*(2*A - 8*B + 21*C)*cos(d*x + c)^3 + (2*A - 8*B + 21*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 105*((2*A - 8*B + 21*C)*cos(d*x + c)^6 + 4*(2*A - 8*B + 21*C)*cos(d*x + c)^5 + 6*(2*A - 8*B + 21*C)*cos(d*x + c)^4 + 4*(2*A - 8*B + 21*C)*cos(d*x + c)^3 + (2*A - 8*B + 21*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(16*(20*A - 83*B + 216*C)*cos(d*x + c)^5 + (1070*A - 4472*B + 11619*C)*cos(d*x + c)^4 + 4*(310*A - 1318*B + 3411*C)*cos(d*x + c)^3 + 4*(130*A - 592*B + 1509*C)*cos(d*x + c)^2 - 210*(B - 2*C)*cos(d*x + c) - 105*C)*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
475,1,328,0,0.476382," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left({\left(B - 4 \, C\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(B - 4 \, C\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(B - 4 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(B - 4 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 4 \, C\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(B - 4 \, C\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(B - 4 \, C\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(B - 4 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(B - 4 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 4 \, C\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(3 \, A - 80 \, B + 332 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(24 \, A - 535 \, B + 2236 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A - 620 \, B + 2636 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(9 \, A - 65 \, B + 296 \, C\right)} \cos\left(d x + c\right) + 105 \, C\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*((B - 4*C)*cos(d*x + c)^5 + 4*(B - 4*C)*cos(d*x + c)^4 + 6*(B - 4*C)*cos(d*x + c)^3 + 4*(B - 4*C)*cos(d*x + c)^2 + (B - 4*C)*cos(d*x + c))*log(sin(d*x + c) + 1) - 105*((B - 4*C)*cos(d*x + c)^5 + 4*(B - 4*C)*cos(d*x + c)^4 + 6*(B - 4*C)*cos(d*x + c)^3 + 4*(B - 4*C)*cos(d*x + c)^2 + (B - 4*C)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(2*(3*A - 80*B + 332*C)*cos(d*x + c)^4 + (24*A - 535*B + 2236*C)*cos(d*x + c)^3 + (39*A - 620*B + 2636*C)*cos(d*x + c)^2 + 4*(9*A - 65*B + 296*C)*cos(d*x + c) + 105*C)*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
476,1,248,0,0.486458," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(C \cos\left(d x + c\right)^{4} + 4 \, C \cos\left(d x + c\right)^{3} + 6 \, C \cos\left(d x + c\right)^{2} + 4 \, C \cos\left(d x + c\right) + C\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(C \cos\left(d x + c\right)^{4} + 4 \, C \cos\left(d x + c\right)^{3} + 6 \, C \cos\left(d x + c\right)^{2} + 4 \, C \cos\left(d x + c\right) + C\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(4 \, A + 3 \, B - 80 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(32 \, A + 24 \, B - 535 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(52 \, A + 39 \, B - 620 \, C\right)} \cos\left(d x + c\right) + 13 \, A + 36 \, B - 260 \, C\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*(C*cos(d*x + c)^4 + 4*C*cos(d*x + c)^3 + 6*C*cos(d*x + c)^2 + 4*C*cos(d*x + c) + C)*log(sin(d*x + c) + 1) - 105*(C*cos(d*x + c)^4 + 4*C*cos(d*x + c)^3 + 6*C*cos(d*x + c)^2 + 4*C*cos(d*x + c) + C)*log(-sin(d*x + c) + 1) + 2*(2*(4*A + 3*B - 80*C)*cos(d*x + c)^3 + (32*A + 24*B - 535*C)*cos(d*x + c)^2 + (52*A + 39*B - 620*C)*cos(d*x + c) + 13*A + 36*B - 260*C)*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
477,1,135,0,0.409247," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(13 \, A + 8 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(13 \, A + 8 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(32 \, A + 52 \, B + 39 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 13 \, B + 36 \, C\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 + 6*C)*cos(d*x + c)^3 + 4*(13*A + 8*B + 6*C)*cos(d*x + c)^2 + (32*A + 52*B + 39*C)*cos(d*x + c) + 8*A + 13*B + 36*C)*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
478,1,135,0,0.409304," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(36 \, A + 13 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A + 52 \, B + 32 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(6 \, A + 8 \, B + 13 \, C\right)} \cos\left(d x + c\right) + 6 \, A + 8 \, B + 13 \, C\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 + 8*C)*cos(d*x + c)^3 + (39*A + 52*B + 32*C)*cos(d*x + c)^2 + 4*(6*A + 8*B + 13*C)*cos(d*x + c) + 6*A + 8*B + 13*C)*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
479,1,192,0,0.452283," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(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({\left(260 \, A - 36 \, B - 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(620 \, A - 39 \, B - 52 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(535 \, A - 24 \, B - 32 \, C\right)} \cos\left(d x + c\right) + 160 \, A - 6 \, B - 8 \, C\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 - ((260*A - 36*B - 13*C)*cos(d*x + c)^3 + (620*A - 39*B - 52*C)*cos(d*x + c)^2 + (535*A - 24*B - 32*C)*cos(d*x + c) + 160*A - 6*B - 8*C)*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
480,1,234,0,0.466061," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""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 + 9 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2636 \, A - 620 \, B + 39 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(2236 \, A - 535 \, B + 24 \, C\right)} \cos\left(d x + c\right) + 664 \, A - 160 \, B + 6 \, C\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 + 9*C)*cos(d*x + c)^3 + (2636*A - 620*B + 39*C)*cos(d*x + c)^2 + (2236*A - 535*B + 24*C)*cos(d*x + c) + 664*A - 160*B + 6*C)*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
481,1,267,0,0.434984," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} d x \cos\left(d x + c\right)^{4} + 420 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} d x \cos\left(d x + c\right)^{3} + 630 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} d x \cos\left(d x + c\right)^{2} + 420 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} d x \cos\left(d x + c\right) + 105 \, {\left(21 \, A - 8 \, B + 2 \, C\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 + 130 \, C\right)} \cos\left(d x + c\right)^{3} - 4 \, {\left(3411 \, A - 1318 \, B + 310 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(11619 \, A - 4472 \, B + 1070 \, C\right)} \cos\left(d x + c\right) - 3456 \, A + 1328 \, B - 320 \, C\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 + 2*C)*d*x*cos(d*x + c)^4 + 420*(21*A - 8*B + 2*C)*d*x*cos(d*x + c)^3 + 630*(21*A - 8*B + 2*C)*d*x*cos(d*x + c)^2 + 420*(21*A - 8*B + 2*C)*d*x*cos(d*x + c) + 105*(21*A - 8*B + 2*C)*d*x + (105*A*cos(d*x + c)^5 - 210*(2*A - B)*cos(d*x + c)^4 - 4*(1509*A - 592*B + 130*C)*cos(d*x + c)^3 - 4*(3411*A - 1318*B + 310*C)*cos(d*x + c)^2 - (11619*A - 4472*B + 1070*C)*cos(d*x + c) - 3456*A + 1328*B - 320*C)*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
482,1,151,0,0.428243," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, {\left(99 \, A + 88 \, B + 80 \, C\right)} \cos\left(d x + c\right)^{5} + 8 \, {\left(99 \, A + 88 \, B + 80 \, C\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(99 \, A + 88 \, B + 80 \, C\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(99 \, A + 88 \, B + 80 \, C\right)} \cos\left(d x + c\right)^{2} + 35 \, {\left(11 \, B + 10 \, C\right)} \cos\left(d x + c\right) + 315 \, C\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*(16*(99*A + 88*B + 80*C)*cos(d*x + c)^5 + 8*(99*A + 88*B + 80*C)*cos(d*x + c)^4 + 6*(99*A + 88*B + 80*C)*cos(d*x + c)^3 + 5*(99*A + 88*B + 80*C)*cos(d*x + c)^2 + 35*(11*B + 10*C)*cos(d*x + c) + 315*C)*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
483,1,131,0,0.440496," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(21 \, A + 18 \, B + 16 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(21 \, A + 18 \, B + 16 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 18 \, B + 16 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, B + 8 \, C\right)} \cos\left(d x + c\right) + 35 \, C\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*(21*A + 18*B + 16*C)*cos(d*x + c)^4 + 4*(21*A + 18*B + 16*C)*cos(d*x + c)^3 + 3*(21*A + 18*B + 16*C)*cos(d*x + c)^2 + 5*(9*B + 8*C)*cos(d*x + c) + 35*C)*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
484,1,110,0,0.427807," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(35 \, A + 28 \, B + 24 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(35 \, A + 28 \, B + 24 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B + 6 \, C\right)} \cos\left(d x + c\right) + 15 \, C\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*(35*A + 28*B + 24*C)*cos(d*x + c)^3 + (35*A + 28*B + 24*C)*cos(d*x + c)^2 + 3*(7*B + 6*C)*cos(d*x + c) + 15*C)*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
485,1,89,0,0.429353," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(15 \, A + 10 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, B + 4 \, C\right)} \cos\left(d x + c\right) + 3 \, C\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*((15*A + 10*B + 8*C)*cos(d*x + c)^2 + (5*B + 4*C)*cos(d*x + c) + 3*C)*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
486,1,304,0,0.506025," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A \cos\left(d x + c\right)^{2} + 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 \, B + 2 \, C\right)} \cos\left(d x + c\right) + C\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 \cos\left(d x + c\right)^{2} + 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 \, B + 2 \, C\right)} \cos\left(d x + c\right) + C\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*cos(d*x + c)^2 + 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*B + 2*C)*cos(d*x + c) + C)*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*cos(d*x + c)^2 + 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*B + 2*C)*cos(d*x + c) + C)*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
487,1,272,0,0.507338," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\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 \cos\left(d x + c\right) + 2 \, C\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(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) - {\left(A \cos\left(d x + c\right) + 2 \, C\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*(((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)) + 2*(A*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -(((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))) - (A*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
488,1,320,0,0.600453," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, A + 4 \, B + 8 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 4 \, B + 8 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 4 \, B + 8 \, C\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 + 8*C)*cos(d*x + c) + 3*A + 4*B + 8*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*(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 + 8*C)*cos(d*x + c) + 3*A + 4*B + 8*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))) - (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
489,1,364,0,0.600470," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, A + 6 \, B + 8 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 6 \, B + 8 \, C\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 + 8 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 6 \, B + 8 \, C\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 + 8 \, C\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 + 8*C)*cos(d*x + c) + 5*A + 6*B + 8*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*(8*A*cos(d*x + c)^3 + 2*(5*A + 6*B)*cos(d*x + c)^2 + 3*(5*A + 6*B + 8*C)*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 + 8*C)*cos(d*x + c) + 5*A + 6*B + 8*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))) - (8*A*cos(d*x + c)^3 + 2*(5*A + 6*B)*cos(d*x + c)^2 + 3*(5*A + 6*B + 8*C)*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
490,1,404,0,0.751857," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(35 \, A + 40 \, B + 48 \, C\right)} \cos\left(d x + c\right) + 35 \, A + 40 \, B + 48 \, C\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} + 2 \, {\left(35 \, A + 40 \, B + 48 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(35 \, A + 40 \, B + 48 \, C\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{3 \, {\left({\left(35 \, A + 40 \, B + 48 \, C\right)} \cos\left(d x + c\right) + 35 \, A + 40 \, B + 48 \, C\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} + 2 \, {\left(35 \, A + 40 \, B + 48 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(35 \, A + 40 \, B + 48 \, C\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*(3*((35*A + 40*B + 48*C)*cos(d*x + c) + 35*A + 40*B + 48*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*(48*A*cos(d*x + c)^4 + 8*(7*A + 8*B)*cos(d*x + c)^3 + 2*(35*A + 40*B + 48*C)*cos(d*x + c)^2 + 3*(35*A + 40*B + 48*C)*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*((35*A + 40*B + 48*C)*cos(d*x + c) + 35*A + 40*B + 48*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))) - (48*A*cos(d*x + c)^4 + 8*(7*A + 8*B)*cos(d*x + c)^3 + 2*(35*A + 40*B + 48*C)*cos(d*x + c)^2 + 3*(35*A + 40*B + 48*C)*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
491,1,157,0,0.433290," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(429 \, A + 374 \, B + 336 \, C\right)} a \cos\left(d x + c\right)^{5} + 4 \, {\left(429 \, A + 374 \, B + 336 \, C\right)} a \cos\left(d x + c\right)^{4} + 3 \, {\left(429 \, A + 374 \, B + 336 \, C\right)} a \cos\left(d x + c\right)^{3} + 5 \, {\left(99 \, A + 187 \, B + 168 \, C\right)} a \cos\left(d x + c\right)^{2} + 35 \, {\left(11 \, B + 21 \, C\right)} a \cos\left(d x + c\right) + 315 \, C a\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*(429*A + 374*B + 336*C)*a*cos(d*x + c)^5 + 4*(429*A + 374*B + 336*C)*a*cos(d*x + c)^4 + 3*(429*A + 374*B + 336*C)*a*cos(d*x + c)^3 + 5*(99*A + 187*B + 168*C)*a*cos(d*x + c)^2 + 35*(11*B + 21*C)*a*cos(d*x + c) + 315*C*a)*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
492,1,135,0,0.442479," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(189 \, A + 156 \, B + 136 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(189 \, A + 156 \, B + 136 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 39 \, B + 34 \, C\right)} a \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, B + 17 \, C\right)} a \cos\left(d x + c\right) + 35 \, C 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*(2*(189*A + 156*B + 136*C)*a*cos(d*x + c)^4 + (189*A + 156*B + 136*C)*a*cos(d*x + c)^3 + 3*(21*A + 39*B + 34*C)*a*cos(d*x + c)^2 + 5*(9*B + 17*C)*a*cos(d*x + c) + 35*C*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
493,1,113,0,0.448185," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(175 \, A + 126 \, B + 104 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(35 \, A + 63 \, B + 52 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B + 13 \, C\right)} a \cos\left(d x + c\right) + 15 \, C 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*((175*A + 126*B + 104*C)*a*cos(d*x + c)^3 + (35*A + 63*B + 52*C)*a*cos(d*x + c)^2 + 3*(7*B + 13*C)*a*cos(d*x + c) + 15*C*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
494,1,364,0,0.469398," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(A a \cos\left(d x + c\right)^{3} + A a \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(15 \, A + 25 \, B + 18 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(5 \, B + 9 \, C\right)} a \cos\left(d x + c\right) + 3 \, C 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)}}, -\frac{2 \, {\left(15 \, {\left(A a \cos\left(d x + c\right)^{3} + A a \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(15 \, A + 25 \, B + 18 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(5 \, B + 9 \, C\right)} a \cos\left(d x + c\right) + 3 \, C 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)}}{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*cos(d*x + c)^3 + A*a*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*((15*A + 25*B + 18*C)*a*cos(d*x + c)^2 + (5*B + 9*C)*a*cos(d*x + c) + 3*C*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), -2/15*(15*(A*a*cos(d*x + c)^3 + A*a*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))) - ((15*A + 25*B + 18*C)*a*cos(d*x + c)^2 + (5*B + 9*C)*a*cos(d*x + c) + 3*C*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
495,1,366,0,0.505491," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(3 \, A + 2 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(3 \, A + 2 \, B\right)} 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(3 \, A a \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B + 5 \, C\right)} a \cos\left(d x + c\right) + 2 \, C a\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(3 \, A + 2 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(3 \, A + 2 \, B\right)} 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(3 \, A a \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B + 5 \, C\right)} a \cos\left(d x + c\right) + 2 \, C 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)}}\right]"," ",0,"[1/6*(3*((3*A + 2*B)*a*cos(d*x + c)^2 + (3*A + 2*B)*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*a*cos(d*x + c)^2 + 2*(3*B + 5*C)*a*cos(d*x + c) + 2*C*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)), -1/3*(3*((3*A + 2*B)*a*cos(d*x + c)^2 + (3*A + 2*B)*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*a*cos(d*x + c)^2 + 2*(3*B + 5*C)*a*cos(d*x + c) + 2*C*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
496,1,340,0,0.620879," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(7 \, A + 12 \, B + 8 \, C\right)} a \cos\left(d x + c\right) + {\left(7 \, A + 12 \, B + 8 \, 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 \, {\left(2 \, A a \cos\left(d x + c\right)^{2} + {\left(7 \, A + 4 \, B\right)} a \cos\left(d x + c\right) + 8 \, C a\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 + 8 \, C\right)} a \cos\left(d x + c\right) + {\left(7 \, A + 12 \, B + 8 \, 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) - {\left(2 \, A a \cos\left(d x + c\right)^{2} + {\left(7 \, A + 4 \, B\right)} a \cos\left(d x + c\right) + 8 \, C a\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 + 8*C)*a*cos(d*x + c) + (7*A + 12*B + 8*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*(2*A*a*cos(d*x + c)^2 + (7*A + 4*B)*a*cos(d*x + c) + 8*C*a)*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 + 8*C)*a*cos(d*x + c) + (7*A + 12*B + 8*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*A*a*cos(d*x + c)^2 + (7*A + 4*B)*a*cos(d*x + c) + 8*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
497,1,378,0,0.594216," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(11 \, A + 14 \, B + 24 \, C\right)} a \cos\left(d x + c\right) + {\left(11 \, A + 14 \, B + 24 \, 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 \, {\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 + 8 \, C\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 + 24 \, C\right)} a \cos\left(d x + c\right) + {\left(11 \, A + 14 \, B + 24 \, 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) - {\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 + 8 \, C\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 + 24*C)*a*cos(d*x + c) + (11*A + 14*B + 24*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*(8*A*a*cos(d*x + c)^3 + 2*(11*A + 6*B)*a*cos(d*x + c)^2 + 3*(11*A + 14*B + 8*C)*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 + 24*C)*a*cos(d*x + c) + (11*A + 14*B + 24*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))) - (8*A*a*cos(d*x + c)^3 + 2*(11*A + 6*B)*a*cos(d*x + c)^2 + 3*(11*A + 14*B + 8*C)*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
498,1,420,0,0.765015," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(75 \, A + 88 \, B + 112 \, C\right)} a \cos\left(d x + c\right) + {\left(75 \, A + 88 \, B + 112 \, 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 \, {\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 + 48 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A + 88 \, B + 112 \, C\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 + 112 \, C\right)} a \cos\left(d x + c\right) + {\left(75 \, A + 88 \, B + 112 \, 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) - {\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 + 48 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A + 88 \, B + 112 \, C\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 + 112*C)*a*cos(d*x + c) + (75*A + 88*B + 112*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*(48*A*a*cos(d*x + c)^4 + 8*(15*A + 8*B)*a*cos(d*x + c)^3 + 2*(75*A + 88*B + 48*C)*a*cos(d*x + c)^2 + 3*(75*A + 88*B + 112*C)*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 + 112*C)*a*cos(d*x + c) + (75*A + 88*B + 112*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))) - (48*A*a*cos(d*x + c)^4 + 8*(15*A + 8*B)*a*cos(d*x + c)^3 + 2*(75*A + 88*B + 48*C)*a*cos(d*x + c)^2 + 3*(75*A + 88*B + 112*C)*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
499,1,462,0,0.756186," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(133 \, A + 150 \, B + 176 \, C\right)} a \cos\left(d x + c\right) + {\left(133 \, A + 150 \, B + 176 \, 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 \, {\left(384 \, A a \cos\left(d x + c\right)^{5} + 48 \, {\left(19 \, A + 10 \, B\right)} a \cos\left(d x + c\right)^{4} + 8 \, {\left(133 \, A + 150 \, B + 80 \, C\right)} a \cos\left(d x + c\right)^{3} + 10 \, {\left(133 \, A + 150 \, B + 176 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(133 \, A + 150 \, B + 176 \, C\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)}{3840 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{15 \, {\left({\left(133 \, A + 150 \, B + 176 \, C\right)} a \cos\left(d x + c\right) + {\left(133 \, A + 150 \, B + 176 \, 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) - {\left(384 \, A a \cos\left(d x + c\right)^{5} + 48 \, {\left(19 \, A + 10 \, B\right)} a \cos\left(d x + c\right)^{4} + 8 \, {\left(133 \, A + 150 \, B + 80 \, C\right)} a \cos\left(d x + c\right)^{3} + 10 \, {\left(133 \, A + 150 \, B + 176 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(133 \, A + 150 \, B + 176 \, C\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)}{1920 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/3840*(15*((133*A + 150*B + 176*C)*a*cos(d*x + c) + (133*A + 150*B + 176*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*(384*A*a*cos(d*x + c)^5 + 48*(19*A + 10*B)*a*cos(d*x + c)^4 + 8*(133*A + 150*B + 80*C)*a*cos(d*x + c)^3 + 10*(133*A + 150*B + 176*C)*a*cos(d*x + c)^2 + 15*(133*A + 150*B + 176*C)*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), -1/1920*(15*((133*A + 150*B + 176*C)*a*cos(d*x + c) + (133*A + 150*B + 176*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))) - (384*A*a*cos(d*x + c)^5 + 48*(19*A + 10*B)*a*cos(d*x + c)^4 + 8*(133*A + 150*B + 80*C)*a*cos(d*x + c)^3 + 10*(133*A + 150*B + 176*C)*a*cos(d*x + c)^2 + 15*(133*A + 150*B + 176*C)*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
500,1,192,0,0.465121," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(10439 \, A + 9230 \, B + 8368 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + 4 \, {\left(10439 \, A + 9230 \, B + 8368 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 3 \, {\left(10439 \, A + 9230 \, B + 8368 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(3718 \, A + 4615 \, B + 4184 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 35 \, {\left(143 \, A + 416 \, B + 523 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 315 \, {\left(13 \, B + 38 \, C\right)} a^{2} \cos\left(d x + c\right) + 3465 \, C 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)}{45045 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"2/45045*(8*(10439*A + 9230*B + 8368*C)*a^2*cos(d*x + c)^6 + 4*(10439*A + 9230*B + 8368*C)*a^2*cos(d*x + c)^5 + 3*(10439*A + 9230*B + 8368*C)*a^2*cos(d*x + c)^4 + 5*(3718*A + 4615*B + 4184*C)*a^2*cos(d*x + c)^3 + 35*(143*A + 416*B + 523*C)*a^2*cos(d*x + c)^2 + 315*(13*B + 38*C)*a^2*cos(d*x + c) + 3465*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^7 + d*cos(d*x + c)^6)","A",0
501,1,168,0,0.452700," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(3795 \, A + 3212 \, B + 2840 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(3795 \, A + 3212 \, B + 2840 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(660 \, A + 803 \, B + 710 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 5 \, {\left(99 \, A + 286 \, B + 355 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 35 \, {\left(11 \, B + 32 \, C\right)} a^{2} \cos\left(d x + c\right) + 315 \, C 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*(2*(3795*A + 3212*B + 2840*C)*a^2*cos(d*x + c)^5 + (3795*A + 3212*B + 2840*C)*a^2*cos(d*x + c)^4 + 3*(660*A + 803*B + 710*C)*a^2*cos(d*x + c)^3 + 5*(99*A + 286*B + 355*C)*a^2*cos(d*x + c)^2 + 35*(11*B + 32*C)*a^2*cos(d*x + c) + 315*C*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
502,1,144,0,0.429635," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(903 \, A + 690 \, B + 584 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(294 \, A + 345 \, B + 292 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 60 \, B + 73 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, B + 26 \, C\right)} a^{2} \cos\left(d x + c\right) + 35 \, C 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*((903*A + 690*B + 584*C)*a^2*cos(d*x + c)^4 + (294*A + 345*B + 292*C)*a^2*cos(d*x + c)^3 + 3*(21*A + 60*B + 73*C)*a^2*cos(d*x + c)^2 + 5*(9*B + 26*C)*a^2*cos(d*x + c) + 35*C*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
503,1,430,0,0.491832," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(A a^{2} \cos\left(d x + c\right)^{4} + A a^{2} \cos\left(d x + c\right)^{3}\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(280 \, A + 301 \, B + 230 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(35 \, A + 98 \, B + 115 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B + 20 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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)}}, -\frac{2 \, {\left(105 \, {\left(A a^{2} \cos\left(d x + c\right)^{4} + A a^{2} \cos\left(d x + c\right)^{3}\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(280 \, A + 301 \, B + 230 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(35 \, A + 98 \, B + 115 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, B + 20 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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)}}{105 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/105*(105*(A*a^2*cos(d*x + c)^4 + A*a^2*cos(d*x + c)^3)*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*((280*A + 301*B + 230*C)*a^2*cos(d*x + c)^3 + (35*A + 98*B + 115*C)*a^2*cos(d*x + c)^2 + 3*(7*B + 20*C)*a^2*cos(d*x + c) + 15*C*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), -2/105*(105*(A*a^2*cos(d*x + c)^4 + A*a^2*cos(d*x + c)^3)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - ((280*A + 301*B + 230*C)*a^2*cos(d*x + c)^3 + (35*A + 98*B + 115*C)*a^2*cos(d*x + c)^2 + 3*(7*B + 20*C)*a^2*cos(d*x + c) + 15*C*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
504,1,440,0,0.523271," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(5 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(5 \, A + 2 \, B\right)} 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(15 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(15 \, A + 40 \, B + 43 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, B + 14 \, C\right)} a^{2} \cos\left(d x + c\right) + 6 \, C 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)}{30 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, -\frac{15 \, {\left({\left(5 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(5 \, A + 2 \, B\right)} 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(15 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(15 \, A + 40 \, B + 43 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, B + 14 \, C\right)} a^{2} \cos\left(d x + c\right) + 6 \, C 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)}}\right]"," ",0,"[1/30*(15*((5*A + 2*B)*a^2*cos(d*x + c)^3 + (5*A + 2*B)*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*(15*A*a^2*cos(d*x + c)^3 + 2*(15*A + 40*B + 43*C)*a^2*cos(d*x + c)^2 + 2*(5*B + 14*C)*a^2*cos(d*x + c) + 6*C*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), -1/15*(15*((5*A + 2*B)*a^2*cos(d*x + c)^3 + (5*A + 2*B)*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))) - (15*A*a^2*cos(d*x + c)^3 + 2*(15*A + 40*B + 43*C)*a^2*cos(d*x + c)^2 + 2*(5*B + 14*C)*a^2*cos(d*x + c) + 6*C*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
505,1,438,0,0.624156," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(19 \, A + 20 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(19 \, A + 20 \, B + 8 \, C\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(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(11 \, A + 4 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, C 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)}{24 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, -\frac{3 \, {\left({\left(19 \, A + 20 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(19 \, A + 20 \, B + 8 \, C\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(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(11 \, A + 4 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, C 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)}{12 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/24*(3*((19*A + 20*B + 8*C)*a^2*cos(d*x + c)^2 + (19*A + 20*B + 8*C)*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*(6*A*a^2*cos(d*x + c)^3 + 3*(11*A + 4*B)*a^2*cos(d*x + c)^2 + 8*(3*B + 8*C)*a^2*cos(d*x + c) + 8*C*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)), -1/12*(3*((19*A + 20*B + 8*C)*a^2*cos(d*x + c)^2 + (19*A + 20*B + 8*C)*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))) - (6*A*a^2*cos(d*x + c)^3 + 3*(11*A + 4*B)*a^2*cos(d*x + c)^2 + 8*(3*B + 8*C)*a^2*cos(d*x + c) + 8*C*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
506,1,410,0,0.622278," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(25 \, A + 38 \, B + 40 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(25 \, A + 38 \, B + 40 \, C\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 + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + 48 \, C 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)}{48 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{3 \, {\left({\left(25 \, A + 38 \, B + 40 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(25 \, A + 38 \, B + 40 \, C\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 + 8 \, C\right)} a^{2} \cos\left(d x + c\right) + 48 \, C 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)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/48*(3*((25*A + 38*B + 40*C)*a^2*cos(d*x + c) + (25*A + 38*B + 40*C)*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 + 8*C)*a^2*cos(d*x + c) + 48*C*a^2)*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 + 40*C)*a^2*cos(d*x + c) + (25*A + 38*B + 40*C)*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 + 8*C)*a^2*cos(d*x + c) + 48*C*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
507,1,444,0,0.768073," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(163 \, A + 200 \, B + 304 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(163 \, A + 200 \, B + 304 \, C\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 + 48 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A + 200 \, B + 176 \, C\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 + 304 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(163 \, A + 200 \, B + 304 \, C\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 + 48 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A + 200 \, B + 176 \, C\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 + 304*C)*a^2*cos(d*x + c) + (163*A + 200*B + 304*C)*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 + 48*C)*a^2*cos(d*x + c)^2 + 3*(163*A + 200*B + 176*C)*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 + 304*C)*a^2*cos(d*x + c) + (163*A + 200*B + 304*C)*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 + 48*C)*a^2*cos(d*x + c)^2 + 3*(163*A + 200*B + 176*C)*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
508,1,490,0,0.752257," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(283 \, A + 326 \, B + 400 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(283 \, A + 326 \, B + 400 \, C\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 + 80 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(283 \, A + 326 \, B + 272 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(283 \, A + 326 \, B + 400 \, C\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 + 400 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(283 \, A + 326 \, B + 400 \, C\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 + 80 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(283 \, A + 326 \, B + 272 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(283 \, A + 326 \, B + 400 \, C\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 + 400*C)*a^2*cos(d*x + c) + (283*A + 326*B + 400*C)*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 + 80*C)*a^2*cos(d*x + c)^3 + 10*(283*A + 326*B + 272*C)*a^2*cos(d*x + c)^2 + 15*(283*A + 326*B + 400*C)*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 + 400*C)*a^2*cos(d*x + c) + (283*A + 326*B + 400*C)*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 + 80*C)*a^2*cos(d*x + c)^3 + 10*(283*A + 326*B + 272*C)*a^2*cos(d*x + c)^2 + 15*(283*A + 326*B + 400*C)*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
509,1,536,0,0.782038," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(1015 \, A + 1132 \, B + 1304 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(1015 \, A + 1132 \, B + 1304 \, C\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(1280 \, A a^{2} \cos\left(d x + c\right)^{6} + 128 \, {\left(35 \, A + 12 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(145 \, A + 116 \, B + 40 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(1015 \, A + 1132 \, B + 920 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(1015 \, A + 1132 \, B + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(1015 \, A + 1132 \, B + 1304 \, C\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)}{15360 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{15 \, {\left({\left(1015 \, A + 1132 \, B + 1304 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(1015 \, A + 1132 \, B + 1304 \, C\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(1280 \, A a^{2} \cos\left(d x + c\right)^{6} + 128 \, {\left(35 \, A + 12 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(145 \, A + 116 \, B + 40 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(1015 \, A + 1132 \, B + 920 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(1015 \, A + 1132 \, B + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(1015 \, A + 1132 \, B + 1304 \, C\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)}{7680 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/15360*(15*((1015*A + 1132*B + 1304*C)*a^2*cos(d*x + c) + (1015*A + 1132*B + 1304*C)*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*(1280*A*a^2*cos(d*x + c)^6 + 128*(35*A + 12*B)*a^2*cos(d*x + c)^5 + 48*(145*A + 116*B + 40*C)*a^2*cos(d*x + c)^4 + 8*(1015*A + 1132*B + 920*C)*a^2*cos(d*x + c)^3 + 10*(1015*A + 1132*B + 1304*C)*a^2*cos(d*x + c)^2 + 15*(1015*A + 1132*B + 1304*C)*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), -1/7680*(15*((1015*A + 1132*B + 1304*C)*a^2*cos(d*x + c) + (1015*A + 1132*B + 1304*C)*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))) - (1280*A*a^2*cos(d*x + c)^6 + 128*(35*A + 12*B)*a^2*cos(d*x + c)^5 + 48*(145*A + 116*B + 40*C)*a^2*cos(d*x + c)^4 + 8*(1015*A + 1132*B + 920*C)*a^2*cos(d*x + c)^3 + 10*(1015*A + 1132*B + 1304*C)*a^2*cos(d*x + c)^2 + 15*(1015*A + 1132*B + 1304*C)*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
510,1,487,0,0.508849," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{315 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{5} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{4}\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(273 \, A - 129 \, B + 257 \, C\right)} \cos\left(d x + c\right)^{4} - {\left(21 \, A - 93 \, B + 29 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A - 3 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, B - C\right)} \cos\left(d x + c\right) + 35 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{630 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}, \frac{2 \, {\left({\left(273 \, A - 129 \, B + 257 \, C\right)} \cos\left(d x + c\right)^{4} - {\left(21 \, A - 93 \, B + 29 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A - 3 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(9 \, B - C\right)} \cos\left(d x + c\right) + 35 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) + \frac{315 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{5} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{4}\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}}}{315 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/630*(315*sqrt(2)*((A - B + C)*a*cos(d*x + c)^5 + (A - B + C)*a*cos(d*x + c)^4)*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*((273*A - 129*B + 257*C)*cos(d*x + c)^4 - (21*A - 93*B + 29*C)*cos(d*x + c)^3 + 3*(21*A - 3*B + 19*C)*cos(d*x + c)^2 + 5*(9*B - C)*cos(d*x + c) + 35*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c)^5 + a*d*cos(d*x + c)^4), 1/315*(2*((273*A - 129*B + 257*C)*cos(d*x + c)^4 - (21*A - 93*B + 29*C)*cos(d*x + c)^3 + 3*(21*A - 3*B + 19*C)*cos(d*x + c)^2 + 5*(9*B - C)*cos(d*x + c) + 35*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 315*sqrt(2)*((A - B + C)*a*cos(d*x + c)^5 + (A - B + C)*a*cos(d*x + c)^4)*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)^5 + a*d*cos(d*x + c)^4)]","A",0
511,1,448,0,0.518568," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B + C\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(35 \, A - 91 \, B + 43 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(35 \, A - 7 \, B + 31 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(7 \, B - C\right)} \cos\left(d x + c\right) - 15 \, C\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(35 \, A - 91 \, B + 43 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(35 \, A - 7 \, B + 31 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(7 \, B - C\right)} \cos\left(d x + c\right) - 15 \, C\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 + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B + C\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 + C)*a*cos(d*x + c)^4 + (A - B + C)*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*((35*A - 91*B + 43*C)*cos(d*x + c)^3 - (35*A - 7*B + 31*C)*cos(d*x + c)^2 - 3*(7*B - C)*cos(d*x + c) - 15*C)*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*((35*A - 91*B + 43*C)*cos(d*x + c)^3 - (35*A - 7*B + 31*C)*cos(d*x + c)^2 - 3*(7*B - C)*cos(d*x + c) - 15*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 105*sqrt(2)*((A - B + C)*a*cos(d*x + c)^4 + (A - B + C)*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
512,1,405,0,0.493814," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B + C\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(15 \, A - 5 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, B - C\right)} \cos\left(d x + c\right) + 3 \, C\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(15 \, A - 5 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, B - C\right)} \cos\left(d x + c\right) + 3 \, C\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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B + C\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 + C)*a*cos(d*x + c)^3 + (A - B + C)*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*((15*A - 5*B + 13*C)*cos(d*x + c)^2 + (5*B - C)*cos(d*x + c) + 3*C)*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*((15*A - 5*B + 13*C)*cos(d*x + c)^2 + (5*B - C)*cos(d*x + c) + 3*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 15*sqrt(2)*((A - B + C)*a*cos(d*x + c)^3 + (A - B + C)*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
513,1,356,0,0.517769," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B + C\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 \, B - C\right)} \cos\left(d x + c\right) + C\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 \, B - C\right)} \cos\left(d x + c\right) + C\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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B + C\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 + C)*a*cos(d*x + c)^2 + (A - B + C)*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*B - C)*cos(d*x + c) + C)*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*B - C)*cos(d*x + c) + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 3*sqrt(2)*((A - B + C)*a*cos(d*x + c)^2 + (A - B + C)*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
514,1,439,0,4.918176," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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) - 2 \, {\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) + 4 \, C \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 \, {\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) - 2 \, C \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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C)*a*cos(d*x + c) + (A - B + C)*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*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*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*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))) - 2*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*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
515,1,462,0,6.261179," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C)*a*cos(d*x + c) + (A - B + C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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
516,1,521,0,15.711376," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + 8 \, C\right)} \cos\left(d x + c\right) + 7 \, A - 4 \, B + 8 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right) + 7 \, A - 4 \, B + 8 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C)*a*cos(d*x + c) + (A - B + C)*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 + 8*C)*cos(d*x + c) + 7*A - 4*B + 8*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*(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 + 8*C)*cos(d*x + c) + 7*A - 4*B + 8*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))) - (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 + C)*a*cos(d*x + c) + (A - B + C)*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
517,1,562,0,15.762691," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{24 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + 8 \, C\right)} \cos\left(d x + c\right) + 9 \, A - 14 \, B + 8 \, C\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 + 8 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right) + 9 \, A - 14 \, B + 8 \, C\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 + 8 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C)*a*cos(d*x + c) + (A - B + C)*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 + 8*C)*cos(d*x + c) + 9*A - 14*B + 8*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*(8*A*cos(d*x + c)^3 - 2*(A - 6*B)*cos(d*x + c)^2 + 3*(7*A - 2*B + 8*C)*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 + 8*C)*cos(d*x + c) + 9*A - 14*B + 8*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))) + (8*A*cos(d*x + c)^3 - 2*(A - 6*B)*cos(d*x + c)^2 + 3*(7*A - 2*B + 8*C)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 24*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*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
518,1,602,0,23.786135," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{192 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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(107 \, A - 72 \, B + 112 \, C\right)} \cos\left(d x + c\right) + 107 \, A - 72 \, B + 112 \, C\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(A - 8 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(43 \, A - 8 \, B + 48 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(21 \, A - 56 \, B + 16 \, C\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(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{3 \, {\left({\left(107 \, A - 72 \, B + 112 \, C\right)} \cos\left(d x + c\right) + 107 \, A - 72 \, B + 112 \, C\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(A - 8 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(43 \, A - 8 \, B + 48 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(21 \, A - 56 \, B + 16 \, C\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{192 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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}}}{192 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/384*(192*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*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*((107*A - 72*B + 112*C)*cos(d*x + c) + 107*A - 72*B + 112*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*(48*A*cos(d*x + c)^4 - 8*(A - 8*B)*cos(d*x + c)^3 + 2*(43*A - 8*B + 48*C)*cos(d*x + c)^2 - 3*(21*A - 56*B + 16*C)*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), -1/192*(3*((107*A - 72*B + 112*C)*cos(d*x + c) + 107*A - 72*B + 112*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))) - (48*A*cos(d*x + c)^4 - 8*(A - 8*B)*cos(d*x + c)^3 + 2*(43*A - 8*B + 48*C)*cos(d*x + c)^2 - 3*(21*A - 56*B + 16*C)*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 192*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*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
519,1,575,0,0.572657," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, \sqrt{2} {\left({\left(11 \, A - 15 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(11 \, A - 15 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(11 \, A - 15 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3}\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(665 \, A - 1029 \, B + 1201 \, C\right)} \cos\left(d x + c\right)^{4} + 12 \, {\left(35 \, A - 63 \, B + 67 \, C\right)} \cos\left(d x + c\right)^{3} - 28 \, {\left(5 \, A - 3 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left(7 \, B - 3 \, C\right)} \cos\left(d x + c\right) - 60 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{840 \, {\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)}}, -\frac{105 \, \sqrt{2} {\left({\left(11 \, A - 15 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(11 \, A - 15 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(11 \, A - 15 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3}\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(665 \, A - 1029 \, B + 1201 \, C\right)} \cos\left(d x + c\right)^{4} + 12 \, {\left(35 \, A - 63 \, B + 67 \, C\right)} \cos\left(d x + c\right)^{3} - 28 \, {\left(5 \, A - 3 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left(7 \, B - 3 \, C\right)} \cos\left(d x + c\right) - 60 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{420 \, {\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)}}\right]"," ",0,"[-1/840*(105*sqrt(2)*((11*A - 15*B + 19*C)*cos(d*x + c)^5 + 2*(11*A - 15*B + 19*C)*cos(d*x + c)^4 + (11*A - 15*B + 19*C)*cos(d*x + c)^3)*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*((665*A - 1029*B + 1201*C)*cos(d*x + c)^4 + 12*(35*A - 63*B + 67*C)*cos(d*x + c)^3 - 28*(5*A - 3*B + 7*C)*cos(d*x + c)^2 - 12*(7*B - 3*C)*cos(d*x + c) - 60*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), -1/420*(105*sqrt(2)*((11*A - 15*B + 19*C)*cos(d*x + c)^5 + 2*(11*A - 15*B + 19*C)*cos(d*x + c)^4 + (11*A - 15*B + 19*C)*cos(d*x + c)^3)*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*((665*A - 1029*B + 1201*C)*cos(d*x + c)^4 + 12*(35*A - 63*B + 67*C)*cos(d*x + c)^3 - 28*(5*A - 3*B + 7*C)*cos(d*x + c)^2 - 12*(7*B - 3*C)*cos(d*x + c) - 60*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
520,1,534,0,0.522012," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left({\left(7 \, A - 11 \, B + 15 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, A - 11 \, B + 15 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A - 11 \, B + 15 \, C\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(75 \, A - 95 \, B + 147 \, C\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(5 \, A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(5 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 12 \, C\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(7 \, A - 11 \, B + 15 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, A - 11 \, B + 15 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A - 11 \, B + 15 \, C\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(75 \, A - 95 \, B + 147 \, C\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(5 \, A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(5 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 12 \, C\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)*((7*A - 11*B + 15*C)*cos(d*x + c)^4 + 2*(7*A - 11*B + 15*C)*cos(d*x + c)^3 + (7*A - 11*B + 15*C)*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*((75*A - 95*B + 147*C)*cos(d*x + c)^3 + 12*(5*A - 5*B + 9*C)*cos(d*x + c)^2 + 4*(5*B - 3*C)*cos(d*x + c) + 12*C)*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)*((7*A - 11*B + 15*C)*cos(d*x + c)^4 + 2*(7*A - 11*B + 15*C)*cos(d*x + c)^3 + (7*A - 11*B + 15*C)*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*((75*A - 95*B + 147*C)*cos(d*x + c)^3 + 12*(5*A - 5*B + 9*C)*cos(d*x + c)^2 + 4*(5*B - 3*C)*cos(d*x + c) + 12*C)*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
521,1,483,0,0.520005," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(3 \, A - 7 \, B + 11 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A - 7 \, B + 11 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - 7 \, B + 11 \, C\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(3 \, A - 15 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left(B - C\right)} \cos\left(d x + c\right) - 4 \, C\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(3 \, A - 7 \, B + 11 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A - 7 \, B + 11 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - 7 \, B + 11 \, C\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(3 \, A - 15 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left(B - C\right)} \cos\left(d x + c\right) - 4 \, C\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)*((3*A - 7*B + 11*C)*cos(d*x + c)^3 + 2*(3*A - 7*B + 11*C)*cos(d*x + c)^2 + (3*A - 7*B + 11*C)*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*((3*A - 15*B + 19*C)*cos(d*x + c)^2 - 12*(B - C)*cos(d*x + c) - 4*C)*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)*((3*A - 7*B + 11*C)*cos(d*x + c)^3 + 2*(3*A - 7*B + 11*C)*cos(d*x + c)^2 + (3*A - 7*B + 11*C)*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*((3*A - 15*B + 19*C)*cos(d*x + c)^2 - 12*(B - C)*cos(d*x + c) - 4*C)*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
522,1,398,0,0.499567," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(A + 3 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 3 \, B - 7 \, C\right)} \cos\left(d x + c\right) + A + 3 \, B - 7 \, C\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 - B + 5 \, C\right)} \cos\left(d x + c\right) + 4 \, C\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(A + 3 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 3 \, B - 7 \, C\right)} \cos\left(d x + c\right) + A + 3 \, B - 7 \, C\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 - B + 5 \, C\right)} \cos\left(d x + c\right) + 4 \, C\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)*((A + 3*B - 7*C)*cos(d*x + c)^2 + 2*(A + 3*B - 7*C)*cos(d*x + c) + A + 3*B - 7*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*((A - B + 5*C)*cos(d*x + c) + 4*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)*((A + 3*B - 7*C)*cos(d*x + c)^2 + 2*(A + 3*B - 7*C)*cos(d*x + c) + A + 3*B - 7*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*((A - B + 5*C)*cos(d*x + c) + 4*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
523,1,568,0,16.664892," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(A - B + C\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 - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - B - 3 \, C\right)} \cos\left(d x + c\right) + 5 \, A - B - 3 \, C\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 + C\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 - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - B - 3 \, C\right)} \cos\left(d x + c\right) + 5 \, A - B - 3 \, C\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 + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((5*A - B - 3*C)*cos(d*x + c)^2 + 2*(5*A - B - 3*C)*cos(d*x + c) + 5*A - B - 3*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)) + 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 + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((5*A - B - 3*C)*cos(d*x + c)^2 + 2*(5*A - B - 3*C)*cos(d*x + c) + 5*A - B - 3*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))) + 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
524,1,618,0,21.970525," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(9 \, A - 5 \, B + C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(9 \, A - 5 \, B + C\right)} \cos\left(d x + c\right) + 9 \, A - 5 \, B + C\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 + C\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 + C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(9 \, A - 5 \, B + C\right)} \cos\left(d x + c\right) + 9 \, A - 5 \, B + C\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 + C\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 + C)*cos(d*x + c)^2 + 2*(9*A - 5*B + C)*cos(d*x + c) + 9*A - 5*B + 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*((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 + C)*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 + C)*cos(d*x + c)^2 + 2*(9*A - 5*B + C)*cos(d*x + c) + 9*A - 5*B + 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))) - 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 + C)*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
525,1,685,0,42.823049," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(13 \, A - 9 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(13 \, A - 9 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 13 \, A - 9 \, B + 5 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(19 \, A - 12 \, B + 8 \, C\right)} \cos\left(d x + c\right) + 19 \, A - 12 \, B + 8 \, C\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 + 2 \, C\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 + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(13 \, A - 9 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 13 \, A - 9 \, B + 5 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(19 \, A - 12 \, B + 8 \, C\right)} \cos\left(d x + c\right) + 19 \, A - 12 \, B + 8 \, C\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 + 2 \, C\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 + 5*C)*cos(d*x + c)^2 + 2*(13*A - 9*B + 5*C)*cos(d*x + c) + 13*A - 9*B + 5*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)) + ((19*A - 12*B + 8*C)*cos(d*x + c)^2 + 2*(19*A - 12*B + 8*C)*cos(d*x + c) + 19*A - 12*B + 8*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*(2*A*cos(d*x + c)^3 - (3*A - 4*B)*cos(d*x + c)^2 - (7*A - 6*B + 2*C)*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 + 5*C)*cos(d*x + c)^2 + 2*(13*A - 9*B + 5*C)*cos(d*x + c) + 13*A - 9*B + 5*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))) - ((19*A - 12*B + 8*C)*cos(d*x + c)^2 + 2*(19*A - 12*B + 8*C)*cos(d*x + c) + 19*A - 12*B + 8*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))) + (2*A*cos(d*x + c)^3 - (3*A - 4*B)*cos(d*x + c)^2 - (7*A - 6*B + 2*C)*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
526,1,724,0,42.708228," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{6 \, \sqrt{2} {\left({\left(17 \, A - 13 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(17 \, A - 13 \, B + 9 \, C\right)} \cos\left(d x + c\right) + 17 \, A - 13 \, B + 9 \, C\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 + 24 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(47 \, A - 38 \, B + 24 \, C\right)} \cos\left(d x + c\right) + 47 \, A - 38 \, B + 24 \, C\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 + 24 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(21 \, A - 14 \, B + 12 \, C\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 + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(17 \, A - 13 \, B + 9 \, C\right)} \cos\left(d x + c\right) + 17 \, A - 13 \, B + 9 \, C\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 + 24 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(47 \, A - 38 \, B + 24 \, C\right)} \cos\left(d x + c\right) + 47 \, A - 38 \, B + 24 \, C\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 + 24 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(21 \, A - 14 \, B + 12 \, C\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 + 9*C)*cos(d*x + c)^2 + 2*(17*A - 13*B + 9*C)*cos(d*x + c) + 17*A - 13*B + 9*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)) + 3*((47*A - 38*B + 24*C)*cos(d*x + c)^2 + 2*(47*A - 38*B + 24*C)*cos(d*x + c) + 47*A - 38*B + 24*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*(8*A*cos(d*x + c)^4 - 6*(A - 2*B)*cos(d*x + c)^3 + (37*A - 18*B + 24*C)*cos(d*x + c)^2 + 3*(21*A - 14*B + 12*C)*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 + 9*C)*cos(d*x + c)^2 + 2*(17*A - 13*B + 9*C)*cos(d*x + c) + 17*A - 13*B + 9*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))) - 3*((47*A - 38*B + 24*C)*cos(d*x + c)^2 + 2*(47*A - 38*B + 24*C)*cos(d*x + c) + 47*A - 38*B + 24*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))) - (8*A*cos(d*x + c)^4 - 6*(A - 2*B)*cos(d*x + c)^3 + (37*A - 18*B + 24*C)*cos(d*x + c)^2 + 3*(21*A - 14*B + 12*C)*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
527,1,638,0,0.570141," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left({\left(75 \, A - 163 \, B + 283 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(75 \, A - 163 \, B + 283 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(75 \, A - 163 \, B + 283 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(75 \, A - 163 \, B + 283 \, C\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(735 \, A - 1495 \, B + 2671 \, C\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(255 \, A - 503 \, B + 911 \, C\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(15 \, A - 25 \, B + 49 \, C\right)} \cos\left(d x + c\right)^{2} + 160 \, {\left(B - C\right)} \cos\left(d x + c\right) + 96 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{960 \, {\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)}}, \frac{15 \, \sqrt{2} {\left({\left(75 \, A - 163 \, B + 283 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(75 \, A - 163 \, B + 283 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(75 \, A - 163 \, B + 283 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(75 \, A - 163 \, B + 283 \, C\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(735 \, A - 1495 \, B + 2671 \, C\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(255 \, A - 503 \, B + 911 \, C\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(15 \, A - 25 \, B + 49 \, C\right)} \cos\left(d x + c\right)^{2} + 160 \, {\left(B - C\right)} \cos\left(d x + c\right) + 96 \, C\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{480 \, {\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)}}\right]"," ",0,"[-1/960*(15*sqrt(2)*((75*A - 163*B + 283*C)*cos(d*x + c)^5 + 3*(75*A - 163*B + 283*C)*cos(d*x + c)^4 + 3*(75*A - 163*B + 283*C)*cos(d*x + c)^3 + (75*A - 163*B + 283*C)*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*((735*A - 1495*B + 2671*C)*cos(d*x + c)^4 + 5*(255*A - 503*B + 911*C)*cos(d*x + c)^3 + 32*(15*A - 25*B + 49*C)*cos(d*x + c)^2 + 160*(B - C)*cos(d*x + c) + 96*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), 1/480*(15*sqrt(2)*((75*A - 163*B + 283*C)*cos(d*x + c)^5 + 3*(75*A - 163*B + 283*C)*cos(d*x + c)^4 + 3*(75*A - 163*B + 283*C)*cos(d*x + c)^3 + (75*A - 163*B + 283*C)*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*((735*A - 1495*B + 2671*C)*cos(d*x + c)^4 + 5*(255*A - 503*B + 911*C)*cos(d*x + c)^3 + 32*(15*A - 25*B + 49*C)*cos(d*x + c)^2 + 160*(B - C)*cos(d*x + c) + 96*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
528,1,593,0,0.505479," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(19 \, A - 75 \, B + 163 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(19 \, A - 75 \, B + 163 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A - 75 \, B + 163 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(19 \, A - 75 \, B + 163 \, C\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(27 \, A - 147 \, B + 299 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A - 255 \, B + 503 \, C\right)} \cos\left(d x + c\right)^{2} - 32 \, {\left(3 \, B - 5 \, C\right)} \cos\left(d x + c\right) - 32 \, C\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(19 \, A - 75 \, B + 163 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(19 \, A - 75 \, B + 163 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A - 75 \, B + 163 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(19 \, A - 75 \, B + 163 \, C\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(27 \, A - 147 \, B + 299 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A - 255 \, B + 503 \, C\right)} \cos\left(d x + c\right)^{2} - 32 \, {\left(3 \, B - 5 \, C\right)} \cos\left(d x + c\right) - 32 \, C\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)*((19*A - 75*B + 163*C)*cos(d*x + c)^4 + 3*(19*A - 75*B + 163*C)*cos(d*x + c)^3 + 3*(19*A - 75*B + 163*C)*cos(d*x + c)^2 + (19*A - 75*B + 163*C)*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*((27*A - 147*B + 299*C)*cos(d*x + c)^3 + (39*A - 255*B + 503*C)*cos(d*x + c)^2 - 32*(3*B - 5*C)*cos(d*x + c) - 32*C)*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)*((19*A - 75*B + 163*C)*cos(d*x + c)^4 + 3*(19*A - 75*B + 163*C)*cos(d*x + c)^3 + 3*(19*A - 75*B + 163*C)*cos(d*x + c)^2 + (19*A - 75*B + 163*C)*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*((27*A - 147*B + 299*C)*cos(d*x + c)^3 + (39*A - 255*B + 503*C)*cos(d*x + c)^2 - 32*(3*B - 5*C)*cos(d*x + c) - 32*C)*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
529,1,516,0,0.509935," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(5 \, A + 19 \, B - 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 19 \, B - 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 19 \, B - 75 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 19 \, B - 75 \, C\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 + 49 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 13 \, B + 85 \, C\right)} \cos\left(d x + c\right) + 32 \, C\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 - 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 19 \, B - 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 19 \, B - 75 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 19 \, B - 75 \, C\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 + 49 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 13 \, B + 85 \, C\right)} \cos\left(d x + c\right) + 32 \, C\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 - 75*C)*cos(d*x + c)^3 + 3*(5*A + 19*B - 75*C)*cos(d*x + c)^2 + 3*(5*A + 19*B - 75*C)*cos(d*x + c) + 5*A + 19*B - 75*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*((A - 9*B + 49*C)*cos(d*x + c)^2 + (5*A - 13*B + 85*C)*cos(d*x + c) + 32*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 - 75*C)*cos(d*x + c)^3 + 3*(5*A + 19*B - 75*C)*cos(d*x + c)^2 + 3*(5*A + 19*B - 75*C)*cos(d*x + c) + 5*A + 19*B - 75*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*((A - 9*B + 49*C)*cos(d*x + c)^2 + (5*A - 13*B + 85*C)*cos(d*x + c) + 32*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
530,1,511,0,0.535728," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(3 \, A + 5 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 5 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 5 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 5 \, B + 19 \, C\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 - 9 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A + 5 \, B - 13 \, C\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 + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 5 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 5 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 5 \, B + 19 \, C\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 - 9 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A + 5 \, B - 13 \, C\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 + 19*C)*cos(d*x + c)^3 + 3*(3*A + 5*B + 19*C)*cos(d*x + c)^2 + 3*(3*A + 5*B + 19*C)*cos(d*x + c) + 3*A + 5*B + 19*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*((7*A + B - 9*C)*cos(d*x + c)^2 + (3*A + 5*B - 13*C)*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 + 19*C)*cos(d*x + c)^3 + 3*(3*A + 5*B + 19*C)*cos(d*x + c)^2 + 3*(3*A + 5*B + 19*C)*cos(d*x + c) + 3*A + 5*B + 19*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*((7*A + B - 9*C)*cos(d*x + c)^2 + (3*A + 5*B - 13*C)*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
531,1,706,0,35.969943," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(43 \, A - 3 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 3 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 3 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 43 \, A - 3 \, B - 5 \, C\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 - C\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, A - 3 \, B - 5 \, C\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 - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 3 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 3 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 43 \, A - 3 \, B - 5 \, C\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 - C\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, A - 3 \, B - 5 \, C\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 - 5*C)*cos(d*x + c)^3 + 3*(43*A - 3*B - 5*C)*cos(d*x + c)^2 + 3*(43*A - 3*B - 5*C)*cos(d*x + c) + 43*A - 3*B - 5*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)) - 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 - C)*cos(d*x + c)^2 + (11*A - 3*B - 5*C)*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 - 5*C)*cos(d*x + c)^3 + 3*(43*A - 3*B - 5*C)*cos(d*x + c)^2 + 3*(43*A - 3*B - 5*C)*cos(d*x + c) + 43*A - 3*B - 5*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))) - 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 - C)*cos(d*x + c)^2 + (11*A - 3*B - 5*C)*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
532,1,774,0,47.706074," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(115 \, A - 43 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, A - 43 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(115 \, A - 43 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 115 \, A - 43 \, B + 3 \, C\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} + {\left(55 \, A - 15 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(35 \, A - 11 \, B + 3 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, A - 43 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(115 \, A - 43 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 115 \, A - 43 \, B + 3 \, C\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} + {\left(55 \, A - 15 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(35 \, A - 11 \, B + 3 \, C\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 + 3*C)*cos(d*x + c)^3 + 3*(115*A - 43*B + 3*C)*cos(d*x + c)^2 + 3*(115*A - 43*B + 3*C)*cos(d*x + c) + 115*A - 43*B + 3*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)) - 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 + (55*A - 15*B + 7*C)*cos(d*x + c)^2 + (35*A - 11*B + 3*C)*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 + 3*C)*cos(d*x + c)^3 + 3*(115*A - 43*B + 3*C)*cos(d*x + c)^2 + 3*(115*A - 43*B + 3*C)*cos(d*x + c) + 115*A - 43*B + 3*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))) - 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 + (55*A - 15*B + 7*C)*cos(d*x + c)^2 + (35*A - 11*B + 3*C)*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
533,1,835,0,84.500643," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(219 \, A - 115 \, B + 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(219 \, A - 115 \, B + 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(219 \, A - 115 \, B + 43 \, C\right)} \cos\left(d x + c\right) + 219 \, A - 115 \, B + 43 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(39 \, A - 20 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(39 \, A - 20 \, B + 8 \, C\right)} \cos\left(d x + c\right) + 39 \, A - 20 \, B + 8 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(63 \, A - 35 \, B + 11 \, C\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 + 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(219 \, A - 115 \, B + 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(219 \, A - 115 \, B + 43 \, C\right)} \cos\left(d x + c\right) + 219 \, A - 115 \, B + 43 \, C\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 + 8 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(39 \, A - 20 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(39 \, A - 20 \, B + 8 \, C\right)} \cos\left(d x + c\right) + 39 \, A - 20 \, B + 8 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(63 \, A - 35 \, B + 11 \, C\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 + 43*C)*cos(d*x + c)^3 + 3*(219*A - 115*B + 43*C)*cos(d*x + c)^2 + 3*(219*A - 115*B + 43*C)*cos(d*x + c) + 219*A - 115*B + 43*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)) + 8*((39*A - 20*B + 8*C)*cos(d*x + c)^3 + 3*(39*A - 20*B + 8*C)*cos(d*x + c)^2 + 3*(39*A - 20*B + 8*C)*cos(d*x + c) + 39*A - 20*B + 8*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)) - 4*(8*A*cos(d*x + c)^4 - 4*(5*A - 4*B)*cos(d*x + c)^3 - 5*(19*A - 11*B + 3*C)*cos(d*x + c)^2 - (63*A - 35*B + 11*C)*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 + 43*C)*cos(d*x + c)^3 + 3*(219*A - 115*B + 43*C)*cos(d*x + c)^2 + 3*(219*A - 115*B + 43*C)*cos(d*x + c) + 219*A - 115*B + 43*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))) - 8*((39*A - 20*B + 8*C)*cos(d*x + c)^3 + 3*(39*A - 20*B + 8*C)*cos(d*x + c)^2 + 3*(39*A - 20*B + 8*C)*cos(d*x + c) + 39*A - 20*B + 8*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))) + 2*(8*A*cos(d*x + c)^4 - 4*(5*A - 4*B)*cos(d*x + c)^3 - 5*(19*A - 11*B + 3*C)*cos(d*x + c)^2 - (63*A - 35*B + 11*C)*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
534,0,0,0,0.452493," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \sec\left(d x + c\right)^{4} + {\left(B + C\right)} 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((C*a*sec(d*x + c)^4 + (B + C)*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
535,0,0,0,0.452967," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*sec(d*x + c)^3 + (B + C)*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)*sqrt(sec(d*x + c)), x)","F",0
536,0,0,0,0.473015," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*sec(d*x + c)^3 + (B + C)*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sqrt(sec(d*x + c)), x)","F",0
537,0,0,0,0.460505," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*sec(d*x + c)^3 + (B + C)*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sec(d*x + c)^(3/2), x)","F",0
538,0,0,0,0.448214," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*sec(d*x + c)^3 + (B + C)*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sec(d*x + c)^(5/2), x)","F",0
539,0,0,0,0.460707," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*sec(d*x + c)^3 + (B + C)*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sec(d*x + c)^(7/2), x)","F",0
540,0,0,0,0.486919," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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{9}{2}}}, x\right)"," ",0,"integral((C*a*sec(d*x + c)^3 + (B + C)*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sec(d*x + c)^(9/2), x)","F",0
541,0,0,0,0.534434," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \sec\left(d x + c\right)^{5} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{4} + {\left(A + 2 \, B + C\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((C*a^2*sec(d*x + c)^5 + (B + 2*C)*a^2*sec(d*x + c)^4 + (A + 2*B + C)*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
542,0,0,0,0.458550," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*sec(d*x + c)^4 + (B + 2*C)*a^2*sec(d*x + c)^3 + (A + 2*B + C)*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
543,0,0,0,0.463497," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*sec(d*x + c)^4 + (B + 2*C)*a^2*sec(d*x + c)^3 + (A + 2*B + C)*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
544,0,0,0,0.466152," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*sec(d*x + c)^4 + (B + 2*C)*a^2*sec(d*x + c)^3 + (A + 2*B + C)*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
545,0,0,0,0.452934," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*sec(d*x + c)^4 + (B + 2*C)*a^2*sec(d*x + c)^3 + (A + 2*B + C)*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
546,0,0,0,0.456388," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*sec(d*x + c)^4 + (B + 2*C)*a^2*sec(d*x + c)^3 + (A + 2*B + C)*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
547,0,0,0,0.463916," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*sec(d*x + c)^4 + (B + 2*C)*a^2*sec(d*x + c)^3 + (A + 2*B + C)*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
548,0,0,0,0.468355," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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{11}{2}}}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + (B + 2*C)*a^2*sec(d*x + c)^3 + (A + 2*B + C)*a^2*sec(d*x + c)^2 + (2*A + B)*a^2*sec(d*x + c) + A*a^2)/sec(d*x + c)^(11/2), x)","F",0
549,0,0,0,0.456498," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \sec\left(d x + c\right)^{6} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{5} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(3 \, A + 3 \, B + C\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((C*a^3*sec(d*x + c)^6 + (B + 3*C)*a^3*sec(d*x + c)^5 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^4 + (3*A + 3*B + C)*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
550,0,0,0,0.453364," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*sec(d*x + c)^5 + (B + 3*C)*a^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^3 + (3*A + 3*B + C)*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
551,0,0,0,0.494320," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*sec(d*x + c)^5 + (B + 3*C)*a^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^3 + (3*A + 3*B + C)*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
552,0,0,0,0.464107," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*sec(d*x + c)^5 + (B + 3*C)*a^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^3 + (3*A + 3*B + C)*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
553,0,0,0,0.450312," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*sec(d*x + c)^5 + (B + 3*C)*a^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^3 + (3*A + 3*B + C)*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
554,0,0,0,0.462211," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*sec(d*x + c)^5 + (B + 3*C)*a^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^3 + (3*A + 3*B + C)*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
555,0,0,0,0.469262," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*sec(d*x + c)^5 + (B + 3*C)*a^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^3 + (3*A + 3*B + C)*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
556,0,0,0,0.502338," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*sec(d*x + c)^5 + (B + 3*C)*a^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^3 + (3*A + 3*B + C)*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
557,0,0,0,0.508268," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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{13}{2}}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + (B + 3*C)*a^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^3 + (3*A + 3*B + C)*a^3*sec(d*x + c)^2 + (3*A + B)*a^3*sec(d*x + c) + A*a^3)/sec(d*x + c)^(13/2), x)","F",0
558,0,0,0,0.467628," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + 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
559,0,0,0,0.466223," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + 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
560,0,0,0,0.462582," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
561,0,0,0,0.444649," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
562,0,0,0,0.461298," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
563,0,0,0,0.480318," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
564,0,0,0,0.465723," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{5} + a \sec\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
565,0,0,0,0.466079," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + 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
566,0,0,0,0.451435," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + 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
567,0,0,0,0.441730," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
568,0,0,0,0.442960," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
569,0,0,0,0.478901," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
570,0,0,0,0.477845," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
571,0,0,0,0.456144," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{5} + 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((C*sec(d*x + c)^5 + 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
572,0,0,0,0.437035," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + 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
573,0,0,0,0.443795," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + 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
574,0,0,0,0.452873," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
575,0,0,0,0.462831," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
576,0,0,0,0.490947," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
577,0,0,0,0.598494," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
578,1,506,0,1.167278," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(48 \, A + 40 \, B + 35 \, C\right)} \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(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 48 \, C\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(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(48 \, A + 40 \, B + 35 \, C\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) + \frac{2 \, {\left(3 \, {\left(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 48 \, C\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*((48*A + 40*B + 35*C)*cos(d*x + c)^4 + (48*A + 40*B + 35*C)*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*(48*A + 40*B + 35*C)*cos(d*x + c)^3 + 2*(48*A + 40*B + 35*C)*cos(d*x + c)^2 + 8*(8*B + 7*C)*cos(d*x + c) + 48*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)^4 + d*cos(d*x + c)^3), 1/384*(3*((48*A + 40*B + 35*C)*cos(d*x + c)^4 + (48*A + 40*B + 35*C)*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*(48*A + 40*B + 35*C)*cos(d*x + c)^3 + 2*(48*A + 40*B + 35*C)*cos(d*x + c)^2 + 8*(8*B + 7*C)*cos(d*x + c) + 48*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)^4 + d*cos(d*x + c)^3)]","A",0
579,1,466,0,0.851018," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, A + 6 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 6 \, B + 5 \, C\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(8 \, A + 6 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 8 \, C\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(8 \, A + 6 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 6 \, B + 5 \, C\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(8 \, A + 6 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 8 \, C\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*((8*A + 6*B + 5*C)*cos(d*x + c)^3 + (8*A + 6*B + 5*C)*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*(8*A + 6*B + 5*C)*cos(d*x + c)^2 + 2*(6*B + 5*C)*cos(d*x + c) + 8*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)^3 + d*cos(d*x + c)^2), 1/48*(3*((8*A + 6*B + 5*C)*cos(d*x + c)^3 + (8*A + 6*B + 5*C)*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*(8*A + 6*B + 5*C)*cos(d*x + c)^2 + 2*(6*B + 5*C)*cos(d*x + c) + 8*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)^3 + d*cos(d*x + c)^2)]","A",0
580,1,414,0,0.832592," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, A + 4 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 4 \, B + 3 \, C\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 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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(8 \, A + 4 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 4 \, B + 3 \, C\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 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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*(((8*A + 4*B + 3*C)*cos(d*x + c)^2 + (8*A + 4*B + 3*C)*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*B + 3*C)*cos(d*x + c) + 2*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)^2 + d*cos(d*x + c)), 1/8*(((8*A + 4*B + 3*C)*cos(d*x + c)^2 + (8*A + 4*B + 3*C)*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*B + 3*C)*cos(d*x + c) + 2*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)^2 + d*cos(d*x + c))]","A",0
581,1,342,0,0.567849," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, B + C\right)} \cos\left(d x + c\right) + 2 \, B + C\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 \cos\left(d x + c\right) + C\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 \, B + C\right)} \cos\left(d x + c\right) + 2 \, B + C\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 \cos\left(d x + c\right) + C\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*B + C)*cos(d*x + c) + 2*B + 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*(2*A*cos(d*x + c) + 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), 1/2*(((2*B + C)*cos(d*x + c) + 2*B + 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*(2*A*cos(d*x + c) + 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
582,1,358,0,0.491490," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(C \cos\left(d x + c\right) + C\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 \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)}{\sqrt{\cos\left(d x + c\right)}}}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{3 \, {\left(C \cos\left(d x + c\right) + C\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 \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)}{\sqrt{\cos\left(d x + c\right)}}}{3 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/6*(3*(C*cos(d*x + c) + 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*(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)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d), 1/3*(3*(C*cos(d*x + c) + 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*(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)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)]","A",0
583,1,94,0,0.460721," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""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} + {\left(8 \, A + 10 \, B + 15 \, C\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 + (8*A + 10*B + 15*C)*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
584,1,115,0,0.432842," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""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} + {\left(24 \, A + 28 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(24 \, A + 28 \, B + 35 \, C\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 + (24*A + 28*B + 35*C)*cos(d*x + c)^2 + 2*(24*A + 28*B + 35*C)*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
585,1,136,0,0.443584," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A \cos\left(d x + c\right)^{5} + 5 \, {\left(8 \, A + 9 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(16 \, A + 18 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(16 \, A + 18 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, A + 18 \, B + 21 \, C\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)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/315*(35*A*cos(d*x + c)^5 + 5*(8*A + 9*B)*cos(d*x + c)^4 + 3*(16*A + 18*B + 21*C)*cos(d*x + c)^3 + 4*(16*A + 18*B + 21*C)*cos(d*x + c)^2 + 8*(16*A + 18*B + 21*C)*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
586,1,560,0,1.147373," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{5} + {\left(176 \, A + 150 \, B + 133 \, C\right)} a \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(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{4} + 10 \, {\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, B + 19 \, C\right)} a \cos\left(d x + c\right) + 384 \, C 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)}}}{7680 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}, \frac{15 \, {\left({\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{5} + {\left(176 \, A + 150 \, B + 133 \, C\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) + \frac{2 \, {\left(15 \, {\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{4} + 10 \, {\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, B + 19 \, C\right)} a \cos\left(d x + c\right) + 384 \, C 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)}}}{3840 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/7680*(15*((176*A + 150*B + 133*C)*a*cos(d*x + c)^5 + (176*A + 150*B + 133*C)*a*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*(176*A + 150*B + 133*C)*a*cos(d*x + c)^4 + 10*(176*A + 150*B + 133*C)*a*cos(d*x + c)^3 + 8*(80*A + 150*B + 133*C)*a*cos(d*x + c)^2 + 48*(10*B + 19*C)*a*cos(d*x + c) + 384*C*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)^5 + d*cos(d*x + c)^4), 1/3840*(15*((176*A + 150*B + 133*C)*a*cos(d*x + c)^5 + (176*A + 150*B + 133*C)*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)) + 2*(15*(176*A + 150*B + 133*C)*a*cos(d*x + c)^4 + 10*(176*A + 150*B + 133*C)*a*cos(d*x + c)^3 + 8*(80*A + 150*B + 133*C)*a*cos(d*x + c)^2 + 48*(10*B + 19*C)*a*cos(d*x + c) + 384*C*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)^5 + d*cos(d*x + c)^4)]","A",0
587,1,518,0,1.163573," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(112 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(112 \, A + 88 \, B + 75 \, C\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(112 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 15 \, C\right)} a \cos\left(d x + c\right) + 48 \, C 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(112 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(112 \, A + 88 \, B + 75 \, C\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(112 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 15 \, C\right)} a \cos\left(d x + c\right) + 48 \, C 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*((112*A + 88*B + 75*C)*a*cos(d*x + c)^4 + (112*A + 88*B + 75*C)*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*(112*A + 88*B + 75*C)*a*cos(d*x + c)^3 + 2*(48*A + 88*B + 75*C)*a*cos(d*x + c)^2 + 8*(8*B + 15*C)*a*cos(d*x + c) + 48*C*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*((112*A + 88*B + 75*C)*a*cos(d*x + c)^4 + (112*A + 88*B + 75*C)*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*(112*A + 88*B + 75*C)*a*cos(d*x + c)^3 + 2*(48*A + 88*B + 75*C)*a*cos(d*x + c)^2 + 8*(8*B + 15*C)*a*cos(d*x + c) + 48*C*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
588,1,476,0,0.833293," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(24 \, A + 14 \, B + 11 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(24 \, A + 14 \, B + 11 \, C\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(8 \, A + 14 \, B + 11 \, C\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 11 \, C\right)} a \cos\left(d x + c\right) + 8 \, C 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(24 \, A + 14 \, B + 11 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(24 \, A + 14 \, B + 11 \, C\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(8 \, A + 14 \, B + 11 \, C\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 11 \, C\right)} a \cos\left(d x + c\right) + 8 \, C 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*((24*A + 14*B + 11*C)*a*cos(d*x + c)^3 + (24*A + 14*B + 11*C)*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*(8*A + 14*B + 11*C)*a*cos(d*x + c)^2 + 2*(6*B + 11*C)*a*cos(d*x + c) + 8*C*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*((24*A + 14*B + 11*C)*a*cos(d*x + c)^3 + (24*A + 14*B + 11*C)*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*(8*A + 14*B + 11*C)*a*cos(d*x + c)^2 + 2*(6*B + 11*C)*a*cos(d*x + c) + 8*C*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
589,1,446,0,0.856170," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, A + 12 \, B + 7 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(8 \, A + 12 \, B + 7 \, C\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(8 \, A a \cos\left(d x + c\right)^{2} + {\left(4 \, B + 7 \, C\right)} a \cos\left(d x + c\right) + 2 \, C 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(8 \, A + 12 \, B + 7 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(8 \, A + 12 \, B + 7 \, C\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(8 \, A a \cos\left(d x + c\right)^{2} + {\left(4 \, B + 7 \, C\right)} a \cos\left(d x + c\right) + 2 \, C 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*(((8*A + 12*B + 7*C)*a*cos(d*x + c)^2 + (8*A + 12*B + 7*C)*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*(8*A*a*cos(d*x + c)^2 + (4*B + 7*C)*a*cos(d*x + c) + 2*C*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*(((8*A + 12*B + 7*C)*a*cos(d*x + c)^2 + (8*A + 12*B + 7*C)*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*(8*A*a*cos(d*x + c)^2 + (4*B + 7*C)*a*cos(d*x + c) + 2*C*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
590,1,404,0,0.587133," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(2 \, B + 3 \, C\right)} a \cos\left(d x + c\right) + {\left(2 \, B + 3 \, C\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)^{2} + 2 \, {\left(5 \, A + 3 \, B\right)} a \cos\left(d x + c\right) + 3 \, C 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)}}}{12 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{3 \, {\left({\left(2 \, B + 3 \, C\right)} a \cos\left(d x + c\right) + {\left(2 \, B + 3 \, C\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)^{2} + 2 \, {\left(5 \, A + 3 \, B\right)} a \cos\left(d x + c\right) + 3 \, C 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)}}}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/12*(3*((2*B + 3*C)*a*cos(d*x + c) + (2*B + 3*C)*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)^2 + 2*(5*A + 3*B)*a*cos(d*x + c) + 3*C*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), 1/6*(3*((2*B + 3*C)*a*cos(d*x + c) + (2*B + 3*C)*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)^2 + 2*(5*A + 3*B)*a*cos(d*x + c) + 3*C*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
591,1,410,0,0.526548," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(C a \cos\left(d x + c\right) + C 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(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 + 15 \, C\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)}}}{30 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{15 \, {\left(C a \cos\left(d x + c\right) + C 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(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 + 15 \, C\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)}}}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/30*(15*(C*a*cos(d*x + c) + C*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*(3*A*a*cos(d*x + c)^3 + (9*A + 5*B)*a*cos(d*x + c)^2 + (18*A + 25*B + 15*C)*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), 1/15*(15*(C*a*cos(d*x + c) + C*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*(3*A*a*cos(d*x + c)^3 + (9*A + 5*B)*a*cos(d*x + c)^2 + (18*A + 25*B + 15*C)*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
592,1,118,0,0.442734," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""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 + 35 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(104 \, A + 126 \, B + 175 \, C\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 + 35*C)*a*cos(d*x + c)^2 + (104*A + 126*B + 175*C)*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
593,1,140,0,0.435089," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""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 + 21 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(136 \, A + 156 \, B + 189 \, C\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(136 \, A + 156 \, B + 189 \, C\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 + 21*C)*a*cos(d*x + c)^3 + (136*A + 156*B + 189*C)*a*cos(d*x + c)^2 + 2*(136*A + 156*B + 189*C)*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
594,1,162,0,0.438225," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, A a \cos\left(d x + c\right)^{6} + 35 \, {\left(21 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{5} + 5 \, {\left(168 \, A + 187 \, B + 99 \, C\right)} a \cos\left(d x + c\right)^{4} + 3 \, {\left(336 \, A + 374 \, B + 429 \, C\right)} a \cos\left(d x + c\right)^{3} + 4 \, {\left(336 \, A + 374 \, B + 429 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(336 \, A + 374 \, B + 429 \, C\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)}{3465 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/3465*(315*A*a*cos(d*x + c)^6 + 35*(21*A + 11*B)*a*cos(d*x + c)^5 + 5*(168*A + 187*B + 99*C)*a*cos(d*x + c)^4 + 3*(336*A + 374*B + 429*C)*a*cos(d*x + c)^3 + 4*(336*A + 374*B + 429*C)*a*cos(d*x + c)^2 + 8*(336*A + 374*B + 429*C)*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
595,1,634,0,1.156721," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{5}\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(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 10 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(920 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 48 \, {\left(40 \, A + 116 \, B + 145 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 128 \, {\left(12 \, B + 35 \, C\right)} a^{2} \cos\left(d x + c\right) + 1280 \, C 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)}}}{30720 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}, \frac{15 \, {\left({\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(1304 \, A + 1132 \, B + 1015 \, C\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) + \frac{2 \, {\left(15 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 10 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(920 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 48 \, {\left(40 \, A + 116 \, B + 145 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 128 \, {\left(12 \, B + 35 \, C\right)} a^{2} \cos\left(d x + c\right) + 1280 \, C 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)}}}{15360 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}\right]"," ",0,"[1/30720*(15*((1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^6 + (1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^5)*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*(1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^5 + 10*(1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^4 + 8*(920*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^3 + 48*(40*A + 116*B + 145*C)*a^2*cos(d*x + c)^2 + 128*(12*B + 35*C)*a^2*cos(d*x + c) + 1280*C*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)^6 + d*cos(d*x + c)^5), 1/15360*(15*((1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^6 + (1304*A + 1132*B + 1015*C)*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)) + 2*(15*(1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^5 + 10*(1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^4 + 8*(920*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^3 + 48*(40*A + 116*B + 145*C)*a^2*cos(d*x + c)^2 + 128*(12*B + 35*C)*a^2*cos(d*x + c) + 1280*C*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)^6 + d*cos(d*x + c)^5)]","A",0
596,1,588,0,1.156405," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(400 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(400 \, A + 326 \, B + 283 \, C\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(400 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(272 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 230 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, B + 29 \, C\right)} a^{2} \cos\left(d x + c\right) + 384 \, C 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(400 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(400 \, A + 326 \, B + 283 \, C\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(400 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(272 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 230 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, B + 29 \, C\right)} a^{2} \cos\left(d x + c\right) + 384 \, C 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*((400*A + 326*B + 283*C)*a^2*cos(d*x + c)^5 + (400*A + 326*B + 283*C)*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*(400*A + 326*B + 283*C)*a^2*cos(d*x + c)^4 + 10*(272*A + 326*B + 283*C)*a^2*cos(d*x + c)^3 + 8*(80*A + 230*B + 283*C)*a^2*cos(d*x + c)^2 + 48*(10*B + 29*C)*a^2*cos(d*x + c) + 384*C*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*((400*A + 326*B + 283*C)*a^2*cos(d*x + c)^5 + (400*A + 326*B + 283*C)*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*(400*A + 326*B + 283*C)*a^2*cos(d*x + c)^4 + 10*(272*A + 326*B + 283*C)*a^2*cos(d*x + c)^3 + 8*(80*A + 230*B + 283*C)*a^2*cos(d*x + c)^2 + 48*(10*B + 29*C)*a^2*cos(d*x + c) + 384*C*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
597,1,542,0,1.185044," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(304 \, A + 200 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(304 \, A + 200 \, B + 163 \, C\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(176 \, A + 200 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 136 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 23 \, C\right)} a^{2} \cos\left(d x + c\right) + 48 \, C 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(304 \, A + 200 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(304 \, A + 200 \, B + 163 \, C\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(176 \, A + 200 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 136 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 23 \, C\right)} a^{2} \cos\left(d x + c\right) + 48 \, C 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*((304*A + 200*B + 163*C)*a^2*cos(d*x + c)^4 + (304*A + 200*B + 163*C)*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*(176*A + 200*B + 163*C)*a^2*cos(d*x + c)^3 + 2*(48*A + 136*B + 163*C)*a^2*cos(d*x + c)^2 + 8*(8*B + 23*C)*a^2*cos(d*x + c) + 48*C*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*((304*A + 200*B + 163*C)*a^2*cos(d*x + c)^4 + (304*A + 200*B + 163*C)*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*(176*A + 200*B + 163*C)*a^2*cos(d*x + c)^3 + 2*(48*A + 136*B + 163*C)*a^2*cos(d*x + c)^2 + 8*(8*B + 23*C)*a^2*cos(d*x + c) + 48*C*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
598,1,524,0,0.851094," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(40 \, A + 38 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(40 \, A + 38 \, B + 25 \, C\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(48 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 22 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 17 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, C 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(40 \, A + 38 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(40 \, A + 38 \, B + 25 \, C\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(48 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 22 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 17 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, C 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*((40*A + 38*B + 25*C)*a^2*cos(d*x + c)^3 + (40*A + 38*B + 25*C)*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*(48*A*a^2*cos(d*x + c)^3 + 3*(8*A + 22*B + 25*C)*a^2*cos(d*x + c)^2 + 2*(6*B + 17*C)*a^2*cos(d*x + c) + 8*C*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*((40*A + 38*B + 25*C)*a^2*cos(d*x + c)^3 + (40*A + 38*B + 25*C)*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*(48*A*a^2*cos(d*x + c)^3 + 3*(8*A + 22*B + 25*C)*a^2*cos(d*x + c)^2 + 2*(6*B + 17*C)*a^2*cos(d*x + c) + 8*C*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
599,1,510,0,0.861563," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, A + 20 \, B + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 20 \, B + 19 \, C\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)^{3} + 8 \, {\left(8 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right) + 6 \, C 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)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{3 \, {\left({\left(8 \, A + 20 \, B + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 20 \, B + 19 \, C\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)^{3} + 8 \, {\left(8 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right) + 6 \, C 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)}}}{24 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/48*(3*((8*A + 20*B + 19*C)*a^2*cos(d*x + c)^2 + (8*A + 20*B + 19*C)*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)^3 + 8*(8*A + 3*B)*a^2*cos(d*x + c)^2 + 3*(4*B + 11*C)*a^2*cos(d*x + c) + 6*C*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)), 1/24*(3*((8*A + 20*B + 19*C)*a^2*cos(d*x + c)^2 + (8*A + 20*B + 19*C)*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)^3 + 8*(8*A + 3*B)*a^2*cos(d*x + c)^2 + 3*(4*B + 11*C)*a^2*cos(d*x + c) + 6*C*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
600,1,470,0,0.662040," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(2 \, B + 5 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(2 \, B + 5 \, C\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(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(43 \, A + 40 \, B + 15 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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)}}}{60 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{15 \, {\left({\left(2 \, B + 5 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(2 \, B + 5 \, C\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(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(43 \, A + 40 \, B + 15 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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)}}}{30 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/60*(15*((2*B + 5*C)*a^2*cos(d*x + c) + (2*B + 5*C)*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*(6*A*a^2*cos(d*x + c)^3 + 2*(14*A + 5*B)*a^2*cos(d*x + c)^2 + 2*(43*A + 40*B + 15*C)*a^2*cos(d*x + c) + 15*C*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), 1/30*(15*((2*B + 5*C)*a^2*cos(d*x + c) + (2*B + 5*C)*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*(6*A*a^2*cos(d*x + c)^3 + 2*(14*A + 5*B)*a^2*cos(d*x + c)^2 + 2*(43*A + 40*B + 15*C)*a^2*cos(d*x + c) + 15*C*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
601,1,476,0,0.540720," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(C a^{2} \cos\left(d x + c\right) + C 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(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 + 35 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(230 \, A + 301 \, B + 280 \, C\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)}}}{210 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{105 \, {\left(C a^{2} \cos\left(d x + c\right) + C 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(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 + 35 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(230 \, A + 301 \, B + 280 \, C\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)}}}{105 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/210*(105*(C*a^2*cos(d*x + c) + C*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*(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 + 35*C)*a^2*cos(d*x + c)^2 + (230*A + 301*B + 280*C)*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), 1/105*(105*(C*a^2*cos(d*x + c) + C*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*(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 + 35*C)*a^2*cos(d*x + c)^2 + (230*A + 301*B + 280*C)*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
602,1,149,0,0.438582," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""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 + 21 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(292 \, A + 345 \, B + 294 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(584 \, A + 690 \, B + 903 \, C\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 + 21*C)*a^2*cos(d*x + c)^3 + (292*A + 345*B + 294*C)*a^2*cos(d*x + c)^2 + (584*A + 690*B + 903*C)*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
603,1,173,0,0.463898," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""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 + 99 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(710 \, A + 803 \, B + 660 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(2840 \, A + 3212 \, B + 3795 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(2840 \, A + 3212 \, B + 3795 \, C\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 + 99*C)*a^2*cos(d*x + c)^4 + 3*(710*A + 803*B + 660*C)*a^2*cos(d*x + c)^3 + (2840*A + 3212*B + 3795*C)*a^2*cos(d*x + c)^2 + 2*(2840*A + 3212*B + 3795*C)*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
604,1,197,0,0.441028," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, A a^{2} \cos\left(d x + c\right)^{7} + 315 \, {\left(38 \, A + 13 \, B\right)} a^{2} \cos\left(d x + c\right)^{6} + 35 \, {\left(523 \, A + 416 \, B + 143 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 5 \, {\left(4184 \, A + 4615 \, B + 3718 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 4 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\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)}{45045 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/45045*(3465*A*a^2*cos(d*x + c)^7 + 315*(38*A + 13*B)*a^2*cos(d*x + c)^6 + 35*(523*A + 416*B + 143*C)*a^2*cos(d*x + c)^5 + 5*(4184*A + 4615*B + 3718*C)*a^2*cos(d*x + c)^4 + 3*(8368*A + 9230*B + 10439*C)*a^2*cos(d*x + c)^3 + 4*(8368*A + 9230*B + 10439*C)*a^2*cos(d*x + c)^2 + 8*(8368*A + 9230*B + 10439*C)*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
605,1,689,0,0.924803," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, A - 14 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A - 14 \, B + 9 \, C\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{48 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B + C\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}} + \frac{4 \, {\left(3 \, {\left(8 \, A - 2 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B - C\right)} \cos\left(d x + c\right) + 8 \, C\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 d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}, -\frac{48 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B + C\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) + 3 \, {\left({\left(8 \, A - 14 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A - 14 \, B + 9 \, C\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(8 \, A - 2 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B - C\right)} \cos\left(d x + c\right) + 8 \, C\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(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/96*(3*((8*A - 14*B + 9*C)*cos(d*x + c)^3 + (8*A - 14*B + 9*C)*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)) + 48*sqrt(2)*((A - B + C)*a*cos(d*x + c)^3 + (A - B + C)*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) + 4*(3*(8*A - 2*B + 7*C)*cos(d*x + c)^2 + 2*(6*B - C)*cos(d*x + c) + 8*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)^3 + a*d*cos(d*x + c)^2), -1/48*(48*sqrt(2)*((A - B + C)*a*cos(d*x + c)^3 + (A - B + C)*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)) + 3*((8*A - 14*B + 9*C)*cos(d*x + c)^3 + (8*A - 14*B + 9*C)*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*(8*A - 2*B + 7*C)*cos(d*x + c)^2 + 2*(6*B - C)*cos(d*x + c) + 8*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)^3 + a*d*cos(d*x + c)^2)]","A",0
606,1,633,0,0.917998," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, A - 4 \, B + 7 \, C\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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B + C\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 \, B - C\right)} \cos\left(d x + c\right) + 2 \, C\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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B + C\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(8 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, A - 4 \, B + 7 \, C\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 \, B - C\right)} \cos\left(d x + c\right) + 2 \, C\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*(((8*A - 4*B + 7*C)*cos(d*x + c)^2 + (8*A - 4*B + 7*C)*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 + C)*a*cos(d*x + c)^2 + (A - B + C)*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*B - C)*cos(d*x + c) + 2*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)^2 + a*d*cos(d*x + c)), 1/8*(8*sqrt(2)*((A - B + C)*a*cos(d*x + c)^2 + (A - B + C)*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)) + ((8*A - 4*B + 7*C)*cos(d*x + c)^2 + (8*A - 4*B + 7*C)*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*B - C)*cos(d*x + c) + 2*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)^2 + a*d*cos(d*x + c))]","A",0
607,1,536,0,0.609773," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, B - C\right)} \cos\left(d x + c\right) + 2 \, B - C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 \, C \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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 \, B - C\right)} \cos\left(d x + c\right) + 2 \, B - C\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 \, C \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*B - C)*cos(d*x + c) + 2*B - 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)) - 2*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*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*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), -1/2*(2*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*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*B - C)*cos(d*x + c) + 2*B - 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*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
608,1,510,0,0.511163," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""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(C \cos\left(d x + c\right) + C\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{\sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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) + {\left(C \cos\left(d x + c\right) + C\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)}{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) + (C*cos(d*x + c) + 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)) + sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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) + (C*cos(d*x + c) + 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) + a*d)]","A",0
609,1,358,0,0.472452," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\frac{3 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C)*a*cos(d*x + c) + (A - B + C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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
610,1,398,0,0.468655," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\frac{15 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + 15 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + 15 \, C\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 + C)*a*cos(d*x + c) + (A - B + C)*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 + 15*C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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 + 15*C)*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
611,1,438,0,0.472026," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\frac{105 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + 35 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(43 \, A - 91 \, B + 35 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + 35 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(43 \, A - 91 \, B + 35 \, C\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 + C)*a*cos(d*x + c) + (A - B + C)*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 + 35*C)*cos(d*x + c)^2 - (43*A - 91*B + 35*C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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 + 35*C)*cos(d*x + c)^2 - (43*A - 91*B + 35*C)*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
612,1,611,0,0.981594," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\frac{4 \, B 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)}} - {\left(2 \, B a + {\left(2 \, A - B\right)} b + {\left(2 \, B a + {\left(2 \, A - B\right)} 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{2 \, \sqrt{2} {\left({\left(A - B\right)} a^{2} - {\left(A - B\right)} a b + {\left({\left(A - B\right)} a^{2} - {\left(A - B\right)} a b\right)} \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) + a d\right)}}, -\frac{2 \, \sqrt{2} {\left({\left(A - B\right)} a^{2} - {\left(A - B\right)} a b + {\left({\left(A - B\right)} a^{2} - {\left(A - B\right)} a b\right)} \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) - \frac{2 \, B 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)}} - {\left(2 \, B a + {\left(2 \, A - B\right)} b + {\left(2 \, B a + {\left(2 \, A - B\right)} 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) + a d\right)}}\right]"," ",0,"[1/4*(4*B*b*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) - (2*B*a + (2*A - B)*b + (2*B*a + (2*A - B)*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)) + 2*sqrt(2)*((A - B)*a^2 - (A - B)*a*b + ((A - B)*a^2 - (A - B)*a*b)*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) + a*d), -1/2*(2*sqrt(2)*((A - B)*a^2 - (A - B)*a*b + ((A - B)*a^2 - (A - B)*a*b)*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*b*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) - (2*B*a + (2*A - B)*b + (2*B*a + (2*A - B)*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) + a*d)]","B",0
613,1,805,0,1.103954," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{2} {\left({\left(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 9 \, B + 13 \, C\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(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, A - 12 \, B + 19 \, C\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(2 \, A - 6 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(4 \, B - 3 \, C\right)} \cos\left(d x + c\right) - 2 \, C\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(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 9 \, B + 13 \, C\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(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, A - 12 \, B + 19 \, C\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(2 \, A - 6 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(4 \, B - 3 \, C\right)} \cos\left(d x + c\right) - 2 \, C\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)*((5*A - 9*B + 13*C)*cos(d*x + c)^3 + 2*(5*A - 9*B + 13*C)*cos(d*x + c)^2 + (5*A - 9*B + 13*C)*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)) + ((8*A - 12*B + 19*C)*cos(d*x + c)^3 + 2*(8*A - 12*B + 19*C)*cos(d*x + c)^2 + (8*A - 12*B + 19*C)*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*((2*A - 6*B + 7*C)*cos(d*x + c)^2 - (4*B - 3*C)*cos(d*x + c) - 2*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)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c)), 1/8*(2*sqrt(2)*((5*A - 9*B + 13*C)*cos(d*x + c)^3 + 2*(5*A - 9*B + 13*C)*cos(d*x + c)^2 + (5*A - 9*B + 13*C)*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))) + ((8*A - 12*B + 19*C)*cos(d*x + c)^3 + 2*(8*A - 12*B + 19*C)*cos(d*x + c)^2 + (8*A - 12*B + 19*C)*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*((2*A - 6*B + 7*C)*cos(d*x + c)^2 - (4*B - 3*C)*cos(d*x + c) - 2*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)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))]","A",0
614,1,681,0,0.677799," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right) + A - 5 \, B + 9 \, C\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 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 2 \, B - 3 \, C\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 - B + 3 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right) + A - 5 \, B + 9 \, C\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 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 2 \, B - 3 \, C\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 - B + 3 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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)*((A - 5*B + 9*C)*cos(d*x + c)^2 + 2*(A - 5*B + 9*C)*cos(d*x + c) + A - 5*B + 9*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)) - 2*((2*B - 3*C)*cos(d*x + c)^2 + 2*(2*B - 3*C)*cos(d*x + c) + 2*B - 3*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*((A - B + 3*C)*cos(d*x + c) + 2*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)*((A - 5*B + 9*C)*cos(d*x + c)^2 + 2*(A - 5*B + 9*C)*cos(d*x + c) + A - 5*B + 9*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*((2*B - 3*C)*cos(d*x + c)^2 + 2*(2*B - 3*C)*cos(d*x + c) + 2*B - 3*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*((A - B + 3*C)*cos(d*x + c) + 2*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
615,1,621,0,0.545956," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A + B - 5 \, C\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 + C\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(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A + B - 5 \, C\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 + C\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(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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)*((3*A + B - 5*C)*cos(d*x + c)^2 + 2*(3*A + B - 5*C)*cos(d*x + c) + 3*A + B - 5*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 - B + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + 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)))/(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 - 5*C)*cos(d*x + c)^2 + 2*(3*A + B - 5*C)*cos(d*x + c) + 3*A + B - 5*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 - B + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + 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)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","B",0
616,1,450,0,0.488024," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(7 \, A - 3 \, B - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 3 \, B - C\right)} \cos\left(d x + c\right) + 7 \, A - 3 \, B - C\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 + C\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 - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 3 \, B - C\right)} \cos\left(d x + c\right) + 7 \, A - 3 \, B - C\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 + C\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 - C)*cos(d*x + c)^2 + 2*(7*A - 3*B - C)*cos(d*x + c) + 7*A - 3*B - 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*(4*A*cos(d*x + c)^2 + (5*A - B + C)*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 - C)*cos(d*x + c)^2 + 2*(7*A - 3*B - C)*cos(d*x + c) + 7*A - 3*B - 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*(4*A*cos(d*x + c)^2 + (5*A - B + C)*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
617,1,488,0,0.505538," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(11 \, A - 7 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A - 7 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 11 \, A - 7 \, B + 3 \, C\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 + 3 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A - 7 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 11 \, A - 7 \, B + 3 \, C\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 + 3 \, C\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 + 3*C)*cos(d*x + c)^2 + 2*(11*A - 7*B + 3*C)*cos(d*x + c) + 11*A - 7*B + 3*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*(4*A*cos(d*x + c)^3 - 12*(A - B)*cos(d*x + c)^2 - (19*A - 15*B + 3*C)*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 + 3*C)*cos(d*x + c)^2 + 2*(11*A - 7*B + 3*C)*cos(d*x + c) + 11*A - 7*B + 3*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*(4*A*cos(d*x + c)^3 - 12*(A - B)*cos(d*x + c)^2 - (19*A - 15*B + 3*C)*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
618,1,530,0,0.515507," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left({\left(15 \, A - 11 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A - 11 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 15 \, A - 11 \, B + 7 \, C\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 + 5 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(147 \, A - 95 \, B + 75 \, C\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 + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A - 11 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 15 \, A - 11 \, B + 7 \, C\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 + 5 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(147 \, A - 95 \, B + 75 \, C\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 + 7*C)*cos(d*x + c)^2 + 2*(15*A - 11*B + 7*C)*cos(d*x + c) + 15*A - 11*B + 7*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*(12*A*cos(d*x + c)^4 - 4*(3*A - 5*B)*cos(d*x + c)^3 + 12*(9*A - 5*B + 5*C)*cos(d*x + c)^2 + (147*A - 95*B + 75*C)*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 + 7*C)*cos(d*x + c)^2 + 2*(15*A - 11*B + 7*C)*cos(d*x + c) + 15*A - 11*B + 7*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*(12*A*cos(d*x + c)^4 - 4*(3*A - 5*B)*cos(d*x + c)^3 + 12*(9*A - 5*B + 5*C)*cos(d*x + c)^2 + (147*A - 95*B + 75*C)*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
619,1,837,0,0.739502," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 43 \, B + 115 \, C\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 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 2 \, B - 5 \, C\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 + 35 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 15 \, B + 55 \, C\right)} \cos\left(d x + c\right) + 16 \, C\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 + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 43 \, B + 115 \, C\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 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 2 \, B - 5 \, C\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 + 35 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 15 \, B + 55 \, C\right)} \cos\left(d x + c\right) + 16 \, C\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 + 115*C)*cos(d*x + c)^3 + 3*(3*A - 43*B + 115*C)*cos(d*x + c)^2 + 3*(3*A - 43*B + 115*C)*cos(d*x + c) + 3*A - 43*B + 115*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)) - 16*((2*B - 5*C)*cos(d*x + c)^3 + 3*(2*B - 5*C)*cos(d*x + c)^2 + 3*(2*B - 5*C)*cos(d*x + c) + 2*B - 5*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*((3*A - 11*B + 35*C)*cos(d*x + c)^2 + (7*A - 15*B + 55*C)*cos(d*x + c) + 16*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 + 115*C)*cos(d*x + c)^3 + 3*(3*A - 43*B + 115*C)*cos(d*x + c)^2 + 3*(3*A - 43*B + 115*C)*cos(d*x + c) + 3*A - 43*B + 115*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))) - 16*((2*B - 5*C)*cos(d*x + c)^3 + 3*(2*B - 5*C)*cos(d*x + c)^2 + 3*(2*B - 5*C)*cos(d*x + c) + 2*B - 5*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*((3*A - 11*B + 35*C)*cos(d*x + c)^2 + (7*A - 15*B + 55*C)*cos(d*x + c) + 16*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
620,1,781,0,0.555846," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B - 43 \, C\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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\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(5 \, A + 3 \, B - 11 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(A + 7 \, B - 15 \, C\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 - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B - 43 \, C\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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\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(5 \, A + 3 \, B - 11 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(A + 7 \, B - 15 \, C\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 - 43*C)*cos(d*x + c)^3 + 3*(5*A + 3*B - 43*C)*cos(d*x + c)^2 + 3*(5*A + 3*B - 43*C)*cos(d*x + c) + 5*A + 3*B - 43*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)) - 32*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 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*((5*A + 3*B - 11*C)*cos(d*x + c)^2 + (A + 7*B - 15*C)*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 - 43*C)*cos(d*x + c)^3 + 3*(5*A + 3*B - 43*C)*cos(d*x + c)^2 + 3*(5*A + 3*B - 43*C)*cos(d*x + c) + 5*A + 3*B - 43*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))) - 32*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 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*((5*A + 3*B - 11*C)*cos(d*x + c)^2 + (A + 7*B - 15*C)*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
621,1,538,0,0.515203," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B + 3 \, C\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 - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A - B - 7 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B + 3 \, C\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 - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A - B - 7 \, C\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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 5*B + 3*C)*cos(d*x + c)^2 + 3*(19*A + 5*B + 3*C)*cos(d*x + c) + 19*A + 5*B + 3*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*((13*A - 5*B - 3*C)*cos(d*x + c)^2 + (9*A - B - 7*C)*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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 5*B + 3*C)*cos(d*x + c)^2 + 3*(19*A + 5*B + 3*C)*cos(d*x + c) + 19*A + 5*B + 3*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*((13*A - 5*B - 3*C)*cos(d*x + c)^2 + (9*A - B - 7*C)*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
622,1,556,0,0.488641," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 75 \, A - 19 \, B - 5 \, C\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 + 5 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(49 \, A - 9 \, B + C\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 - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 75 \, A - 19 \, B - 5 \, C\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 + 5 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(49 \, A - 9 \, B + C\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 - 5*C)*cos(d*x + c)^3 + 3*(75*A - 19*B - 5*C)*cos(d*x + c)^2 + 3*(75*A - 19*B - 5*C)*cos(d*x + c) + 75*A - 19*B - 5*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*(32*A*cos(d*x + c)^3 + (85*A - 13*B + 5*C)*cos(d*x + c)^2 + (49*A - 9*B + C)*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 - 5*C)*cos(d*x + c)^3 + 3*(75*A - 19*B - 5*C)*cos(d*x + c)^2 + 3*(75*A - 19*B - 5*C)*cos(d*x + c) + 75*A - 19*B - 5*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*(32*A*cos(d*x + c)^3 + (85*A - 13*B + 5*C)*cos(d*x + c)^2 + (49*A - 9*B + C)*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
623,1,600,0,0.500126," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 163 \, A - 75 \, B + 19 \, C\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 + 39 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(299 \, A - 147 \, B + 27 \, C\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 + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 163 \, A - 75 \, B + 19 \, C\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 + 39 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(299 \, A - 147 \, B + 27 \, C\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 + 19*C)*cos(d*x + c)^3 + 3*(163*A - 75*B + 19*C)*cos(d*x + c)^2 + 3*(163*A - 75*B + 19*C)*cos(d*x + c) + 163*A - 75*B + 19*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*(32*A*cos(d*x + c)^4 - 32*(5*A - 3*B)*cos(d*x + c)^3 - (503*A - 255*B + 39*C)*cos(d*x + c)^2 - (299*A - 147*B + 27*C)*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 + 19*C)*cos(d*x + c)^3 + 3*(163*A - 75*B + 19*C)*cos(d*x + c)^2 + 3*(163*A - 75*B + 19*C)*cos(d*x + c) + 163*A - 75*B + 19*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*(32*A*cos(d*x + c)^4 - 32*(5*A - 3*B)*cos(d*x + c)^3 - (503*A - 255*B + 39*C)*cos(d*x + c)^2 - (299*A - 147*B + 27*C)*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
624,1,634,0,0.489983," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left({\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right) + 283 \, A - 163 \, B + 75 \, C\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 + 15 \, C\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(911 \, A - 503 \, B + 255 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(2671 \, A - 1495 \, B + 735 \, C\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 + 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right) + 283 \, A - 163 \, B + 75 \, C\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 + 15 \, C\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(911 \, A - 503 \, B + 255 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(2671 \, A - 1495 \, B + 735 \, C\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 + 75*C)*cos(d*x + c)^3 + 3*(283*A - 163*B + 75*C)*cos(d*x + c)^2 + 3*(283*A - 163*B + 75*C)*cos(d*x + c) + 283*A - 163*B + 75*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*(96*A*cos(d*x + c)^5 - 160*(A - B)*cos(d*x + c)^4 + 32*(49*A - 25*B + 15*C)*cos(d*x + c)^3 + 5*(911*A - 503*B + 255*C)*cos(d*x + c)^2 + (2671*A - 1495*B + 735*C)*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 + 75*C)*cos(d*x + c)^3 + 3*(283*A - 163*B + 75*C)*cos(d*x + c)^2 + 3*(283*A - 163*B + 75*C)*cos(d*x + c) + 283*A - 163*B + 75*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*(96*A*cos(d*x + c)^5 - 160*(A - B)*cos(d*x + c)^4 + 32*(49*A - 25*B + 15*C)*cos(d*x + c)^3 + 5*(911*A - 503*B + 255*C)*cos(d*x + c)^2 + (2671*A - 1495*B + 735*C)*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
625,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(7/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,0,0,0,0.848447," ","integrate(sec(d*x+c)^m*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^m, x)","F",0
634,0,0,0,0.937059," ","integrate(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{-n - 1}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1), x)","F",0
635,1,58,0,0.742543," ","integrate((a+a*sec(d*x+c))^n*(-a*(A*n+B*n+B)-a*C*(1+n)*sec(d*x+c))/a/(1+n)/(sec(d*x+c)^n)+sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{A \left(\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}\right)^{n} \frac{1}{\cos\left(d x + c\right)}^{-n - 1} \sin\left(d x + c\right)}{{\left(d n + d\right)} \cos\left(d x + c\right)}"," ",0,"A*((a*cos(d*x + c) + a)/cos(d*x + c))^n*(1/cos(d*x + c))^(-n - 1)*sin(d*x + c)/((d*n + d)*cos(d*x + c))","A",0
636,0,0,0,0.436459," ","integrate((a+a*sec(d*x+c))^m*(B-C+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + B - C\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + B - C)*(a*sec(d*x + c) + a)^m, x)","F",0
637,1,147,0,0.458328," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, C\right)} a \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, A + 3 \, C\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 \, C\right)} b \cos\left(d x + c\right)^{4} + 15 \, {\left(4 \, A + 3 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 4 \, C\right)} b \cos\left(d x + c\right)^{2} + 30 \, C a \cos\left(d x + c\right) + 24 \, C b\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(4*A + 3*C)*a*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*A + 3*C)*a*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(5*A + 4*C)*b*cos(d*x + c)^4 + 15*(4*A + 3*C)*a*cos(d*x + c)^3 + 8*(5*A + 4*C)*b*cos(d*x + c)^2 + 30*C*a*cos(d*x + c) + 24*C*b)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
638,1,129,0,0.490151," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A + 3 \, C\right)} b \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, A + 3 \, C\right)} b \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(3 \, A + 2 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 3 \, C\right)} b \cos\left(d x + c\right)^{2} + 8 \, C a \cos\left(d x + c\right) + 6 \, C b\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(4*A + 3*C)*b*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*A + 3*C)*b*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(3*A + 2*C)*a*cos(d*x + c)^3 + 3*(4*A + 3*C)*b*cos(d*x + c)^2 + 8*C*a*cos(d*x + c) + 6*C*b)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
639,1,107,0,0.468487," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + C\right)} a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A + C\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 \, C\right)} b \cos\left(d x + c\right)^{2} + 3 \, C a \cos\left(d x + c\right) + 2 \, C b\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(2*A + C)*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*A + C)*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(3*A + 2*C)*b*cos(d*x + c)^2 + 3*C*a*cos(d*x + c) + 2*C*b)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
640,1,101,0,0.454225," ","integrate((a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, A a d x \cos\left(d x + c\right)^{2} + {\left(2 \, A + C\right)} b \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, A + C\right)} b \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a \cos\left(d x + c\right) + C b\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*A*a*d*x*cos(d*x + c)^2 + (2*A + C)*b*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*A + C)*b*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*a*cos(d*x + c) + C*b)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
641,1,86,0,0.458823," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, A b d x \cos\left(d x + c\right) + C a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - C a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a \cos\left(d x + c\right) + C b\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*A*b*d*x*cos(d*x + c) + C*a*cos(d*x + c)*log(sin(d*x + c) + 1) - C*a*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(A*a*cos(d*x + c) + C*b)*sin(d*x + c))/(d*cos(d*x + c))","B",0
642,1,63,0,0.457179," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(A + 2 \, C\right)} a d x + C b \log\left(\sin\left(d x + c\right) + 1\right) - C b \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(A a \cos\left(d x + c\right) + 2 \, A b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((A + 2*C)*a*d*x + C*b*log(sin(d*x + c) + 1) - C*b*log(-sin(d*x + c) + 1) + (A*a*cos(d*x + c) + 2*A*b)*sin(d*x + c))/d","A",0
643,1,56,0,0.437738," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(A + 2 \, C\right)} b d x + {\left(2 \, A a \cos\left(d x + c\right)^{2} + 3 \, A b \cos\left(d x + c\right) + 2 \, {\left(2 \, A + 3 \, C\right)} a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(A + 2*C)*b*d*x + (2*A*a*cos(d*x + c)^2 + 3*A*b*cos(d*x + c) + 2*(2*A + 3*C)*a)*sin(d*x + c))/d","A",0
644,1,76,0,0.445274," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 4 \, C\right)} a d x + {\left(6 \, A a \cos\left(d x + c\right)^{3} + 8 \, A b \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 4 \, C\right)} a \cos\left(d x + c\right) + 8 \, {\left(2 \, A + 3 \, C\right)} b\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*A + 4*C)*a*d*x + (6*A*a*cos(d*x + c)^3 + 8*A*b*cos(d*x + c)^2 + 3*(3*A + 4*C)*a*cos(d*x + c) + 8*(2*A + 3*C)*b)*sin(d*x + c))/d","A",0
645,1,94,0,0.464491," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, A + 4 \, C\right)} b d x + {\left(24 \, A a \cos\left(d x + c\right)^{4} + 30 \, A b \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, A + 5 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, A + 4 \, C\right)} b \cos\left(d x + c\right) + 16 \, {\left(4 \, A + 5 \, C\right)} a\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(3*A + 4*C)*b*d*x + (24*A*a*cos(d*x + c)^4 + 30*A*b*cos(d*x + c)^3 + 8*(4*A + 5*C)*a*cos(d*x + c)^2 + 15*(3*A + 4*C)*b*cos(d*x + c) + 16*(4*A + 5*C)*a)*sin(d*x + c))/d","A",0
646,1,180,0,0.468071," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, C\right)} a b \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, A + 3 \, C\right)} a b \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(15 \, {\left(4 \, A + 3 \, C\right)} a b \cos\left(d x + c\right)^{3} + 4 \, {\left(5 \, {\left(3 \, A + 2 \, C\right)} a^{2} + 2 \, {\left(5 \, A + 4 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} + 30 \, C a b \cos\left(d x + c\right) + 12 \, C b^{2} + 4 \, {\left(5 \, C a^{2} + {\left(5 \, A + 4 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{120 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/120*(15*(4*A + 3*C)*a*b*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*A + 3*C)*a*b*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(15*(4*A + 3*C)*a*b*cos(d*x + c)^3 + 4*(5*(3*A + 2*C)*a^2 + 2*(5*A + 4*C)*b^2)*cos(d*x + c)^4 + 30*C*a*b*cos(d*x + c) + 12*C*b^2 + 4*(5*C*a^2 + (5*A + 4*C)*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
647,1,171,0,0.461812," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{2} + {\left(4 \, A + 3 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{2} + {\left(4 \, A + 3 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(3 \, A + 2 \, C\right)} a b \cos\left(d x + c\right)^{3} + 16 \, C a b \cos\left(d x + c\right) + 6 \, C b^{2} + 3 \, {\left(4 \, C a^{2} + {\left(4 \, A + 3 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(4*(2*A + C)*a^2 + (4*A + 3*C)*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*(2*A + C)*a^2 + (4*A + 3*C)*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(3*A + 2*C)*a*b*cos(d*x + c)^3 + 16*C*a*b*cos(d*x + c) + 6*C*b^2 + 3*(4*C*a^2 + (4*A + 3*C)*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
648,1,136,0,0.461668," ","integrate((a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{6 \, A a^{2} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A + C\right)} a b \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A + C\right)} a b \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, C a b \cos\left(d x + c\right) + C b^{2} + {\left(3 \, C a^{2} + {\left(3 \, A + 2 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(6*A*a^2*d*x*cos(d*x + c)^3 + 3*(2*A + C)*a*b*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*A + C)*a*b*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(3*C*a*b*cos(d*x + c) + C*b^2 + (3*C*a^2 + (3*A + 2*C)*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
649,1,139,0,0.469032," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{8 \, A a b d x \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{2} + {\left(2 \, A + C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, C a^{2} + {\left(2 \, A + C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + 4 \, C a b \cos\left(d x + c\right) + C b^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(8*A*a*b*d*x*cos(d*x + c)^2 + (2*C*a^2 + (2*A + C)*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*C*a^2 + (2*A + C)*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a^2*cos(d*x + c)^2 + 4*C*a*b*cos(d*x + c) + C*b^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
650,1,119,0,0.460068," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, C a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, C a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left({\left(A + 2 \, C\right)} a^{2} + 2 \, A b^{2}\right)} d x \cos\left(d x + c\right) + {\left(A a^{2} \cos\left(d x + c\right)^{2} + 4 \, A a b \cos\left(d x + c\right) + 2 \, C b^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*C*a*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 2*C*a*b*cos(d*x + c)*log(-sin(d*x + c) + 1) + ((A + 2*C)*a^2 + 2*A*b^2)*d*x*cos(d*x + c) + (A*a^2*cos(d*x + c)^2 + 4*A*a*b*cos(d*x + c) + 2*C*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
651,1,99,0,0.496449," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{6 \, {\left(A + 2 \, C\right)} a b d x + 3 \, C b^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, C b^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{2} \cos\left(d x + c\right)^{2} + 3 \, A a b \cos\left(d x + c\right) + {\left(2 \, A + 3 \, C\right)} a^{2} + 3 \, A b^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(6*(A + 2*C)*a*b*d*x + 3*C*b^2*log(sin(d*x + c) + 1) - 3*C*b^2*log(-sin(d*x + c) + 1) + 2*(A*a^2*cos(d*x + c)^2 + 3*A*a*b*cos(d*x + c) + (2*A + 3*C)*a^2 + 3*A*b^2)*sin(d*x + c))/d","A",0
652,1,104,0,0.466183," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{2} + 4 \, {\left(A + 2 \, C\right)} b^{2}\right)} d x + {\left(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 16 \, A a b \cos\left(d x + c\right)^{2} + 16 \, {\left(2 \, A + 3 \, C\right)} a b + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{2} + 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 + 4*C)*a^2 + 4*(A + 2*C)*b^2)*d*x + (6*A*a^2*cos(d*x + c)^3 + 16*A*a*b*cos(d*x + c)^2 + 16*(2*A + 3*C)*a*b + 3*((3*A + 4*C)*a^2 + 4*A*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
653,1,123,0,0.465884," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, A + 4 \, C\right)} a b d x + {\left(12 \, A a^{2} \cos\left(d x + c\right)^{4} + 30 \, A a b \cos\left(d x + c\right)^{3} + 15 \, {\left(3 \, A + 4 \, C\right)} a b \cos\left(d x + c\right) + 8 \, {\left(4 \, A + 5 \, C\right)} a^{2} + 20 \, {\left(2 \, A + 3 \, C\right)} b^{2} + 4 \, {\left({\left(4 \, A + 5 \, C\right)} a^{2} + 5 \, A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(15*(3*A + 4*C)*a*b*d*x + (12*A*a^2*cos(d*x + c)^4 + 30*A*a*b*cos(d*x + c)^3 + 15*(3*A + 4*C)*a*b*cos(d*x + c) + 8*(4*A + 5*C)*a^2 + 20*(2*A + 3*C)*b^2 + 4*((4*A + 5*C)*a^2 + 5*A*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
654,1,262,0,0.492122," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, {\left(4 \, A + 3 \, C\right)} a^{2} b + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(6 \, {\left(4 \, A + 3 \, C\right)} a^{2} b + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(5 \, {\left(3 \, A + 2 \, C\right)} a^{3} + 6 \, {\left(5 \, A + 4 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{5} + 144 \, C a b^{2} \cos\left(d x + c\right) + 15 \, {\left(6 \, {\left(4 \, A + 3 \, C\right)} a^{2} b + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{4} + 40 \, C b^{3} + 16 \, {\left(5 \, C a^{3} + 3 \, {\left(5 \, A + 4 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(18 \, C a^{2} b + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(6*(4*A + 3*C)*a^2*b + (6*A + 5*C)*b^3)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(6*(4*A + 3*C)*a^2*b + (6*A + 5*C)*b^3)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(5*(3*A + 2*C)*a^3 + 6*(5*A + 4*C)*a*b^2)*cos(d*x + c)^5 + 144*C*a*b^2*cos(d*x + c) + 15*(6*(4*A + 3*C)*a^2*b + (6*A + 5*C)*b^3)*cos(d*x + c)^4 + 40*C*b^3 + 16*(5*C*a^3 + 3*(5*A + 4*C)*a*b^2)*cos(d*x + c)^3 + 10*(18*C*a^2*b + (6*A + 5*C)*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
655,1,225,0,0.504641," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, {\left(2 \, A + C\right)} a^{3} + 3 \, {\left(4 \, A + 3 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, {\left(2 \, A + C\right)} a^{3} + 3 \, {\left(4 \, A + 3 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(90 \, C a b^{2} \cos\left(d x + c\right) + 8 \, {\left(15 \, {\left(3 \, A + 2 \, C\right)} a^{2} b + 2 \, {\left(5 \, A + 4 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{4} + 24 \, C b^{3} + 15 \, {\left(4 \, C a^{3} + 3 \, {\left(4 \, A + 3 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, C a^{2} b + {\left(5 \, A + 4 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(4*(2*A + C)*a^3 + 3*(4*A + 3*C)*a*b^2)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*(2*A + C)*a^3 + 3*(4*A + 3*C)*a*b^2)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(90*C*a*b^2*cos(d*x + c) + 8*(15*(3*A + 2*C)*a^2*b + 2*(5*A + 4*C)*b^3)*cos(d*x + c)^4 + 24*C*b^3 + 15*(4*C*a^3 + 3*(4*A + 3*C)*a*b^2)*cos(d*x + c)^3 + 8*(15*C*a^2*b + (5*A + 4*C)*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
656,1,199,0,0.476864," ","integrate((a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{16 \, A a^{3} d x \cos\left(d x + c\right)^{4} + {\left(12 \, {\left(2 \, A + C\right)} a^{2} b + {\left(4 \, A + 3 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(12 \, {\left(2 \, A + C\right)} a^{2} b + {\left(4 \, A + 3 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, C a b^{2} \cos\left(d x + c\right) + 2 \, C b^{3} + 8 \, {\left(C a^{3} + {\left(3 \, A + 2 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, C a^{2} b + {\left(4 \, A + 3 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*A*a^3*d*x*cos(d*x + c)^4 + (12*(2*A + C)*a^2*b + (4*A + 3*C)*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (12*(2*A + C)*a^2*b + (4*A + 3*C)*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*C*a*b^2*cos(d*x + c) + 2*C*b^3 + 8*(C*a^3 + (3*A + 2*C)*a*b^2)*cos(d*x + c)^3 + (12*C*a^2*b + (4*A + 3*C)*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
657,1,178,0,0.474333," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{36 \, A a^{2} b d x \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{3} + 3 \, {\left(2 \, A + C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, C a^{3} + 3 \, {\left(2 \, A + C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, A a^{3} \cos\left(d x + c\right)^{3} + 9 \, C a b^{2} \cos\left(d x + c\right) + 2 \, C b^{3} + 2 \, {\left(9 \, C a^{2} b + {\left(3 \, A + 2 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(36*A*a^2*b*d*x*cos(d*x + c)^3 + 3*(2*C*a^3 + 3*(2*A + C)*a*b^2)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*C*a^3 + 3*(2*A + C)*a*b^2)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*A*a^3*cos(d*x + c)^3 + 9*C*a*b^2*cos(d*x + c) + 2*C*b^3 + 2*(9*C*a^2*b + (3*A + 2*C)*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
658,1,171,0,0.508005," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(A + 2 \, C\right)} a^{3} + 6 \, A a b^{2}\right)} d x \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{2} b + {\left(2 \, A + C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(6 \, C a^{2} b + {\left(2 \, A + C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{3} \cos\left(d x + c\right)^{3} + 6 \, A a^{2} b \cos\left(d x + c\right)^{2} + 6 \, C a b^{2} \cos\left(d x + c\right) + C b^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*((A + 2*C)*a^3 + 6*A*a*b^2)*d*x*cos(d*x + c)^2 + (6*C*a^2*b + (2*A + C)*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (6*C*a^2*b + (2*A + C)*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a^3*cos(d*x + c)^3 + 6*A*a^2*b*cos(d*x + c)^2 + 6*C*a*b^2*cos(d*x + c) + C*b^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
659,1,158,0,0.502054," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{9 \, C a b^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, C a b^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(3 \, {\left(A + 2 \, C\right)} a^{2} b + 2 \, A b^{3}\right)} d x \cos\left(d x + c\right) + {\left(2 \, A a^{3} \cos\left(d x + c\right)^{3} + 9 \, A a^{2} b \cos\left(d x + c\right)^{2} + 6 \, C b^{3} + 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{3} + 9 \, A a 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*(9*C*a*b^2*cos(d*x + c)*log(sin(d*x + c) + 1) - 9*C*a*b^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + 3*(3*(A + 2*C)*a^2*b + 2*A*b^3)*d*x*cos(d*x + c) + (2*A*a^3*cos(d*x + c)^3 + 9*A*a^2*b*cos(d*x + c)^2 + 6*C*b^3 + 2*((2*A + 3*C)*a^3 + 9*A*a*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
660,1,146,0,0.476199," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, C b^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 4 \, C b^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left({\left(3 \, A + 4 \, C\right)} a^{3} + 12 \, {\left(A + 2 \, C\right)} a b^{2}\right)} d x + {\left(2 \, A a^{3} \cos\left(d x + c\right)^{3} + 8 \, A a^{2} b \cos\left(d x + c\right)^{2} + 8 \, {\left(2 \, A + 3 \, C\right)} a^{2} b + 8 \, A b^{3} + {\left({\left(3 \, A + 4 \, C\right)} a^{3} + 12 \, A a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(4*C*b^3*log(sin(d*x + c) + 1) - 4*C*b^3*log(-sin(d*x + c) + 1) + ((3*A + 4*C)*a^3 + 12*(A + 2*C)*a*b^2)*d*x + (2*A*a^3*cos(d*x + c)^3 + 8*A*a^2*b*cos(d*x + c)^2 + 8*(2*A + 3*C)*a^2*b + 8*A*b^3 + ((3*A + 4*C)*a^3 + 12*A*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
661,1,153,0,0.473477," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, {\left(3 \, A + 4 \, C\right)} a^{2} b + 4 \, {\left(A + 2 \, C\right)} b^{3}\right)} d x + {\left(24 \, A a^{3} \cos\left(d x + c\right)^{4} + 90 \, A a^{2} b \cos\left(d x + c\right)^{3} + 16 \, {\left(4 \, A + 5 \, C\right)} a^{3} + 120 \, {\left(2 \, A + 3 \, C\right)} a b^{2} + 8 \, {\left({\left(4 \, A + 5 \, C\right)} a^{3} + 15 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, {\left(3 \, A + 4 \, C\right)} a^{2} b + 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*(3*A + 4*C)*a^2*b + 4*(A + 2*C)*b^3)*d*x + (24*A*a^3*cos(d*x + c)^4 + 90*A*a^2*b*cos(d*x + c)^3 + 16*(4*A + 5*C)*a^3 + 120*(2*A + 3*C)*a*b^2 + 8*((4*A + 5*C)*a^3 + 15*A*a*b^2)*cos(d*x + c)^2 + 15*(3*(3*A + 4*C)*a^2*b + 4*A*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
662,1,189,0,0.460486," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 6 \, {\left(3 \, A + 4 \, C\right)} a b^{2}\right)} d x + {\left(40 \, A a^{3} \cos\left(d x + c\right)^{5} + 144 \, A a^{2} b \cos\left(d x + c\right)^{4} + 96 \, {\left(4 \, A + 5 \, C\right)} a^{2} b + 80 \, {\left(2 \, A + 3 \, C\right)} b^{3} + 10 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 18 \, A a b^{2}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(3 \, {\left(4 \, A + 5 \, C\right)} a^{2} b + 5 \, A b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 6 \, {\left(3 \, A + 4 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*((5*A + 6*C)*a^3 + 6*(3*A + 4*C)*a*b^2)*d*x + (40*A*a^3*cos(d*x + c)^5 + 144*A*a^2*b*cos(d*x + c)^4 + 96*(4*A + 5*C)*a^2*b + 80*(2*A + 3*C)*b^3 + 10*((5*A + 6*C)*a^3 + 18*A*a*b^2)*cos(d*x + c)^3 + 16*(3*(4*A + 5*C)*a^2*b + 5*A*b^3)*cos(d*x + c)^2 + 15*((5*A + 6*C)*a^3 + 6*(3*A + 4*C)*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
663,1,325,0,0.479817," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(2 \, {\left(4 \, A + 3 \, C\right)} a^{3} b + {\left(6 \, A + 5 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(2 \, {\left(4 \, A + 3 \, C\right)} a^{3} b + {\left(6 \, A + 5 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, {\left(35 \, {\left(3 \, A + 2 \, C\right)} a^{4} + 84 \, {\left(5 \, A + 4 \, C\right)} a^{2} b^{2} + 8 \, {\left(7 \, A + 6 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{6} + 280 \, C a b^{3} \cos\left(d x + c\right) + 105 \, {\left(2 \, {\left(4 \, A + 3 \, C\right)} a^{3} b + {\left(6 \, A + 5 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{5} + 60 \, C b^{4} + 4 \, {\left(35 \, C a^{4} + 42 \, {\left(5 \, A + 4 \, C\right)} a^{2} b^{2} + 4 \, {\left(7 \, A + 6 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left(6 \, C a^{3} b + {\left(6 \, A + 5 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(42 \, C a^{2} b^{2} + {\left(7 \, A + 6 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{840 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/840*(105*(2*(4*A + 3*C)*a^3*b + (6*A + 5*C)*a*b^3)*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(2*(4*A + 3*C)*a^3*b + (6*A + 5*C)*a*b^3)*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 2*(4*(35*(3*A + 2*C)*a^4 + 84*(5*A + 4*C)*a^2*b^2 + 8*(7*A + 6*C)*b^4)*cos(d*x + c)^6 + 280*C*a*b^3*cos(d*x + c) + 105*(2*(4*A + 3*C)*a^3*b + (6*A + 5*C)*a*b^3)*cos(d*x + c)^5 + 60*C*b^4 + 4*(35*C*a^4 + 42*(5*A + 4*C)*a^2*b^2 + 4*(7*A + 6*C)*b^4)*cos(d*x + c)^4 + 70*(6*C*a^3*b + (6*A + 5*C)*a*b^3)*cos(d*x + c)^3 + 12*(42*C*a^2*b^2 + (7*A + 6*C)*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
664,1,297,0,0.489871," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, {\left(2 \, A + C\right)} a^{4} + 12 \, {\left(4 \, A + 3 \, C\right)} a^{2} b^{2} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, {\left(2 \, A + C\right)} a^{4} + 12 \, {\left(4 \, A + 3 \, C\right)} a^{2} b^{2} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(192 \, C a b^{3} \cos\left(d x + c\right) + 64 \, {\left(5 \, {\left(3 \, A + 2 \, C\right)} a^{3} b + 2 \, {\left(5 \, A + 4 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{5} + 40 \, C b^{4} + 15 \, {\left(8 \, C a^{4} + 12 \, {\left(4 \, A + 3 \, C\right)} a^{2} b^{2} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} + 64 \, {\left(5 \, C a^{3} b + {\left(5 \, A + 4 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(36 \, C a^{2} b^{2} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(8*(2*A + C)*a^4 + 12*(4*A + 3*C)*a^2*b^2 + (6*A + 5*C)*b^4)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(8*(2*A + C)*a^4 + 12*(4*A + 3*C)*a^2*b^2 + (6*A + 5*C)*b^4)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(192*C*a*b^3*cos(d*x + c) + 64*(5*(3*A + 2*C)*a^3*b + 2*(5*A + 4*C)*a*b^3)*cos(d*x + c)^5 + 40*C*b^4 + 15*(8*C*a^4 + 12*(4*A + 3*C)*a^2*b^2 + (6*A + 5*C)*b^4)*cos(d*x + c)^4 + 64*(5*C*a^3*b + (5*A + 4*C)*a*b^3)*cos(d*x + c)^3 + 10*(36*C*a^2*b^2 + (6*A + 5*C)*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
665,1,251,0,0.510396," ","integrate((a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{60 \, A a^{4} d x \cos\left(d x + c\right)^{5} + 15 \, {\left(4 \, {\left(2 \, A + C\right)} a^{3} b + {\left(4 \, A + 3 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, {\left(2 \, A + C\right)} a^{3} b + {\left(4 \, A + 3 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(30 \, C a b^{3} \cos\left(d x + c\right) + 6 \, C b^{4} + 2 \, {\left(15 \, C a^{4} + 30 \, {\left(3 \, A + 2 \, C\right)} a^{2} b^{2} + 2 \, {\left(5 \, A + 4 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(4 \, C a^{3} b + {\left(4 \, A + 3 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(30 \, C a^{2} b^{2} + {\left(5 \, A + 4 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/60*(60*A*a^4*d*x*cos(d*x + c)^5 + 15*(4*(2*A + C)*a^3*b + (4*A + 3*C)*a*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*(2*A + C)*a^3*b + (4*A + 3*C)*a*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(30*C*a*b^3*cos(d*x + c) + 6*C*b^4 + 2*(15*C*a^4 + 30*(3*A + 2*C)*a^2*b^2 + 2*(5*A + 4*C)*b^4)*cos(d*x + c)^4 + 15*(4*C*a^3*b + (4*A + 3*C)*a*b^3)*cos(d*x + c)^3 + 2*(30*C*a^2*b^2 + (5*A + 4*C)*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
666,1,236,0,0.501402," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{192 \, A a^{3} b d x \cos\left(d x + c\right)^{4} + 3 \, {\left(8 \, C a^{4} + 24 \, {\left(2 \, A + C\right)} a^{2} b^{2} + {\left(4 \, A + 3 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, C a^{4} + 24 \, {\left(2 \, A + C\right)} a^{2} b^{2} + {\left(4 \, A + 3 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, A a^{4} \cos\left(d x + c\right)^{4} + 32 \, C a b^{3} \cos\left(d x + c\right) + 6 \, C b^{4} + 32 \, {\left(3 \, C a^{3} b + {\left(3 \, A + 2 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(24 \, C a^{2} b^{2} + {\left(4 \, A + 3 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(192*A*a^3*b*d*x*cos(d*x + c)^4 + 3*(8*C*a^4 + 24*(2*A + C)*a^2*b^2 + (4*A + 3*C)*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*C*a^4 + 24*(2*A + C)*a^2*b^2 + (4*A + 3*C)*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*A*a^4*cos(d*x + c)^4 + 32*C*a*b^3*cos(d*x + c) + 6*C*b^4 + 32*(3*C*a^3*b + (3*A + 2*C)*a*b^3)*cos(d*x + c)^3 + 3*(24*C*a^2*b^2 + (4*A + 3*C)*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
667,1,208,0,0.516051," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(A + 2 \, C\right)} a^{4} + 12 \, A a^{2} b^{2}\right)} d x \cos\left(d x + c\right)^{3} + 6 \, {\left(2 \, C a^{3} b + {\left(2 \, A + C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left(2 \, C a^{3} b + {\left(2 \, A + C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(3 \, A a^{4} \cos\left(d x + c\right)^{4} + 24 \, A a^{3} b \cos\left(d x + c\right)^{3} + 12 \, C a b^{3} \cos\left(d x + c\right) + 2 \, C b^{4} + 2 \, {\left(18 \, C a^{2} b^{2} + {\left(3 \, A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(3*((A + 2*C)*a^4 + 12*A*a^2*b^2)*d*x*cos(d*x + c)^3 + 6*(2*C*a^3*b + (2*A + C)*a*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 6*(2*C*a^3*b + (2*A + C)*a*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + (3*A*a^4*cos(d*x + c)^4 + 24*A*a^3*b*cos(d*x + c)^3 + 12*C*a*b^3*cos(d*x + c) + 2*C*b^4 + 2*(18*C*a^2*b^2 + (3*A + 2*C)*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
668,1,210,0,0.491689," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{24 \, {\left({\left(A + 2 \, C\right)} a^{3} b + 2 \, A a b^{3}\right)} d x \cos\left(d x + c\right)^{2} + 3 \, {\left(12 \, C a^{2} b^{2} + {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(12 \, C a^{2} b^{2} + {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{4} \cos\left(d x + c\right)^{4} + 12 \, A a^{3} b \cos\left(d x + c\right)^{3} + 24 \, C a b^{3} \cos\left(d x + c\right) + 3 \, C b^{4} + 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{4} + 18 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(24*((A + 2*C)*a^3*b + 2*A*a*b^3)*d*x*cos(d*x + c)^2 + 3*(12*C*a^2*b^2 + (2*A + C)*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*(12*C*a^2*b^2 + (2*A + C)*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a^4*cos(d*x + c)^4 + 12*A*a^3*b*cos(d*x + c)^3 + 24*C*a*b^3*cos(d*x + c) + 3*C*b^4 + 2*((2*A + 3*C)*a^4 + 18*A*a^2*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
669,1,203,0,0.499717," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{48 \, C a b^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 48 \, C a b^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{4} + 24 \, {\left(A + 2 \, C\right)} a^{2} b^{2} + 8 \, A b^{4}\right)} d x \cos\left(d x + c\right) + {\left(6 \, A a^{4} \cos\left(d x + c\right)^{4} + 32 \, A a^{3} b \cos\left(d x + c\right)^{3} + 24 \, C b^{4} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{4} + 24 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 32 \, {\left({\left(2 \, A + 3 \, C\right)} a^{3} b + 3 \, A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}"," ",0,"1/24*(48*C*a*b^3*cos(d*x + c)*log(sin(d*x + c) + 1) - 48*C*a*b^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + 3*((3*A + 4*C)*a^4 + 24*(A + 2*C)*a^2*b^2 + 8*A*b^4)*d*x*cos(d*x + c) + (6*A*a^4*cos(d*x + c)^4 + 32*A*a^3*b*cos(d*x + c)^3 + 24*C*b^4 + 3*((3*A + 4*C)*a^4 + 24*A*a^2*b^2)*cos(d*x + c)^2 + 32*((2*A + 3*C)*a^3*b + 3*A*a*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
670,1,195,0,0.512993," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, C b^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, C b^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 15 \, {\left({\left(3 \, A + 4 \, C\right)} a^{3} b + 4 \, {\left(A + 2 \, C\right)} a b^{3}\right)} d x + {\left(6 \, A a^{4} \cos\left(d x + c\right)^{4} + 30 \, A a^{3} b \cos\left(d x + c\right)^{3} + 4 \, {\left(4 \, A + 5 \, C\right)} a^{4} + 60 \, {\left(2 \, A + 3 \, C\right)} a^{2} b^{2} + 30 \, A b^{4} + 2 \, {\left({\left(4 \, A + 5 \, C\right)} a^{4} + 30 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left({\left(3 \, A + 4 \, C\right)} a^{3} b + 4 \, A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(15*C*b^4*log(sin(d*x + c) + 1) - 15*C*b^4*log(-sin(d*x + c) + 1) + 15*((3*A + 4*C)*a^3*b + 4*(A + 2*C)*a*b^3)*d*x + (6*A*a^4*cos(d*x + c)^4 + 30*A*a^3*b*cos(d*x + c)^3 + 4*(4*A + 5*C)*a^4 + 60*(2*A + 3*C)*a^2*b^2 + 30*A*b^4 + 2*((4*A + 5*C)*a^4 + 30*A*a^2*b^2)*cos(d*x + c)^2 + 15*((3*A + 4*C)*a^3*b + 4*A*a*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
671,1,212,0,0.523782," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 12 \, {\left(3 \, A + 4 \, C\right)} a^{2} b^{2} + 8 \, {\left(A + 2 \, C\right)} b^{4}\right)} d x + {\left(40 \, A a^{4} \cos\left(d x + c\right)^{5} + 192 \, A a^{3} b \cos\left(d x + c\right)^{4} + 128 \, {\left(4 \, A + 5 \, C\right)} a^{3} b + 320 \, {\left(2 \, A + 3 \, C\right)} a b^{3} + 10 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 36 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + 64 \, {\left({\left(4 \, A + 5 \, C\right)} a^{3} b + 5 \, A a b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 12 \, {\left(3 \, A + 4 \, C\right)} a^{2} b^{2} + 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 + 6*C)*a^4 + 12*(3*A + 4*C)*a^2*b^2 + 8*(A + 2*C)*b^4)*d*x + (40*A*a^4*cos(d*x + c)^5 + 192*A*a^3*b*cos(d*x + c)^4 + 128*(4*A + 5*C)*a^3*b + 320*(2*A + 3*C)*a*b^3 + 10*((5*A + 6*C)*a^4 + 36*A*a^2*b^2)*cos(d*x + c)^3 + 64*((4*A + 5*C)*a^3*b + 5*A*a*b^3)*cos(d*x + c)^2 + 15*((5*A + 6*C)*a^4 + 12*(3*A + 4*C)*a^2*b^2 + 8*A*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
672,1,251,0,0.467702," ","integrate(cos(d*x+c)^7*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} b + 2 \, {\left(3 \, A + 4 \, C\right)} a b^{3}\right)} d x + {\left(60 \, A a^{4} \cos\left(d x + c\right)^{6} + 280 \, A a^{3} b \cos\left(d x + c\right)^{5} + 32 \, {\left(6 \, A + 7 \, C\right)} a^{4} + 336 \, {\left(4 \, A + 5 \, C\right)} a^{2} b^{2} + 140 \, {\left(2 \, A + 3 \, C\right)} b^{4} + 12 \, {\left({\left(6 \, A + 7 \, C\right)} a^{4} + 42 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} b + 6 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(4 \, {\left(6 \, A + 7 \, C\right)} a^{4} + 42 \, {\left(4 \, A + 5 \, C\right)} a^{2} b^{2} + 35 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} + 105 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} b + 2 \, {\left(3 \, A + 4 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{420 \, d}"," ",0,"1/420*(105*((5*A + 6*C)*a^3*b + 2*(3*A + 4*C)*a*b^3)*d*x + (60*A*a^4*cos(d*x + c)^6 + 280*A*a^3*b*cos(d*x + c)^5 + 32*(6*A + 7*C)*a^4 + 336*(4*A + 5*C)*a^2*b^2 + 140*(2*A + 3*C)*b^4 + 12*((6*A + 7*C)*a^4 + 42*A*a^2*b^2)*cos(d*x + c)^4 + 70*((5*A + 6*C)*a^3*b + 6*A*a*b^3)*cos(d*x + c)^3 + 4*(4*(6*A + 7*C)*a^4 + 42*(4*A + 5*C)*a^2*b^2 + 35*A*b^4)*cos(d*x + c)^2 + 105*((5*A + 6*C)*a^3*b + 2*(3*A + 4*C)*a*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
673,1,181,0,0.496100," ","integrate((a+b*sec(d*x+c))^3*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{16 \, a^{5} d x \cos\left(d x + c\right)^{4} + {\left(24 \, a^{4} b - 8 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(24 \, a^{4} b - 8 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(8 \, a b^{4} \cos\left(d x + c\right) + 2 \, b^{5} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*a^5*d*x*cos(d*x + c)^4 + (24*a^4*b - 8*a^2*b^3 - 3*b^5)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (24*a^4*b - 8*a^2*b^3 - 3*b^5)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 2*(8*a*b^4*cos(d*x + c) + 2*b^5 - 16*(a^3*b^2 - a*b^4)*cos(d*x + c)^3 + (8*a^2*b^3 + 3*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
674,1,132,0,0.485205," ","integrate((a+b*sec(d*x+c))^2*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{6 \, a^{4} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, a^{3} b - 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^{4} \cos\left(d x + c\right)^{2} + 3 \, a b^{3} \cos\left(d x + c\right) + b^{4}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(6*a^4*d*x*cos(d*x + c)^3 + 3*(2*a^3*b - a*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*a^3*b - a*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - 2*(2*b^4*cos(d*x + c)^2 + 3*a*b^3*cos(d*x + c) + b^4)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
675,1,116,0,0.472566," ","integrate((a+b*sec(d*x+c))*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, a^{3} d x \cos\left(d x + c\right)^{2} + {\left(2 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, a^{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 b^{2} \cos\left(d x + c\right) + b^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*a^3*d*x*cos(d*x + c)^2 + (2*a^2*b - b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*a^2*b - b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(2*a*b^2*cos(d*x + c) + b^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
676,1,663,0,3.079895," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(C a^{4} + A a^{2} b^{2}\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 \, C a^{5} + {\left(2 \, A - C\right)} a^{3} b^{2} - {\left(2 \, A + C\right)} a b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, C a^{5} + {\left(2 \, A - C\right)} a^{3} b^{2} - {\left(2 \, A + C\right)} a b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{2} b^{3} - 2 \, C b^{5} + 2 \, {\left(3 \, C a^{4} b + {\left(3 \, A - C\right)} a^{2} b^{3} - {\left(3 \, A + 2 \, C\right)} b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - C a b^{4}\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(C a^{4} + A a^{2} 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) \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, C a^{5} + {\left(2 \, A - C\right)} a^{3} b^{2} - {\left(2 \, A + C\right)} a b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, C a^{5} + {\left(2 \, A - C\right)} a^{3} b^{2} - {\left(2 \, A + C\right)} a b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{2} b^{3} - 2 \, C b^{5} + 2 \, {\left(3 \, C a^{4} b + {\left(3 \, A - C\right)} a^{2} b^{3} - {\left(3 \, A + 2 \, C\right)} b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - C a b^{4}\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*(C*a^4 + A*a^2*b^2)*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*C*a^5 + (2*A - C)*a^3*b^2 - (2*A + C)*a*b^4)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(2*C*a^5 + (2*A - C)*a^3*b^2 - (2*A + C)*a*b^4)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*C*a^2*b^3 - 2*C*b^5 + 2*(3*C*a^4*b + (3*A - C)*a^2*b^3 - (3*A + 2*C)*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - C*a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d*cos(d*x + c)^3), 1/12*(12*(C*a^4 + A*a^2*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)))*cos(d*x + c)^3 - 3*(2*C*a^5 + (2*A - C)*a^3*b^2 - (2*A + C)*a*b^4)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(2*C*a^5 + (2*A - C)*a^3*b^2 - (2*A + C)*a*b^4)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*C*a^2*b^3 - 2*C*b^5 + 2*(3*C*a^4*b + (3*A - C)*a^2*b^3 - (3*A + 2*C)*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - C*a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d*cos(d*x + c)^3)]","A",0
677,1,559,0,3.123258," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{3} + A a b^{2}\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 \, C a^{4} + {\left(2 \, A - C\right)} a^{2} b^{2} - {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, C a^{4} + {\left(2 \, A - C\right)} a^{2} b^{2} - {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{2} b^{2} - C b^{4} - 2 \, {\left(C a^{3} b - C a b^{3}\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(C a^{3} + A 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) \cos\left(d x + c\right)^{2} - {\left(2 \, C a^{4} + {\left(2 \, A - C\right)} a^{2} b^{2} - {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{4} + {\left(2 \, A - C\right)} a^{2} b^{2} - {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{2} b^{2} - C b^{4} - 2 \, {\left(C a^{3} b - C a b^{3}\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*(C*a^3 + A*a*b^2)*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*C*a^4 + (2*A - C)*a^2*b^2 - (2*A + C)*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*C*a^4 + (2*A - C)*a^2*b^2 - (2*A + C)*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(C*a^2*b^2 - C*b^4 - 2*(C*a^3*b - C*a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d*cos(d*x + c)^2), -1/4*(4*(C*a^3 + A*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)))*cos(d*x + c)^2 - (2*C*a^4 + (2*A - C)*a^2*b^2 - (2*A + C)*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (2*C*a^4 + (2*A - C)*a^2*b^2 - (2*A + C)*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(C*a^2*b^2 - C*b^4 - 2*(C*a^3*b - C*a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d*cos(d*x + c)^2)]","B",0
678,1,424,0,1.073416," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(C a^{2} + A b^{2}\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(C a^{3} - C a b^{2}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{3} - C a b^{2}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{2} b - C 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(C a^{2} + 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) \cos\left(d x + c\right) - {\left(C a^{3} - C a b^{2}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{3} - C a b^{2}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{2} b - C 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*((C*a^2 + A*b^2)*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)) - (C*a^3 - C*a*b^2)*cos(d*x + c)*log(sin(d*x + c) + 1) + (C*a^3 - C*a*b^2)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d*cos(d*x + c)), 1/2*(2*(C*a^2 + 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)))*cos(d*x + c) - (C*a^3 - C*a*b^2)*cos(d*x + c)*log(sin(d*x + c) + 1) + (C*a^3 - C*a*b^2)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d*cos(d*x + c))]","B",0
679,1,362,0,1.067600," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(A a^{2} b - A b^{3}\right)} d x + {\left(C a^{2} + 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) + {\left(C a^{3} - C a b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{3} - C a b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} b - a b^{3}\right)} d}, \frac{2 \, {\left(A a^{2} b - A b^{3}\right)} d x - 2 \, {\left(C a^{2} + 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(C a^{3} - C a b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{3} - C a b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} b - a b^{3}\right)} d}\right]"," ",0,"[1/2*(2*(A*a^2*b - A*b^3)*d*x + (C*a^2 + 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)) + (C*a^3 - C*a*b^2)*log(sin(d*x + c) + 1) - (C*a^3 - C*a*b^2)*log(-sin(d*x + c) + 1))/((a^3*b - a*b^3)*d), 1/2*(2*(A*a^2*b - A*b^3)*d*x - 2*(C*a^2 + 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))) + (C*a^3 - C*a*b^2)*log(sin(d*x + c) + 1) - (C*a^3 - C*a*b^2)*log(-sin(d*x + c) + 1))/((a^3*b - a*b^3)*d)]","A",0
680,1,306,0,0.509050," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(A a^{2} b - A b^{3}\right)} d x - {\left(C a^{2} + 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(A a^{2} b - A b^{3}\right)} d x - {\left(C a^{2} + 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*(A*a^2*b - A*b^3)*d*x - (C*a^2 + 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), -((A*a^2*b - A*b^3)*d*x - (C*a^2 + 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
681,1,386,0,0.514878," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left({\left(A + 2 \, C\right)} a^{4} + {\left(A - 2 \, C\right)} a^{2} b^{2} - 2 \, A b^{4}\right)} d x + {\left(C a^{2} b + 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 \, A a^{3} b - 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({\left(A + 2 \, C\right)} a^{4} + {\left(A - 2 \, C\right)} a^{2} b^{2} - 2 \, A b^{4}\right)} d x - 2 \, {\left(C a^{2} b + 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 \, A a^{3} b - 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 + 2*C)*a^4 + (A - 2*C)*a^2*b^2 - 2*A*b^4)*d*x + (C*a^2*b + 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*A*a^3*b - 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 + 2*C)*a^4 + (A - 2*C)*a^2*b^2 - 2*A*b^4)*d*x - 2*(C*a^2*b + 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*A*a^3*b - 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
682,1,483,0,0.526977," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(A + 2 \, C\right)} a^{4} b + {\left(A - 2 \, C\right)} a^{2} b^{3} - 2 \, A b^{5}\right)} d x - 3 \, {\left(C a^{2} b^{2} + 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(2 \, {\left(2 \, A + 3 \, C\right)} a^{5} + 2 \, {\left(A - 3 \, C\right)} a^{3} b^{2} - 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(A a^{4} b - 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({\left(A + 2 \, C\right)} a^{4} b + {\left(A - 2 \, C\right)} a^{2} b^{3} - 2 \, A b^{5}\right)} d x - 6 \, {\left(C a^{2} b^{2} + 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(2 \, {\left(2 \, A + 3 \, C\right)} a^{5} + 2 \, {\left(A - 3 \, C\right)} a^{3} b^{2} - 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(A a^{4} b - 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*((A + 2*C)*a^4*b + (A - 2*C)*a^2*b^3 - 2*A*b^5)*d*x - 3*(C*a^2*b^2 + 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)) - (2*(2*A + 3*C)*a^5 + 2*(A - 3*C)*a^3*b^2 - 6*A*a*b^4 + 2*(A*a^5 - A*a^3*b^2)*cos(d*x + c)^2 - 3*(A*a^4*b - A*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d), -1/6*(3*((A + 2*C)*a^4*b + (A - 2*C)*a^2*b^3 - 2*A*b^5)*d*x - 6*(C*a^2*b^2 + 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))) - (2*(2*A + 3*C)*a^5 + 2*(A - 3*C)*a^3*b^2 - 6*A*a*b^4 + 2*(A*a^5 - A*a^3*b^2)*cos(d*x + c)^2 - 3*(A*a^4*b - A*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d)]","A",0
683,1,599,0,0.575341," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{6} + {\left(A + 4 \, C\right)} a^{4} b^{2} + 4 \, {\left(A - 2 \, C\right)} a^{2} b^{4} - 8 \, A b^{6}\right)} d x + 12 \, {\left(C a^{2} b^{3} + 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(8 \, {\left(2 \, A + 3 \, C\right)} a^{5} b + 8 \, {\left(A - 3 \, C\right)} a^{3} b^{3} - 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(A a^{5} b - A a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{6} + {\left(A - 4 \, C\right)} a^{4} b^{2} - 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({\left(3 \, A + 4 \, C\right)} a^{6} + {\left(A + 4 \, C\right)} a^{4} b^{2} + 4 \, {\left(A - 2 \, C\right)} a^{2} b^{4} - 8 \, A b^{6}\right)} d x - 24 \, {\left(C a^{2} b^{3} + 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(8 \, {\left(2 \, A + 3 \, C\right)} a^{5} b + 8 \, {\left(A - 3 \, C\right)} a^{3} b^{3} - 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(A a^{5} b - A a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{6} + {\left(A - 4 \, C\right)} a^{4} b^{2} - 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 + 4*C)*a^6 + (A + 4*C)*a^4*b^2 + 4*(A - 2*C)*a^2*b^4 - 8*A*b^6)*d*x + 12*(C*a^2*b^3 + 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)) - (8*(2*A + 3*C)*a^5*b + 8*(A - 3*C)*a^3*b^3 - 24*A*a*b^5 - 6*(A*a^6 - A*a^4*b^2)*cos(d*x + c)^3 + 8*(A*a^5*b - A*a^3*b^3)*cos(d*x + c)^2 - 3*((3*A + 4*C)*a^6 + (A - 4*C)*a^4*b^2 - 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 + 4*C)*a^6 + (A + 4*C)*a^4*b^2 + 4*(A - 2*C)*a^2*b^4 - 8*A*b^6)*d*x - 24*(C*a^2*b^3 + 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))) - (8*(2*A + 3*C)*a^5*b + 8*(A - 3*C)*a^3*b^3 - 24*A*a*b^5 - 6*(A*a^6 - A*a^4*b^2)*cos(d*x + c)^3 + 8*(A*a^5*b - A*a^3*b^3)*cos(d*x + c)^2 - 3*((3*A + 4*C)*a^6 + (A - 4*C)*a^4*b^2 - 4*A*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^7 - a^5*b^2)*d)]","A",0
684,1,1135,0,13.316922," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(3 \, C a^{6} + {\left(A - 4 \, C\right)} a^{4} b^{2} - 2 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, C a^{5} b + {\left(A - 4 \, C\right)} a^{3} b^{3} - 2 \, A a b^{5}\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 \, C a^{7} + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} - 4 \, {\left(A - C\right)} a^{3} b^{4} + {\left(2 \, A + C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{2} b^{5} + {\left(2 \, A + C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(6 \, C a^{7} + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} - 4 \, {\left(A - C\right)} a^{3} b^{4} + {\left(2 \, A + C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{2} b^{5} + {\left(2 \, A + C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7} - 2 \, {\left(3 \, C a^{6} b + {\left(A - 5 \, C\right)} a^{4} b^{3} - {\left(A - 2 \, C\right)} a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{5} b^{2} - 2 \, C a^{3} b^{4} + C a b^{6}\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 \, C a^{6} + {\left(A - 4 \, C\right)} a^{4} b^{2} - 2 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, C a^{5} b + {\left(A - 4 \, C\right)} a^{3} b^{3} - 2 \, A a b^{5}\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 \, C a^{7} + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} - 4 \, {\left(A - C\right)} a^{3} b^{4} + {\left(2 \, A + C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{2} b^{5} + {\left(2 \, A + C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(6 \, C a^{7} + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} - 4 \, {\left(A - C\right)} a^{3} b^{4} + {\left(2 \, A + C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{2} b^{5} + {\left(2 \, A + C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7} - 2 \, {\left(3 \, C a^{6} b + {\left(A - 5 \, C\right)} a^{4} b^{3} - {\left(A - 2 \, C\right)} a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{5} b^{2} - 2 \, C a^{3} b^{4} + C a b^{6}\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*C*a^6 + (A - 4*C)*a^4*b^2 - 2*A*a^2*b^4)*cos(d*x + c)^3 + (3*C*a^5*b + (A - 4*C)*a^3*b^3 - 2*A*a*b^5)*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*C*a^7 + (2*A - 11*C)*a^5*b^2 - 4*(A - C)*a^3*b^4 + (2*A + C)*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b + (2*A - 11*C)*a^4*b^3 - 4*(A - C)*a^2*b^5 + (2*A + C)*b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((6*C*a^7 + (2*A - 11*C)*a^5*b^2 - 4*(A - C)*a^3*b^4 + (2*A + C)*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b + (2*A - 11*C)*a^4*b^3 - 4*(A - C)*a^2*b^5 + (2*A + C)*b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7 - 2*(3*C*a^6*b + (A - 5*C)*a^4*b^3 - (A - 2*C)*a^2*b^5)*cos(d*x + c)^2 - 3*(C*a^5*b^2 - 2*C*a^3*b^4 + C*a*b^6)*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*C*a^6 + (A - 4*C)*a^4*b^2 - 2*A*a^2*b^4)*cos(d*x + c)^3 + (3*C*a^5*b + (A - 4*C)*a^3*b^3 - 2*A*a*b^5)*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*C*a^7 + (2*A - 11*C)*a^5*b^2 - 4*(A - C)*a^3*b^4 + (2*A + C)*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b + (2*A - 11*C)*a^4*b^3 - 4*(A - C)*a^2*b^5 + (2*A + C)*b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((6*C*a^7 + (2*A - 11*C)*a^5*b^2 - 4*(A - C)*a^3*b^4 + (2*A + C)*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b + (2*A - 11*C)*a^4*b^3 - 4*(A - C)*a^2*b^5 + (2*A + C)*b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7 - 2*(3*C*a^6*b + (A - 5*C)*a^4*b^3 - (A - 2*C)*a^2*b^5)*cos(d*x + c)^2 - 3*(C*a^5*b^2 - 2*C*a^3*b^4 + C*a*b^6)*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
685,1,852,0,3.344233," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, C a^{5} - 3 \, C a^{3} b^{2} - A a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{4} b - 3 \, C a^{2} b^{3} - 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({\left(C a^{6} - 2 \, C a^{4} b^{2} + C a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{5} b - 2 \, C a^{3} b^{3} + C a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(C a^{6} - 2 \, C a^{4} b^{2} + C a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{5} b - 2 \, C a^{3} b^{3} + C a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C b^{6} + {\left(2 \, C a^{5} b + {\left(A - 3 \, C\right)} a^{3} b^{3} - {\left(A - C\right)} 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{{\left({\left(2 \, C a^{5} - 3 \, C a^{3} b^{2} - A a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{4} b - 3 \, C a^{2} b^{3} - 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({\left(C a^{6} - 2 \, C a^{4} b^{2} + C a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{5} b - 2 \, C a^{3} b^{3} + C a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(C a^{6} - 2 \, C a^{4} b^{2} + C a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{5} b - 2 \, C a^{3} b^{3} + C a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C b^{6} + {\left(2 \, C a^{5} b + {\left(A - 3 \, C\right)} a^{3} b^{3} - {\left(A - C\right)} a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\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]"," ",0,"[1/2*(((2*C*a^5 - 3*C*a^3*b^2 - A*a*b^4)*cos(d*x + c)^2 + (2*C*a^4*b - 3*C*a^2*b^3 - 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*((C*a^6 - 2*C*a^4*b^2 + C*a^2*b^4)*cos(d*x + c)^2 + (C*a^5*b - 2*C*a^3*b^3 + C*a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + 2*((C*a^6 - 2*C*a^4*b^2 + C*a^2*b^4)*cos(d*x + c)^2 + (C*a^5*b - 2*C*a^3*b^3 + C*a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(C*a^4*b^2 - 2*C*a^2*b^4 + C*b^6 + (2*C*a^5*b + (A - 3*C)*a^3*b^3 - (A - C)*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)), (((2*C*a^5 - 3*C*a^3*b^2 - A*a*b^4)*cos(d*x + c)^2 + (2*C*a^4*b - 3*C*a^2*b^3 - 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))) - ((C*a^6 - 2*C*a^4*b^2 + C*a^2*b^4)*cos(d*x + c)^2 + (C*a^5*b - 2*C*a^3*b^3 + C*a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((C*a^6 - 2*C*a^4*b^2 + C*a^2*b^4)*cos(d*x + c)^2 + (C*a^5*b - 2*C*a^3*b^3 + C*a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (C*a^4*b^2 - 2*C*a^2*b^4 + C*b^6 + (2*C*a^5*b + (A - 3*C)*a^3*b^3 - (A - C)*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
686,1,676,0,2.513372," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(C a^{3} b - {\left(A + 2 \, C\right)} a b^{3} + {\left(C a^{4} - {\left(A + 2 \, C\right)} a^{2} b^{2}\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(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{4} b + {\left(A - C\right)} a^{2} b^{3} - A b^{5}\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(C a^{3} b - {\left(A + 2 \, C\right)} a b^{3} + {\left(C a^{4} - {\left(A + 2 \, C\right)} a^{2} b^{2}\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(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b + {\left(A - C\right)} a^{2} b^{3} - A b^{5}\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*((C*a^3*b - (A + 2*C)*a*b^3 + (C*a^4 - (A + 2*C)*a^2*b^2)*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)) + (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) - (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(C*a^4*b + (A - C)*a^2*b^3 - A*b^5)*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*(C*a^3*b - (A + 2*C)*a*b^3 + (C*a^4 - (A + 2*C)*a^2*b^2)*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))) - (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) + (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(C*a^4*b + (A - C)*a^2*b^3 - A*b^5)*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
687,1,543,0,0.503464," ","integrate((A+C*sec(d*x+c)^2)/(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({\left(2 \, A + C\right)} a^{2} b^{2} - A b^{4} + {\left({\left(2 \, A + C\right)} 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(C a^{5} + {\left(A - C\right)} a^{3} b^{2} - 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({\left(2 \, A + C\right)} a^{2} b^{2} - A b^{4} + {\left({\left(2 \, A + C\right)} 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(C a^{5} + {\left(A - C\right)} a^{3} b^{2} - 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 - ((2*A + C)*a^2*b^2 - A*b^4 + ((2*A + C)*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*(C*a^5 + (A - C)*a^3*b^2 - 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 - ((2*A + C)*a^2*b^2 - A*b^4 + ((2*A + C)*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))) + (C*a^5 + (A - C)*a^3*b^2 - 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
688,1,642,0,0.529577," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(A a^{5} b - 2 \, A a^{3} b^{3} + A a b^{5}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(A a^{4} b^{2} - 2 \, A a^{2} b^{4} + A b^{6}\right)} d x + {\left(C a^{4} b + 3 \, A a^{2} b^{3} - 2 \, A b^{5} + {\left(C a^{5} + 3 \, A a^{3} b^{2} - 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({\left(A - C\right)} a^{5} b - {\left(3 \, A - C\right)} a^{3} b^{3} + 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{2 \, {\left(A a^{5} b - 2 \, A a^{3} b^{3} + A a b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(A a^{4} b^{2} - 2 \, A a^{2} b^{4} + A b^{6}\right)} d x - {\left(C a^{4} b + 3 \, A a^{2} b^{3} - 2 \, A b^{5} + {\left(C a^{5} + 3 \, A a^{3} b^{2} - 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(A - C\right)} a^{5} b - {\left(3 \, A - C\right)} a^{3} b^{3} + 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*(4*(A*a^5*b - 2*A*a^3*b^3 + A*a*b^5)*d*x*cos(d*x + c) + 4*(A*a^4*b^2 - 2*A*a^2*b^4 + A*b^6)*d*x + (C*a^4*b + 3*A*a^2*b^3 - 2*A*b^5 + (C*a^5 + 3*A*a^3*b^2 - 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 - C)*a^5*b - (3*A - C)*a^3*b^3 + 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), -(2*(A*a^5*b - 2*A*a^3*b^3 + A*a*b^5)*d*x*cos(d*x + c) + 2*(A*a^4*b^2 - 2*A*a^2*b^4 + A*b^6)*d*x - (C*a^4*b + 3*A*a^2*b^3 - 2*A*b^5 + (C*a^5 + 3*A*a^3*b^2 - 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 - C)*a^5*b - (3*A - C)*a^3*b^3 + 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)]","A",0
689,1,838,0,0.594820," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(A + 2 \, C\right)} a^{7} + 4 \, {\left(A - C\right)} a^{5} b^{2} - {\left(11 \, A - 2 \, C\right)} a^{3} b^{4} + 6 \, A a b^{6}\right)} d x \cos\left(d x + c\right) + {\left({\left(A + 2 \, C\right)} a^{6} b + 4 \, {\left(A - C\right)} a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} + 6 \, A b^{7}\right)} d x + {\left(2 \, C a^{4} b^{2} + {\left(4 \, A - C\right)} a^{2} b^{4} - 3 \, A b^{6} + {\left(2 \, C a^{5} b + {\left(4 \, A - C\right)} a^{3} b^{3} - 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 \, {\left(2 \, A - C\right)} a^{5} b^{2} - 2 \, {\left(5 \, A - C\right)} a^{3} b^{4} + 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} + 3 \, {\left(A a^{6} b - 2 \, A a^{4} b^{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({\left(A + 2 \, C\right)} a^{7} + 4 \, {\left(A - C\right)} a^{5} b^{2} - {\left(11 \, A - 2 \, C\right)} a^{3} b^{4} + 6 \, A a b^{6}\right)} d x \cos\left(d x + c\right) + {\left({\left(A + 2 \, C\right)} a^{6} b + 4 \, {\left(A - C\right)} a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} + 6 \, A b^{7}\right)} d x - 2 \, {\left(2 \, C a^{4} b^{2} + {\left(4 \, A - C\right)} a^{2} b^{4} - 3 \, A b^{6} + {\left(2 \, C a^{5} b + {\left(4 \, A - C\right)} a^{3} b^{3} - 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 \, {\left(2 \, A - C\right)} a^{5} b^{2} - 2 \, {\left(5 \, A - C\right)} a^{3} b^{4} + 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} + 3 \, {\left(A a^{6} b - 2 \, A a^{4} b^{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 + 2*C)*a^7 + 4*(A - C)*a^5*b^2 - (11*A - 2*C)*a^3*b^4 + 6*A*a*b^6)*d*x*cos(d*x + c) + ((A + 2*C)*a^6*b + 4*(A - C)*a^4*b^3 - (11*A - 2*C)*a^2*b^5 + 6*A*b^7)*d*x + (2*C*a^4*b^2 + (4*A - C)*a^2*b^4 - 3*A*b^6 + (2*C*a^5*b + (4*A - C)*a^3*b^3 - 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*(2*A - C)*a^5*b^2 - 2*(5*A - C)*a^3*b^4 + 6*A*a*b^6 - (A*a^7 - 2*A*a^5*b^2 + A*a^3*b^4)*cos(d*x + c)^2 + 3*(A*a^6*b - 2*A*a^4*b^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 + 2*C)*a^7 + 4*(A - C)*a^5*b^2 - (11*A - 2*C)*a^3*b^4 + 6*A*a*b^6)*d*x*cos(d*x + c) + ((A + 2*C)*a^6*b + 4*(A - C)*a^4*b^3 - (11*A - 2*C)*a^2*b^5 + 6*A*b^7)*d*x - 2*(2*C*a^4*b^2 + (4*A - C)*a^2*b^4 - 3*A*b^6 + (2*C*a^5*b + (4*A - C)*a^3*b^3 - 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*(2*A - C)*a^5*b^2 - 2*(5*A - C)*a^3*b^4 + 6*A*a*b^6 - (A*a^7 - 2*A*a^5*b^2 + A*a^3*b^4)*cos(d*x + c)^2 + 3*(A*a^6*b - 2*A*a^4*b^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
690,1,989,0,0.577541," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left({\left(A + 2 \, C\right)} a^{7} b + 2 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - {\left(7 \, A - 2 \, C\right)} a^{3} b^{5} + 4 \, A a b^{7}\right)} d x \cos\left(d x + c\right) + 6 \, {\left({\left(A + 2 \, C\right)} a^{6} b^{2} + 2 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 4 \, A b^{8}\right)} d x - 3 \, {\left(3 \, C a^{4} b^{3} + {\left(5 \, A - 2 \, C\right)} a^{2} b^{5} - 4 \, A b^{7} + {\left(3 \, C a^{5} b^{2} + {\left(5 \, A - 2 \, C\right)} a^{3} b^{4} - 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) - 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{7} b + {\left(5 \, A - 9 \, C\right)} a^{5} b^{3} - {\left(19 \, A - 6 \, C\right)} a^{3} b^{5} + 12 \, A a b^{7} + {\left(A a^{8} - 2 \, A a^{6} b^{2} + A a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(A a^{7} b - 2 \, A a^{5} b^{3} + A a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(2 \, A + 3 \, C\right)} a^{8} + 2 \, {\left(A - 3 \, C\right)} a^{6} b^{2} - {\left(10 \, A - 3 \, C\right)} a^{4} b^{4} + 6 \, 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({\left(A + 2 \, C\right)} a^{7} b + 2 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - {\left(7 \, A - 2 \, C\right)} a^{3} b^{5} + 4 \, A a b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left({\left(A + 2 \, C\right)} a^{6} b^{2} + 2 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 4 \, A b^{8}\right)} d x - 3 \, {\left(3 \, C a^{4} b^{3} + {\left(5 \, A - 2 \, C\right)} a^{2} b^{5} - 4 \, A b^{7} + {\left(3 \, C a^{5} b^{2} + {\left(5 \, A - 2 \, C\right)} a^{3} b^{4} - 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({\left(2 \, A + 3 \, C\right)} a^{7} b + {\left(5 \, A - 9 \, C\right)} a^{5} b^{3} - {\left(19 \, A - 6 \, C\right)} a^{3} b^{5} + 12 \, A a b^{7} + {\left(A a^{8} - 2 \, A a^{6} b^{2} + A a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(A a^{7} b - 2 \, A a^{5} b^{3} + A a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(2 \, A + 3 \, C\right)} a^{8} + 2 \, {\left(A - 3 \, C\right)} a^{6} b^{2} - {\left(10 \, A - 3 \, C\right)} a^{4} b^{4} + 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\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*(6*((A + 2*C)*a^7*b + 2*(A - 2*C)*a^5*b^3 - (7*A - 2*C)*a^3*b^5 + 4*A*a*b^7)*d*x*cos(d*x + c) + 6*((A + 2*C)*a^6*b^2 + 2*(A - 2*C)*a^4*b^4 - (7*A - 2*C)*a^2*b^6 + 4*A*b^8)*d*x - 3*(3*C*a^4*b^3 + (5*A - 2*C)*a^2*b^5 - 4*A*b^7 + (3*C*a^5*b^2 + (5*A - 2*C)*a^3*b^4 - 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)) - 2*((2*A + 3*C)*a^7*b + (5*A - 9*C)*a^5*b^3 - (19*A - 6*C)*a^3*b^5 + 12*A*a*b^7 + (A*a^8 - 2*A*a^6*b^2 + A*a^4*b^4)*cos(d*x + c)^3 - 2*(A*a^7*b - 2*A*a^5*b^3 + A*a^3*b^5)*cos(d*x + c)^2 + ((2*A + 3*C)*a^8 + 2*(A - 3*C)*a^6*b^2 - (10*A - 3*C)*a^4*b^4 + 6*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), -1/3*(3*((A + 2*C)*a^7*b + 2*(A - 2*C)*a^5*b^3 - (7*A - 2*C)*a^3*b^5 + 4*A*a*b^7)*d*x*cos(d*x + c) + 3*((A + 2*C)*a^6*b^2 + 2*(A - 2*C)*a^4*b^4 - (7*A - 2*C)*a^2*b^6 + 4*A*b^8)*d*x - 3*(3*C*a^4*b^3 + (5*A - 2*C)*a^2*b^5 - 4*A*b^7 + (3*C*a^5*b^2 + (5*A - 2*C)*a^3*b^4 - 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))) - ((2*A + 3*C)*a^7*b + (5*A - 9*C)*a^5*b^3 - (19*A - 6*C)*a^3*b^5 + 12*A*a*b^7 + (A*a^8 - 2*A*a^6*b^2 + A*a^4*b^4)*cos(d*x + c)^3 - 2*(A*a^7*b - 2*A*a^5*b^3 + A*a^3*b^5)*cos(d*x + c)^2 + ((2*A + 3*C)*a^8 + 2*(A - 3*C)*a^6*b^2 - (10*A - 3*C)*a^4*b^4 + 6*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
691,1,2084,0,34.689653," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(12 \, C a^{9} + {\left(2 \, A - 29 \, C\right)} a^{7} b^{2} - 5 \, {\left(A - 4 \, C\right)} a^{5} b^{4} + 6 \, A a^{3} b^{6}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, C a^{8} b + {\left(2 \, A - 29 \, C\right)} a^{6} b^{3} - 5 \, {\left(A - 4 \, C\right)} a^{4} b^{5} + 6 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, C a^{7} b^{2} + {\left(2 \, A - 29 \, C\right)} a^{5} b^{4} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} + 6 \, A a b^{8}\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 \, C a^{10} + {\left(2 \, A - 35 \, C\right)} a^{8} b^{2} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{6} b^{4} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{4} b^{6} - {\left(2 \, A + C\right)} a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, C a^{9} b + {\left(2 \, A - 35 \, C\right)} a^{7} b^{3} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{5} b^{5} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{3} b^{7} - {\left(2 \, A + C\right)} a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, C a^{8} b^{2} + {\left(2 \, A - 35 \, C\right)} a^{6} b^{4} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{4} b^{6} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{2} b^{8} - {\left(2 \, A + C\right)} b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(12 \, C a^{10} + {\left(2 \, A - 35 \, C\right)} a^{8} b^{2} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{6} b^{4} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{4} b^{6} - {\left(2 \, A + C\right)} a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, C a^{9} b + {\left(2 \, A - 35 \, C\right)} a^{7} b^{3} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{5} b^{5} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{3} b^{7} - {\left(2 \, A + C\right)} a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, C a^{8} b^{2} + {\left(2 \, A - 35 \, C\right)} a^{6} b^{4} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{4} b^{6} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{2} b^{8} - {\left(2 \, A + C\right)} b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{6} b^{4} - 3 \, C a^{4} b^{6} + 3 \, C a^{2} b^{8} - C b^{10} - {\left(12 \, C a^{9} b + {\left(2 \, A - 33 \, C\right)} a^{7} b^{3} - {\left(7 \, A - 27 \, C\right)} a^{5} b^{5} + {\left(5 \, A - 6 \, C\right)} a^{3} b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(18 \, C a^{8} b^{2} + {\left(3 \, A - 50 \, C\right)} a^{6} b^{4} - {\left(9 \, A - 43 \, C\right)} a^{4} b^{6} + {\left(6 \, A - 11 \, C\right)} a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(C a^{7} b^{3} - 3 \, C a^{5} b^{5} + 3 \, C a^{3} b^{7} - C a b^{9}\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 \, C a^{9} + {\left(2 \, A - 29 \, C\right)} a^{7} b^{2} - 5 \, {\left(A - 4 \, C\right)} a^{5} b^{4} + 6 \, A a^{3} b^{6}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, C a^{8} b + {\left(2 \, A - 29 \, C\right)} a^{6} b^{3} - 5 \, {\left(A - 4 \, C\right)} a^{4} b^{5} + 6 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, C a^{7} b^{2} + {\left(2 \, A - 29 \, C\right)} a^{5} b^{4} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} + 6 \, A a b^{8}\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 \, C a^{10} + {\left(2 \, A - 35 \, C\right)} a^{8} b^{2} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{6} b^{4} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{4} b^{6} - {\left(2 \, A + C\right)} a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, C a^{9} b + {\left(2 \, A - 35 \, C\right)} a^{7} b^{3} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{5} b^{5} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{3} b^{7} - {\left(2 \, A + C\right)} a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, C a^{8} b^{2} + {\left(2 \, A - 35 \, C\right)} a^{6} b^{4} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{4} b^{6} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{2} b^{8} - {\left(2 \, A + C\right)} b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(12 \, C a^{10} + {\left(2 \, A - 35 \, C\right)} a^{8} b^{2} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{6} b^{4} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{4} b^{6} - {\left(2 \, A + C\right)} a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, C a^{9} b + {\left(2 \, A - 35 \, C\right)} a^{7} b^{3} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{5} b^{5} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{3} b^{7} - {\left(2 \, A + C\right)} a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, C a^{8} b^{2} + {\left(2 \, A - 35 \, C\right)} a^{6} b^{4} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{4} b^{6} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{2} b^{8} - {\left(2 \, A + C\right)} b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{6} b^{4} - 3 \, C a^{4} b^{6} + 3 \, C a^{2} b^{8} - C b^{10} - {\left(12 \, C a^{9} b + {\left(2 \, A - 33 \, C\right)} a^{7} b^{3} - {\left(7 \, A - 27 \, C\right)} a^{5} b^{5} + {\left(5 \, A - 6 \, C\right)} a^{3} b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(18 \, C a^{8} b^{2} + {\left(3 \, A - 50 \, C\right)} a^{6} b^{4} - {\left(9 \, A - 43 \, C\right)} a^{4} b^{6} + {\left(6 \, A - 11 \, C\right)} a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(C a^{7} b^{3} - 3 \, C a^{5} b^{5} + 3 \, C a^{3} b^{7} - C a b^{9}\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*C*a^9 + (2*A - 29*C)*a^7*b^2 - 5*(A - 4*C)*a^5*b^4 + 6*A*a^3*b^6)*cos(d*x + c)^4 + 2*(12*C*a^8*b + (2*A - 29*C)*a^6*b^3 - 5*(A - 4*C)*a^4*b^5 + 6*A*a^2*b^7)*cos(d*x + c)^3 + (12*C*a^7*b^2 + (2*A - 29*C)*a^5*b^4 - 5*(A - 4*C)*a^3*b^6 + 6*A*a*b^8)*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*C*a^10 + (2*A - 35*C)*a^8*b^2 - 3*(2*A - 11*C)*a^6*b^4 + 3*(2*A - 3*C)*a^4*b^6 - (2*A + C)*a^2*b^8)*cos(d*x + c)^4 + 2*(12*C*a^9*b + (2*A - 35*C)*a^7*b^3 - 3*(2*A - 11*C)*a^5*b^5 + 3*(2*A - 3*C)*a^3*b^7 - (2*A + C)*a*b^9)*cos(d*x + c)^3 + (12*C*a^8*b^2 + (2*A - 35*C)*a^6*b^4 - 3*(2*A - 11*C)*a^4*b^6 + 3*(2*A - 3*C)*a^2*b^8 - (2*A + C)*b^10)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((12*C*a^10 + (2*A - 35*C)*a^8*b^2 - 3*(2*A - 11*C)*a^6*b^4 + 3*(2*A - 3*C)*a^4*b^6 - (2*A + C)*a^2*b^8)*cos(d*x + c)^4 + 2*(12*C*a^9*b + (2*A - 35*C)*a^7*b^3 - 3*(2*A - 11*C)*a^5*b^5 + 3*(2*A - 3*C)*a^3*b^7 - (2*A + C)*a*b^9)*cos(d*x + c)^3 + (12*C*a^8*b^2 + (2*A - 35*C)*a^6*b^4 - 3*(2*A - 11*C)*a^4*b^6 + 3*(2*A - 3*C)*a^2*b^8 - (2*A + C)*b^10)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(C*a^6*b^4 - 3*C*a^4*b^6 + 3*C*a^2*b^8 - C*b^10 - (12*C*a^9*b + (2*A - 33*C)*a^7*b^3 - (7*A - 27*C)*a^5*b^5 + (5*A - 6*C)*a^3*b^7)*cos(d*x + c)^3 - (18*C*a^8*b^2 + (3*A - 50*C)*a^6*b^4 - (9*A - 43*C)*a^4*b^6 + (6*A - 11*C)*a^2*b^8)*cos(d*x + c)^2 - 4*(C*a^7*b^3 - 3*C*a^5*b^5 + 3*C*a^3*b^7 - C*a*b^9)*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*C*a^9 + (2*A - 29*C)*a^7*b^2 - 5*(A - 4*C)*a^5*b^4 + 6*A*a^3*b^6)*cos(d*x + c)^4 + 2*(12*C*a^8*b + (2*A - 29*C)*a^6*b^3 - 5*(A - 4*C)*a^4*b^5 + 6*A*a^2*b^7)*cos(d*x + c)^3 + (12*C*a^7*b^2 + (2*A - 29*C)*a^5*b^4 - 5*(A - 4*C)*a^3*b^6 + 6*A*a*b^8)*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*C*a^10 + (2*A - 35*C)*a^8*b^2 - 3*(2*A - 11*C)*a^6*b^4 + 3*(2*A - 3*C)*a^4*b^6 - (2*A + C)*a^2*b^8)*cos(d*x + c)^4 + 2*(12*C*a^9*b + (2*A - 35*C)*a^7*b^3 - 3*(2*A - 11*C)*a^5*b^5 + 3*(2*A - 3*C)*a^3*b^7 - (2*A + C)*a*b^9)*cos(d*x + c)^3 + (12*C*a^8*b^2 + (2*A - 35*C)*a^6*b^4 - 3*(2*A - 11*C)*a^4*b^6 + 3*(2*A - 3*C)*a^2*b^8 - (2*A + C)*b^10)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((12*C*a^10 + (2*A - 35*C)*a^8*b^2 - 3*(2*A - 11*C)*a^6*b^4 + 3*(2*A - 3*C)*a^4*b^6 - (2*A + C)*a^2*b^8)*cos(d*x + c)^4 + 2*(12*C*a^9*b + (2*A - 35*C)*a^7*b^3 - 3*(2*A - 11*C)*a^5*b^5 + 3*(2*A - 3*C)*a^3*b^7 - (2*A + C)*a*b^9)*cos(d*x + c)^3 + (12*C*a^8*b^2 + (2*A - 35*C)*a^6*b^4 - 3*(2*A - 11*C)*a^4*b^6 + 3*(2*A - 3*C)*a^2*b^8 - (2*A + C)*b^10)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(C*a^6*b^4 - 3*C*a^4*b^6 + 3*C*a^2*b^8 - C*b^10 - (12*C*a^9*b + (2*A - 33*C)*a^7*b^3 - (7*A - 27*C)*a^5*b^5 + (5*A - 6*C)*a^3*b^7)*cos(d*x + c)^3 - (18*C*a^8*b^2 + (3*A - 50*C)*a^6*b^4 - (9*A - 43*C)*a^4*b^6 + (6*A - 11*C)*a^2*b^8)*cos(d*x + c)^2 - 4*(C*a^7*b^3 - 3*C*a^5*b^5 + 3*C*a^3*b^7 - C*a*b^9)*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
692,1,1552,0,12.351632," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(6 \, C a^{8} - 15 \, C a^{6} b^{2} + {\left(A + 12 \, C\right)} a^{4} b^{4} + 2 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, C a^{7} b - 15 \, C a^{5} b^{3} + {\left(A + 12 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{6} b^{2} - 15 \, C a^{4} b^{4} + {\left(A + 12 \, C\right)} a^{2} b^{6} + 2 \, 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) - 6 \, {\left({\left(C a^{9} - 3 \, C a^{7} b^{2} + 3 \, C a^{5} b^{4} - C a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(C a^{8} b - 3 \, C a^{6} b^{3} + 3 \, C a^{4} b^{5} - C a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{7} b^{2} - 3 \, C a^{5} b^{4} + 3 \, C a^{3} b^{6} - C a b^{8}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, {\left({\left(C a^{9} - 3 \, C a^{7} b^{2} + 3 \, C a^{5} b^{4} - C a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(C a^{8} b - 3 \, C a^{6} b^{3} + 3 \, C a^{4} b^{5} - C a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{7} b^{2} - 3 \, C a^{5} b^{4} + 3 \, C a^{3} b^{6} - C a b^{8}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{6} b^{3} - 6 \, C a^{4} b^{5} + 6 \, C a^{2} b^{7} - 2 \, C b^{9} + {\left(6 \, C a^{8} b - 17 \, C a^{6} b^{3} - {\left(3 \, A - 13 \, C\right)} a^{4} b^{5} + {\left(3 \, A - 2 \, C\right)} a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} + {\left(A - 25 \, C\right)} a^{5} b^{4} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} + 4 \, {\left(A - C\right)} 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 \, C a^{8} - 15 \, C a^{6} b^{2} + {\left(A + 12 \, C\right)} a^{4} b^{4} + 2 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, C a^{7} b - 15 \, C a^{5} b^{3} + {\left(A + 12 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{6} b^{2} - 15 \, C a^{4} b^{4} + {\left(A + 12 \, C\right)} a^{2} b^{6} + 2 \, 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) - 3 \, {\left({\left(C a^{9} - 3 \, C a^{7} b^{2} + 3 \, C a^{5} b^{4} - C a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(C a^{8} b - 3 \, C a^{6} b^{3} + 3 \, C a^{4} b^{5} - C a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{7} b^{2} - 3 \, C a^{5} b^{4} + 3 \, C a^{3} b^{6} - C a b^{8}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(C a^{9} - 3 \, C a^{7} b^{2} + 3 \, C a^{5} b^{4} - C a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(C a^{8} b - 3 \, C a^{6} b^{3} + 3 \, C a^{4} b^{5} - C a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{7} b^{2} - 3 \, C a^{5} b^{4} + 3 \, C a^{3} b^{6} - C a b^{8}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{6} b^{3} - 6 \, C a^{4} b^{5} + 6 \, C a^{2} b^{7} - 2 \, C b^{9} + {\left(6 \, C a^{8} b - 17 \, C a^{6} b^{3} - {\left(3 \, A - 13 \, C\right)} a^{4} b^{5} + {\left(3 \, A - 2 \, C\right)} a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} + {\left(A - 25 \, C\right)} a^{5} b^{4} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} + 4 \, {\left(A - C\right)} 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*C*a^8 - 15*C*a^6*b^2 + (A + 12*C)*a^4*b^4 + 2*A*a^2*b^6)*cos(d*x + c)^3 + 2*(6*C*a^7*b - 15*C*a^5*b^3 + (A + 12*C)*a^3*b^5 + 2*A*a*b^7)*cos(d*x + c)^2 + (6*C*a^6*b^2 - 15*C*a^4*b^4 + (A + 12*C)*a^2*b^6 + 2*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)) - 6*((C*a^9 - 3*C*a^7*b^2 + 3*C*a^5*b^4 - C*a^3*b^6)*cos(d*x + c)^3 + 2*(C*a^8*b - 3*C*a^6*b^3 + 3*C*a^4*b^5 - C*a^2*b^7)*cos(d*x + c)^2 + (C*a^7*b^2 - 3*C*a^5*b^4 + 3*C*a^3*b^6 - C*a*b^8)*cos(d*x + c))*log(sin(d*x + c) + 1) + 6*((C*a^9 - 3*C*a^7*b^2 + 3*C*a^5*b^4 - C*a^3*b^6)*cos(d*x + c)^3 + 2*(C*a^8*b - 3*C*a^6*b^3 + 3*C*a^4*b^5 - C*a^2*b^7)*cos(d*x + c)^2 + (C*a^7*b^2 - 3*C*a^5*b^4 + 3*C*a^3*b^6 - C*a*b^8)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(2*C*a^6*b^3 - 6*C*a^4*b^5 + 6*C*a^2*b^7 - 2*C*b^9 + (6*C*a^8*b - 17*C*a^6*b^3 - (3*A - 13*C)*a^4*b^5 + (3*A - 2*C)*a^2*b^7)*cos(d*x + c)^2 + (9*C*a^7*b^2 + (A - 25*C)*a^5*b^4 - 5*(A - 4*C)*a^3*b^6 + 4*(A - C)*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*C*a^8 - 15*C*a^6*b^2 + (A + 12*C)*a^4*b^4 + 2*A*a^2*b^6)*cos(d*x + c)^3 + 2*(6*C*a^7*b - 15*C*a^5*b^3 + (A + 12*C)*a^3*b^5 + 2*A*a*b^7)*cos(d*x + c)^2 + (6*C*a^6*b^2 - 15*C*a^4*b^4 + (A + 12*C)*a^2*b^6 + 2*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))) - 3*((C*a^9 - 3*C*a^7*b^2 + 3*C*a^5*b^4 - C*a^3*b^6)*cos(d*x + c)^3 + 2*(C*a^8*b - 3*C*a^6*b^3 + 3*C*a^4*b^5 - C*a^2*b^7)*cos(d*x + c)^2 + (C*a^7*b^2 - 3*C*a^5*b^4 + 3*C*a^3*b^6 - C*a*b^8)*cos(d*x + c))*log(sin(d*x + c) + 1) + 3*((C*a^9 - 3*C*a^7*b^2 + 3*C*a^5*b^4 - C*a^3*b^6)*cos(d*x + c)^3 + 2*(C*a^8*b - 3*C*a^6*b^3 + 3*C*a^4*b^5 - C*a^2*b^7)*cos(d*x + c)^2 + (C*a^7*b^2 - 3*C*a^5*b^4 + 3*C*a^3*b^6 - C*a*b^8)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (2*C*a^6*b^3 - 6*C*a^4*b^5 + 6*C*a^2*b^7 - 2*C*b^9 + (6*C*a^8*b - 17*C*a^6*b^3 - (3*A - 13*C)*a^4*b^5 + (3*A - 2*C)*a^2*b^7)*cos(d*x + c)^2 + (9*C*a^7*b^2 + (A - 25*C)*a^5*b^4 - 5*(A - 4*C)*a^3*b^6 + 4*(A - C)*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
693,1,1317,0,7.508992," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} + 3 \, {\left(A + 2 \, C\right)} a b^{6} + {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} + 3 \, {\left(A + 2 \, C\right)} a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} + 3 \, {\left(A + 2 \, C\right)} a^{2} 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(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(3 \, C a^{6} b^{2} - {\left(A + 9 \, C\right)} a^{4} b^{4} - {\left(A - 6 \, C\right)} a^{2} b^{6} + 2 \, A b^{8} + {\left(2 \, C a^{7} b - {\left(2 \, A + 7 \, C\right)} a^{5} b^{3} + {\left(A + 5 \, C\right)} a^{3} b^{5} + A a b^{7}\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 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} + 3 \, {\left(A + 2 \, C\right)} a b^{6} + {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} + 3 \, {\left(A + 2 \, C\right)} a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} + 3 \, {\left(A + 2 \, C\right)} a^{2} 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(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(3 \, C a^{6} b^{2} - {\left(A + 9 \, C\right)} a^{4} b^{4} - {\left(A - 6 \, C\right)} a^{2} b^{6} + 2 \, A b^{8} + {\left(2 \, C a^{7} b - {\left(2 \, A + 7 \, C\right)} a^{5} b^{3} + {\left(A + 5 \, C\right)} a^{3} b^{5} + A a b^{7}\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*C*a^5*b^2 - 5*C*a^3*b^4 + 3*(A + 2*C)*a*b^6 + (2*C*a^7 - 5*C*a^5*b^2 + 3*(A + 2*C)*a^3*b^4)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 + 3*(A + 2*C)*a^2*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*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) - 2*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(3*C*a^6*b^2 - (A + 9*C)*a^4*b^4 - (A - 6*C)*a^2*b^6 + 2*A*b^8 + (2*C*a^7*b - (2*A + 7*C)*a^5*b^3 + (A + 5*C)*a^3*b^5 + A*a*b^7)*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*C*a^5*b^2 - 5*C*a^3*b^4 + 3*(A + 2*C)*a*b^6 + (2*C*a^7 - 5*C*a^5*b^2 + 3*(A + 2*C)*a^3*b^4)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 + 3*(A + 2*C)*a^2*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))) - (C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + (C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (3*C*a^6*b^2 - (A + 9*C)*a^4*b^4 - (A - 6*C)*a^2*b^6 + 2*A*b^8 + (2*C*a^7*b - (2*A + 7*C)*a^5*b^3 + (A + 5*C)*a^3*b^5 + A*a*b^7)*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
694,1,718,0,0.565509," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, A + C\right)} a^{2} b^{2} + {\left(A + 2 \, C\right)} b^{4} + {\left({\left(2 \, A + C\right)} a^{4} + {\left(A + 2 \, C\right)} a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, A + C\right)} a^{3} b + {\left(A + 2 \, C\right)} 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(C a^{5} - {\left(3 \, A + 5 \, C\right)} a^{3} b^{2} + {\left(3 \, A + 4 \, C\right)} a b^{4} - {\left({\left(4 \, A + 3 \, C\right)} a^{4} b - {\left(5 \, A + 3 \, C\right)} a^{2} b^{3} + 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({\left(2 \, A + C\right)} a^{2} b^{2} + {\left(A + 2 \, C\right)} b^{4} + {\left({\left(2 \, A + C\right)} a^{4} + {\left(A + 2 \, C\right)} a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, A + C\right)} a^{3} b + {\left(A + 2 \, C\right)} 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(C a^{5} - {\left(3 \, A + 5 \, C\right)} a^{3} b^{2} + {\left(3 \, A + 4 \, C\right)} a b^{4} - {\left({\left(4 \, A + 3 \, C\right)} a^{4} b - {\left(5 \, A + 3 \, C\right)} a^{2} b^{3} + 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 + C)*a^2*b^2 + (A + 2*C)*b^4 + ((2*A + C)*a^4 + (A + 2*C)*a^2*b^2)*cos(d*x + c)^2 + 2*((2*A + C)*a^3*b + (A + 2*C)*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*(C*a^5 - (3*A + 5*C)*a^3*b^2 + (3*A + 4*C)*a*b^4 - ((4*A + 3*C)*a^4*b - (5*A + 3*C)*a^2*b^3 + 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 + C)*a^2*b^2 + (A + 2*C)*b^4 + ((2*A + C)*a^4 + (A + 2*C)*a^2*b^2)*cos(d*x + c)^2 + 2*((2*A + C)*a^3*b + (A + 2*C)*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))) + (C*a^5 - (3*A + 5*C)*a^3*b^2 + (3*A + 4*C)*a*b^4 - ((4*A + 3*C)*a^4*b - (5*A + 3*C)*a^2*b^3 + 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
695,1,1059,0,0.556720," ","integrate((A+C*sec(d*x+c)^2)/(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(3 \, {\left(2 \, A + C\right)} a^{4} b^{3} - 5 \, A a^{2} b^{5} + 2 \, A b^{7} + {\left(3 \, {\left(2 \, A + C\right)} a^{6} b - 5 \, A a^{4} b^{3} + 2 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, A + C\right)} a^{5} b^{2} - 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(C a^{7} b + {\left(5 \, A + C\right)} a^{5} b^{3} - {\left(7 \, A + 2 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7} + {\left(2 \, C a^{8} + {\left(6 \, A - C\right)} a^{6} b^{2} - {\left(9 \, A + C\right)} a^{4} b^{4} + 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(3 \, {\left(2 \, A + C\right)} a^{4} b^{3} - 5 \, A a^{2} b^{5} + 2 \, A b^{7} + {\left(3 \, {\left(2 \, A + C\right)} a^{6} b - 5 \, A a^{4} b^{3} + 2 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, A + C\right)} a^{5} b^{2} - 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(C a^{7} b + {\left(5 \, A + C\right)} a^{5} b^{3} - {\left(7 \, A + 2 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7} + {\left(2 \, C a^{8} + {\left(6 \, A - C\right)} a^{6} b^{2} - {\left(9 \, A + C\right)} a^{4} b^{4} + 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 + (3*(2*A + C)*a^4*b^3 - 5*A*a^2*b^5 + 2*A*b^7 + (3*(2*A + C)*a^6*b - 5*A*a^4*b^3 + 2*A*a^2*b^5)*cos(d*x + c)^2 + 2*(3*(2*A + C)*a^5*b^2 - 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*(C*a^7*b + (5*A + C)*a^5*b^3 - (7*A + 2*C)*a^3*b^5 + 2*A*a*b^7 + (2*C*a^8 + (6*A - C)*a^6*b^2 - (9*A + C)*a^4*b^4 + 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 - (3*(2*A + C)*a^4*b^3 - 5*A*a^2*b^5 + 2*A*b^7 + (3*(2*A + C)*a^6*b - 5*A*a^4*b^3 + 2*A*a^2*b^5)*cos(d*x + c)^2 + 2*(3*(2*A + C)*a^5*b^2 - 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))) + (C*a^7*b + (5*A + C)*a^5*b^3 - (7*A + 2*C)*a^3*b^5 + 2*A*a*b^7 + (2*C*a^8 + (6*A - C)*a^6*b^2 - (9*A + C)*a^4*b^4 + 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
696,1,1219,0,0.591810," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(A a^{8} b - 3 \, A a^{6} b^{3} + 3 \, A a^{4} b^{5} - A a^{2} b^{7}\right)} d x \cos\left(d x + c\right)^{2} + 24 \, {\left(A a^{7} b^{2} - 3 \, A a^{5} b^{4} + 3 \, A a^{3} b^{6} - A a b^{8}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(A a^{6} b^{3} - 3 \, A a^{4} b^{5} + 3 \, A a^{2} b^{7} - A b^{9}\right)} d x - {\left(2 \, C a^{6} b^{2} + {\left(12 \, A + C\right)} a^{4} b^{4} - 15 \, A a^{2} b^{6} + 6 \, A b^{8} + {\left(2 \, C a^{8} + {\left(12 \, A + C\right)} a^{6} b^{2} - 15 \, A a^{4} b^{4} + 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{7} b + {\left(12 \, A + C\right)} a^{5} b^{3} - 15 \, A a^{3} b^{5} + 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(2 \, A - 3 \, C\right)} a^{7} b^{2} - {\left(13 \, A - 3 \, C\right)} a^{5} b^{4} + 17 \, A a^{3} b^{6} - 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 \, {\left(A - C\right)} a^{8} b - 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} + {\left(25 \, A - C\right)} a^{4} b^{5} - 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{6 \, {\left(A a^{8} b - 3 \, A a^{6} b^{3} + 3 \, A a^{4} b^{5} - A a^{2} b^{7}\right)} d x \cos\left(d x + c\right)^{2} + 12 \, {\left(A a^{7} b^{2} - 3 \, A a^{5} b^{4} + 3 \, A a^{3} b^{6} - A a b^{8}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(A a^{6} b^{3} - 3 \, A a^{4} b^{5} + 3 \, A a^{2} b^{7} - A b^{9}\right)} d x - {\left(2 \, C a^{6} b^{2} + {\left(12 \, A + C\right)} a^{4} b^{4} - 15 \, A a^{2} b^{6} + 6 \, A b^{8} + {\left(2 \, C a^{8} + {\left(12 \, A + C\right)} a^{6} b^{2} - 15 \, A a^{4} b^{4} + 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{7} b + {\left(12 \, A + C\right)} a^{5} b^{3} - 15 \, A a^{3} b^{5} + 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(2 \, A - 3 \, C\right)} a^{7} b^{2} - {\left(13 \, A - 3 \, C\right)} a^{5} b^{4} + 17 \, A a^{3} b^{6} - 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 \, {\left(A - C\right)} a^{8} b - 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} + {\left(25 \, A - C\right)} a^{4} b^{5} - 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*(12*(A*a^8*b - 3*A*a^6*b^3 + 3*A*a^4*b^5 - A*a^2*b^7)*d*x*cos(d*x + c)^2 + 24*(A*a^7*b^2 - 3*A*a^5*b^4 + 3*A*a^3*b^6 - A*a*b^8)*d*x*cos(d*x + c) + 12*(A*a^6*b^3 - 3*A*a^4*b^5 + 3*A*a^2*b^7 - A*b^9)*d*x - (2*C*a^6*b^2 + (12*A + C)*a^4*b^4 - 15*A*a^2*b^6 + 6*A*b^8 + (2*C*a^8 + (12*A + C)*a^6*b^2 - 15*A*a^4*b^4 + 6*A*a^2*b^6)*cos(d*x + c)^2 + 2*(2*C*a^7*b + (12*A + C)*a^5*b^3 - 15*A*a^3*b^5 + 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 - 3*C)*a^7*b^2 - (13*A - 3*C)*a^5*b^4 + 17*A*a^3*b^6 - 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 - C)*a^8*b - 5*(4*A - C)*a^6*b^3 + (25*A - C)*a^4*b^5 - 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*(6*(A*a^8*b - 3*A*a^6*b^3 + 3*A*a^4*b^5 - A*a^2*b^7)*d*x*cos(d*x + c)^2 + 12*(A*a^7*b^2 - 3*A*a^5*b^4 + 3*A*a^3*b^6 - A*a*b^8)*d*x*cos(d*x + c) + 6*(A*a^6*b^3 - 3*A*a^4*b^5 + 3*A*a^2*b^7 - A*b^9)*d*x - (2*C*a^6*b^2 + (12*A + C)*a^4*b^4 - 15*A*a^2*b^6 + 6*A*b^8 + (2*C*a^8 + (12*A + C)*a^6*b^2 - 15*A*a^4*b^4 + 6*A*a^2*b^6)*cos(d*x + c)^2 + 2*(2*C*a^7*b + (12*A + C)*a^5*b^3 - 15*A*a^3*b^5 + 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 - 3*C)*a^7*b^2 - (13*A - 3*C)*a^5*b^4 + 17*A*a^3*b^6 - 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 - C)*a^8*b - 5*(4*A - C)*a^6*b^3 + (25*A - C)*a^4*b^5 - 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
697,1,1554,0,0.667440," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(A + 2 \, C\right)} a^{10} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{8} b^{2} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{6} b^{4} + {\left(35 \, A - 2 \, C\right)} a^{4} b^{6} - 12 \, A a^{2} b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(A + 2 \, C\right)} a^{9} b + 3 \, {\left(3 \, A - 2 \, C\right)} a^{7} b^{3} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{5} b^{5} + {\left(35 \, A - 2 \, C\right)} a^{3} b^{7} - 12 \, A a b^{9}\right)} d x \cos\left(d x + c\right) + 2 \, {\left({\left(A + 2 \, C\right)} a^{8} b^{2} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{6} b^{4} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{4} b^{6} + {\left(35 \, A - 2 \, C\right)} a^{2} b^{8} - 12 \, A b^{10}\right)} d x + {\left(6 \, C a^{6} b^{3} + 5 \, {\left(4 \, A - C\right)} a^{4} b^{5} - {\left(29 \, A - 2 \, C\right)} a^{2} b^{7} + 12 \, A b^{9} + {\left(6 \, C a^{8} b + 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} - {\left(29 \, A - 2 \, C\right)} a^{4} b^{5} + 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, C a^{7} b^{2} + 5 \, {\left(4 \, A - C\right)} a^{5} b^{4} - {\left(29 \, A - 2 \, C\right)} a^{3} b^{6} + 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({\left(6 \, A - 5 \, C\right)} a^{7} b^{3} - {\left(27 \, A - 7 \, C\right)} a^{5} b^{5} + {\left(33 \, A - 2 \, C\right)} a^{3} b^{7} - 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} + 4 \, {\left(A a^{9} b - 3 \, A a^{7} b^{3} + 3 \, A a^{5} b^{5} - A a^{3} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(11 \, A - 6 \, C\right)} a^{8} b^{2} - {\left(43 \, A - 9 \, C\right)} a^{6} b^{4} + {\left(50 \, A - 3 \, C\right)} a^{4} b^{6} - 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({\left(A + 2 \, C\right)} a^{10} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{8} b^{2} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{6} b^{4} + {\left(35 \, A - 2 \, C\right)} a^{4} b^{6} - 12 \, A a^{2} b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(A + 2 \, C\right)} a^{9} b + 3 \, {\left(3 \, A - 2 \, C\right)} a^{7} b^{3} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{5} b^{5} + {\left(35 \, A - 2 \, C\right)} a^{3} b^{7} - 12 \, A a b^{9}\right)} d x \cos\left(d x + c\right) + {\left({\left(A + 2 \, C\right)} a^{8} b^{2} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{6} b^{4} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{4} b^{6} + {\left(35 \, A - 2 \, C\right)} a^{2} b^{8} - 12 \, A b^{10}\right)} d x - {\left(6 \, C a^{6} b^{3} + 5 \, {\left(4 \, A - C\right)} a^{4} b^{5} - {\left(29 \, A - 2 \, C\right)} a^{2} b^{7} + 12 \, A b^{9} + {\left(6 \, C a^{8} b + 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} - {\left(29 \, A - 2 \, C\right)} a^{4} b^{5} + 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, C a^{7} b^{2} + 5 \, {\left(4 \, A - C\right)} a^{5} b^{4} - {\left(29 \, A - 2 \, C\right)} a^{3} b^{6} + 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({\left(6 \, A - 5 \, C\right)} a^{7} b^{3} - {\left(27 \, A - 7 \, C\right)} a^{5} b^{5} + {\left(33 \, A - 2 \, C\right)} a^{3} b^{7} - 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} + 4 \, {\left(A a^{9} b - 3 \, A a^{7} b^{3} + 3 \, A a^{5} b^{5} - A a^{3} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(11 \, A - 6 \, C\right)} a^{8} b^{2} - {\left(43 \, A - 9 \, C\right)} a^{6} b^{4} + {\left(50 \, A - 3 \, C\right)} a^{4} b^{6} - 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 + 2*C)*a^10 + 3*(3*A - 2*C)*a^8*b^2 - 3*(11*A - 2*C)*a^6*b^4 + (35*A - 2*C)*a^4*b^6 - 12*A*a^2*b^8)*d*x*cos(d*x + c)^2 + 4*((A + 2*C)*a^9*b + 3*(3*A - 2*C)*a^7*b^3 - 3*(11*A - 2*C)*a^5*b^5 + (35*A - 2*C)*a^3*b^7 - 12*A*a*b^9)*d*x*cos(d*x + c) + 2*((A + 2*C)*a^8*b^2 + 3*(3*A - 2*C)*a^6*b^4 - 3*(11*A - 2*C)*a^4*b^6 + (35*A - 2*C)*a^2*b^8 - 12*A*b^10)*d*x + (6*C*a^6*b^3 + 5*(4*A - C)*a^4*b^5 - (29*A - 2*C)*a^2*b^7 + 12*A*b^9 + (6*C*a^8*b + 5*(4*A - C)*a^6*b^3 - (29*A - 2*C)*a^4*b^5 + 12*A*a^2*b^7)*cos(d*x + c)^2 + 2*(6*C*a^7*b^2 + 5*(4*A - C)*a^5*b^4 - (29*A - 2*C)*a^3*b^6 + 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*((6*A - 5*C)*a^7*b^3 - (27*A - 7*C)*a^5*b^5 + (33*A - 2*C)*a^3*b^7 - 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 + 4*(A*a^9*b - 3*A*a^7*b^3 + 3*A*a^5*b^5 - A*a^3*b^7)*cos(d*x + c)^2 + ((11*A - 6*C)*a^8*b^2 - (43*A - 9*C)*a^6*b^4 + (50*A - 3*C)*a^4*b^6 - 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 + 2*C)*a^10 + 3*(3*A - 2*C)*a^8*b^2 - 3*(11*A - 2*C)*a^6*b^4 + (35*A - 2*C)*a^4*b^6 - 12*A*a^2*b^8)*d*x*cos(d*x + c)^2 + 2*((A + 2*C)*a^9*b + 3*(3*A - 2*C)*a^7*b^3 - 3*(11*A - 2*C)*a^5*b^5 + (35*A - 2*C)*a^3*b^7 - 12*A*a*b^9)*d*x*cos(d*x + c) + ((A + 2*C)*a^8*b^2 + 3*(3*A - 2*C)*a^6*b^4 - 3*(11*A - 2*C)*a^4*b^6 + (35*A - 2*C)*a^2*b^8 - 12*A*b^10)*d*x - (6*C*a^6*b^3 + 5*(4*A - C)*a^4*b^5 - (29*A - 2*C)*a^2*b^7 + 12*A*b^9 + (6*C*a^8*b + 5*(4*A - C)*a^6*b^3 - (29*A - 2*C)*a^4*b^5 + 12*A*a^2*b^7)*cos(d*x + c)^2 + 2*(6*C*a^7*b^2 + 5*(4*A - C)*a^5*b^4 - (29*A - 2*C)*a^3*b^6 + 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))) - ((6*A - 5*C)*a^7*b^3 - (27*A - 7*C)*a^5*b^5 + (33*A - 2*C)*a^3*b^7 - 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 + 4*(A*a^9*b - 3*A*a^7*b^3 + 3*A*a^5*b^5 - A*a^3*b^7)*cos(d*x + c)^2 + ((11*A - 6*C)*a^8*b^2 - (43*A - 9*C)*a^6*b^4 + (50*A - 3*C)*a^4*b^6 - 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
698,1,2424,0,29.411506," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, C a^{11} - 28 \, C a^{9} b^{2} + 35 \, C a^{7} b^{4} - {\left(3 \, A + 20 \, C\right)} a^{5} b^{6} - 2 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(8 \, C a^{10} b - 28 \, C a^{8} b^{3} + 35 \, C a^{6} b^{5} - {\left(3 \, A + 20 \, C\right)} a^{4} b^{7} - 2 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, C a^{9} b^{2} - 28 \, C a^{7} b^{4} + 35 \, C a^{5} b^{6} - {\left(3 \, A + 20 \, C\right)} a^{3} b^{8} - 2 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, C a^{8} b^{3} - 28 \, C a^{6} b^{5} + 35 \, C a^{4} b^{7} - {\left(3 \, A + 20 \, C\right)} a^{2} b^{9} - 2 \, 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) - 24 \, {\left({\left(C a^{12} - 4 \, C a^{10} b^{2} + 6 \, C a^{8} b^{4} - 4 \, C a^{6} b^{6} + C a^{4} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(C a^{11} b - 4 \, C a^{9} b^{3} + 6 \, C a^{7} b^{5} - 4 \, C a^{5} b^{7} + C a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b^{2} - 4 \, C a^{8} b^{4} + 6 \, C a^{6} b^{6} - 4 \, C a^{4} b^{8} + C a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{9} b^{3} - 4 \, C a^{7} b^{5} + 6 \, C a^{5} b^{7} - 4 \, C a^{3} b^{9} + C a b^{11}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 24 \, {\left({\left(C a^{12} - 4 \, C a^{10} b^{2} + 6 \, C a^{8} b^{4} - 4 \, C a^{6} b^{6} + C a^{4} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(C a^{11} b - 4 \, C a^{9} b^{3} + 6 \, C a^{7} b^{5} - 4 \, C a^{5} b^{7} + C a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b^{2} - 4 \, C a^{8} b^{4} + 6 \, C a^{6} b^{6} - 4 \, C a^{4} b^{8} + C a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{9} b^{3} - 4 \, C a^{7} b^{5} + 6 \, C a^{5} b^{7} - 4 \, C a^{3} b^{9} + C a b^{11}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, C a^{8} b^{4} - 24 \, C a^{6} b^{6} + 36 \, C a^{4} b^{8} - 24 \, C a^{2} b^{10} + 6 \, C b^{12} + {\left(24 \, C a^{11} b - 92 \, C a^{9} b^{3} + {\left(4 \, A + 133 \, C\right)} a^{7} b^{5} + {\left(7 \, A - 71 \, C\right)} a^{5} b^{7} - {\left(11 \, A - 6 \, C\right)} a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, C a^{10} b^{2} - 77 \, C a^{8} b^{4} + {\left(A + 110 \, C\right)} a^{6} b^{6} + {\left(8 \, A - 59 \, C\right)} a^{4} b^{8} - 3 \, {\left(3 \, A - 2 \, C\right)} a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(44 \, C a^{9} b^{3} + {\left(2 \, A - 169 \, C\right)} a^{7} b^{5} - {\left(7 \, A - 239 \, C\right)} a^{5} b^{7} + {\left(23 \, A - 132 \, C\right)} a^{3} b^{9} - 18 \, {\left(A - C\right)} 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 \, C a^{11} - 28 \, C a^{9} b^{2} + 35 \, C a^{7} b^{4} - {\left(3 \, A + 20 \, C\right)} a^{5} b^{6} - 2 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(8 \, C a^{10} b - 28 \, C a^{8} b^{3} + 35 \, C a^{6} b^{5} - {\left(3 \, A + 20 \, C\right)} a^{4} b^{7} - 2 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, C a^{9} b^{2} - 28 \, C a^{7} b^{4} + 35 \, C a^{5} b^{6} - {\left(3 \, A + 20 \, C\right)} a^{3} b^{8} - 2 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, C a^{8} b^{3} - 28 \, C a^{6} b^{5} + 35 \, C a^{4} b^{7} - {\left(3 \, A + 20 \, C\right)} a^{2} b^{9} - 2 \, 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) - 12 \, {\left({\left(C a^{12} - 4 \, C a^{10} b^{2} + 6 \, C a^{8} b^{4} - 4 \, C a^{6} b^{6} + C a^{4} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(C a^{11} b - 4 \, C a^{9} b^{3} + 6 \, C a^{7} b^{5} - 4 \, C a^{5} b^{7} + C a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b^{2} - 4 \, C a^{8} b^{4} + 6 \, C a^{6} b^{6} - 4 \, C a^{4} b^{8} + C a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{9} b^{3} - 4 \, C a^{7} b^{5} + 6 \, C a^{5} b^{7} - 4 \, C a^{3} b^{9} + C a b^{11}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 12 \, {\left({\left(C a^{12} - 4 \, C a^{10} b^{2} + 6 \, C a^{8} b^{4} - 4 \, C a^{6} b^{6} + C a^{4} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(C a^{11} b - 4 \, C a^{9} b^{3} + 6 \, C a^{7} b^{5} - 4 \, C a^{5} b^{7} + C a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b^{2} - 4 \, C a^{8} b^{4} + 6 \, C a^{6} b^{6} - 4 \, C a^{4} b^{8} + C a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{9} b^{3} - 4 \, C a^{7} b^{5} + 6 \, C a^{5} b^{7} - 4 \, C a^{3} b^{9} + C a b^{11}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, C a^{8} b^{4} - 24 \, C a^{6} b^{6} + 36 \, C a^{4} b^{8} - 24 \, C a^{2} b^{10} + 6 \, C b^{12} + {\left(24 \, C a^{11} b - 92 \, C a^{9} b^{3} + {\left(4 \, A + 133 \, C\right)} a^{7} b^{5} + {\left(7 \, A - 71 \, C\right)} a^{5} b^{7} - {\left(11 \, A - 6 \, C\right)} a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, C a^{10} b^{2} - 77 \, C a^{8} b^{4} + {\left(A + 110 \, C\right)} a^{6} b^{6} + {\left(8 \, A - 59 \, C\right)} a^{4} b^{8} - 3 \, {\left(3 \, A - 2 \, C\right)} a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(44 \, C a^{9} b^{3} + {\left(2 \, A - 169 \, C\right)} a^{7} b^{5} - {\left(7 \, A - 239 \, C\right)} a^{5} b^{7} + {\left(23 \, A - 132 \, C\right)} a^{3} b^{9} - 18 \, {\left(A - C\right)} 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*C*a^11 - 28*C*a^9*b^2 + 35*C*a^7*b^4 - (3*A + 20*C)*a^5*b^6 - 2*A*a^3*b^8)*cos(d*x + c)^4 + 3*(8*C*a^10*b - 28*C*a^8*b^3 + 35*C*a^6*b^5 - (3*A + 20*C)*a^4*b^7 - 2*A*a^2*b^9)*cos(d*x + c)^3 + 3*(8*C*a^9*b^2 - 28*C*a^7*b^4 + 35*C*a^5*b^6 - (3*A + 20*C)*a^3*b^8 - 2*A*a*b^10)*cos(d*x + c)^2 + (8*C*a^8*b^3 - 28*C*a^6*b^5 + 35*C*a^4*b^7 - (3*A + 20*C)*a^2*b^9 - 2*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)) - 24*((C*a^12 - 4*C*a^10*b^2 + 6*C*a^8*b^4 - 4*C*a^6*b^6 + C*a^4*b^8)*cos(d*x + c)^4 + 3*(C*a^11*b - 4*C*a^9*b^3 + 6*C*a^7*b^5 - 4*C*a^5*b^7 + C*a^3*b^9)*cos(d*x + c)^3 + 3*(C*a^10*b^2 - 4*C*a^8*b^4 + 6*C*a^6*b^6 - 4*C*a^4*b^8 + C*a^2*b^10)*cos(d*x + c)^2 + (C*a^9*b^3 - 4*C*a^7*b^5 + 6*C*a^5*b^7 - 4*C*a^3*b^9 + C*a*b^11)*cos(d*x + c))*log(sin(d*x + c) + 1) + 24*((C*a^12 - 4*C*a^10*b^2 + 6*C*a^8*b^4 - 4*C*a^6*b^6 + C*a^4*b^8)*cos(d*x + c)^4 + 3*(C*a^11*b - 4*C*a^9*b^3 + 6*C*a^7*b^5 - 4*C*a^5*b^7 + C*a^3*b^9)*cos(d*x + c)^3 + 3*(C*a^10*b^2 - 4*C*a^8*b^4 + 6*C*a^6*b^6 - 4*C*a^4*b^8 + C*a^2*b^10)*cos(d*x + c)^2 + (C*a^9*b^3 - 4*C*a^7*b^5 + 6*C*a^5*b^7 - 4*C*a^3*b^9 + C*a*b^11)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(6*C*a^8*b^4 - 24*C*a^6*b^6 + 36*C*a^4*b^8 - 24*C*a^2*b^10 + 6*C*b^12 + (24*C*a^11*b - 92*C*a^9*b^3 + (4*A + 133*C)*a^7*b^5 + (7*A - 71*C)*a^5*b^7 - (11*A - 6*C)*a^3*b^9)*cos(d*x + c)^3 + 3*(20*C*a^10*b^2 - 77*C*a^8*b^4 + (A + 110*C)*a^6*b^6 + (8*A - 59*C)*a^4*b^8 - 3*(3*A - 2*C)*a^2*b^10)*cos(d*x + c)^2 + (44*C*a^9*b^3 + (2*A - 169*C)*a^7*b^5 - (7*A - 239*C)*a^5*b^7 + (23*A - 132*C)*a^3*b^9 - 18*(A - C)*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*C*a^11 - 28*C*a^9*b^2 + 35*C*a^7*b^4 - (3*A + 20*C)*a^5*b^6 - 2*A*a^3*b^8)*cos(d*x + c)^4 + 3*(8*C*a^10*b - 28*C*a^8*b^3 + 35*C*a^6*b^5 - (3*A + 20*C)*a^4*b^7 - 2*A*a^2*b^9)*cos(d*x + c)^3 + 3*(8*C*a^9*b^2 - 28*C*a^7*b^4 + 35*C*a^5*b^6 - (3*A + 20*C)*a^3*b^8 - 2*A*a*b^10)*cos(d*x + c)^2 + (8*C*a^8*b^3 - 28*C*a^6*b^5 + 35*C*a^4*b^7 - (3*A + 20*C)*a^2*b^9 - 2*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))) - 12*((C*a^12 - 4*C*a^10*b^2 + 6*C*a^8*b^4 - 4*C*a^6*b^6 + C*a^4*b^8)*cos(d*x + c)^4 + 3*(C*a^11*b - 4*C*a^9*b^3 + 6*C*a^7*b^5 - 4*C*a^5*b^7 + C*a^3*b^9)*cos(d*x + c)^3 + 3*(C*a^10*b^2 - 4*C*a^8*b^4 + 6*C*a^6*b^6 - 4*C*a^4*b^8 + C*a^2*b^10)*cos(d*x + c)^2 + (C*a^9*b^3 - 4*C*a^7*b^5 + 6*C*a^5*b^7 - 4*C*a^3*b^9 + C*a*b^11)*cos(d*x + c))*log(sin(d*x + c) + 1) + 12*((C*a^12 - 4*C*a^10*b^2 + 6*C*a^8*b^4 - 4*C*a^6*b^6 + C*a^4*b^8)*cos(d*x + c)^4 + 3*(C*a^11*b - 4*C*a^9*b^3 + 6*C*a^7*b^5 - 4*C*a^5*b^7 + C*a^3*b^9)*cos(d*x + c)^3 + 3*(C*a^10*b^2 - 4*C*a^8*b^4 + 6*C*a^6*b^6 - 4*C*a^4*b^8 + C*a^2*b^10)*cos(d*x + c)^2 + (C*a^9*b^3 - 4*C*a^7*b^5 + 6*C*a^5*b^7 - 4*C*a^3*b^9 + C*a*b^11)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (6*C*a^8*b^4 - 24*C*a^6*b^6 + 36*C*a^4*b^8 - 24*C*a^2*b^10 + 6*C*b^12 + (24*C*a^11*b - 92*C*a^9*b^3 + (4*A + 133*C)*a^7*b^5 + (7*A - 71*C)*a^5*b^7 - (11*A - 6*C)*a^3*b^9)*cos(d*x + c)^3 + 3*(20*C*a^10*b^2 - 77*C*a^8*b^4 + (A + 110*C)*a^6*b^6 + (8*A - 59*C)*a^4*b^8 - 3*(3*A - 2*C)*a^2*b^10)*cos(d*x + c)^2 + (44*C*a^9*b^3 + (2*A - 169*C)*a^7*b^5 - (7*A - 239*C)*a^5*b^7 + (23*A - 132*C)*a^3*b^9 - 18*(A - C)*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
699,1,2156,0,22.982542," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, C a^{7} b^{3} - 7 \, C a^{5} b^{5} - {\left(A - 8 \, C\right)} a^{3} b^{7} - 4 \, {\left(A + 2 \, C\right)} a b^{9} + {\left(2 \, C a^{10} - 7 \, C a^{8} b^{2} - {\left(A - 8 \, C\right)} a^{6} b^{4} - 4 \, {\left(A + 2 \, C\right)} a^{4} b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{9} b - 7 \, C a^{7} b^{3} - {\left(A - 8 \, C\right)} a^{5} b^{5} - 4 \, {\left(A + 2 \, C\right)} a^{3} b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{8} b^{2} - 7 \, C a^{6} b^{4} - {\left(A - 8 \, C\right)} a^{4} b^{6} - 4 \, {\left(A + 2 \, C\right)} a^{2} 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) + 6 \, {\left(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11} + {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11} + {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(11 \, C a^{8} b^{3} - {\left(A + 43 \, C\right)} a^{6} b^{5} + {\left(11 \, A + 68 \, C\right)} a^{4} b^{7} - 4 \, {\left(A + 9 \, C\right)} a^{2} b^{9} - 6 \, A b^{11} + {\left(6 \, C a^{10} b - 23 \, C a^{8} b^{3} + {\left(13 \, A + 43 \, C\right)} a^{6} b^{5} - {\left(11 \, A + 26 \, C\right)} a^{4} b^{7} - 2 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, C a^{9} b^{2} - {\left(A + 20 \, C\right)} a^{7} b^{4} + 5 \, {\left(2 \, A + 7 \, C\right)} a^{5} b^{6} - {\left(7 \, A + 20 \, C\right)} a^{3} b^{8} - 2 \, A a b^{10}\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 \, C a^{7} b^{3} - 7 \, C a^{5} b^{5} - {\left(A - 8 \, C\right)} a^{3} b^{7} - 4 \, {\left(A + 2 \, C\right)} a b^{9} + {\left(2 \, C a^{10} - 7 \, C a^{8} b^{2} - {\left(A - 8 \, C\right)} a^{6} b^{4} - 4 \, {\left(A + 2 \, C\right)} a^{4} b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{9} b - 7 \, C a^{7} b^{3} - {\left(A - 8 \, C\right)} a^{5} b^{5} - 4 \, {\left(A + 2 \, C\right)} a^{3} b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{8} b^{2} - 7 \, C a^{6} b^{4} - {\left(A - 8 \, C\right)} a^{4} b^{6} - 4 \, {\left(A + 2 \, C\right)} a^{2} 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) - 3 \, {\left(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11} + {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11} + {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(11 \, C a^{8} b^{3} - {\left(A + 43 \, C\right)} a^{6} b^{5} + {\left(11 \, A + 68 \, C\right)} a^{4} b^{7} - 4 \, {\left(A + 9 \, C\right)} a^{2} b^{9} - 6 \, A b^{11} + {\left(6 \, C a^{10} b - 23 \, C a^{8} b^{3} + {\left(13 \, A + 43 \, C\right)} a^{6} b^{5} - {\left(11 \, A + 26 \, C\right)} a^{4} b^{7} - 2 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, C a^{9} b^{2} - {\left(A + 20 \, C\right)} a^{7} b^{4} + 5 \, {\left(2 \, A + 7 \, C\right)} a^{5} b^{6} - {\left(7 \, A + 20 \, C\right)} a^{3} b^{8} - 2 \, A a b^{10}\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*C*a^7*b^3 - 7*C*a^5*b^5 - (A - 8*C)*a^3*b^7 - 4*(A + 2*C)*a*b^9 + (2*C*a^10 - 7*C*a^8*b^2 - (A - 8*C)*a^6*b^4 - 4*(A + 2*C)*a^4*b^6)*cos(d*x + c)^3 + 3*(2*C*a^9*b - 7*C*a^7*b^3 - (A - 8*C)*a^5*b^5 - 4*(A + 2*C)*a^3*b^7)*cos(d*x + c)^2 + 3*(2*C*a^8*b^2 - 7*C*a^6*b^4 - (A - 8*C)*a^4*b^6 - 4*(A + 2*C)*a^2*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)) + 6*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11 + (C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*cos(d*x + c)^3 + 3*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*cos(d*x + c)^2 + 3*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*cos(d*x + c))*log(sin(d*x + c) + 1) - 6*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11 + (C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*cos(d*x + c)^3 + 3*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*cos(d*x + c)^2 + 3*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(11*C*a^8*b^3 - (A + 43*C)*a^6*b^5 + (11*A + 68*C)*a^4*b^7 - 4*(A + 9*C)*a^2*b^9 - 6*A*b^11 + (6*C*a^10*b - 23*C*a^8*b^3 + (13*A + 43*C)*a^6*b^5 - (11*A + 26*C)*a^4*b^7 - 2*A*a^2*b^9)*cos(d*x + c)^2 + 3*(5*C*a^9*b^2 - (A + 20*C)*a^7*b^4 + 5*(2*A + 7*C)*a^5*b^6 - (7*A + 20*C)*a^3*b^8 - 2*A*a*b^10)*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*C*a^7*b^3 - 7*C*a^5*b^5 - (A - 8*C)*a^3*b^7 - 4*(A + 2*C)*a*b^9 + (2*C*a^10 - 7*C*a^8*b^2 - (A - 8*C)*a^6*b^4 - 4*(A + 2*C)*a^4*b^6)*cos(d*x + c)^3 + 3*(2*C*a^9*b - 7*C*a^7*b^3 - (A - 8*C)*a^5*b^5 - 4*(A + 2*C)*a^3*b^7)*cos(d*x + c)^2 + 3*(2*C*a^8*b^2 - 7*C*a^6*b^4 - (A - 8*C)*a^4*b^6 - 4*(A + 2*C)*a^2*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))) - 3*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11 + (C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*cos(d*x + c)^3 + 3*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*cos(d*x + c)^2 + 3*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*cos(d*x + c))*log(sin(d*x + c) + 1) + 3*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11 + (C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*cos(d*x + c)^3 + 3*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*cos(d*x + c)^2 + 3*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (11*C*a^8*b^3 - (A + 43*C)*a^6*b^5 + (11*A + 68*C)*a^4*b^7 - 4*(A + 9*C)*a^2*b^9 - 6*A*b^11 + (6*C*a^10*b - 23*C*a^8*b^3 + (13*A + 43*C)*a^6*b^5 - (11*A + 26*C)*a^4*b^7 - 2*A*a^2*b^9)*cos(d*x + c)^2 + 3*(5*C*a^9*b^2 - (A + 20*C)*a^7*b^4 + 5*(2*A + 7*C)*a^5*b^6 - (7*A + 20*C)*a^3*b^8 - 2*A*a*b^10)*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
700,1,1113,0,0.593427," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(4 \, A + 3 \, C\right)} a^{2} b^{4} + {\left(A + 2 \, C\right)} b^{6} + {\left({\left(4 \, A + 3 \, C\right)} a^{5} b + {\left(A + 2 \, C\right)} a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(4 \, A + 3 \, C\right)} a^{4} b^{2} + {\left(A + 2 \, C\right)} a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(4 \, A + 3 \, C\right)} a^{3} b^{3} + {\left(A + 2 \, C\right)} 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 \, C a^{7} + {\left(2 \, A - 7 \, C\right)} a^{5} b^{2} + {\left(11 \, A + 23 \, C\right)} a^{3} b^{4} - {\left(13 \, A + 18 \, C\right)} a b^{6} + {\left(2 \, {\left(3 \, A + 2 \, C\right)} a^{7} + {\left(4 \, A + 7 \, C\right)} a^{5} b^{2} - 11 \, {\left(A + C\right)} a^{3} b^{4} + A a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{6} b + {\left(7 \, A + 8 \, C\right)} a^{4} b^{3} - {\left(10 \, A + 9 \, C\right)} a^{2} b^{5} + 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({\left(4 \, A + 3 \, C\right)} a^{2} b^{4} + {\left(A + 2 \, C\right)} b^{6} + {\left({\left(4 \, A + 3 \, C\right)} a^{5} b + {\left(A + 2 \, C\right)} a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(4 \, A + 3 \, C\right)} a^{4} b^{2} + {\left(A + 2 \, C\right)} a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(4 \, A + 3 \, C\right)} a^{3} b^{3} + {\left(A + 2 \, C\right)} 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 \, C a^{7} + {\left(2 \, A - 7 \, C\right)} a^{5} b^{2} + {\left(11 \, A + 23 \, C\right)} a^{3} b^{4} - {\left(13 \, A + 18 \, C\right)} a b^{6} + {\left(2 \, {\left(3 \, A + 2 \, C\right)} a^{7} + {\left(4 \, A + 7 \, C\right)} a^{5} b^{2} - 11 \, {\left(A + C\right)} a^{3} b^{4} + A a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{6} b + {\left(7 \, A + 8 \, C\right)} a^{4} b^{3} - {\left(10 \, A + 9 \, C\right)} a^{2} b^{5} + 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*((4*A + 3*C)*a^2*b^4 + (A + 2*C)*b^6 + ((4*A + 3*C)*a^5*b + (A + 2*C)*a^3*b^3)*cos(d*x + c)^3 + 3*((4*A + 3*C)*a^4*b^2 + (A + 2*C)*a^2*b^4)*cos(d*x + c)^2 + 3*((4*A + 3*C)*a^3*b^3 + (A + 2*C)*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*C*a^7 + (2*A - 7*C)*a^5*b^2 + (11*A + 23*C)*a^3*b^4 - (13*A + 18*C)*a*b^6 + (2*(3*A + 2*C)*a^7 + (4*A + 7*C)*a^5*b^2 - 11*(A + C)*a^3*b^4 + A*a*b^6)*cos(d*x + c)^2 + 3*((2*A + C)*a^6*b + (7*A + 8*C)*a^4*b^3 - (10*A + 9*C)*a^2*b^5 + 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*((4*A + 3*C)*a^2*b^4 + (A + 2*C)*b^6 + ((4*A + 3*C)*a^5*b + (A + 2*C)*a^3*b^3)*cos(d*x + c)^3 + 3*((4*A + 3*C)*a^4*b^2 + (A + 2*C)*a^2*b^4)*cos(d*x + c)^2 + 3*((4*A + 3*C)*a^3*b^3 + (A + 2*C)*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*C*a^7 + (2*A - 7*C)*a^5*b^2 + (11*A + 23*C)*a^3*b^4 - (13*A + 18*C)*a*b^6 + (2*(3*A + 2*C)*a^7 + (4*A + 7*C)*a^5*b^2 - 11*(A + C)*a^3*b^4 + A*a*b^6)*cos(d*x + c)^2 + 3*((2*A + C)*a^6*b + (7*A + 8*C)*a^4*b^3 - (10*A + 9*C)*a^2*b^5 + 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
701,1,1114,0,0.611849," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, A + C\right)} a^{3} b^{3} + {\left(3 \, A + 4 \, C\right)} a b^{5} + {\left({\left(2 \, A + C\right)} a^{6} + {\left(3 \, A + 4 \, C\right)} a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(2 \, A + C\right)} a^{5} b + {\left(3 \, A + 4 \, C\right)} a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{4} b^{2} + {\left(3 \, A + 4 \, C\right)} a^{2} 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(C a^{6} b - 11 \, {\left(A + C\right)} a^{4} b^{3} + {\left(7 \, A + 4 \, C\right)} a^{2} b^{5} + 2 \, {\left(2 \, A + 3 \, C\right)} b^{7} - {\left({\left(18 \, A + 13 \, C\right)} a^{6} b - {\left(23 \, A + 11 \, C\right)} a^{4} b^{3} + {\left(7 \, A - 2 \, C\right)} a^{2} b^{5} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{7} - {\left(9 \, A + 10 \, C\right)} a^{5} b^{2} + {\left(8 \, A + 7 \, C\right)} a^{3} b^{4} + {\left(A + 2 \, C\right)} 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({\left(2 \, A + C\right)} a^{3} b^{3} + {\left(3 \, A + 4 \, C\right)} a b^{5} + {\left({\left(2 \, A + C\right)} a^{6} + {\left(3 \, A + 4 \, C\right)} a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(2 \, A + C\right)} a^{5} b + {\left(3 \, A + 4 \, C\right)} a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{4} b^{2} + {\left(3 \, A + 4 \, C\right)} a^{2} 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(C a^{6} b - 11 \, {\left(A + C\right)} a^{4} b^{3} + {\left(7 \, A + 4 \, C\right)} a^{2} b^{5} + 2 \, {\left(2 \, A + 3 \, C\right)} b^{7} - {\left({\left(18 \, A + 13 \, C\right)} a^{6} b - {\left(23 \, A + 11 \, C\right)} a^{4} b^{3} + {\left(7 \, A - 2 \, C\right)} a^{2} b^{5} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{7} - {\left(9 \, A + 10 \, C\right)} a^{5} b^{2} + {\left(8 \, A + 7 \, C\right)} a^{3} b^{4} + {\left(A + 2 \, C\right)} 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*((2*A + C)*a^3*b^3 + (3*A + 4*C)*a*b^5 + ((2*A + C)*a^6 + (3*A + 4*C)*a^4*b^2)*cos(d*x + c)^3 + 3*((2*A + C)*a^5*b + (3*A + 4*C)*a^3*b^3)*cos(d*x + c)^2 + 3*((2*A + C)*a^4*b^2 + (3*A + 4*C)*a^2*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*(C*a^6*b - 11*(A + C)*a^4*b^3 + (7*A + 4*C)*a^2*b^5 + 2*(2*A + 3*C)*b^7 - ((18*A + 13*C)*a^6*b - (23*A + 11*C)*a^4*b^3 + (7*A - 2*C)*a^2*b^5 - 2*A*b^7)*cos(d*x + c)^2 + 3*(C*a^7 - (9*A + 10*C)*a^5*b^2 + (8*A + 7*C)*a^3*b^4 + (A + 2*C)*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*((2*A + C)*a^3*b^3 + (3*A + 4*C)*a*b^5 + ((2*A + C)*a^6 + (3*A + 4*C)*a^4*b^2)*cos(d*x + c)^3 + 3*((2*A + C)*a^5*b + (3*A + 4*C)*a^3*b^3)*cos(d*x + c)^2 + 3*((2*A + C)*a^4*b^2 + (3*A + 4*C)*a^2*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))) + (C*a^6*b - 11*(A + C)*a^4*b^3 + (7*A + 4*C)*a^2*b^5 + 2*(2*A + 3*C)*b^7 - ((18*A + 13*C)*a^6*b - (23*A + 11*C)*a^4*b^3 + (7*A - 2*C)*a^2*b^5 - 2*A*b^7)*cos(d*x + c)^2 + 3*(C*a^7 - (9*A + 10*C)*a^5*b^2 + (8*A + 7*C)*a^3*b^4 + (A + 2*C)*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
702,1,1756,0,0.660970," ","integrate((A+C*sec(d*x+c)^2)/(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(4 \, {\left(2 \, A + C\right)} a^{6} b^{4} - {\left(8 \, A - C\right)} a^{4} b^{6} + 7 \, A a^{2} b^{8} - 2 \, A b^{10} + {\left(4 \, {\left(2 \, A + C\right)} a^{9} b - {\left(8 \, A - C\right)} 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(4 \, {\left(2 \, A + C\right)} a^{8} b^{2} - {\left(8 \, A - C\right)} 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(4 \, {\left(2 \, A + C\right)} a^{7} b^{3} - {\left(8 \, A - C\right)} 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(2 \, C a^{9} b^{2} + {\left(26 \, A + 11 \, C\right)} a^{7} b^{4} - {\left(43 \, A + 13 \, C\right)} a^{5} b^{6} + 23 \, A a^{3} b^{8} - 6 \, A a b^{10} + {\left(6 \, C a^{11} + 4 \, {\left(9 \, A + C\right)} a^{9} b^{2} - {\left(68 \, A + 11 \, C\right)} a^{7} b^{4} + {\left(43 \, A + C\right)} a^{5} b^{6} - 11 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{10} b + {\left(20 \, A + 7 \, C\right)} a^{8} b^{3} - 5 \, {\left(7 \, A + 2 \, C\right)} a^{6} b^{5} + {\left(20 \, A + C\right)} 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(4 \, {\left(2 \, A + C\right)} a^{6} b^{4} - {\left(8 \, A - C\right)} a^{4} b^{6} + 7 \, A a^{2} b^{8} - 2 \, A b^{10} + {\left(4 \, {\left(2 \, A + C\right)} a^{9} b - {\left(8 \, A - C\right)} 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(4 \, {\left(2 \, A + C\right)} a^{8} b^{2} - {\left(8 \, A - C\right)} 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(4 \, {\left(2 \, A + C\right)} a^{7} b^{3} - {\left(8 \, A - C\right)} 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(2 \, C a^{9} b^{2} + {\left(26 \, A + 11 \, C\right)} a^{7} b^{4} - {\left(43 \, A + 13 \, C\right)} a^{5} b^{6} + 23 \, A a^{3} b^{8} - 6 \, A a b^{10} + {\left(6 \, C a^{11} + 4 \, {\left(9 \, A + C\right)} a^{9} b^{2} - {\left(68 \, A + 11 \, C\right)} a^{7} b^{4} + {\left(43 \, A + C\right)} a^{5} b^{6} - 11 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{10} b + {\left(20 \, A + 7 \, C\right)} a^{8} b^{3} - 5 \, {\left(7 \, A + 2 \, C\right)} a^{6} b^{5} + {\left(20 \, A + C\right)} 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*(4*(2*A + C)*a^6*b^4 - (8*A - C)*a^4*b^6 + 7*A*a^2*b^8 - 2*A*b^10 + (4*(2*A + C)*a^9*b - (8*A - C)*a^7*b^3 + 7*A*a^5*b^5 - 2*A*a^3*b^7)*cos(d*x + c)^3 + 3*(4*(2*A + C)*a^8*b^2 - (8*A - C)*a^6*b^4 + 7*A*a^4*b^6 - 2*A*a^2*b^8)*cos(d*x + c)^2 + 3*(4*(2*A + C)*a^7*b^3 - (8*A - C)*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*(2*C*a^9*b^2 + (26*A + 11*C)*a^7*b^4 - (43*A + 13*C)*a^5*b^6 + 23*A*a^3*b^8 - 6*A*a*b^10 + (6*C*a^11 + 4*(9*A + C)*a^9*b^2 - (68*A + 11*C)*a^7*b^4 + (43*A + C)*a^5*b^6 - 11*A*a^3*b^8)*cos(d*x + c)^2 + 3*(2*C*a^10*b + (20*A + 7*C)*a^8*b^3 - 5*(7*A + 2*C)*a^6*b^5 + (20*A + C)*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*(4*(2*A + C)*a^6*b^4 - (8*A - C)*a^4*b^6 + 7*A*a^2*b^8 - 2*A*b^10 + (4*(2*A + C)*a^9*b - (8*A - C)*a^7*b^3 + 7*A*a^5*b^5 - 2*A*a^3*b^7)*cos(d*x + c)^3 + 3*(4*(2*A + C)*a^8*b^2 - (8*A - C)*a^6*b^4 + 7*A*a^4*b^6 - 2*A*a^2*b^8)*cos(d*x + c)^2 + 3*(4*(2*A + C)*a^7*b^3 - (8*A - C)*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))) + (2*C*a^9*b^2 + (26*A + 11*C)*a^7*b^4 - (43*A + 13*C)*a^5*b^6 + 23*A*a^3*b^8 - 6*A*a*b^10 + (6*C*a^11 + 4*(9*A + C)*a^9*b^2 - (68*A + 11*C)*a^7*b^4 + (43*A + C)*a^5*b^6 - 11*A*a^3*b^8)*cos(d*x + c)^2 + 3*(2*C*a^10*b + (20*A + 7*C)*a^8*b^3 - 5*(7*A + 2*C)*a^6*b^5 + (20*A + C)*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
703,1,1925,0,0.723562," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{48 \, {\left(A a^{11} b - 4 \, A a^{9} b^{3} + 6 \, A a^{7} b^{5} - 4 \, A a^{5} b^{7} + A a^{3} b^{9}\right)} d x \cos\left(d x + c\right)^{3} + 144 \, {\left(A a^{10} b^{2} - 4 \, A a^{8} b^{4} + 6 \, A a^{6} b^{6} - 4 \, A a^{4} b^{8} + A a^{2} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 144 \, {\left(A a^{9} b^{3} - 4 \, A a^{7} b^{5} + 6 \, A a^{5} b^{7} - 4 \, A a^{3} b^{9} + A a b^{11}\right)} d x \cos\left(d x + c\right) + 48 \, {\left(A a^{8} b^{4} - 4 \, A a^{6} b^{6} + 6 \, A a^{4} b^{8} - 4 \, A a^{2} b^{10} + A b^{12}\right)} d x - 3 \, {\left(2 \, C a^{8} b^{3} + {\left(20 \, A + 3 \, C\right)} a^{6} b^{5} - 35 \, A a^{4} b^{7} + 28 \, A a^{2} b^{9} - 8 \, A b^{11} + {\left(2 \, C a^{11} + {\left(20 \, A + 3 \, C\right)} a^{9} b^{2} - 35 \, A a^{7} b^{4} + 28 \, A a^{5} b^{6} - 8 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{10} b + {\left(20 \, A + 3 \, C\right)} a^{8} b^{3} - 35 \, A a^{6} b^{5} + 28 \, A a^{4} b^{7} - 8 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{9} b^{2} + {\left(20 \, A + 3 \, C\right)} a^{7} b^{4} - 35 \, A a^{5} b^{6} + 28 \, A a^{3} b^{8} - 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({\left(6 \, A - 11 \, C\right)} a^{9} b^{3} - {\left(71 \, A - 7 \, C\right)} a^{7} b^{5} + {\left(133 \, A + 4 \, C\right)} a^{5} b^{7} - 92 \, A a^{3} b^{9} + 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 \, {\left(A - C\right)} a^{11} b - {\left(132 \, A - 23 \, C\right)} a^{9} b^{3} + {\left(239 \, A - 7 \, C\right)} a^{7} b^{5} - {\left(169 \, A - 2 \, C\right)} a^{5} b^{7} + 44 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, {\left(2 \, A - 3 \, C\right)} a^{10} b^{2} - {\left(59 \, A - 8 \, C\right)} a^{8} b^{4} + {\left(110 \, A + C\right)} a^{6} b^{6} - 77 \, A a^{4} b^{8} + 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{24 \, {\left(A a^{11} b - 4 \, A a^{9} b^{3} + 6 \, A a^{7} b^{5} - 4 \, A a^{5} b^{7} + A a^{3} b^{9}\right)} d x \cos\left(d x + c\right)^{3} + 72 \, {\left(A a^{10} b^{2} - 4 \, A a^{8} b^{4} + 6 \, A a^{6} b^{6} - 4 \, A a^{4} b^{8} + A a^{2} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 72 \, {\left(A a^{9} b^{3} - 4 \, A a^{7} b^{5} + 6 \, A a^{5} b^{7} - 4 \, A a^{3} b^{9} + A a b^{11}\right)} d x \cos\left(d x + c\right) + 24 \, {\left(A a^{8} b^{4} - 4 \, A a^{6} b^{6} + 6 \, A a^{4} b^{8} - 4 \, A a^{2} b^{10} + A b^{12}\right)} d x - 3 \, {\left(2 \, C a^{8} b^{3} + {\left(20 \, A + 3 \, C\right)} a^{6} b^{5} - 35 \, A a^{4} b^{7} + 28 \, A a^{2} b^{9} - 8 \, A b^{11} + {\left(2 \, C a^{11} + {\left(20 \, A + 3 \, C\right)} a^{9} b^{2} - 35 \, A a^{7} b^{4} + 28 \, A a^{5} b^{6} - 8 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{10} b + {\left(20 \, A + 3 \, C\right)} a^{8} b^{3} - 35 \, A a^{6} b^{5} + 28 \, A a^{4} b^{7} - 8 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{9} b^{2} + {\left(20 \, A + 3 \, C\right)} a^{7} b^{4} - 35 \, A a^{5} b^{6} + 28 \, A a^{3} b^{8} - 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({\left(6 \, A - 11 \, C\right)} a^{9} b^{3} - {\left(71 \, A - 7 \, C\right)} a^{7} b^{5} + {\left(133 \, A + 4 \, C\right)} a^{5} b^{7} - 92 \, A a^{3} b^{9} + 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 \, {\left(A - C\right)} a^{11} b - {\left(132 \, A - 23 \, C\right)} a^{9} b^{3} + {\left(239 \, A - 7 \, C\right)} a^{7} b^{5} - {\left(169 \, A - 2 \, C\right)} a^{5} b^{7} + 44 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, {\left(2 \, A - 3 \, C\right)} a^{10} b^{2} - {\left(59 \, A - 8 \, C\right)} a^{8} b^{4} + {\left(110 \, A + C\right)} a^{6} b^{6} - 77 \, A a^{4} b^{8} + 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*(48*(A*a^11*b - 4*A*a^9*b^3 + 6*A*a^7*b^5 - 4*A*a^5*b^7 + A*a^3*b^9)*d*x*cos(d*x + c)^3 + 144*(A*a^10*b^2 - 4*A*a^8*b^4 + 6*A*a^6*b^6 - 4*A*a^4*b^8 + A*a^2*b^10)*d*x*cos(d*x + c)^2 + 144*(A*a^9*b^3 - 4*A*a^7*b^5 + 6*A*a^5*b^7 - 4*A*a^3*b^9 + A*a*b^11)*d*x*cos(d*x + c) + 48*(A*a^8*b^4 - 4*A*a^6*b^6 + 6*A*a^4*b^8 - 4*A*a^2*b^10 + A*b^12)*d*x - 3*(2*C*a^8*b^3 + (20*A + 3*C)*a^6*b^5 - 35*A*a^4*b^7 + 28*A*a^2*b^9 - 8*A*b^11 + (2*C*a^11 + (20*A + 3*C)*a^9*b^2 - 35*A*a^7*b^4 + 28*A*a^5*b^6 - 8*A*a^3*b^8)*cos(d*x + c)^3 + 3*(2*C*a^10*b + (20*A + 3*C)*a^8*b^3 - 35*A*a^6*b^5 + 28*A*a^4*b^7 - 8*A*a^2*b^9)*cos(d*x + c)^2 + 3*(2*C*a^9*b^2 + (20*A + 3*C)*a^7*b^4 - 35*A*a^5*b^6 + 28*A*a^3*b^8 - 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 - 11*C)*a^9*b^3 - (71*A - 7*C)*a^7*b^5 + (133*A + 4*C)*a^5*b^7 - 92*A*a^3*b^9 + 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 - C)*a^11*b - (132*A - 23*C)*a^9*b^3 + (239*A - 7*C)*a^7*b^5 - (169*A - 2*C)*a^5*b^7 + 44*A*a^3*b^9)*cos(d*x + c)^2 + 3*(3*(2*A - 3*C)*a^10*b^2 - (59*A - 8*C)*a^8*b^4 + (110*A + C)*a^6*b^6 - 77*A*a^4*b^8 + 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*(24*(A*a^11*b - 4*A*a^9*b^3 + 6*A*a^7*b^5 - 4*A*a^5*b^7 + A*a^3*b^9)*d*x*cos(d*x + c)^3 + 72*(A*a^10*b^2 - 4*A*a^8*b^4 + 6*A*a^6*b^6 - 4*A*a^4*b^8 + A*a^2*b^10)*d*x*cos(d*x + c)^2 + 72*(A*a^9*b^3 - 4*A*a^7*b^5 + 6*A*a^5*b^7 - 4*A*a^3*b^9 + A*a*b^11)*d*x*cos(d*x + c) + 24*(A*a^8*b^4 - 4*A*a^6*b^6 + 6*A*a^4*b^8 - 4*A*a^2*b^10 + A*b^12)*d*x - 3*(2*C*a^8*b^3 + (20*A + 3*C)*a^6*b^5 - 35*A*a^4*b^7 + 28*A*a^2*b^9 - 8*A*b^11 + (2*C*a^11 + (20*A + 3*C)*a^9*b^2 - 35*A*a^7*b^4 + 28*A*a^5*b^6 - 8*A*a^3*b^8)*cos(d*x + c)^3 + 3*(2*C*a^10*b + (20*A + 3*C)*a^8*b^3 - 35*A*a^6*b^5 + 28*A*a^4*b^7 - 8*A*a^2*b^9)*cos(d*x + c)^2 + 3*(2*C*a^9*b^2 + (20*A + 3*C)*a^7*b^4 - 35*A*a^5*b^6 + 28*A*a^3*b^8 - 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 - 11*C)*a^9*b^3 - (71*A - 7*C)*a^7*b^5 + (133*A + 4*C)*a^5*b^7 - 92*A*a^3*b^9 + 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 - C)*a^11*b - (132*A - 23*C)*a^9*b^3 + (239*A - 7*C)*a^7*b^5 - (169*A - 2*C)*a^5*b^7 + 44*A*a^3*b^9)*cos(d*x + c)^2 + 3*(3*(2*A - 3*C)*a^10*b^2 - (59*A - 8*C)*a^8*b^4 + (110*A + C)*a^6*b^6 - 77*A*a^4*b^8 + 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
704,1,2465,0,0.908303," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{6 \, {\left({\left(A + 2 \, C\right)} a^{13} + 8 \, {\left(2 \, A - C\right)} a^{11} b^{2} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{9} b^{4} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{7} b^{6} - {\left(79 \, A - 2 \, C\right)} a^{5} b^{8} + 20 \, A a^{3} b^{10}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left({\left(A + 2 \, C\right)} a^{12} b + 8 \, {\left(2 \, A - C\right)} a^{10} b^{3} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{8} b^{5} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{6} b^{7} - {\left(79 \, A - 2 \, C\right)} a^{4} b^{9} + 20 \, A a^{2} b^{11}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left({\left(A + 2 \, C\right)} a^{11} b^{2} + 8 \, {\left(2 \, A - C\right)} a^{9} b^{4} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{7} b^{6} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{5} b^{8} - {\left(79 \, A - 2 \, C\right)} a^{3} b^{10} + 20 \, A a b^{12}\right)} d x \cos\left(d x + c\right) + 6 \, {\left({\left(A + 2 \, C\right)} a^{10} b^{3} + 8 \, {\left(2 \, A - C\right)} a^{8} b^{5} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{6} b^{7} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{4} b^{9} - {\left(79 \, A - 2 \, C\right)} a^{2} b^{11} + 20 \, A b^{13}\right)} d x + 3 \, {\left(8 \, C a^{8} b^{4} + 8 \, {\left(5 \, A - C\right)} a^{6} b^{6} - 7 \, {\left(12 \, A - C\right)} a^{4} b^{8} + {\left(69 \, A - 2 \, C\right)} a^{2} b^{10} - 20 \, A b^{12} + {\left(8 \, C a^{11} b + 8 \, {\left(5 \, A - C\right)} a^{9} b^{3} - 7 \, {\left(12 \, A - C\right)} a^{7} b^{5} + {\left(69 \, A - 2 \, C\right)} a^{5} b^{7} - 20 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, C a^{10} b^{2} + 8 \, {\left(5 \, A - C\right)} a^{8} b^{4} - 7 \, {\left(12 \, A - C\right)} a^{6} b^{6} + {\left(69 \, A - 2 \, C\right)} a^{4} b^{8} - 20 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, C a^{9} b^{3} + 8 \, {\left(5 \, A - C\right)} a^{7} b^{5} - 7 \, {\left(12 \, A - C\right)} a^{5} b^{7} + {\left(69 \, A - 2 \, C\right)} a^{3} b^{9} - 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(2 \, {\left(12 \, A - 13 \, C\right)} a^{9} b^{4} - {\left(170 \, A - 43 \, C\right)} a^{7} b^{6} + {\left(313 \, A - 23 \, C\right)} a^{5} b^{8} - {\left(227 \, A - 6 \, C\right)} a^{3} b^{10} + 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} + 15 \, {\left(A a^{12} b - 4 \, A a^{10} b^{3} + 6 \, A a^{8} b^{5} - 4 \, A a^{6} b^{7} + A a^{4} b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(9 \, {\left(7 \, A - 4 \, C\right)} a^{11} b^{2} - 2 \, {\left(171 \, A - 34 \, C\right)} a^{9} b^{4} + {\left(590 \, A - 43 \, C\right)} a^{7} b^{6} - {\left(421 \, A - 11 \, C\right)} a^{5} b^{8} + 110 \, A a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(23 \, A - 20 \, C\right)} a^{10} b^{3} - {\left(146 \, A - 35 \, C\right)} a^{8} b^{5} + {\left(263 \, A - 20 \, C\right)} a^{6} b^{7} - 5 \, {\left(38 \, A - C\right)} a^{4} b^{9} + 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({\left(A + 2 \, C\right)} a^{13} + 8 \, {\left(2 \, A - C\right)} a^{11} b^{2} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{9} b^{4} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{7} b^{6} - {\left(79 \, A - 2 \, C\right)} a^{5} b^{8} + 20 \, A a^{3} b^{10}\right)} d x \cos\left(d x + c\right)^{3} + 9 \, {\left({\left(A + 2 \, C\right)} a^{12} b + 8 \, {\left(2 \, A - C\right)} a^{10} b^{3} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{8} b^{5} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{6} b^{7} - {\left(79 \, A - 2 \, C\right)} a^{4} b^{9} + 20 \, A a^{2} b^{11}\right)} d x \cos\left(d x + c\right)^{2} + 9 \, {\left({\left(A + 2 \, C\right)} a^{11} b^{2} + 8 \, {\left(2 \, A - C\right)} a^{9} b^{4} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{7} b^{6} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{5} b^{8} - {\left(79 \, A - 2 \, C\right)} a^{3} b^{10} + 20 \, A a b^{12}\right)} d x \cos\left(d x + c\right) + 3 \, {\left({\left(A + 2 \, C\right)} a^{10} b^{3} + 8 \, {\left(2 \, A - C\right)} a^{8} b^{5} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{6} b^{7} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{4} b^{9} - {\left(79 \, A - 2 \, C\right)} a^{2} b^{11} + 20 \, A b^{13}\right)} d x - 3 \, {\left(8 \, C a^{8} b^{4} + 8 \, {\left(5 \, A - C\right)} a^{6} b^{6} - 7 \, {\left(12 \, A - C\right)} a^{4} b^{8} + {\left(69 \, A - 2 \, C\right)} a^{2} b^{10} - 20 \, A b^{12} + {\left(8 \, C a^{11} b + 8 \, {\left(5 \, A - C\right)} a^{9} b^{3} - 7 \, {\left(12 \, A - C\right)} a^{7} b^{5} + {\left(69 \, A - 2 \, C\right)} a^{5} b^{7} - 20 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, C a^{10} b^{2} + 8 \, {\left(5 \, A - C\right)} a^{8} b^{4} - 7 \, {\left(12 \, A - C\right)} a^{6} b^{6} + {\left(69 \, A - 2 \, C\right)} a^{4} b^{8} - 20 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, C a^{9} b^{3} + 8 \, {\left(5 \, A - C\right)} a^{7} b^{5} - 7 \, {\left(12 \, A - C\right)} a^{5} b^{7} + {\left(69 \, A - 2 \, C\right)} a^{3} b^{9} - 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(2 \, {\left(12 \, A - 13 \, C\right)} a^{9} b^{4} - {\left(170 \, A - 43 \, C\right)} a^{7} b^{6} + {\left(313 \, A - 23 \, C\right)} a^{5} b^{8} - {\left(227 \, A - 6 \, C\right)} a^{3} b^{10} + 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} + 15 \, {\left(A a^{12} b - 4 \, A a^{10} b^{3} + 6 \, A a^{8} b^{5} - 4 \, A a^{6} b^{7} + A a^{4} b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(9 \, {\left(7 \, A - 4 \, C\right)} a^{11} b^{2} - 2 \, {\left(171 \, A - 34 \, C\right)} a^{9} b^{4} + {\left(590 \, A - 43 \, C\right)} a^{7} b^{6} - {\left(421 \, A - 11 \, C\right)} a^{5} b^{8} + 110 \, A a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(23 \, A - 20 \, C\right)} a^{10} b^{3} - {\left(146 \, A - 35 \, C\right)} a^{8} b^{5} + {\left(263 \, A - 20 \, C\right)} a^{6} b^{7} - 5 \, {\left(38 \, A - C\right)} a^{4} b^{9} + 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 + 2*C)*a^13 + 8*(2*A - C)*a^11*b^2 - 2*(37*A - 6*C)*a^9*b^4 + 4*(29*A - 2*C)*a^7*b^6 - (79*A - 2*C)*a^5*b^8 + 20*A*a^3*b^10)*d*x*cos(d*x + c)^3 + 18*((A + 2*C)*a^12*b + 8*(2*A - C)*a^10*b^3 - 2*(37*A - 6*C)*a^8*b^5 + 4*(29*A - 2*C)*a^6*b^7 - (79*A - 2*C)*a^4*b^9 + 20*A*a^2*b^11)*d*x*cos(d*x + c)^2 + 18*((A + 2*C)*a^11*b^2 + 8*(2*A - C)*a^9*b^4 - 2*(37*A - 6*C)*a^7*b^6 + 4*(29*A - 2*C)*a^5*b^8 - (79*A - 2*C)*a^3*b^10 + 20*A*a*b^12)*d*x*cos(d*x + c) + 6*((A + 2*C)*a^10*b^3 + 8*(2*A - C)*a^8*b^5 - 2*(37*A - 6*C)*a^6*b^7 + 4*(29*A - 2*C)*a^4*b^9 - (79*A - 2*C)*a^2*b^11 + 20*A*b^13)*d*x + 3*(8*C*a^8*b^4 + 8*(5*A - C)*a^6*b^6 - 7*(12*A - C)*a^4*b^8 + (69*A - 2*C)*a^2*b^10 - 20*A*b^12 + (8*C*a^11*b + 8*(5*A - C)*a^9*b^3 - 7*(12*A - C)*a^7*b^5 + (69*A - 2*C)*a^5*b^7 - 20*A*a^3*b^9)*cos(d*x + c)^3 + 3*(8*C*a^10*b^2 + 8*(5*A - C)*a^8*b^4 - 7*(12*A - C)*a^6*b^6 + (69*A - 2*C)*a^4*b^8 - 20*A*a^2*b^10)*cos(d*x + c)^2 + 3*(8*C*a^9*b^3 + 8*(5*A - C)*a^7*b^5 - 7*(12*A - C)*a^5*b^7 + (69*A - 2*C)*a^3*b^9 - 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*(2*(12*A - 13*C)*a^9*b^4 - (170*A - 43*C)*a^7*b^6 + (313*A - 23*C)*a^5*b^8 - (227*A - 6*C)*a^3*b^10 + 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 + 15*(A*a^12*b - 4*A*a^10*b^3 + 6*A*a^8*b^5 - 4*A*a^6*b^7 + A*a^4*b^9)*cos(d*x + c)^3 + (9*(7*A - 4*C)*a^11*b^2 - 2*(171*A - 34*C)*a^9*b^4 + (590*A - 43*C)*a^7*b^6 - (421*A - 11*C)*a^5*b^8 + 110*A*a^3*b^10)*cos(d*x + c)^2 + 3*((23*A - 20*C)*a^10*b^3 - (146*A - 35*C)*a^8*b^5 + (263*A - 20*C)*a^6*b^7 - 5*(38*A - C)*a^4*b^9 + 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 + 2*C)*a^13 + 8*(2*A - C)*a^11*b^2 - 2*(37*A - 6*C)*a^9*b^4 + 4*(29*A - 2*C)*a^7*b^6 - (79*A - 2*C)*a^5*b^8 + 20*A*a^3*b^10)*d*x*cos(d*x + c)^3 + 9*((A + 2*C)*a^12*b + 8*(2*A - C)*a^10*b^3 - 2*(37*A - 6*C)*a^8*b^5 + 4*(29*A - 2*C)*a^6*b^7 - (79*A - 2*C)*a^4*b^9 + 20*A*a^2*b^11)*d*x*cos(d*x + c)^2 + 9*((A + 2*C)*a^11*b^2 + 8*(2*A - C)*a^9*b^4 - 2*(37*A - 6*C)*a^7*b^6 + 4*(29*A - 2*C)*a^5*b^8 - (79*A - 2*C)*a^3*b^10 + 20*A*a*b^12)*d*x*cos(d*x + c) + 3*((A + 2*C)*a^10*b^3 + 8*(2*A - C)*a^8*b^5 - 2*(37*A - 6*C)*a^6*b^7 + 4*(29*A - 2*C)*a^4*b^9 - (79*A - 2*C)*a^2*b^11 + 20*A*b^13)*d*x - 3*(8*C*a^8*b^4 + 8*(5*A - C)*a^6*b^6 - 7*(12*A - C)*a^4*b^8 + (69*A - 2*C)*a^2*b^10 - 20*A*b^12 + (8*C*a^11*b + 8*(5*A - C)*a^9*b^3 - 7*(12*A - C)*a^7*b^5 + (69*A - 2*C)*a^5*b^7 - 20*A*a^3*b^9)*cos(d*x + c)^3 + 3*(8*C*a^10*b^2 + 8*(5*A - C)*a^8*b^4 - 7*(12*A - C)*a^6*b^6 + (69*A - 2*C)*a^4*b^8 - 20*A*a^2*b^10)*cos(d*x + c)^2 + 3*(8*C*a^9*b^3 + 8*(5*A - C)*a^7*b^5 - 7*(12*A - C)*a^5*b^7 + (69*A - 2*C)*a^3*b^9 - 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))) - (2*(12*A - 13*C)*a^9*b^4 - (170*A - 43*C)*a^7*b^6 + (313*A - 23*C)*a^5*b^8 - (227*A - 6*C)*a^3*b^10 + 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 + 15*(A*a^12*b - 4*A*a^10*b^3 + 6*A*a^8*b^5 - 4*A*a^6*b^7 + A*a^4*b^9)*cos(d*x + c)^3 + (9*(7*A - 4*C)*a^11*b^2 - 2*(171*A - 34*C)*a^9*b^4 + (590*A - 43*C)*a^7*b^6 - (421*A - 11*C)*a^5*b^8 + 110*A*a^3*b^10)*cos(d*x + c)^2 + 3*((23*A - 20*C)*a^10*b^3 - (146*A - 35*C)*a^8*b^5 + (263*A - 20*C)*a^6*b^7 - 5*(38*A - C)*a^4*b^9 + 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
705,1,36,0,0.459350," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d x - b \log\left(\sin\left(d x + c\right) + 1\right) + b \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, d}"," ",0,"1/2*(2*a*d*x - b*log(sin(d*x + c) + 1) + b*log(-sin(d*x + c) + 1))/d","B",0
706,1,226,0,0.520888," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} - b^{2}\right)} 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)}{{\left(a^{2} - b^{2}\right)} d}, \frac{{\left(a^{2} - b^{2}\right)} d x - 2 \, \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)}{{\left(a^{2} - b^{2}\right)} d}\right]"," ",0,"[((a^2 - b^2)*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 - b^2)*d), ((a^2 - b^2)*d*x - 2*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 - b^2)*d)]","A",0
707,1,481,0,0.513964," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x + {\left(3 \, a^{2} b^{2} - b^{4} + {\left(3 \, a^{3} 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) + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d\right)}}, \frac{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \cos\left(d x + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x - {\left(3 \, a^{2} b^{2} - b^{4} + {\left(3 \, a^{3} 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) + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d}\right]"," ",0,"[1/2*(2*(a^5 - 2*a^3*b^2 + a*b^4)*d*x*cos(d*x + c) + 2*(a^4*b - 2*a^2*b^3 + b^5)*d*x + (3*a^2*b^2 - b^4 + (3*a^3*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)) + 4*(a^3*b^2 - a*b^4)*sin(d*x + c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*d*cos(d*x + c) + (a^5*b - 2*a^3*b^3 + a*b^5)*d), ((a^5 - 2*a^3*b^2 + a*b^4)*d*x*cos(d*x + c) + (a^4*b - 2*a^2*b^3 + b^5)*d*x - (3*a^2*b^2 - b^4 + (3*a^3*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))) + 2*(a^3*b^2 - a*b^4)*sin(d*x + c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*d*cos(d*x + c) + (a^5*b - 2*a^3*b^3 + a*b^5)*d)]","B",0
708,1,906,0,0.564301," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d x + {\left(4 \, a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + {\left(4 \, a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{5} b^{2} - 2 \, a^{3} b^{4} + 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(4 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + a b^{7} + {\left(5 \, a^{6} b^{2} - 7 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8}\right)} d\right)}}, \frac{{\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \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 x \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 x - {\left(4 \, a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + {\left(4 \, a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{5} b^{2} - 2 \, a^{3} b^{4} + 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^{5} b^{3} - 5 \, a^{3} b^{5} + a b^{7} + {\left(5 \, a^{6} b^{2} - 7 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{2} - 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8}\right)} d}\right]"," ",0,"[1/2*(2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*cos(d*x + c)^2 + 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x*cos(d*x + c) + 2*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*x + (4*a^4*b^3 - 2*a^2*b^5 + b^7 + (4*a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c)^2 + 2*(4*a^5*b^2 - 2*a^3*b^4 + 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*(4*a^5*b^3 - 5*a^3*b^5 + a*b^7 + (5*a^6*b^2 - 7*a^4*b^4 + 2*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*d*cos(d*x + c)^2 + 2*(a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*d*cos(d*x + c) + (a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8)*d), ((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x*cos(d*x + c) + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*x - (4*a^4*b^3 - 2*a^2*b^5 + b^7 + (4*a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c)^2 + 2*(4*a^5*b^2 - 2*a^3*b^4 + 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^5*b^3 - 5*a^3*b^5 + a*b^7 + (5*a^6*b^2 - 7*a^4*b^4 + 2*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*d*cos(d*x + c)^2 + 2*(a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*d*cos(d*x + c) + (a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 - a^2*b^8)*d)]","B",0
709,0,0,0,0.524560," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{5} + A \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^5 + A*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
710,0,0,0,0.482489," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^4 + A*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
711,0,0,0,0.455127," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^3 + A*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
712,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,0,0,0,32.397564," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)*sec(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
714,0,0,0,2.121374," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2*sec(d*x + c)^2 + A*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
715,0,0,0,2.112148," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^3*sec(d*x + c)^2 + A*cos(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
716,0,0,0,70.297889," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^4*sec(d*x + c)^2 + A*cos(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
717,0,0,0,0.568022," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{6} + C a \sec\left(d x + c\right)^{5} + A b \sec\left(d x + c\right)^{4} + A a \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^6 + C*a*sec(d*x + c)^5 + A*b*sec(d*x + c)^4 + A*a*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
718,0,0,0,0.478200," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{5} + C a \sec\left(d x + c\right)^{4} + A b \sec\left(d x + c\right)^{3} + A a \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^5 + C*a*sec(d*x + c)^4 + A*b*sec(d*x + c)^3 + A*a*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
719,0,0,0,0.575253," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{4} + C a \sec\left(d x + c\right)^{3} + A b \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^4 + C*a*sec(d*x + c)^3 + A*b*sec(d*x + c)^2 + A*a*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
720,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
721,0,0,0,1.461934," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + C a \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) + A a \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)*sec(d*x + c)^3 + C*a*cos(d*x + c)*sec(d*x + c)^2 + A*b*cos(d*x + c)*sec(d*x + c) + A*a*cos(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
722,0,0,0,57.496488," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + C a \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) + A a \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^2*sec(d*x + c)^3 + C*a*cos(d*x + c)^2*sec(d*x + c)^2 + A*b*cos(d*x + c)^2*sec(d*x + c) + A*a*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
723,0,0,0,58.099915," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A a \cos\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3*sec(d*x + c)^3 + C*a*cos(d*x + c)^3*sec(d*x + c)^2 + A*b*cos(d*x + c)^3*sec(d*x + c) + A*a*cos(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
724,0,0,0,2.262230," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + A a \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^4*sec(d*x + c)^3 + C*a*cos(d*x + c)^4*sec(d*x + c)^2 + A*b*cos(d*x + c)^4*sec(d*x + c) + A*a*cos(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
725,0,0,0,0.555577," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{7} + 2 \, C a b \sec\left(d x + c\right)^{6} + 2 \, A a b \sec\left(d x + c\right)^{4} + A a^{2} \sec\left(d x + c\right)^{3} + {\left(C a^{2} + A b^{2}\right)} \sec\left(d x + c\right)^{5}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^7 + 2*C*a*b*sec(d*x + c)^6 + 2*A*a*b*sec(d*x + c)^4 + A*a^2*sec(d*x + c)^3 + (C*a^2 + A*b^2)*sec(d*x + c)^5)*sqrt(b*sec(d*x + c) + a), x)","F",0
726,0,0,0,0.536849," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{6} + 2 \, C a b \sec\left(d x + c\right)^{5} + 2 \, A a b \sec\left(d x + c\right)^{3} + A a^{2} \sec\left(d x + c\right)^{2} + {\left(C a^{2} + A b^{2}\right)} \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^6 + 2*C*a*b*sec(d*x + c)^5 + 2*A*a*b*sec(d*x + c)^3 + A*a^2*sec(d*x + c)^2 + (C*a^2 + A*b^2)*sec(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
727,0,0,0,0.512333," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{5} + 2 \, C a b \sec\left(d x + c\right)^{4} + 2 \, A a b \sec\left(d x + c\right)^{2} + A a^{2} \sec\left(d x + c\right) + {\left(C a^{2} + A b^{2}\right)} \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^5 + 2*C*a*b*sec(d*x + c)^4 + 2*A*a*b*sec(d*x + c)^2 + A*a^2*sec(d*x + c) + (C*a^2 + A*b^2)*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
728,0,0,0,0.941151," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{4} + 2 \, C a b \sec\left(d x + c\right)^{3} + 2 \, A a b \sec\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^4 + 2*C*a*b*sec(d*x + c)^3 + 2*A*a*b*sec(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
729,0,0,0,1.027339," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) \sec\left(d x + c\right) + A a^{2} \cos\left(d x + c\right) + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)*sec(d*x + c)^4 + 2*C*a*b*cos(d*x + c)*sec(d*x + c)^3 + 2*A*a*b*cos(d*x + c)*sec(d*x + c) + A*a^2*cos(d*x + c) + (C*a^2 + A*b^2)*cos(d*x + c)*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
730,0,0,0,1.482279," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A a^{2} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^2*sec(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^2*sec(d*x + c)^3 + 2*A*a*b*cos(d*x + c)^2*sec(d*x + c) + A*a^2*cos(d*x + c)^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
731,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,0,0,0,64.068116," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + A a^{2} \cos\left(d x + c\right)^{4} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4*sec(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^4*sec(d*x + c)^3 + 2*A*a*b*cos(d*x + c)^4*sec(d*x + c) + A*a^2*cos(d*x + c)^4 + (C*a^2 + A*b^2)*cos(d*x + c)^4*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
733,0,0,0,0.836363," ","integrate((a+b*sec(d*x+c))^(3/2)*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{3} \sec\left(d x + c\right)^{3} + a b^{2} \sec\left(d x + c\right)^{2} - a^{2} b \sec\left(d x + c\right) - a^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(b^3*sec(d*x + c)^3 + a*b^2*sec(d*x + c)^2 - a^2*b*sec(d*x + c) - a^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
734,0,0,0,0.826123," ","integrate((a^2-b^2*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \sec\left(d x + c\right)^{2} - a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(b^2*sec(d*x + c)^2 - a^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
735,0,0,0,0.507978," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{5} + A \sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*sec(d*x + c)^5 + A*sec(d*x + c)^3)/sqrt(b*sec(d*x + c) + a), x)","F",0
736,0,0,0,0.519961," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{4} + A \sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*sec(d*x + c)^4 + A*sec(d*x + c)^2)/sqrt(b*sec(d*x + c) + a), x)","F",0
737,0,0,0,0.494763," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{3} + A \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*sec(d*x + c)^3 + A*sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
738,0,0,0,0.849027," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)/sqrt(b*sec(d*x + c) + a), x)","F",0
739,0,0,0,0.883724," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)*sec(d*x + c)^2 + A*cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
740,0,0,0,1.471534," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2*sec(d*x + c)^2 + A*cos(d*x + c)^2)/sqrt(b*sec(d*x + c) + a), x)","F",0
741,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
742,0,0,0,0.817674," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{5} + 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((C*sec(d*x + c)^5 + 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
743,0,0,0,0.764803," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + 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
744,0,0,0,0.487602," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + 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
745,0,0,0,23.836515," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\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((C*sec(d*x + c)^2 + A)*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
746,0,0,0,23.868615," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
747,0,0,0,1.569474," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
748,0,0,0,0.572773," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{5} + 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((C*sec(d*x + c)^5 + 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
749,0,0,0,0.537882," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + 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
750,0,0,0,0.522186," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + 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
751,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
752,0,0,0,43.218032," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
753,0,0,0,3.531681," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
754,0,0,0,1.690892," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{4} \sec\left(d x + c\right)^{4} + 4 \, a b^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{3} b \sec\left(d x + c\right) + a^{4}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)/(b^4*sec(d*x + c)^4 + 4*a*b^3*sec(d*x + c)^3 + 6*a^2*b^2*sec(d*x + c)^2 + 4*a^3*b*sec(d*x + c) + a^4), x)","F",0
755,0,0,0,32.085980," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\sqrt{b \sec\left(d x + c\right) + a} {\left(b \sec\left(d x + c\right) - a\right)}, x\right)"," ",0,"integral(-sqrt(b*sec(d*x + c) + a)*(b*sec(d*x + c) - a), x)","F",0
756,0,0,0,1.197053," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),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
757,0,0,0,31.254263," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sec\left(d x + c\right) + a} {\left(b \sec\left(d x + c\right) - a\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(-sqrt(b*sec(d*x + c) + a)*(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
758,0,0,0,23.689486," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sec\left(d x + c\right) + a} {\left(b \sec\left(d x + c\right) - a\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(-sqrt(b*sec(d*x + c) + a)*(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
759,0,0,0,107.979307," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c)^2 + a*sec(d*x + c)), x)","F",0
760,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
761,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
762,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
764,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
765,1,151,0,0.975806," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{45 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 45 \, {\left(C a + B b\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 + 4 \, C b\right)} \cos\left(d x + c\right)^{4} + 45 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, B a + 4 \, C b\right)} \cos\left(d x + c\right)^{2} + 24 \, C b + 30 \, {\left(C a + B b\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*(45*(C*a + B*b)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 45*(C*a + B*b)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(5*B*a + 4*C*b)*cos(d*x + c)^4 + 45*(C*a + B*b)*cos(d*x + c)^3 + 8*(5*B*a + 4*C*b)*cos(d*x + c)^2 + 24*C*b + 30*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
766,1,136,0,0.932258," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, B a + 3 \, C b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, B a + 3 \, C b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, B a + 3 \, C b\right)} \cos\left(d x + c\right)^{2} + 6 \, C b + 8 \, {\left(C a + B 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*B*a + 3*C*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*B*a + 3*C*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(C*a + B*b)*cos(d*x + c)^3 + 3*(4*B*a + 3*C*b)*cos(d*x + c)^2 + 6*C*b + 8*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
767,1,115,0,0.480936," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(3 \, B a + 2 \, C b\right)} \cos\left(d x + c\right)^{2} + 2 \, C b + 3 \, {\left(C a + B 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*(C*a + B*b)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(C*a + B*b)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(3*B*a + 2*C*b)*cos(d*x + c)^2 + 2*C*b + 3*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
768,1,96,0,0.540255," ","integrate((a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(2 \, B a + C b\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, B a + C b\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C b + 2 \, {\left(C a + B 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*B*a + C*b)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*B*a + C*b)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(C*b + 2*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
769,1,85,0,0.497664," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, B a d x \cos\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a + B b\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, C b \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*B*a*d*x*cos(d*x + c) + (C*a + B*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - (C*a + B*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*C*b*sin(d*x + c))/(d*cos(d*x + c))","B",0
770,1,54,0,0.652436," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(C a + B b\right)} d x + C b \log\left(\sin\left(d x + c\right) + 1\right) - C b \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(C*a + B*b)*d*x + C*b*log(sin(d*x + c) + 1) - C*b*log(-sin(d*x + c) + 1) + 2*B*a*sin(d*x + c))/d","A",0
771,1,42,0,0.593928," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(B a + 2 \, C b\right)} d x + {\left(B a \cos\left(d x + c\right) + 2 \, C a + 2 \, B b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((B*a + 2*C*b)*d*x + (B*a*cos(d*x + c) + 2*C*a + 2*B*b)*sin(d*x + c))/d","A",0
772,1,60,0,0.468944," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(C a + B b\right)} d x + {\left(2 \, B a \cos\left(d x + c\right)^{2} + 4 \, B a + 6 \, C b + 3 \, {\left(C a + B b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(C*a + B*b)*d*x + (2*B*a*cos(d*x + c)^2 + 4*B*a + 6*C*b + 3*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
773,1,81,0,0.715375," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, B a + 4 \, C b\right)} d x + {\left(6 \, B a \cos\left(d x + c\right)^{3} + 8 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{2} + 16 \, C a + 16 \, B b + 3 \, {\left(3 \, B a + 4 \, C b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*B*a + 4*C*b)*d*x + (6*B*a*cos(d*x + c)^3 + 8*(C*a + B*b)*cos(d*x + c)^2 + 16*C*a + 16*B*b + 3*(3*B*a + 4*C*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
774,1,96,0,0.579916," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{45 \, {\left(C a + B b\right)} d x + {\left(24 \, B a \cos\left(d x + c\right)^{4} + 30 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, B a + 5 \, C b\right)} \cos\left(d x + c\right)^{2} + 64 \, B a + 80 \, C b + 45 \, {\left(C a + B b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(45*(C*a + B*b)*d*x + (24*B*a*cos(d*x + c)^4 + 30*(C*a + B*b)*cos(d*x + c)^3 + 8*(4*B*a + 5*C*b)*cos(d*x + c)^2 + 64*B*a + 80*C*b + 45*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
775,1,208,0,0.594943," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, B a^{2} + 6 \, C a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, B a^{2} + 6 \, C a b + 3 \, B 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 \, C a^{2} + 10 \, B a b + 4 \, C b^{2}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(4 \, B a^{2} + 6 \, C a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{3} + 24 \, C b^{2} + 8 \, {\left(5 \, C a^{2} + 10 \, B a b + 4 \, C b^{2}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(2 \, C a b + B 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*B*a^2 + 6*C*a*b + 3*B*b^2)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*B*a^2 + 6*C*a*b + 3*B*b^2)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(5*C*a^2 + 10*B*a*b + 4*C*b^2)*cos(d*x + c)^4 + 15*(4*B*a^2 + 6*C*a*b + 3*B*b^2)*cos(d*x + c)^3 + 24*C*b^2 + 8*(5*C*a^2 + 10*B*a*b + 4*C*b^2)*cos(d*x + c)^2 + 30*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
776,1,180,0,0.917093," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, C a^{2} + 8 \, B a b + 3 \, C b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, C a^{2} + 8 \, B a b + 3 \, C 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 \, B a^{2} + 4 \, C a b + 2 \, B b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, C b^{2} + 3 \, {\left(4 \, C a^{2} + 8 \, B a b + 3 \, C b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(2 \, C a b + B 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*C*a^2 + 8*B*a*b + 3*C*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*C*a^2 + 8*B*a*b + 3*C*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(3*B*a^2 + 4*C*a*b + 2*B*b^2)*cos(d*x + c)^3 + 6*C*b^2 + 3*(4*C*a^2 + 8*B*a*b + 3*C*b^2)*cos(d*x + c)^2 + 8*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
777,1,150,0,0.450198," ","integrate((a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, B a^{2} + 2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, B a^{2} + 2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C b^{2} + 2 \, {\left(3 \, C a^{2} + 6 \, B a b + 2 \, C b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a b + B 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*B*a^2 + 2*C*a*b + B*b^2)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*B*a^2 + 2*C*a*b + B*b^2)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*C*b^2 + 2*(3*C*a^2 + 6*B*a*b + 2*C*b^2)*cos(d*x + c)^2 + 3*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
778,1,136,0,0.452527," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, B a^{2} d x \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{2} + 4 \, B a b + C b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, C a^{2} + 4 \, B a b + C b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C b^{2} + 2 \, {\left(2 \, C a b + B 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*B*a^2*d*x*cos(d*x + c)^2 + (2*C*a^2 + 4*B*a*b + C*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*C*a^2 + 4*B*a*b + C*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(C*b^2 + 2*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
779,1,117,0,0.454773," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(C a^{2} + 2 \, B a b\right)} d x \cos\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{2} \cos\left(d x + c\right) + C b^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(C*a^2 + 2*B*a*b)*d*x*cos(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)*log(sin(d*x + c) + 1) - (2*C*a*b + B*b^2)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(B*a^2*cos(d*x + c) + C*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
780,1,87,0,0.458817," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{C b^{2} \log\left(\sin\left(d x + c\right) + 1\right) - C b^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(B a^{2} + 4 \, C a b + 2 \, B b^{2}\right)} d x + {\left(B a^{2} \cos\left(d x + c\right) + 2 \, C a^{2} + 4 \, B a b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(C*b^2*log(sin(d*x + c) + 1) - C*b^2*log(-sin(d*x + c) + 1) + (B*a^2 + 4*C*a*b + 2*B*b^2)*d*x + (B*a^2*cos(d*x + c) + 2*C*a^2 + 4*B*a*b)*sin(d*x + c))/d","A",0
781,1,85,0,0.474888," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(C a^{2} + 2 \, B a b + 2 \, C b^{2}\right)} d x + {\left(2 \, B a^{2} \cos\left(d x + c\right)^{2} + 4 \, B a^{2} + 12 \, C a b + 6 \, B b^{2} + 3 \, {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(C*a^2 + 2*B*a*b + 2*C*b^2)*d*x + (2*B*a^2*cos(d*x + c)^2 + 4*B*a^2 + 12*C*a*b + 6*B*b^2 + 3*(C*a^2 + 2*B*a*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
782,1,114,0,0.494550," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, B a^{2} + 8 \, C a b + 4 \, B b^{2}\right)} d x + {\left(6 \, B a^{2} \cos\left(d x + c\right)^{3} + 16 \, C a^{2} + 32 \, B a b + 24 \, C b^{2} + 8 \, {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, B a^{2} + 8 \, C a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*B*a^2 + 8*C*a*b + 4*B*b^2)*d*x + (6*B*a^2*cos(d*x + c)^3 + 16*C*a^2 + 32*B*a*b + 24*C*b^2 + 8*(C*a^2 + 2*B*a*b)*cos(d*x + c)^2 + 3*(3*B*a^2 + 8*C*a*b + 4*B*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
783,1,142,0,0.453450," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, C a^{2} + 6 \, B a b + 4 \, C b^{2}\right)} d x + {\left(24 \, B a^{2} \cos\left(d x + c\right)^{4} + 30 \, {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{3} + 64 \, B a^{2} + 160 \, C a b + 80 \, B b^{2} + 8 \, {\left(4 \, B a^{2} + 10 \, C a b + 5 \, B b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, C a^{2} + 6 \, B a b + 4 \, C b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(3*C*a^2 + 6*B*a*b + 4*C*b^2)*d*x + (24*B*a^2*cos(d*x + c)^4 + 30*(C*a^2 + 2*B*a*b)*cos(d*x + c)^3 + 64*B*a^2 + 160*C*a*b + 80*B*b^2 + 8*(4*B*a^2 + 10*C*a*b + 5*B*b^2)*cos(d*x + c)^2 + 15*(3*C*a^2 + 6*B*a*b + 4*C*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
784,1,286,0,0.464751," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, B a^{3} + 18 \, C a^{2} b + 18 \, B a b^{2} + 5 \, C b^{3}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, B a^{3} + 18 \, C a^{2} b + 18 \, B a b^{2} + 5 \, C b^{3}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(32 \, {\left(5 \, C a^{3} + 15 \, B a^{2} b + 12 \, C a b^{2} + 4 \, B b^{3}\right)} \cos\left(d x + c\right)^{5} + 15 \, {\left(8 \, B a^{3} + 18 \, C a^{2} b + 18 \, B a b^{2} + 5 \, C b^{3}\right)} \cos\left(d x + c\right)^{4} + 40 \, C b^{3} + 16 \, {\left(5 \, C a^{3} + 15 \, B a^{2} b + 12 \, C a b^{2} + 4 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(18 \, C a^{2} b + 18 \, B a b^{2} + 5 \, C b^{3}\right)} \cos\left(d x + c\right)^{2} + 48 \, {\left(3 \, C a b^{2} + B b^{3}\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^3 + 18*C*a^2*b + 18*B*a*b^2 + 5*C*b^3)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(8*B*a^3 + 18*C*a^2*b + 18*B*a*b^2 + 5*C*b^3)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(32*(5*C*a^3 + 15*B*a^2*b + 12*C*a*b^2 + 4*B*b^3)*cos(d*x + c)^5 + 15*(8*B*a^3 + 18*C*a^2*b + 18*B*a*b^2 + 5*C*b^3)*cos(d*x + c)^4 + 40*C*b^3 + 16*(5*C*a^3 + 15*B*a^2*b + 12*C*a*b^2 + 4*B*b^3)*cos(d*x + c)^3 + 10*(18*C*a^2*b + 18*B*a*b^2 + 5*C*b^3)*cos(d*x + c)^2 + 48*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
785,1,249,0,0.759358," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, C a^{3} + 12 \, B a^{2} b + 9 \, C a b^{2} + 3 \, B b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, C a^{3} + 12 \, B a^{2} b + 9 \, C a b^{2} + 3 \, B 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 \, B a^{3} + 30 \, C a^{2} b + 30 \, B a b^{2} + 8 \, C b^{3}\right)} \cos\left(d x + c\right)^{4} + 24 \, C b^{3} + 15 \, {\left(4 \, C a^{3} + 12 \, B a^{2} b + 9 \, C a b^{2} + 3 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, C a^{2} b + 15 \, B a b^{2} + 4 \, C b^{3}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(3 \, C a b^{2} + B 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*C*a^3 + 12*B*a^2*b + 9*C*a*b^2 + 3*B*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*C*a^3 + 12*B*a^2*b + 9*C*a*b^2 + 3*B*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(15*B*a^3 + 30*C*a^2*b + 30*B*a*b^2 + 8*C*b^3)*cos(d*x + c)^4 + 24*C*b^3 + 15*(4*C*a^3 + 12*B*a^2*b + 9*C*a*b^2 + 3*B*b^3)*cos(d*x + c)^3 + 8*(15*C*a^2*b + 15*B*a*b^2 + 4*C*b^3)*cos(d*x + c)^2 + 30*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
786,1,211,0,0.844035," ","integrate((a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 3 \, C b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 3 \, C b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, C b^{3} + 8 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b + 6 \, C a b^{2} + 2 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} + 9 \, {\left(4 \, C a^{2} b + 4 \, B a b^{2} + C b^{3}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, C a b^{2} + B 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*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 3*C*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 3*C*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(6*C*b^3 + 8*(3*C*a^3 + 9*B*a^2*b + 6*C*a*b^2 + 2*B*b^3)*cos(d*x + c)^3 + 9*(4*C*a^2*b + 4*B*a*b^2 + C*b^3)*cos(d*x + c)^2 + 8*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
787,1,189,0,0.631731," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{12 \, B a^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C b^{3} + 2 \, {\left(9 \, C a^{2} b + 9 \, B a b^{2} + 2 \, C b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, C a b^{2} + B 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*B*a^3*d*x*cos(d*x + c)^3 + 3*(2*C*a^3 + 6*B*a^2*b + 3*C*a*b^2 + B*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*C*a^3 + 6*B*a^2*b + 3*C*a*b^2 + B*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*C*b^3 + 2*(9*C*a^2*b + 9*B*a*b^2 + 2*C*b^3)*cos(d*x + c)^2 + 3*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
788,1,167,0,0.614235," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} d x \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{2} b + 6 \, B a b^{2} + C b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(6 \, C a^{2} b + 6 \, B a b^{2} + C b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B a^{3} \cos\left(d x + c\right)^{2} + C b^{3} + 2 \, {\left(3 \, C a b^{2} + B 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*(C*a^3 + 3*B*a^2*b)*d*x*cos(d*x + c)^2 + (6*C*a^2*b + 6*B*a*b^2 + C*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (6*C*a^2*b + 6*B*a*b^2 + C*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*B*a^3*cos(d*x + c)^2 + C*b^3 + 2*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
789,1,152,0,0.806933," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(B a^{3} + 6 \, C a^{2} b + 6 \, B a b^{2}\right)} d x \cos\left(d x + c\right) + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(B a^{3} \cos\left(d x + c\right)^{2} + 2 \, C b^{3} + 2 \, {\left(C a^{3} + 3 \, B 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*((B*a^3 + 6*C*a^2*b + 6*B*a*b^2)*d*x*cos(d*x + c) + (3*C*a*b^2 + B*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) - (3*C*a*b^2 + B*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (B*a^3*cos(d*x + c)^2 + 2*C*b^3 + 2*(C*a^3 + 3*B*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
790,1,131,0,0.543668," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, C b^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, C b^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(C a^{3} + 3 \, B a^{2} b + 6 \, C a b^{2} + 2 \, B b^{3}\right)} d x + {\left(2 \, B a^{3} \cos\left(d x + c\right)^{2} + 4 \, B a^{3} + 18 \, C a^{2} b + 18 \, B a b^{2} + 3 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*C*b^3*log(sin(d*x + c) + 1) - 3*C*b^3*log(-sin(d*x + c) + 1) + 3*(C*a^3 + 3*B*a^2*b + 6*C*a*b^2 + 2*B*b^3)*d*x + (2*B*a^3*cos(d*x + c)^2 + 4*B*a^3 + 18*C*a^2*b + 18*B*a*b^2 + 3*(C*a^3 + 3*B*a^2*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
791,1,136,0,1.314949," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 8 \, C b^{3}\right)} d x + {\left(6 \, B a^{3} \cos\left(d x + c\right)^{3} + 16 \, C a^{3} + 48 \, B a^{2} b + 72 \, C a b^{2} + 24 \, B b^{3} + 8 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(B a^{3} + 4 \, C a^{2} b + 4 \, B a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 8*C*b^3)*d*x + (6*B*a^3*cos(d*x + c)^3 + 16*C*a^3 + 48*B*a^2*b + 72*C*a*b^2 + 24*B*b^3 + 8*(C*a^3 + 3*B*a^2*b)*cos(d*x + c)^2 + 9*(B*a^3 + 4*C*a^2*b + 4*B*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
792,1,174,0,0.531816," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b + 12 \, C a b^{2} + 4 \, B b^{3}\right)} d x + {\left(24 \, B a^{3} \cos\left(d x + c\right)^{4} + 64 \, B a^{3} + 240 \, C a^{2} b + 240 \, B a b^{2} + 120 \, C b^{3} + 30 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, B a^{3} + 15 \, C a^{2} b + 15 \, B a b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b + 12 \, C a b^{2} + 4 \, B b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(3*C*a^3 + 9*B*a^2*b + 12*C*a*b^2 + 4*B*b^3)*d*x + (24*B*a^3*cos(d*x + c)^4 + 64*B*a^3 + 240*C*a^2*b + 240*B*a*b^2 + 120*C*b^3 + 30*(C*a^3 + 3*B*a^2*b)*cos(d*x + c)^3 + 8*(4*B*a^3 + 15*C*a^2*b + 15*B*a*b^2)*cos(d*x + c)^2 + 15*(3*C*a^3 + 9*B*a^2*b + 12*C*a*b^2 + 4*B*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
793,1,743,0,1.249722," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(C a^{4} - B 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 \, C a^{5} - 2 \, B a^{4} b - C a^{3} b^{2} + B a^{2} b^{3} - C a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, C a^{5} - 2 \, B a^{4} b - C a^{3} b^{2} + B a^{2} b^{3} - C a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, C a^{2} b^{3} - 2 \, C b^{5} + 2 \, {\left(3 \, C a^{4} b - 3 \, B a^{3} b^{2} - C a^{2} b^{3} + 3 \, B a b^{4} - 2 \, C b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} - C a b^{4} + B 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(C a^{4} - B 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 \, C a^{5} - 2 \, B a^{4} b - C a^{3} b^{2} + B a^{2} b^{3} - C a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, C a^{5} - 2 \, B a^{4} b - C a^{3} b^{2} + B a^{2} b^{3} - C a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{2} b^{3} - 2 \, C b^{5} + 2 \, {\left(3 \, C a^{4} b - 3 \, B a^{3} b^{2} - C a^{2} b^{3} + 3 \, B a b^{4} - 2 \, C b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} - C a b^{4} + B 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*(C*a^4 - B*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*C*a^5 - 2*B*a^4*b - C*a^3*b^2 + B*a^2*b^3 - C*a*b^4 + B*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*C*a^5 - 2*B*a^4*b - C*a^3*b^2 + B*a^2*b^3 - C*a*b^4 + B*b^5)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - 2*(2*C*a^2*b^3 - 2*C*b^5 + 2*(3*C*a^4*b - 3*B*a^3*b^2 - C*a^2*b^3 + 3*B*a*b^4 - 2*C*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - B*a^2*b^3 - C*a*b^4 + B*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*(C*a^4 - B*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*C*a^5 - 2*B*a^4*b - C*a^3*b^2 + B*a^2*b^3 - C*a*b^4 + B*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(2*C*a^5 - 2*B*a^4*b - C*a^3*b^2 + B*a^2*b^3 - C*a*b^4 + B*b^5)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*C*a^2*b^3 - 2*C*b^5 + 2*(3*C*a^4*b - 3*B*a^3*b^2 - C*a^2*b^3 + 3*B*a*b^4 - 2*C*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - B*a^2*b^3 - C*a*b^4 + B*b^5)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d*cos(d*x + c)^3)]","B",0
794,1,609,0,5.292763," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(C a^{3} - B 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 \, C a^{4} - 2 \, B a^{3} b - C a^{2} b^{2} + 2 \, B a b^{3} - C b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{4} - 2 \, B a^{3} b - C a^{2} b^{2} + 2 \, B a b^{3} - C b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{2} b^{2} - C b^{4} - 2 \, {\left(C a^{3} b - B a^{2} b^{2} - C a b^{3} + B 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(C a^{3} - B 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 \, C a^{4} - 2 \, B a^{3} b - C a^{2} b^{2} + 2 \, B a b^{3} - C b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{4} - 2 \, B a^{3} b - C a^{2} b^{2} + 2 \, B a b^{3} - C b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{2} b^{2} - C b^{4} - 2 \, {\left(C a^{3} b - B a^{2} b^{2} - C a b^{3} + B 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*(C*a^3 - B*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*C*a^4 - 2*B*a^3*b - C*a^2*b^2 + 2*B*a*b^3 - C*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (2*C*a^4 - 2*B*a^3*b - C*a^2*b^2 + 2*B*a*b^3 - C*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(C*a^2*b^2 - C*b^4 - 2*(C*a^3*b - B*a^2*b^2 - C*a*b^3 + B*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*(C*a^3 - B*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*C*a^4 - 2*B*a^3*b - C*a^2*b^2 + 2*B*a*b^3 - C*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (2*C*a^4 - 2*B*a^3*b - C*a^2*b^2 + 2*B*a*b^3 - C*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(C*a^2*b^2 - C*b^4 - 2*(C*a^3*b - B*a^2*b^2 - C*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d*cos(d*x + c)^2)]","B",0
795,1,472,0,0.850930," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{{\left(C a^{2} - B 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(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{2} b - C 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(C a^{2} - B 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(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{2} b - C 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*((C*a^2 - B*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)) + (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) - (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) - 2*(C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d*cos(d*x + c)), 1/2*(2*(C*a^2 - B*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) - (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) + (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d*cos(d*x + c))]","B",0
796,1,316,0,2.463099," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{{\left(C a - B 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(C a^{2} - C b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{2} - C 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(C a - B 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(C a^{2} - C b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{2} - C 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*((C*a - B*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)) - (C*a^2 - C*b^2)*log(sin(d*x + c) + 1) + (C*a^2 - C*b^2)*log(-sin(d*x + c) + 1))/((a^2*b - b^3)*d), -1/2*(2*(C*a - B*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))) - (C*a^2 - C*b^2)*log(sin(d*x + c) + 1) + (C*a^2 - C*b^2)*log(-sin(d*x + c) + 1))/((a^2*b - b^3)*d)]","A",0
797,1,250,0,0.832917," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a^{2} - B b^{2}\right)} d x - {\left(C a - B 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(B a^{2} - B b^{2}\right)} d x + {\left(C a - B 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*(B*a^2 - B*b^2)*d*x - (C*a - B*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), ((B*a^2 - B*b^2)*d*x + (C*a - B*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
798,1,328,0,0.663172," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} d x - {\left(C a b - B 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(B a^{3} - B a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d}, \frac{{\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} d x - {\left(C a b - B 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(B a^{3} - B a b^{2}\right)} \sin\left(d x + c\right)}{{\left(a^{4} - a^{2} b^{2}\right)} d}\right]"," ",0,"[1/2*(2*(C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*d*x - (C*a*b - B*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*(B*a^3 - B*a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d), ((C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*d*x - (C*a*b - B*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))) + (B*a^3 - B*a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d)]","A",0
799,1,427,0,0.748098," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(B a^{4} - 2 \, C a^{3} b + B a^{2} b^{2} + 2 \, C a b^{3} - 2 \, B b^{4}\right)} d x - {\left(C a b^{2} - B 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 \, C a^{4} - 2 \, B a^{3} b - 2 \, C a^{2} b^{2} + 2 \, B a b^{3} + {\left(B a^{4} - B 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(B a^{4} - 2 \, C a^{3} b + B a^{2} b^{2} + 2 \, C a b^{3} - 2 \, B b^{4}\right)} d x + 2 \, {\left(C a b^{2} - B 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 \, C a^{4} - 2 \, B a^{3} b - 2 \, C a^{2} b^{2} + 2 \, B a b^{3} + {\left(B a^{4} - B 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*((B*a^4 - 2*C*a^3*b + B*a^2*b^2 + 2*C*a*b^3 - 2*B*b^4)*d*x - (C*a*b^2 - B*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*C*a^4 - 2*B*a^3*b - 2*C*a^2*b^2 + 2*B*a*b^3 + (B*a^4 - B*a^2*b^2)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d), 1/2*((B*a^4 - 2*C*a^3*b + B*a^2*b^2 + 2*C*a*b^3 - 2*B*b^4)*d*x + 2*(C*a*b^2 - B*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*C*a^4 - 2*B*a^3*b - 2*C*a^2*b^2 + 2*B*a*b^3 + (B*a^4 - B*a^2*b^2)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d)]","A",0
800,1,547,0,0.832232," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(C a^{5} - B a^{4} b + C a^{3} b^{2} - B a^{2} b^{3} - 2 \, C a b^{4} + 2 \, B b^{5}\right)} d x - 3 \, {\left(C a b^{3} - B 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 \, B a^{5} - 6 \, C a^{4} b + 2 \, B a^{3} b^{2} + 6 \, C a^{2} b^{3} - 6 \, B a b^{4} + 2 \, {\left(B a^{5} - B a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{5} - B a^{4} b - C a^{3} b^{2} + B 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(C a^{5} - B a^{4} b + C a^{3} b^{2} - B a^{2} b^{3} - 2 \, C a b^{4} + 2 \, B b^{5}\right)} d x - 6 \, {\left(C a b^{3} - B 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 \, B a^{5} - 6 \, C a^{4} b + 2 \, B a^{3} b^{2} + 6 \, C a^{2} b^{3} - 6 \, B a b^{4} + 2 \, {\left(B a^{5} - B a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{5} - B a^{4} b - C a^{3} b^{2} + B 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*(C*a^5 - B*a^4*b + C*a^3*b^2 - B*a^2*b^3 - 2*C*a*b^4 + 2*B*b^5)*d*x - 3*(C*a*b^3 - B*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*B*a^5 - 6*C*a^4*b + 2*B*a^3*b^2 + 6*C*a^2*b^3 - 6*B*a*b^4 + 2*(B*a^5 - B*a^3*b^2)*cos(d*x + c)^2 + 3*(C*a^5 - B*a^4*b - C*a^3*b^2 + B*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d), 1/6*(3*(C*a^5 - B*a^4*b + C*a^3*b^2 - B*a^2*b^3 - 2*C*a*b^4 + 2*B*b^5)*d*x - 6*(C*a*b^3 - B*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*B*a^5 - 6*C*a^4*b + 2*B*a^3*b^2 + 6*C*a^2*b^3 - 6*B*a*b^4 + 2*(B*a^5 - B*a^3*b^2)*cos(d*x + c)^2 + 3*(C*a^5 - B*a^4*b - C*a^3*b^2 + B*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d)]","A",0
801,1,1343,0,21.846952," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(3 \, C a^{6} - 2 \, B a^{5} b - 4 \, C a^{4} b^{2} + 3 \, B a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, C a^{5} b - 2 \, B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 3 \, B 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 \, C a^{7} - 4 \, B a^{6} b - 11 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3} + 4 \, C a^{3} b^{4} - 4 \, B a^{2} b^{5} + C a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} - 11 \, C a^{4} b^{3} + 8 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} - 4 \, B a b^{6} + C b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(6 \, C a^{7} - 4 \, B a^{6} b - 11 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3} + 4 \, C a^{3} b^{4} - 4 \, B a^{2} b^{5} + C a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} - 11 \, C a^{4} b^{3} + 8 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} - 4 \, B a b^{6} + C b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7} - 2 \, {\left(3 \, C a^{6} b - 2 \, B a^{5} b^{2} - 5 \, C a^{4} b^{3} + 3 \, B a^{3} b^{4} + 2 \, C a^{2} b^{5} - B a b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} - 6 \, C a^{3} b^{4} + 4 \, B a^{2} b^{5} + 3 \, C a b^{6} - 2 \, B 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 \, C a^{6} - 2 \, B a^{5} b - 4 \, C a^{4} b^{2} + 3 \, B a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, C a^{5} b - 2 \, B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 3 \, B 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 \, C a^{7} - 4 \, B a^{6} b - 11 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3} + 4 \, C a^{3} b^{4} - 4 \, B a^{2} b^{5} + C a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} - 11 \, C a^{4} b^{3} + 8 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} - 4 \, B a b^{6} + C b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(6 \, C a^{7} - 4 \, B a^{6} b - 11 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3} + 4 \, C a^{3} b^{4} - 4 \, B a^{2} b^{5} + C a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} - 11 \, C a^{4} b^{3} + 8 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} - 4 \, B a b^{6} + C b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7} - 2 \, {\left(3 \, C a^{6} b - 2 \, B a^{5} b^{2} - 5 \, C a^{4} b^{3} + 3 \, B a^{3} b^{4} + 2 \, C a^{2} b^{5} - B a b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} - 6 \, C a^{3} b^{4} + 4 \, B a^{2} b^{5} + 3 \, C a b^{6} - 2 \, B 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*C*a^6 - 2*B*a^5*b - 4*C*a^4*b^2 + 3*B*a^3*b^3)*cos(d*x + c)^3 + (3*C*a^5*b - 2*B*a^4*b^2 - 4*C*a^3*b^3 + 3*B*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*C*a^7 - 4*B*a^6*b - 11*C*a^5*b^2 + 8*B*a^4*b^3 + 4*C*a^3*b^4 - 4*B*a^2*b^5 + C*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b - 4*B*a^5*b^2 - 11*C*a^4*b^3 + 8*B*a^3*b^4 + 4*C*a^2*b^5 - 4*B*a*b^6 + C*b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((6*C*a^7 - 4*B*a^6*b - 11*C*a^5*b^2 + 8*B*a^4*b^3 + 4*C*a^3*b^4 - 4*B*a^2*b^5 + C*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b - 4*B*a^5*b^2 - 11*C*a^4*b^3 + 8*B*a^3*b^4 + 4*C*a^2*b^5 - 4*B*a*b^6 + C*b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7 - 2*(3*C*a^6*b - 2*B*a^5*b^2 - 5*C*a^4*b^3 + 3*B*a^3*b^4 + 2*C*a^2*b^5 - B*a*b^6)*cos(d*x + c)^2 - (3*C*a^5*b^2 - 2*B*a^4*b^3 - 6*C*a^3*b^4 + 4*B*a^2*b^5 + 3*C*a*b^6 - 2*B*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*C*a^6 - 2*B*a^5*b - 4*C*a^4*b^2 + 3*B*a^3*b^3)*cos(d*x + c)^3 + (3*C*a^5*b - 2*B*a^4*b^2 - 4*C*a^3*b^3 + 3*B*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*C*a^7 - 4*B*a^6*b - 11*C*a^5*b^2 + 8*B*a^4*b^3 + 4*C*a^3*b^4 - 4*B*a^2*b^5 + C*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b - 4*B*a^5*b^2 - 11*C*a^4*b^3 + 8*B*a^3*b^4 + 4*C*a^2*b^5 - 4*B*a*b^6 + C*b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((6*C*a^7 - 4*B*a^6*b - 11*C*a^5*b^2 + 8*B*a^4*b^3 + 4*C*a^3*b^4 - 4*B*a^2*b^5 + C*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b - 4*B*a^5*b^2 - 11*C*a^4*b^3 + 8*B*a^3*b^4 + 4*C*a^2*b^5 - 4*B*a*b^6 + C*b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7 - 2*(3*C*a^6*b - 2*B*a^5*b^2 - 5*C*a^4*b^3 + 3*B*a^3*b^4 + 2*C*a^2*b^5 - B*a*b^6)*cos(d*x + c)^2 - (3*C*a^5*b^2 - 2*B*a^4*b^3 - 6*C*a^3*b^4 + 4*B*a^2*b^5 + 3*C*a*b^6 - 2*B*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
802,1,1114,0,19.706624," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, C a^{5} - B a^{4} b - 3 \, C a^{3} b^{2} + 2 \, B a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{4} b - B a^{3} b^{2} - 3 \, C a^{2} b^{3} + 2 \, B 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 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(2 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C b^{6} + {\left(2 \, C a^{5} b - B a^{4} b^{2} - 3 \, C a^{3} b^{3} + B a^{2} b^{4} + C 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 \, C a^{5} - B a^{4} b - 3 \, C a^{3} b^{2} + 2 \, B a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{4} b - B a^{3} b^{2} - 3 \, C a^{2} b^{3} + 2 \, B 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 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(2 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C b^{6} + {\left(2 \, C a^{5} b - B a^{4} b^{2} - 3 \, C a^{3} b^{3} + B a^{2} b^{4} + C 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*C*a^5 - B*a^4*b - 3*C*a^3*b^2 + 2*B*a^2*b^3)*cos(d*x + c)^2 + (2*C*a^4*b - B*a^3*b^2 - 3*C*a^2*b^3 + 2*B*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*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + (2*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((2*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + (2*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(C*a^4*b^2 - 2*C*a^2*b^4 + C*b^6 + (2*C*a^5*b - B*a^4*b^2 - 3*C*a^3*b^3 + B*a^2*b^4 + C*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*C*a^5 - B*a^4*b - 3*C*a^3*b^2 + 2*B*a^2*b^3)*cos(d*x + c)^2 + (2*C*a^4*b - B*a^3*b^2 - 3*C*a^2*b^3 + 2*B*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*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + (2*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((2*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + (2*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(C*a^4*b^2 - 2*C*a^2*b^4 + C*b^6 + (2*C*a^5*b - B*a^4*b^2 - 3*C*a^3*b^3 + B*a^2*b^4 + C*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
803,1,694,0,6.408909," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(C a^{3} b - 2 \, C a b^{3} + B b^{4} + {\left(C a^{4} - 2 \, C a^{2} b^{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) + {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{4} b - B a^{3} b^{2} - C a^{2} b^{3} + B 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(C a^{3} b - 2 \, C a b^{3} + B b^{4} + {\left(C a^{4} - 2 \, C a^{2} b^{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(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b - B a^{3} b^{2} - C a^{2} b^{3} + B 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*((C*a^3*b - 2*C*a*b^3 + B*b^4 + (C*a^4 - 2*C*a^2*b^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)) + (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) - (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(C*a^4*b - B*a^3*b^2 - C*a^2*b^3 + B*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*(C*a^3*b - 2*C*a*b^3 + B*b^4 + (C*a^4 - 2*C*a^2*b^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))) - (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) + (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(C*a^4*b - B*a^3*b^2 - C*a^2*b^3 + B*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
804,1,389,0,0.911443," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(B a b - C b^{2} + {\left(B a^{2} - C 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(C a^{3} - B a^{2} b - C a b^{2} + B 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(B a b - C b^{2} + {\left(B a^{2} - C 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(C a^{3} - B a^{2} b - C a b^{2} + B 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*((B*a*b - C*b^2 + (B*a^2 - C*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*(C*a^3 - B*a^2*b - C*a*b^2 + B*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), ((B*a*b - C*b^2 + (B*a^2 - C*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))) + (C*a^3 - B*a^2*b - C*a*b^2 + B*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
805,1,561,0,0.832318," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5}\right)} d x - {\left(C a^{3} b - 2 \, B a^{2} b^{2} + B b^{4} + {\left(C a^{4} - 2 \, B a^{3} b + 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(C a^{4} b - B a^{3} b^{2} - C a^{2} b^{3} + B 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(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4}\right)} d x \cos\left(d x + c\right) + {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5}\right)} d x + {\left(C a^{3} b - 2 \, B a^{2} b^{2} + B b^{4} + {\left(C a^{4} - 2 \, B a^{3} b + 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(C a^{4} b - B a^{3} b^{2} - C a^{2} b^{3} + B 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*(B*a^5 - 2*B*a^3*b^2 + B*a*b^4)*d*x*cos(d*x + c) + 2*(B*a^4*b - 2*B*a^2*b^3 + B*b^5)*d*x - (C*a^3*b - 2*B*a^2*b^2 + B*b^4 + (C*a^4 - 2*B*a^3*b + 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*(C*a^4*b - B*a^3*b^2 - C*a^2*b^3 + B*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*a^5 - 2*B*a^3*b^2 + B*a*b^4)*d*x*cos(d*x + c) + (B*a^4*b - 2*B*a^2*b^3 + B*b^5)*d*x + (C*a^3*b - 2*B*a^2*b^2 + B*b^4 + (C*a^4 - 2*B*a^3*b + 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))) - (C*a^4*b - B*a^3*b^2 - C*a^2*b^3 + B*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
806,1,788,0,0.813179," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{6} - 2 \, B a^{5} b - 2 \, C a^{4} b^{2} + 4 \, B a^{3} b^{3} + C a^{2} b^{4} - 2 \, B a b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{5} b - 2 \, B a^{4} b^{2} - 2 \, C a^{3} b^{3} + 4 \, B a^{2} b^{4} + C a b^{5} - 2 \, B b^{6}\right)} d x + {\left(2 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - C a b^{4} + 2 \, B b^{5} + {\left(2 \, C a^{4} b - 3 \, B a^{3} b^{2} - C a^{2} b^{3} + 2 \, B 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(B a^{5} b + C a^{4} b^{2} - 3 \, B a^{3} b^{3} - C a^{2} b^{4} + 2 \, B a b^{5} + {\left(B a^{6} - 2 \, B a^{4} b^{2} + B 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(C a^{6} - 2 \, B a^{5} b - 2 \, C a^{4} b^{2} + 4 \, B a^{3} b^{3} + C a^{2} b^{4} - 2 \, B a b^{5}\right)} d x \cos\left(d x + c\right) + {\left(C a^{5} b - 2 \, B a^{4} b^{2} - 2 \, C a^{3} b^{3} + 4 \, B a^{2} b^{4} + C a b^{5} - 2 \, B b^{6}\right)} d x - {\left(2 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - C a b^{4} + 2 \, B b^{5} + {\left(2 \, C a^{4} b - 3 \, B a^{3} b^{2} - C a^{2} b^{3} + 2 \, B 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(B a^{5} b + C a^{4} b^{2} - 3 \, B a^{3} b^{3} - C a^{2} b^{4} + 2 \, B a b^{5} + {\left(B a^{6} - 2 \, B a^{4} b^{2} + B 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*(C*a^6 - 2*B*a^5*b - 2*C*a^4*b^2 + 4*B*a^3*b^3 + C*a^2*b^4 - 2*B*a*b^5)*d*x*cos(d*x + c) + 2*(C*a^5*b - 2*B*a^4*b^2 - 2*C*a^3*b^3 + 4*B*a^2*b^4 + C*a*b^5 - 2*B*b^6)*d*x + (2*C*a^3*b^2 - 3*B*a^2*b^3 - C*a*b^4 + 2*B*b^5 + (2*C*a^4*b - 3*B*a^3*b^2 - C*a^2*b^3 + 2*B*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^5*b + C*a^4*b^2 - 3*B*a^3*b^3 - C*a^2*b^4 + 2*B*a*b^5 + (B*a^6 - 2*B*a^4*b^2 + B*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), ((C*a^6 - 2*B*a^5*b - 2*C*a^4*b^2 + 4*B*a^3*b^3 + C*a^2*b^4 - 2*B*a*b^5)*d*x*cos(d*x + c) + (C*a^5*b - 2*B*a^4*b^2 - 2*C*a^3*b^3 + 4*B*a^2*b^4 + C*a*b^5 - 2*B*b^6)*d*x - (2*C*a^3*b^2 - 3*B*a^2*b^3 - C*a*b^4 + 2*B*b^5 + (2*C*a^4*b - 3*B*a^3*b^2 - C*a^2*b^3 + 2*B*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))) + (B*a^5*b + C*a^4*b^2 - 3*B*a^3*b^3 - C*a^2*b^4 + 2*B*a*b^5 + (B*a^6 - 2*B*a^4*b^2 + B*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
807,1,970,0,1.720267," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(B a^{7} - 4 \, C a^{6} b + 4 \, B a^{5} b^{2} + 8 \, C a^{4} b^{3} - 11 \, B a^{3} b^{4} - 4 \, C a^{2} b^{5} + 6 \, B a b^{6}\right)} d x \cos\left(d x + c\right) + {\left(B a^{6} b - 4 \, C a^{5} b^{2} + 4 \, B a^{4} b^{3} + 8 \, C a^{3} b^{4} - 11 \, B a^{2} b^{5} - 4 \, C a b^{6} + 6 \, B b^{7}\right)} d x + {\left(3 \, C a^{3} b^{3} - 4 \, B a^{2} b^{4} - 2 \, C a b^{5} + 3 \, B b^{6} + {\left(3 \, C a^{4} b^{2} - 4 \, B a^{3} b^{3} - 2 \, C a^{2} b^{4} + 3 \, 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) + {\left(2 \, C a^{6} b - 4 \, B a^{5} b^{2} - 6 \, C a^{4} b^{3} + 10 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} - 6 \, B a b^{6} + {\left(B a^{7} - 2 \, B a^{5} b^{2} + B a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{7} - 3 \, B a^{6} b - 4 \, C a^{5} b^{2} + 6 \, B a^{4} b^{3} + 2 \, C a^{3} b^{4} - 3 \, B 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(B a^{7} - 4 \, C a^{6} b + 4 \, B a^{5} b^{2} + 8 \, C a^{4} b^{3} - 11 \, B a^{3} b^{4} - 4 \, C a^{2} b^{5} + 6 \, B a b^{6}\right)} d x \cos\left(d x + c\right) + {\left(B a^{6} b - 4 \, C a^{5} b^{2} + 4 \, B a^{4} b^{3} + 8 \, C a^{3} b^{4} - 11 \, B a^{2} b^{5} - 4 \, C a b^{6} + 6 \, B b^{7}\right)} d x + 2 \, {\left(3 \, C a^{3} b^{3} - 4 \, B a^{2} b^{4} - 2 \, C a b^{5} + 3 \, B b^{6} + {\left(3 \, C a^{4} b^{2} - 4 \, B a^{3} b^{3} - 2 \, C a^{2} b^{4} + 3 \, 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 \, C a^{6} b - 4 \, B a^{5} b^{2} - 6 \, C a^{4} b^{3} + 10 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} - 6 \, B a b^{6} + {\left(B a^{7} - 2 \, B a^{5} b^{2} + B a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{7} - 3 \, B a^{6} b - 4 \, C a^{5} b^{2} + 6 \, B a^{4} b^{3} + 2 \, C a^{3} b^{4} - 3 \, B 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*((B*a^7 - 4*C*a^6*b + 4*B*a^5*b^2 + 8*C*a^4*b^3 - 11*B*a^3*b^4 - 4*C*a^2*b^5 + 6*B*a*b^6)*d*x*cos(d*x + c) + (B*a^6*b - 4*C*a^5*b^2 + 4*B*a^4*b^3 + 8*C*a^3*b^4 - 11*B*a^2*b^5 - 4*C*a*b^6 + 6*B*b^7)*d*x + (3*C*a^3*b^3 - 4*B*a^2*b^4 - 2*C*a*b^5 + 3*B*b^6 + (3*C*a^4*b^2 - 4*B*a^3*b^3 - 2*C*a^2*b^4 + 3*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*C*a^6*b - 4*B*a^5*b^2 - 6*C*a^4*b^3 + 10*B*a^3*b^4 + 4*C*a^2*b^5 - 6*B*a*b^6 + (B*a^7 - 2*B*a^5*b^2 + B*a^3*b^4)*cos(d*x + c)^2 + (2*C*a^7 - 3*B*a^6*b - 4*C*a^5*b^2 + 6*B*a^4*b^3 + 2*C*a^3*b^4 - 3*B*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*((B*a^7 - 4*C*a^6*b + 4*B*a^5*b^2 + 8*C*a^4*b^3 - 11*B*a^3*b^4 - 4*C*a^2*b^5 + 6*B*a*b^6)*d*x*cos(d*x + c) + (B*a^6*b - 4*C*a^5*b^2 + 4*B*a^4*b^3 + 8*C*a^3*b^4 - 11*B*a^2*b^5 - 4*C*a*b^6 + 6*B*b^7)*d*x + 2*(3*C*a^3*b^3 - 4*B*a^2*b^4 - 2*C*a*b^5 + 3*B*b^6 + (3*C*a^4*b^2 - 4*B*a^3*b^3 - 2*C*a^2*b^4 + 3*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*C*a^6*b - 4*B*a^5*b^2 - 6*C*a^4*b^3 + 10*B*a^3*b^4 + 4*C*a^2*b^5 - 6*B*a*b^6 + (B*a^7 - 2*B*a^5*b^2 + B*a^3*b^4)*cos(d*x + c)^2 + (2*C*a^7 - 3*B*a^6*b - 4*C*a^5*b^2 + 6*B*a^4*b^3 + 2*C*a^3*b^4 - 3*B*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
808,1,2111,0,54.847538," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(6 \, C a^{8} - 2 \, B a^{7} b - 15 \, C a^{6} b^{2} + 5 \, B a^{5} b^{3} + 12 \, C a^{4} b^{4} - 6 \, B a^{3} b^{5}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, C a^{7} b - 2 \, B a^{6} b^{2} - 15 \, C a^{5} b^{3} + 5 \, B a^{4} b^{4} + 12 \, C a^{3} b^{5} - 6 \, B a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{6} b^{2} - 2 \, B a^{5} b^{3} - 15 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 12 \, C a^{2} b^{6} - 6 \, B 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 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(3 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, C a^{6} b^{3} - 6 \, C a^{4} b^{5} + 6 \, C a^{2} b^{7} - 2 \, C b^{9} + {\left(6 \, C a^{8} b - 2 \, B a^{7} b^{2} - 17 \, C a^{6} b^{3} + 7 \, B a^{5} b^{4} + 13 \, C a^{4} b^{5} - 5 \, B a^{3} b^{6} - 2 \, C a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} - 25 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 20 \, C a^{3} b^{6} - 6 \, B a^{2} b^{7} - 4 \, C 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 \, C a^{8} - 2 \, B a^{7} b - 15 \, C a^{6} b^{2} + 5 \, B a^{5} b^{3} + 12 \, C a^{4} b^{4} - 6 \, B a^{3} b^{5}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, C a^{7} b - 2 \, B a^{6} b^{2} - 15 \, C a^{5} b^{3} + 5 \, B a^{4} b^{4} + 12 \, C a^{3} b^{5} - 6 \, B a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{6} b^{2} - 2 \, B a^{5} b^{3} - 15 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 12 \, C a^{2} b^{6} - 6 \, B 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 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(3 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{6} b^{3} - 6 \, C a^{4} b^{5} + 6 \, C a^{2} b^{7} - 2 \, C b^{9} + {\left(6 \, C a^{8} b - 2 \, B a^{7} b^{2} - 17 \, C a^{6} b^{3} + 7 \, B a^{5} b^{4} + 13 \, C a^{4} b^{5} - 5 \, B a^{3} b^{6} - 2 \, C a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} - 25 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 20 \, C a^{3} b^{6} - 6 \, B a^{2} b^{7} - 4 \, C 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*C*a^8 - 2*B*a^7*b - 15*C*a^6*b^2 + 5*B*a^5*b^3 + 12*C*a^4*b^4 - 6*B*a^3*b^5)*cos(d*x + c)^3 + 2*(6*C*a^7*b - 2*B*a^6*b^2 - 15*C*a^5*b^3 + 5*B*a^4*b^4 + 12*C*a^3*b^5 - 6*B*a^2*b^6)*cos(d*x + c)^2 + (6*C*a^6*b^2 - 2*B*a^5*b^3 - 15*C*a^4*b^4 + 5*B*a^3*b^5 + 12*C*a^2*b^6 - 6*B*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*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*cos(d*x + c)^3 + 2*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*cos(d*x + c)^2 + (3*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) - 2*((3*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*cos(d*x + c)^3 + 2*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*cos(d*x + c)^2 + (3*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*C*a^6*b^3 - 6*C*a^4*b^5 + 6*C*a^2*b^7 - 2*C*b^9 + (6*C*a^8*b - 2*B*a^7*b^2 - 17*C*a^6*b^3 + 7*B*a^5*b^4 + 13*C*a^4*b^5 - 5*B*a^3*b^6 - 2*C*a^2*b^7)*cos(d*x + c)^2 + (9*C*a^7*b^2 - 3*B*a^6*b^3 - 25*C*a^5*b^4 + 9*B*a^4*b^5 + 20*C*a^3*b^6 - 6*B*a^2*b^7 - 4*C*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*C*a^8 - 2*B*a^7*b - 15*C*a^6*b^2 + 5*B*a^5*b^3 + 12*C*a^4*b^4 - 6*B*a^3*b^5)*cos(d*x + c)^3 + 2*(6*C*a^7*b - 2*B*a^6*b^2 - 15*C*a^5*b^3 + 5*B*a^4*b^4 + 12*C*a^3*b^5 - 6*B*a^2*b^6)*cos(d*x + c)^2 + (6*C*a^6*b^2 - 2*B*a^5*b^3 - 15*C*a^4*b^4 + 5*B*a^3*b^5 + 12*C*a^2*b^6 - 6*B*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*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*cos(d*x + c)^3 + 2*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*cos(d*x + c)^2 + (3*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((3*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*cos(d*x + c)^3 + 2*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*cos(d*x + c)^2 + (3*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (2*C*a^6*b^3 - 6*C*a^4*b^5 + 6*C*a^2*b^7 - 2*C*b^9 + (6*C*a^8*b - 2*B*a^7*b^2 - 17*C*a^6*b^3 + 7*B*a^5*b^4 + 13*C*a^4*b^5 - 5*B*a^3*b^6 - 2*C*a^2*b^7)*cos(d*x + c)^2 + (9*C*a^7*b^2 - 3*B*a^6*b^3 - 25*C*a^5*b^4 + 9*B*a^4*b^5 + 20*C*a^3*b^6 - 6*B*a^2*b^7 - 4*C*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
809,1,1419,0,22.683043," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} - B a^{2} b^{5} + 6 \, C a b^{6} - 2 \, B b^{7} + {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} - B a^{4} b^{3} + 6 \, C a^{3} b^{4} - 2 \, B a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} - B a^{3} b^{4} + 6 \, C a^{2} b^{5} - 2 \, B 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(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, C a^{6} b^{2} - B a^{5} b^{3} - 9 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 6 \, C a^{2} b^{6} - 4 \, B a b^{7} + {\left(2 \, C a^{7} b - 7 \, C a^{5} b^{3} + 3 \, B a^{4} b^{4} + 5 \, C a^{3} b^{5} - 3 \, B 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 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} - B a^{2} b^{5} + 6 \, C a b^{6} - 2 \, B b^{7} + {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} - B a^{4} b^{3} + 6 \, C a^{3} b^{4} - 2 \, B a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} - B a^{3} b^{4} + 6 \, C a^{2} b^{5} - 2 \, B 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(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(3 \, C a^{6} b^{2} - B a^{5} b^{3} - 9 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 6 \, C a^{2} b^{6} - 4 \, B a b^{7} + {\left(2 \, C a^{7} b - 7 \, C a^{5} b^{3} + 3 \, B a^{4} b^{4} + 5 \, C a^{3} b^{5} - 3 \, B 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*C*a^5*b^2 - 5*C*a^3*b^4 - B*a^2*b^5 + 6*C*a*b^6 - 2*B*b^7 + (2*C*a^7 - 5*C*a^5*b^2 - B*a^4*b^3 + 6*C*a^3*b^4 - 2*B*a^2*b^5)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 - B*a^3*b^4 + 6*C*a^2*b^5 - 2*B*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*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + 2*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(3*C*a^6*b^2 - B*a^5*b^3 - 9*C*a^4*b^4 + 5*B*a^3*b^5 + 6*C*a^2*b^6 - 4*B*a*b^7 + (2*C*a^7*b - 7*C*a^5*b^3 + 3*B*a^4*b^4 + 5*C*a^3*b^5 - 3*B*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*C*a^5*b^2 - 5*C*a^3*b^4 - B*a^2*b^5 + 6*C*a*b^6 - 2*B*b^7 + (2*C*a^7 - 5*C*a^5*b^2 - B*a^4*b^3 + 6*C*a^3*b^4 - 2*B*a^2*b^5)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 - B*a^3*b^4 + 6*C*a^2*b^5 - 2*B*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))) - (C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + (C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (3*C*a^6*b^2 - B*a^5*b^3 - 9*C*a^4*b^4 + 5*B*a^3*b^5 + 6*C*a^2*b^6 - 4*B*a*b^7 + (2*C*a^7*b - 7*C*a^5*b^3 + 3*B*a^4*b^4 + 5*C*a^3*b^5 - 3*B*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
810,1,750,0,0.601371," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(C a^{2} b^{2} - 3 \, B a b^{3} + 2 \, C b^{4} + {\left(C a^{4} - 3 \, B a^{3} b + 2 \, C a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{3} b - 3 \, B a^{2} b^{2} + 2 \, C 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(C a^{5} + B a^{4} b - 5 \, C a^{3} b^{2} + B a^{2} b^{3} + 4 \, C a b^{4} - 2 \, B b^{5} + {\left(2 \, B a^{5} - 3 \, C a^{4} b - B a^{3} b^{2} + 3 \, C a^{2} b^{3} - B 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(C a^{2} b^{2} - 3 \, B a b^{3} + 2 \, C b^{4} + {\left(C a^{4} - 3 \, B a^{3} b + 2 \, C a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{3} b - 3 \, B a^{2} b^{2} + 2 \, C 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(C a^{5} + B a^{4} b - 5 \, C a^{3} b^{2} + B a^{2} b^{3} + 4 \, C a b^{4} - 2 \, B b^{5} + {\left(2 \, B a^{5} - 3 \, C a^{4} b - B a^{3} b^{2} + 3 \, C a^{2} b^{3} - B 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*((C*a^2*b^2 - 3*B*a*b^3 + 2*C*b^4 + (C*a^4 - 3*B*a^3*b + 2*C*a^2*b^2)*cos(d*x + c)^2 + 2*(C*a^3*b - 3*B*a^2*b^2 + 2*C*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*(C*a^5 + B*a^4*b - 5*C*a^3*b^2 + B*a^2*b^3 + 4*C*a*b^4 - 2*B*b^5 + (2*B*a^5 - 3*C*a^4*b - B*a^3*b^2 + 3*C*a^2*b^3 - B*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*((C*a^2*b^2 - 3*B*a*b^3 + 2*C*b^4 + (C*a^4 - 3*B*a^3*b + 2*C*a^2*b^2)*cos(d*x + c)^2 + 2*(C*a^3*b - 3*B*a^2*b^2 + 2*C*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))) + (C*a^5 + B*a^4*b - 5*C*a^3*b^2 + B*a^2*b^3 + 4*C*a*b^4 - 2*B*b^5 + (2*B*a^5 - 3*C*a^4*b - B*a^3*b^2 + 3*C*a^2*b^3 - B*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
811,1,752,0,0.983751," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a^{2} b^{2} - 3 \, C a b^{3} + B b^{4} + {\left(2 \, B a^{4} - 3 \, C a^{3} b + B a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{3} b - 3 \, C a^{2} b^{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(C a^{4} b - 3 \, B a^{3} b^{2} + C a^{2} b^{3} + 3 \, B a b^{4} - 2 \, C b^{5} + {\left(2 \, C a^{5} - 4 \, B a^{4} b - C a^{3} b^{2} + 5 \, B a^{2} b^{3} - C a b^{4} - B 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 \, B a^{2} b^{2} - 3 \, C a b^{3} + B b^{4} + {\left(2 \, B a^{4} - 3 \, C a^{3} b + B a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{3} b - 3 \, C a^{2} b^{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(C a^{4} b - 3 \, B a^{3} b^{2} + C a^{2} b^{3} + 3 \, B a b^{4} - 2 \, C b^{5} + {\left(2 \, C a^{5} - 4 \, B a^{4} b - C a^{3} b^{2} + 5 \, B a^{2} b^{3} - C a b^{4} - B 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*B*a^2*b^2 - 3*C*a*b^3 + B*b^4 + (2*B*a^4 - 3*C*a^3*b + B*a^2*b^2)*cos(d*x + c)^2 + 2*(2*B*a^3*b - 3*C*a^2*b^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*(C*a^4*b - 3*B*a^3*b^2 + C*a^2*b^3 + 3*B*a*b^4 - 2*C*b^5 + (2*C*a^5 - 4*B*a^4*b - C*a^3*b^2 + 5*B*a^2*b^3 - C*a*b^4 - B*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*B*a^2*b^2 - 3*C*a*b^3 + B*b^4 + (2*B*a^4 - 3*C*a^3*b + B*a^2*b^2)*cos(d*x + c)^2 + 2*(2*B*a^3*b - 3*C*a^2*b^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))) + (C*a^4*b - 3*B*a^3*b^2 + C*a^2*b^3 + 3*B*a*b^4 - 2*C*b^5 + (2*C*a^5 - 4*B*a^4*b - C*a^3*b^2 + 5*B*a^2*b^3 - C*a*b^4 - B*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
812,1,1152,0,0.555691," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8}\right)} d x - {\left(2 \, C a^{5} b^{2} - 6 \, B a^{4} b^{3} + C a^{3} b^{4} + 5 \, B a^{2} b^{5} - 2 \, B b^{7} + {\left(2 \, C a^{7} - 6 \, B a^{6} b + C a^{5} b^{2} + 5 \, B a^{4} b^{3} - 2 \, B a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 6 \, B a^{5} b^{2} + C a^{4} b^{3} + 5 \, B a^{3} b^{4} - 2 \, B 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 \, C a^{6} b^{2} - 5 \, B a^{5} b^{3} - 3 \, C a^{4} b^{4} + 7 \, B a^{3} b^{5} - 2 \, B a b^{7} + {\left(4 \, C a^{7} b - 6 \, B a^{6} b^{2} - 5 \, C a^{5} b^{3} + 9 \, B a^{4} b^{4} + C a^{3} b^{5} - 3 \, B 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(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8}\right)} d x + {\left(2 \, C a^{5} b^{2} - 6 \, B a^{4} b^{3} + C a^{3} b^{4} + 5 \, B a^{2} b^{5} - 2 \, B b^{7} + {\left(2 \, C a^{7} - 6 \, B a^{6} b + C a^{5} b^{2} + 5 \, B a^{4} b^{3} - 2 \, B a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 6 \, B a^{5} b^{2} + C a^{4} b^{3} + 5 \, B a^{3} b^{4} - 2 \, B 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 \, C a^{6} b^{2} - 5 \, B a^{5} b^{3} - 3 \, C a^{4} b^{4} + 7 \, B a^{3} b^{5} - 2 \, B a b^{7} + {\left(4 \, C a^{7} b - 6 \, B a^{6} b^{2} - 5 \, C a^{5} b^{3} + 9 \, B a^{4} b^{4} + C a^{3} b^{5} - 3 \, B 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*(B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6)*d*x*cos(d*x + c)^2 + 8*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*d*x*cos(d*x + c) + 4*(B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8)*d*x - (2*C*a^5*b^2 - 6*B*a^4*b^3 + C*a^3*b^4 + 5*B*a^2*b^5 - 2*B*b^7 + (2*C*a^7 - 6*B*a^6*b + C*a^5*b^2 + 5*B*a^4*b^3 - 2*B*a^2*b^5)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 6*B*a^5*b^2 + C*a^4*b^3 + 5*B*a^3*b^4 - 2*B*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*C*a^6*b^2 - 5*B*a^5*b^3 - 3*C*a^4*b^4 + 7*B*a^3*b^5 - 2*B*a*b^7 + (4*C*a^7*b - 6*B*a^6*b^2 - 5*C*a^5*b^3 + 9*B*a^4*b^4 + C*a^3*b^5 - 3*B*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*(B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6)*d*x*cos(d*x + c)^2 + 4*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*d*x*cos(d*x + c) + 2*(B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8)*d*x + (2*C*a^5*b^2 - 6*B*a^4*b^3 + C*a^3*b^4 + 5*B*a^2*b^5 - 2*B*b^7 + (2*C*a^7 - 6*B*a^6*b + C*a^5*b^2 + 5*B*a^4*b^3 - 2*B*a^2*b^5)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 6*B*a^5*b^2 + C*a^4*b^3 + 5*B*a^3*b^4 - 2*B*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*C*a^6*b^2 - 5*B*a^5*b^3 - 3*C*a^4*b^4 + 7*B*a^3*b^5 - 2*B*a*b^7 + (4*C*a^7*b - 6*B*a^6*b^2 - 5*C*a^5*b^3 + 9*B*a^4*b^4 + C*a^3*b^5 - 3*B*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
813,1,1568,0,0.609604," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(C a^{9} - 3 \, B a^{8} b - 3 \, C a^{7} b^{2} + 9 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} - C a^{3} b^{6} + 3 \, B a^{2} b^{7}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(C a^{8} b - 3 \, B a^{7} b^{2} - 3 \, C a^{6} b^{3} + 9 \, B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 9 \, B a^{3} b^{6} - C a^{2} b^{7} + 3 \, B a b^{8}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(C a^{7} b^{2} - 3 \, B a^{6} b^{3} - 3 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B a^{2} b^{7} - C a b^{8} + 3 \, B b^{9}\right)} d x - {\left(6 \, C a^{5} b^{3} - 12 \, B a^{4} b^{4} - 5 \, C a^{3} b^{5} + 15 \, B a^{2} b^{6} + 2 \, C a b^{7} - 6 \, B b^{8} + {\left(6 \, C a^{7} b - 12 \, B a^{6} b^{2} - 5 \, C a^{5} b^{3} + 15 \, B a^{4} b^{4} + 2 \, C a^{3} b^{5} - 6 \, B a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, C a^{6} b^{2} - 12 \, B a^{5} b^{3} - 5 \, C a^{4} b^{4} + 15 \, B a^{3} b^{5} + 2 \, C a^{2} b^{6} - 6 \, B 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 \, B a^{7} b^{2} + 5 \, C a^{6} b^{3} - 13 \, B a^{5} b^{4} - 7 \, C a^{4} b^{5} + 17 \, B a^{3} b^{6} + 2 \, C a^{2} b^{7} - 6 \, B a b^{8} + 2 \, {\left(B a^{9} - 3 \, B a^{7} b^{2} + 3 \, B a^{5} b^{4} - B a^{3} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, B a^{8} b + 6 \, C a^{7} b^{2} - 20 \, B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 25 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B 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(C a^{9} - 3 \, B a^{8} b - 3 \, C a^{7} b^{2} + 9 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} - C a^{3} b^{6} + 3 \, B a^{2} b^{7}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(C a^{8} b - 3 \, B a^{7} b^{2} - 3 \, C a^{6} b^{3} + 9 \, B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 9 \, B a^{3} b^{6} - C a^{2} b^{7} + 3 \, B a b^{8}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{7} b^{2} - 3 \, B a^{6} b^{3} - 3 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B a^{2} b^{7} - C a b^{8} + 3 \, B b^{9}\right)} d x - {\left(6 \, C a^{5} b^{3} - 12 \, B a^{4} b^{4} - 5 \, C a^{3} b^{5} + 15 \, B a^{2} b^{6} + 2 \, C a b^{7} - 6 \, B b^{8} + {\left(6 \, C a^{7} b - 12 \, B a^{6} b^{2} - 5 \, C a^{5} b^{3} + 15 \, B a^{4} b^{4} + 2 \, C a^{3} b^{5} - 6 \, B a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, C a^{6} b^{2} - 12 \, B a^{5} b^{3} - 5 \, C a^{4} b^{4} + 15 \, B a^{3} b^{5} + 2 \, C a^{2} b^{6} - 6 \, B 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 \, B a^{7} b^{2} + 5 \, C a^{6} b^{3} - 13 \, B a^{5} b^{4} - 7 \, C a^{4} b^{5} + 17 \, B a^{3} b^{6} + 2 \, C a^{2} b^{7} - 6 \, B a b^{8} + 2 \, {\left(B a^{9} - 3 \, B a^{7} b^{2} + 3 \, B a^{5} b^{4} - B a^{3} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, B a^{8} b + 6 \, C a^{7} b^{2} - 20 \, B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 25 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B 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*(C*a^9 - 3*B*a^8*b - 3*C*a^7*b^2 + 9*B*a^6*b^3 + 3*C*a^5*b^4 - 9*B*a^4*b^5 - C*a^3*b^6 + 3*B*a^2*b^7)*d*x*cos(d*x + c)^2 + 8*(C*a^8*b - 3*B*a^7*b^2 - 3*C*a^6*b^3 + 9*B*a^5*b^4 + 3*C*a^4*b^5 - 9*B*a^3*b^6 - C*a^2*b^7 + 3*B*a*b^8)*d*x*cos(d*x + c) + 4*(C*a^7*b^2 - 3*B*a^6*b^3 - 3*C*a^5*b^4 + 9*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*a^2*b^7 - C*a*b^8 + 3*B*b^9)*d*x - (6*C*a^5*b^3 - 12*B*a^4*b^4 - 5*C*a^3*b^5 + 15*B*a^2*b^6 + 2*C*a*b^7 - 6*B*b^8 + (6*C*a^7*b - 12*B*a^6*b^2 - 5*C*a^5*b^3 + 15*B*a^4*b^4 + 2*C*a^3*b^5 - 6*B*a^2*b^6)*cos(d*x + c)^2 + 2*(6*C*a^6*b^2 - 12*B*a^5*b^3 - 5*C*a^4*b^4 + 15*B*a^3*b^5 + 2*C*a^2*b^6 - 6*B*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*B*a^7*b^2 + 5*C*a^6*b^3 - 13*B*a^5*b^4 - 7*C*a^4*b^5 + 17*B*a^3*b^6 + 2*C*a^2*b^7 - 6*B*a*b^8 + 2*(B*a^9 - 3*B*a^7*b^2 + 3*B*a^5*b^4 - B*a^3*b^6)*cos(d*x + c)^2 + (4*B*a^8*b + 6*C*a^7*b^2 - 20*B*a^6*b^3 - 9*C*a^5*b^4 + 25*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*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*(C*a^9 - 3*B*a^8*b - 3*C*a^7*b^2 + 9*B*a^6*b^3 + 3*C*a^5*b^4 - 9*B*a^4*b^5 - C*a^3*b^6 + 3*B*a^2*b^7)*d*x*cos(d*x + c)^2 + 4*(C*a^8*b - 3*B*a^7*b^2 - 3*C*a^6*b^3 + 9*B*a^5*b^4 + 3*C*a^4*b^5 - 9*B*a^3*b^6 - C*a^2*b^7 + 3*B*a*b^8)*d*x*cos(d*x + c) + 2*(C*a^7*b^2 - 3*B*a^6*b^3 - 3*C*a^5*b^4 + 9*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*a^2*b^7 - C*a*b^8 + 3*B*b^9)*d*x - (6*C*a^5*b^3 - 12*B*a^4*b^4 - 5*C*a^3*b^5 + 15*B*a^2*b^6 + 2*C*a*b^7 - 6*B*b^8 + (6*C*a^7*b - 12*B*a^6*b^2 - 5*C*a^5*b^3 + 15*B*a^4*b^4 + 2*C*a^3*b^5 - 6*B*a^2*b^6)*cos(d*x + c)^2 + 2*(6*C*a^6*b^2 - 12*B*a^5*b^3 - 5*C*a^4*b^4 + 15*B*a^3*b^5 + 2*C*a^2*b^6 - 6*B*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*B*a^7*b^2 + 5*C*a^6*b^3 - 13*B*a^5*b^4 - 7*C*a^4*b^5 + 17*B*a^3*b^6 + 2*C*a^2*b^7 - 6*B*a*b^8 + 2*(B*a^9 - 3*B*a^7*b^2 + 3*B*a^5*b^4 - B*a^3*b^6)*cos(d*x + c)^2 + (4*B*a^8*b + 6*C*a^7*b^2 - 20*B*a^6*b^3 - 9*C*a^5*b^4 + 25*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*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
814,0,0,0,0.530637," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{5} + B \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^5 + B*sec(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
815,0,0,0,0.661031," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{4} + B \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^4 + B*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
816,0,0,0,0.912011," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{3} + B \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^3 + B*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
817,0,0,0,0.593048," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
818,0,0,0,1.687133," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + B \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((C*cos(d*x + c)*sec(d*x + c)^2 + B*cos(d*x + c)*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
819,0,0,0,51.956238," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + B \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((C*cos(d*x + c)^2*sec(d*x + c)^2 + B*cos(d*x + c)^2*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
820,0,0,0,1.757359," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + B \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((C*cos(d*x + c)^3*sec(d*x + c)^2 + B*cos(d*x + c)^3*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
821,0,0,0,0.948652," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{6} + B a \sec\left(d x + c\right)^{4} + {\left(C a + B b\right)} \sec\left(d x + c\right)^{5}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^6 + B*a*sec(d*x + c)^4 + (C*a + B*b)*sec(d*x + c)^5)*sqrt(b*sec(d*x + c) + a), x)","F",0
822,0,0,0,0.681680," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{5} + B a \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^5 + B*a*sec(d*x + c)^3 + (C*a + B*b)*sec(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
823,0,0,0,0.607162," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{4} + B a \sec\left(d x + c\right)^{2} + {\left(C a + B b\right)} \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^4 + B*a*sec(d*x + c)^2 + (C*a + B*b)*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
824,0,0,0,0.623572," ","integrate((a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{3} + B a \sec\left(d x + c\right) + {\left(C a + B b\right)} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^3 + B*a*sec(d*x + c) + (C*a + B*b)*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
825,0,0,0,29.172175," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + B a \cos\left(d x + c\right) \sec\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)*sec(d*x + c)^3 + B*a*cos(d*x + c)*sec(d*x + c) + (C*a + B*b)*cos(d*x + c)*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
826,0,0,0,52.921952," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + B a \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^2*sec(d*x + c)^3 + B*a*cos(d*x + c)^2*sec(d*x + c) + (C*a + B*b)*cos(d*x + c)^2*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
827,0,0,0,2.332927," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + B a \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3*sec(d*x + c)^3 + B*a*cos(d*x + c)^3*sec(d*x + c) + (C*a + B*b)*cos(d*x + c)^3*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
828,0,0,0,2.923144," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + B a \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^4*sec(d*x + c)^3 + B*a*cos(d*x + c)^4*sec(d*x + c) + (C*a + B*b)*cos(d*x + c)^4*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
829,0,0,0,0.843943," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{6} + B a^{2} \sec\left(d x + c\right)^{3} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{5} + {\left(C a^{2} + 2 \, B a b\right)} \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^6 + B*a^2*sec(d*x + c)^3 + (2*C*a*b + B*b^2)*sec(d*x + c)^5 + (C*a^2 + 2*B*a*b)*sec(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
830,0,0,0,0.506008," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{5} + B a^{2} \sec\left(d x + c\right)^{2} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{4} + {\left(C a^{2} + 2 \, B a b\right)} \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^5 + B*a^2*sec(d*x + c)^2 + (2*C*a*b + B*b^2)*sec(d*x + c)^4 + (C*a^2 + 2*B*a*b)*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
831,0,0,0,0.503257," ","integrate((a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{4} + B a^{2} \sec\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^4 + B*a^2*sec(d*x + c) + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + (C*a^2 + 2*B*a*b)*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
832,0,0,0,29.545099," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)*sec(d*x + c)^4 + B*a^2*cos(d*x + c)*sec(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)*sec(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
833,0,0,0,56.939259," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^2*sec(d*x + c)^4 + B*a^2*cos(d*x + c)^2*sec(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^2*sec(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^2*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
834,0,0,0,65.532316," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^3*sec(d*x + c)^4 + B*a^2*cos(d*x + c)^3*sec(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^3*sec(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^3*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
835,0,0,0,72.282953," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4*sec(d*x + c)^4 + B*a^2*cos(d*x + c)^4*sec(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^4*sec(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^4*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
836,0,0,0,73.045194," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^5*sec(d*x + c)^4 + B*a^2*cos(d*x + c)^5*sec(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^5*sec(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^5*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
837,0,0,0,0.566498," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{5} + B \sec\left(d x + c\right)^{4}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*sec(d*x + c)^5 + B*sec(d*x + c)^4)/sqrt(b*sec(d*x + c) + a), x)","F",0
838,0,0,0,0.681083," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{4} + B \sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*sec(d*x + c)^4 + B*sec(d*x + c)^3)/sqrt(b*sec(d*x + c) + a), x)","F",0
839,0,0,0,0.630524," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{3} + B \sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*sec(d*x + c)^3 + B*sec(d*x + c)^2)/sqrt(b*sec(d*x + c) + a), x)","F",0
840,0,0,0,0.519083," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
841,0,0,0,1.170751," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right) \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)*sec(d*x + c)^2 + B*cos(d*x + c)*sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
842,0,0,0,52.120659," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2*sec(d*x + c)^2 + B*cos(d*x + c)^2*sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
843,0,0,0,0.502883," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{5} + B \sec\left(d x + c\right)^{4}\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((C*sec(d*x + c)^5 + B*sec(d*x + c)^4)*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
844,0,0,0,0.635548," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + B \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((C*sec(d*x + c)^4 + B*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
845,0,0,0,0.564803," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + B \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((C*sec(d*x + c)^3 + B*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
846,0,0,0,0.613017," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*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
847,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,0,0,0,2.916537," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{2} \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((C*cos(d*x + c)^2*sec(d*x + c)^2 + B*cos(d*x + c)^2*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
849,0,0,0,1.297161," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{5} + B \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((C*sec(d*x + c)^5 + B*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
850,0,0,0,1.694899," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + B \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((C*sec(d*x + c)^4 + B*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
851,0,0,0,1.913294," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + B \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((C*sec(d*x + c)^3 + B*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
852,0,0,0,0.685453," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}}{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((C*sec(d*x + c)^2 + B*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
853,0,0,0,27.243725," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right) \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((C*cos(d*x + c)*sec(d*x + c)^2 + B*cos(d*x + c)*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
854,0,0,0,0.642816," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{4} \sec\left(d x + c\right)^{4} + 4 \, a b^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{3} b \sec\left(d x + c\right) + a^{4}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)/(b^4*sec(d*x + c)^4 + 4*a*b^3*sec(d*x + c)^3 + 6*a^2*b^2*sec(d*x + c)^2 + 4*a^3*b*sec(d*x + c) + a^4), x)","F",0
855,-1,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
856,-1,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
857,0,0,0,1.436923," ","integrate((a+b*sec(d*x+c))^(2/3)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(2/3), x)","F",0
858,0,0,0,1.412593," ","integrate((a+b*sec(d*x+c))^(1/3)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(1/3), x)","F",0
859,0,0,0,0.718037," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))/(b*sec(d*x + c) + a)^(1/3), x)","F",0
860,0,0,0,0.861770," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))/(b*sec(d*x + c) + a)^(2/3), x)","F",0
861,1,182,0,1.061564," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left({\left(4 \, A + 3 \, C\right)} a + 3 \, B b\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(4 \, A + 3 \, C\right)} a + 3 \, B b\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 + {\left(5 \, A + 4 \, C\right)} b\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left({\left(4 \, A + 3 \, C\right)} a + 3 \, B b\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, B a + {\left(5 \, A + 4 \, C\right)} b\right)} \cos\left(d x + c\right)^{2} + 24 \, C b + 30 \, {\left(C a + B b\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 + 3*C)*a + 3*B*b)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*((4*A + 3*C)*a + 3*B*b)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(5*B*a + (5*A + 4*C)*b)*cos(d*x + c)^4 + 15*((4*A + 3*C)*a + 3*B*b)*cos(d*x + c)^3 + 8*(5*B*a + (5*A + 4*C)*b)*cos(d*x + c)^2 + 24*C*b + 30*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
862,1,158,0,0.884170," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, B a + {\left(4 \, A + 3 \, C\right)} b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, B a + {\left(4 \, A + 3 \, C\right)} b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left({\left(3 \, A + 2 \, C\right)} a + 2 \, B b\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, B a + {\left(4 \, A + 3 \, C\right)} b\right)} \cos\left(d x + c\right)^{2} + 6 \, C b + 8 \, {\left(C a + B 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*B*a + (4*A + 3*C)*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*B*a + (4*A + 3*C)*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*((3*A + 2*C)*a + 2*B*b)*cos(d*x + c)^3 + 3*(4*B*a + (4*A + 3*C)*b)*cos(d*x + c)^2 + 6*C*b + 8*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
863,1,128,0,1.149571," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(2 \, A + C\right)} a + B b\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(2 \, A + C\right)} a + B b\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(3 \, B a + {\left(3 \, A + 2 \, C\right)} b\right)} \cos\left(d x + c\right)^{2} + 2 \, C b + 3 \, {\left(C a + B 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*((2*A + C)*a + B*b)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*((2*A + C)*a + B*b)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(3*B*a + (3*A + 2*C)*b)*cos(d*x + c)^2 + 2*C*b + 3*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
864,1,118,0,0.570430," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, A a d x \cos\left(d x + c\right)^{2} + {\left(2 \, B a + {\left(2 \, A + C\right)} b\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, B a + {\left(2 \, A + C\right)} b\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C b + 2 \, {\left(C a + B 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*(4*A*a*d*x*cos(d*x + c)^2 + (2*B*a + (2*A + C)*b)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*B*a + (2*A + C)*b)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(C*b + 2*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
865,1,101,0,0.507735," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(B a + A b\right)} d x \cos\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a + B b\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a \cos\left(d x + c\right) + C b\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(B*a + A*b)*d*x*cos(d*x + c) + (C*a + B*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - (C*a + B*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(A*a*cos(d*x + c) + C*b)*sin(d*x + c))/(d*cos(d*x + c))","A",0
866,1,73,0,0.702229," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left({\left(A + 2 \, C\right)} a + 2 \, B b\right)} d x + C b \log\left(\sin\left(d x + c\right) + 1\right) - C b \log\left(-\sin\left(d x + c\right) + 1\right) + {\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 + 2*C)*a + 2*B*b)*d*x + C*b*log(sin(d*x + c) + 1) - C*b*log(-sin(d*x + c) + 1) + (A*a*cos(d*x + c) + 2*B*a + 2*A*b)*sin(d*x + c))/d","A",0
867,1,70,0,0.494447," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(B a + {\left(A + 2 \, C\right)} b\right)} d x + {\left(2 \, A a \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A + 3 \, C\right)} 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 + 2*C)*b)*d*x + (2*A*a*cos(d*x + c)^2 + 2*(2*A + 3*C)*a + 6*B*b + 3*(B*a + A*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
868,1,97,0,0.622434," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(3 \, A + 4 \, C\right)} 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 + 8 \, {\left(2 \, A + 3 \, C\right)} b + 3 \, {\left({\left(3 \, A + 4 \, C\right)} 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 + 4*C)*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 + 8*(2*A + 3*C)*b + 3*((3*A + 4*C)*a + 4*B*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
869,1,121,0,1.010877," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a + {\left(3 \, A + 4 \, C\right)} b\right)} d x + {\left(24 \, A a \cos\left(d x + c\right)^{4} + 30 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left({\left(4 \, A + 5 \, C\right)} a + 5 \, B b\right)} \cos\left(d x + c\right)^{2} + 16 \, {\left(4 \, A + 5 \, C\right)} a + 80 \, B b + 15 \, {\left(3 \, B a + {\left(3 \, A + 4 \, C\right)} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(3*B*a + (3*A + 4*C)*b)*d*x + (24*A*a*cos(d*x + c)^4 + 30*(B*a + A*b)*cos(d*x + c)^3 + 8*((4*A + 5*C)*a + 5*B*b)*cos(d*x + c)^2 + 16*(4*A + 5*C)*a + 80*B*b + 15*(3*B*a + (3*A + 4*C)*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
870,1,243,0,0.927994," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, B a^{2} + 2 \, {\left(4 \, A + 3 \, C\right)} a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, B a^{2} + 2 \, {\left(4 \, A + 3 \, C\right)} a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(5 \, {\left(3 \, A + 2 \, C\right)} a^{2} + 20 \, B a b + 2 \, {\left(5 \, A + 4 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(4 \, B a^{2} + 2 \, {\left(4 \, A + 3 \, C\right)} a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{3} + 24 \, C b^{2} + 8 \, {\left(5 \, C a^{2} + 10 \, B a b + {\left(5 \, A + 4 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(2 \, C a b + B 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*B*a^2 + 2*(4*A + 3*C)*a*b + 3*B*b^2)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*B*a^2 + 2*(4*A + 3*C)*a*b + 3*B*b^2)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(5*(3*A + 2*C)*a^2 + 20*B*a*b + 2*(5*A + 4*C)*b^2)*cos(d*x + c)^4 + 15*(4*B*a^2 + 2*(4*A + 3*C)*a*b + 3*B*b^2)*cos(d*x + c)^3 + 24*C*b^2 + 8*(5*C*a^2 + 10*B*a*b + (5*A + 4*C)*b^2)*cos(d*x + c)^2 + 30*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
871,1,209,0,0.772096," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{2} + 8 \, B a b + {\left(4 \, A + 3 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{2} + 8 \, B a b + {\left(4 \, A + 3 \, C\right)} 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 \, B a^{2} + 2 \, {\left(3 \, A + 2 \, C\right)} a b + 2 \, B b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, C b^{2} + 3 \, {\left(4 \, C a^{2} + 8 \, B a b + {\left(4 \, A + 3 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(2 \, C a b + B 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*(2*A + C)*a^2 + 8*B*a*b + (4*A + 3*C)*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*(2*A + C)*a^2 + 8*B*a*b + (4*A + 3*C)*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(3*B*a^2 + 2*(3*A + 2*C)*a*b + 2*B*b^2)*cos(d*x + c)^3 + 6*C*b^2 + 3*(4*C*a^2 + 8*B*a*b + (4*A + 3*C)*b^2)*cos(d*x + c)^2 + 8*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
872,1,179,0,0.755266," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{12 \, A a^{2} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{2} + 2 \, {\left(2 \, A + C\right)} a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, B a^{2} + 2 \, {\left(2 \, A + C\right)} a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C b^{2} + 2 \, {\left(3 \, C a^{2} + 6 \, B a b + {\left(3 \, A + 2 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a b + B 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*(12*A*a^2*d*x*cos(d*x + c)^3 + 3*(2*B*a^2 + 2*(2*A + C)*a*b + B*b^2)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*B*a^2 + 2*(2*A + C)*a*b + B*b^2)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*C*b^2 + 2*(3*C*a^2 + 6*B*a*b + (3*A + 2*C)*b^2)*cos(d*x + c)^2 + 3*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
873,1,165,0,0.978567," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, {\left(B a^{2} + 2 \, A a b\right)} d x \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{2} + 4 \, B a b + {\left(2 \, A + C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, C a^{2} + 4 \, B a b + {\left(2 \, A + C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + C b^{2} + 2 \, {\left(2 \, C a b + B 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*(B*a^2 + 2*A*a*b)*d*x*cos(d*x + c)^2 + (2*C*a^2 + 4*B*a*b + (2*A + C)*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*C*a^2 + 4*B*a*b + (2*A + C)*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a^2*cos(d*x + c)^2 + C*b^2 + 2*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
874,1,147,0,0.725549," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left({\left(A + 2 \, C\right)} a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} d x \cos\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(A a^{2} \cos\left(d x + c\right)^{2} + 2 \, C b^{2} + 2 \, {\left(B a^{2} + 2 \, A a 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 + 2*C)*a^2 + 4*B*a*b + 2*A*b^2)*d*x*cos(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)*log(sin(d*x + c) + 1) - (2*C*a*b + B*b^2)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (A*a^2*cos(d*x + c)^2 + 2*C*b^2 + 2*(B*a^2 + 2*A*a*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
875,1,127,0,0.520429," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, C b^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, C b^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(B a^{2} + 2 \, {\left(A + 2 \, C\right)} a b + 2 \, B b^{2}\right)} d x + {\left(2 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A + 3 \, C\right)} 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*C*b^2*log(sin(d*x + c) + 1) - 3*C*b^2*log(-sin(d*x + c) + 1) + 3*(B*a^2 + 2*(A + 2*C)*a*b + 2*B*b^2)*d*x + (2*A*a^2*cos(d*x + c)^2 + 2*(2*A + 3*C)*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
876,1,134,0,0.520079," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{2} + 8 \, B a b + 4 \, {\left(A + 2 \, C\right)} b^{2}\right)} d x + {\left(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 16 \, B a^{2} + 16 \, {\left(2 \, A + 3 \, C\right)} 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({\left(3 \, A + 4 \, C\right)} 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 + 4*C)*a^2 + 8*B*a*b + 4*(A + 2*C)*b^2)*d*x + (6*A*a^2*cos(d*x + c)^3 + 16*B*a^2 + 16*(2*A + 3*C)*a*b + 24*B*b^2 + 8*(B*a^2 + 2*A*a*b)*cos(d*x + c)^2 + 3*((3*A + 4*C)*a^2 + 8*B*a*b + 4*A*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
877,1,171,0,0.549600," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a^{2} + 2 \, {\left(3 \, A + 4 \, C\right)} 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} + 16 \, {\left(4 \, A + 5 \, C\right)} a^{2} + 160 \, B a b + 40 \, {\left(2 \, A + 3 \, C\right)} b^{2} + 8 \, {\left({\left(4 \, A + 5 \, C\right)} a^{2} + 10 \, B a b + 5 \, A b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, B a^{2} + 2 \, {\left(3 \, A + 4 \, C\right)} 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 + 2*(3*A + 4*C)*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 + 16*(4*A + 5*C)*a^2 + 160*B*a*b + 40*(2*A + 3*C)*b^2 + 8*((4*A + 5*C)*a^2 + 10*B*a*b + 5*A*b^2)*cos(d*x + c)^2 + 15*(3*B*a^2 + 2*(3*A + 4*C)*a*b + 4*B*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
878,1,342,0,0.753871," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, B a^{3} + 6 \, {\left(4 \, A + 3 \, C\right)} a^{2} b + 18 \, B a b^{2} + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, B a^{3} + 6 \, {\left(4 \, A + 3 \, C\right)} a^{2} b + 18 \, B a b^{2} + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(5 \, {\left(3 \, A + 2 \, C\right)} a^{3} + 30 \, B a^{2} b + 6 \, {\left(5 \, A + 4 \, C\right)} a b^{2} + 8 \, B b^{3}\right)} \cos\left(d x + c\right)^{5} + 15 \, {\left(8 \, B a^{3} + 6 \, {\left(4 \, A + 3 \, C\right)} a^{2} b + 18 \, B a b^{2} + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{4} + 40 \, C b^{3} + 16 \, {\left(5 \, C a^{3} + 15 \, B a^{2} b + 3 \, {\left(5 \, A + 4 \, C\right)} a b^{2} + 4 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(18 \, C a^{2} b + 18 \, B a b^{2} + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} + 48 \, {\left(3 \, C a b^{2} + B b^{3}\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^3 + 6*(4*A + 3*C)*a^2*b + 18*B*a*b^2 + (6*A + 5*C)*b^3)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(8*B*a^3 + 6*(4*A + 3*C)*a^2*b + 18*B*a*b^2 + (6*A + 5*C)*b^3)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(5*(3*A + 2*C)*a^3 + 30*B*a^2*b + 6*(5*A + 4*C)*a*b^2 + 8*B*b^3)*cos(d*x + c)^5 + 15*(8*B*a^3 + 6*(4*A + 3*C)*a^2*b + 18*B*a*b^2 + (6*A + 5*C)*b^3)*cos(d*x + c)^4 + 40*C*b^3 + 16*(5*C*a^3 + 15*B*a^2*b + 3*(5*A + 4*C)*a*b^2 + 4*B*b^3)*cos(d*x + c)^3 + 10*(18*C*a^2*b + 18*B*a*b^2 + (6*A + 5*C)*b^3)*cos(d*x + c)^2 + 48*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
879,1,292,0,0.491004," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, {\left(2 \, A + C\right)} a^{3} + 12 \, B a^{2} b + 3 \, {\left(4 \, A + 3 \, C\right)} a b^{2} + 3 \, B b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, {\left(2 \, A + C\right)} a^{3} + 12 \, B a^{2} b + 3 \, {\left(4 \, A + 3 \, C\right)} a b^{2} + 3 \, B 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 \, B a^{3} + 15 \, {\left(3 \, A + 2 \, C\right)} a^{2} b + 30 \, B a b^{2} + 2 \, {\left(5 \, A + 4 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{4} + 24 \, C b^{3} + 15 \, {\left(4 \, C a^{3} + 12 \, B a^{2} b + 3 \, {\left(4 \, A + 3 \, C\right)} a b^{2} + 3 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, C a^{2} b + 15 \, B a b^{2} + {\left(5 \, A + 4 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(3 \, C a b^{2} + B 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*(2*A + C)*a^3 + 12*B*a^2*b + 3*(4*A + 3*C)*a*b^2 + 3*B*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*(2*A + C)*a^3 + 12*B*a^2*b + 3*(4*A + 3*C)*a*b^2 + 3*B*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(15*B*a^3 + 15*(3*A + 2*C)*a^2*b + 30*B*a*b^2 + 2*(5*A + 4*C)*b^3)*cos(d*x + c)^4 + 24*C*b^3 + 15*(4*C*a^3 + 12*B*a^2*b + 3*(4*A + 3*C)*a*b^2 + 3*B*b^3)*cos(d*x + c)^3 + 8*(15*C*a^2*b + 15*B*a*b^2 + (5*A + 4*C)*b^3)*cos(d*x + c)^2 + 30*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
880,1,257,0,0.575288," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{48 \, A a^{3} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(8 \, B a^{3} + 12 \, {\left(2 \, A + C\right)} a^{2} b + 12 \, B a b^{2} + {\left(4 \, A + 3 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, B a^{3} + 12 \, {\left(2 \, A + C\right)} a^{2} b + 12 \, B a b^{2} + {\left(4 \, A + 3 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, C b^{3} + 8 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b + 3 \, {\left(3 \, A + 2 \, C\right)} a b^{2} + 2 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(12 \, C a^{2} b + 12 \, B a b^{2} + {\left(4 \, A + 3 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, C a b^{2} + B 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*(48*A*a^3*d*x*cos(d*x + c)^4 + 3*(8*B*a^3 + 12*(2*A + C)*a^2*b + 12*B*a*b^2 + (4*A + 3*C)*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*B*a^3 + 12*(2*A + C)*a^2*b + 12*B*a*b^2 + (4*A + 3*C)*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(6*C*b^3 + 8*(3*C*a^3 + 9*B*a^2*b + 3*(3*A + 2*C)*a*b^2 + 2*B*b^3)*cos(d*x + c)^3 + 3*(12*C*a^2*b + 12*B*a*b^2 + (4*A + 3*C)*b^3)*cos(d*x + c)^2 + 8*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
881,1,225,0,0.810561," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{12 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 3 \, {\left(2 \, A + C\right)} a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 3 \, {\left(2 \, A + C\right)} a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, A a^{3} \cos\left(d x + c\right)^{3} + 2 \, C b^{3} + 2 \, {\left(9 \, C a^{2} b + 9 \, B a b^{2} + {\left(3 \, A + 2 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, C a b^{2} + B 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*(B*a^3 + 3*A*a^2*b)*d*x*cos(d*x + c)^3 + 3*(2*C*a^3 + 6*B*a^2*b + 3*(2*A + C)*a*b^2 + B*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*C*a^3 + 6*B*a^2*b + 3*(2*A + C)*a*b^2 + B*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*A*a^3*cos(d*x + c)^3 + 2*C*b^3 + 2*(9*C*a^2*b + 9*B*a*b^2 + (3*A + 2*C)*b^3)*cos(d*x + c)^2 + 3*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
882,1,208,0,1.067741," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(A + 2 \, C\right)} a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2}\right)} d x \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{2} b + 6 \, B a b^{2} + {\left(2 \, A + C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(6 \, C a^{2} b + 6 \, B a b^{2} + {\left(2 \, A + C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{3} \cos\left(d x + c\right)^{3} + C b^{3} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, C a b^{2} + B 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*(2*((A + 2*C)*a^3 + 6*B*a^2*b + 6*A*a*b^2)*d*x*cos(d*x + c)^2 + (6*C*a^2*b + 6*B*a*b^2 + (2*A + C)*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (6*C*a^2*b + 6*B*a*b^2 + (2*A + C)*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a^3*cos(d*x + c)^3 + C*b^3 + 2*(B*a^3 + 3*A*a^2*b)*cos(d*x + c)^2 + 2*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
883,1,201,0,0.833912," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(B a^{3} + 3 \, {\left(A + 2 \, C\right)} a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, A a^{3} \cos\left(d x + c\right)^{3} + 6 \, C b^{3} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{3} + 9 \, B a^{2} b + 9 \, A a 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^3 + 3*(A + 2*C)*a^2*b + 6*B*a*b^2 + 2*A*b^3)*d*x*cos(d*x + c) + 3*(3*C*a*b^2 + B*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*(3*C*a*b^2 + B*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*A*a^3*cos(d*x + c)^3 + 6*C*b^3 + 3*(B*a^3 + 3*A*a^2*b)*cos(d*x + c)^2 + 2*((2*A + 3*C)*a^3 + 9*B*a^2*b + 9*A*a*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
884,1,189,0,0.593818," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{12 \, C b^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, C b^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{3} + 12 \, B a^{2} b + 12 \, {\left(A + 2 \, C\right)} 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} + 24 \, {\left(2 \, A + 3 \, C\right)} 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} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(12*C*b^3*log(sin(d*x + c) + 1) - 12*C*b^3*log(-sin(d*x + c) + 1) + 3*((3*A + 4*C)*a^3 + 12*B*a^2*b + 12*(A + 2*C)*a*b^2 + 8*B*b^3)*d*x + (6*A*a^3*cos(d*x + c)^3 + 16*B*a^3 + 24*(2*A + 3*C)*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 + 3*((3*A + 4*C)*a^3 + 12*B*a^2*b + 12*A*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
885,1,207,0,0.762435," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a^{3} + 3 \, {\left(3 \, A + 4 \, C\right)} a^{2} b + 12 \, B a b^{2} + 4 \, {\left(A + 2 \, C\right)} b^{3}\right)} d x + {\left(24 \, A a^{3} \cos\left(d x + c\right)^{4} + 16 \, {\left(4 \, A + 5 \, C\right)} a^{3} + 240 \, B a^{2} b + 120 \, {\left(2 \, A + 3 \, C\right)} 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({\left(4 \, A + 5 \, C\right)} 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} + 3 \, {\left(3 \, A + 4 \, C\right)} 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 + 3*(3*A + 4*C)*a^2*b + 12*B*a*b^2 + 4*(A + 2*C)*b^3)*d*x + (24*A*a^3*cos(d*x + c)^4 + 16*(4*A + 5*C)*a^3 + 240*B*a^2*b + 120*(2*A + 3*C)*a*b^2 + 120*B*b^3 + 30*(B*a^3 + 3*A*a^2*b)*cos(d*x + c)^3 + 8*((4*A + 5*C)*a^3 + 15*B*a^2*b + 15*A*a*b^2)*cos(d*x + c)^2 + 15*(3*B*a^3 + 3*(3*A + 4*C)*a^2*b + 12*B*a*b^2 + 4*A*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
886,1,256,0,0.802670," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 18 \, B a^{2} b + 6 \, {\left(3 \, A + 4 \, C\right)} a b^{2} + 8 \, B b^{3}\right)} d x + {\left(40 \, A a^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)^{4} + 128 \, B a^{3} + 96 \, {\left(4 \, A + 5 \, C\right)} a^{2} b + 480 \, B a b^{2} + 80 \, {\left(2 \, A + 3 \, C\right)} b^{3} + 10 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(4 \, B a^{3} + 3 \, {\left(4 \, A + 5 \, C\right)} a^{2} b + 15 \, B a b^{2} + 5 \, A b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 18 \, B a^{2} b + 6 \, {\left(3 \, A + 4 \, C\right)} a b^{2} + 8 \, B b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*((5*A + 6*C)*a^3 + 18*B*a^2*b + 6*(3*A + 4*C)*a*b^2 + 8*B*b^3)*d*x + (40*A*a^3*cos(d*x + c)^5 + 48*(B*a^3 + 3*A*a^2*b)*cos(d*x + c)^4 + 128*B*a^3 + 96*(4*A + 5*C)*a^2*b + 480*B*a*b^2 + 80*(2*A + 3*C)*b^3 + 10*((5*A + 6*C)*a^3 + 18*B*a^2*b + 18*A*a*b^2)*cos(d*x + c)^3 + 16*(4*B*a^3 + 3*(4*A + 5*C)*a^2*b + 15*B*a*b^2 + 5*A*b^3)*cos(d*x + c)^2 + 15*((5*A + 6*C)*a^3 + 18*B*a^2*b + 6*(3*A + 4*C)*a*b^2 + 8*B*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
887,1,450,0,0.982180," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(8 \, B a^{4} + 8 \, {\left(4 \, A + 3 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 4 \, {\left(6 \, A + 5 \, C\right)} a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(8 \, B a^{4} + 8 \, {\left(4 \, A + 3 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 4 \, {\left(6 \, A + 5 \, C\right)} a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(35 \, {\left(3 \, A + 2 \, C\right)} a^{4} + 280 \, B a^{3} b + 84 \, {\left(5 \, A + 4 \, C\right)} a^{2} b^{2} + 224 \, B a b^{3} + 8 \, {\left(7 \, A + 6 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{6} + 105 \, {\left(8 \, B a^{4} + 8 \, {\left(4 \, A + 3 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 4 \, {\left(6 \, A + 5 \, C\right)} a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)^{5} + 240 \, C b^{4} + 16 \, {\left(35 \, C a^{4} + 140 \, B a^{3} b + 42 \, {\left(5 \, A + 4 \, C\right)} a^{2} b^{2} + 112 \, B a b^{3} + 4 \, {\left(7 \, A + 6 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left(24 \, C a^{3} b + 36 \, B a^{2} b^{2} + 4 \, {\left(6 \, A + 5 \, C\right)} a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)^{3} + 48 \, {\left(42 \, C a^{2} b^{2} + 28 \, B a b^{3} + {\left(7 \, A + 6 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 280 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3360 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/3360*(105*(8*B*a^4 + 8*(4*A + 3*C)*a^3*b + 36*B*a^2*b^2 + 4*(6*A + 5*C)*a*b^3 + 5*B*b^4)*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(8*B*a^4 + 8*(4*A + 3*C)*a^3*b + 36*B*a^2*b^2 + 4*(6*A + 5*C)*a*b^3 + 5*B*b^4)*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 2*(16*(35*(3*A + 2*C)*a^4 + 280*B*a^3*b + 84*(5*A + 4*C)*a^2*b^2 + 224*B*a*b^3 + 8*(7*A + 6*C)*b^4)*cos(d*x + c)^6 + 105*(8*B*a^4 + 8*(4*A + 3*C)*a^3*b + 36*B*a^2*b^2 + 4*(6*A + 5*C)*a*b^3 + 5*B*b^4)*cos(d*x + c)^5 + 240*C*b^4 + 16*(35*C*a^4 + 140*B*a^3*b + 42*(5*A + 4*C)*a^2*b^2 + 112*B*a*b^3 + 4*(7*A + 6*C)*b^4)*cos(d*x + c)^4 + 70*(24*C*a^3*b + 36*B*a^2*b^2 + 4*(6*A + 5*C)*a*b^3 + 5*B*b^4)*cos(d*x + c)^3 + 48*(42*C*a^2*b^2 + 28*B*a*b^3 + (7*A + 6*C)*b^4)*cos(d*x + c)^2 + 280*(4*C*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
888,1,391,0,0.732276," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, {\left(2 \, A + C\right)} a^{4} + 32 \, B a^{3} b + 12 \, {\left(4 \, A + 3 \, C\right)} a^{2} b^{2} + 24 \, B a b^{3} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, {\left(2 \, A + C\right)} a^{4} + 32 \, B a^{3} b + 12 \, {\left(4 \, A + 3 \, C\right)} a^{2} b^{2} + 24 \, B a b^{3} + {\left(6 \, A + 5 \, C\right)} 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 \, B a^{4} + 20 \, {\left(3 \, A + 2 \, C\right)} a^{3} b + 60 \, B a^{2} b^{2} + 8 \, {\left(5 \, A + 4 \, C\right)} a b^{3} + 8 \, B b^{4}\right)} \cos\left(d x + c\right)^{5} + 40 \, C b^{4} + 15 \, {\left(8 \, C a^{4} + 32 \, B a^{3} b + 12 \, {\left(4 \, A + 3 \, C\right)} a^{2} b^{2} + 24 \, B a b^{3} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} + 32 \, {\left(10 \, C a^{3} b + 15 \, B a^{2} b^{2} + 2 \, {\left(5 \, A + 4 \, C\right)} a b^{3} + 2 \, B b^{4}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(36 \, C a^{2} b^{2} + 24 \, B a b^{3} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 48 \, {\left(4 \, C a b^{3} + B 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*(2*A + C)*a^4 + 32*B*a^3*b + 12*(4*A + 3*C)*a^2*b^2 + 24*B*a*b^3 + (6*A + 5*C)*b^4)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(8*(2*A + C)*a^4 + 32*B*a^3*b + 12*(4*A + 3*C)*a^2*b^2 + 24*B*a*b^3 + (6*A + 5*C)*b^4)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(15*B*a^4 + 20*(3*A + 2*C)*a^3*b + 60*B*a^2*b^2 + 8*(5*A + 4*C)*a*b^3 + 8*B*b^4)*cos(d*x + c)^5 + 40*C*b^4 + 15*(8*C*a^4 + 32*B*a^3*b + 12*(4*A + 3*C)*a^2*b^2 + 24*B*a*b^3 + (6*A + 5*C)*b^4)*cos(d*x + c)^4 + 32*(10*C*a^3*b + 15*B*a^2*b^2 + 2*(5*A + 4*C)*a*b^3 + 2*B*b^4)*cos(d*x + c)^3 + 10*(36*C*a^2*b^2 + 24*B*a*b^3 + (6*A + 5*C)*b^4)*cos(d*x + c)^2 + 48*(4*C*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
889,1,340,0,0.882771," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{240 \, A a^{4} d x \cos\left(d x + c\right)^{5} + 15 \, {\left(8 \, B a^{4} + 16 \, {\left(2 \, A + C\right)} a^{3} b + 24 \, B a^{2} b^{2} + 4 \, {\left(4 \, A + 3 \, C\right)} a b^{3} + 3 \, B b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, B a^{4} + 16 \, {\left(2 \, A + C\right)} a^{3} b + 24 \, B a^{2} b^{2} + 4 \, {\left(4 \, A + 3 \, C\right)} a b^{3} + 3 \, B b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, C b^{4} + 8 \, {\left(15 \, C a^{4} + 60 \, B a^{3} b + 30 \, {\left(3 \, A + 2 \, C\right)} a^{2} b^{2} + 40 \, B a b^{3} + 2 \, {\left(5 \, A + 4 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 4 \, {\left(4 \, A + 3 \, C\right)} a b^{3} + 3 \, B b^{4}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(30 \, C a^{2} b^{2} + 20 \, B a b^{3} + {\left(5 \, A + 4 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(4 \, C a b^{3} + B 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*(240*A*a^4*d*x*cos(d*x + c)^5 + 15*(8*B*a^4 + 16*(2*A + C)*a^3*b + 24*B*a^2*b^2 + 4*(4*A + 3*C)*a*b^3 + 3*B*b^4)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(8*B*a^4 + 16*(2*A + C)*a^3*b + 24*B*a^2*b^2 + 4*(4*A + 3*C)*a*b^3 + 3*B*b^4)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(24*C*b^4 + 8*(15*C*a^4 + 60*B*a^3*b + 30*(3*A + 2*C)*a^2*b^2 + 40*B*a*b^3 + 2*(5*A + 4*C)*b^4)*cos(d*x + c)^4 + 15*(16*C*a^3*b + 24*B*a^2*b^2 + 4*(4*A + 3*C)*a*b^3 + 3*B*b^4)*cos(d*x + c)^3 + 8*(30*C*a^2*b^2 + 20*B*a*b^3 + (5*A + 4*C)*b^4)*cos(d*x + c)^2 + 30*(4*C*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
890,1,302,0,0.569258," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{48 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(8 \, C a^{4} + 32 \, B a^{3} b + 24 \, {\left(2 \, A + C\right)} a^{2} b^{2} + 16 \, B a b^{3} + {\left(4 \, A + 3 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, C a^{4} + 32 \, B a^{3} b + 24 \, {\left(2 \, A + C\right)} a^{2} b^{2} + 16 \, B a b^{3} + {\left(4 \, A + 3 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, A a^{4} \cos\left(d x + c\right)^{4} + 6 \, C b^{4} + 16 \, {\left(6 \, C a^{3} b + 9 \, B a^{2} b^{2} + 2 \, {\left(3 \, A + 2 \, C\right)} a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(24 \, C a^{2} b^{2} + 16 \, B a b^{3} + {\left(4 \, A + 3 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(4 \, C a b^{3} + B 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*(B*a^4 + 4*A*a^3*b)*d*x*cos(d*x + c)^4 + 3*(8*C*a^4 + 32*B*a^3*b + 24*(2*A + C)*a^2*b^2 + 16*B*a*b^3 + (4*A + 3*C)*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*C*a^4 + 32*B*a^3*b + 24*(2*A + C)*a^2*b^2 + 16*B*a*b^3 + (4*A + 3*C)*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*A*a^4*cos(d*x + c)^4 + 6*C*b^4 + 16*(6*C*a^3*b + 9*B*a^2*b^2 + 2*(3*A + 2*C)*a*b^3 + B*b^4)*cos(d*x + c)^3 + 3*(24*C*a^2*b^2 + 16*B*a*b^3 + (4*A + 3*C)*b^4)*cos(d*x + c)^2 + 8*(4*C*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
891,1,269,0,0.738216," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{6 \, {\left({\left(A + 2 \, C\right)} a^{4} + 8 \, B a^{3} b + 12 \, A a^{2} b^{2}\right)} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, C a^{3} b + 12 \, B a^{2} b^{2} + 4 \, {\left(2 \, A + C\right)} a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, C a^{3} b + 12 \, B a^{2} b^{2} + 4 \, {\left(2 \, A + C\right)} a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, A a^{4} \cos\left(d x + c\right)^{4} + 2 \, C b^{4} + 6 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(18 \, C a^{2} b^{2} + 12 \, B a b^{3} + {\left(3 \, A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, C a b^{3} + B 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*(6*((A + 2*C)*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*d*x*cos(d*x + c)^3 + 3*(8*C*a^3*b + 12*B*a^2*b^2 + 4*(2*A + C)*a*b^3 + B*b^4)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(8*C*a^3*b + 12*B*a^2*b^2 + 4*(2*A + C)*a*b^3 + B*b^4)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(3*A*a^4*cos(d*x + c)^4 + 2*C*b^4 + 6*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)^3 + 2*(18*C*a^2*b^2 + 12*B*a*b^3 + (3*A + 2*C)*b^4)*cos(d*x + c)^2 + 3*(4*C*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
892,1,262,0,0.797665," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{6 \, {\left(B a^{4} + 4 \, {\left(A + 2 \, C\right)} a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} d x \cos\left(d x + c\right)^{2} + 3 \, {\left(12 \, C a^{2} b^{2} + 8 \, B a b^{3} + {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(12 \, C a^{2} b^{2} + 8 \, B a b^{3} + {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{4} \cos\left(d x + c\right)^{4} + 3 \, C b^{4} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{4} + 12 \, B a^{3} b + 18 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(6*(B*a^4 + 4*(A + 2*C)*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3)*d*x*cos(d*x + c)^2 + 3*(12*C*a^2*b^2 + 8*B*a*b^3 + (2*A + C)*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*(12*C*a^2*b^2 + 8*B*a*b^3 + (2*A + C)*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a^4*cos(d*x + c)^4 + 3*C*b^4 + 3*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)^3 + 2*((2*A + 3*C)*a^4 + 12*B*a^3*b + 18*A*a^2*b^2)*cos(d*x + c)^2 + 6*(4*C*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
893,1,263,0,0.720641," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{4} + 16 \, B a^{3} b + 24 \, {\left(A + 2 \, C\right)} a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, A a^{4} \cos\left(d x + c\right)^{4} + 24 \, C b^{4} + 8 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 16 \, {\left(B a^{4} + 2 \, {\left(2 \, A + 3 \, C\right)} a^{3} b + 9 \, B a^{2} b^{2} + 6 \, A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}"," ",0,"1/24*(3*((3*A + 4*C)*a^4 + 16*B*a^3*b + 24*(A + 2*C)*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*d*x*cos(d*x + c) + 12*(4*C*a*b^3 + B*b^4)*cos(d*x + c)*log(sin(d*x + c) + 1) - 12*(4*C*a*b^3 + B*b^4)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (6*A*a^4*cos(d*x + c)^4 + 24*C*b^4 + 8*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)^3 + 3*((3*A + 4*C)*a^4 + 16*B*a^3*b + 24*A*a^2*b^2)*cos(d*x + c)^2 + 16*(B*a^4 + 2*(2*A + 3*C)*a^3*b + 9*B*a^2*b^2 + 6*A*a*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
894,1,262,0,0.743809," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{60 \, C b^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 60 \, C b^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 15 \, {\left(3 \, B a^{4} + 4 \, {\left(3 \, A + 4 \, C\right)} a^{3} b + 24 \, B a^{2} b^{2} + 16 \, {\left(A + 2 \, C\right)} a b^{3} + 8 \, B b^{4}\right)} d x + {\left(24 \, A a^{4} \cos\left(d x + c\right)^{4} + 16 \, {\left(4 \, A + 5 \, C\right)} a^{4} + 320 \, B a^{3} b + 240 \, {\left(2 \, A + 3 \, C\right)} 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} + 8 \, {\left({\left(4 \, A + 5 \, C\right)} a^{4} + 20 \, B a^{3} b + 30 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, B a^{4} + 4 \, {\left(3 \, A + 4 \, C\right)} 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*(60*C*b^4*log(sin(d*x + c) + 1) - 60*C*b^4*log(-sin(d*x + c) + 1) + 15*(3*B*a^4 + 4*(3*A + 4*C)*a^3*b + 24*B*a^2*b^2 + 16*(A + 2*C)*a*b^3 + 8*B*b^4)*d*x + (24*A*a^4*cos(d*x + c)^4 + 16*(4*A + 5*C)*a^4 + 320*B*a^3*b + 240*(2*A + 3*C)*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 + 8*((4*A + 5*C)*a^4 + 20*B*a^3*b + 30*A*a^2*b^2)*cos(d*x + c)^2 + 15*(3*B*a^4 + 4*(3*A + 4*C)*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
895,1,292,0,0.936108," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 24 \, B a^{3} b + 12 \, {\left(3 \, A + 4 \, C\right)} a^{2} b^{2} + 32 \, B a b^{3} + 8 \, {\left(A + 2 \, C\right)} b^{4}\right)} d x + {\left(40 \, A a^{4} \cos\left(d x + c\right)^{5} + 128 \, B a^{4} + 128 \, {\left(4 \, A + 5 \, C\right)} a^{3} b + 960 \, B a^{2} b^{2} + 320 \, {\left(2 \, A + 3 \, C\right)} 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({\left(5 \, A + 6 \, C\right)} 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} + 2 \, {\left(4 \, A + 5 \, C\right)} a^{3} b + 15 \, B a^{2} b^{2} + 10 \, A a b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 24 \, B a^{3} b + 12 \, {\left(3 \, A + 4 \, C\right)} 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 + 6*C)*a^4 + 24*B*a^3*b + 12*(3*A + 4*C)*a^2*b^2 + 32*B*a*b^3 + 8*(A + 2*C)*b^4)*d*x + (40*A*a^4*cos(d*x + c)^5 + 128*B*a^4 + 128*(4*A + 5*C)*a^3*b + 960*B*a^2*b^2 + 320*(2*A + 3*C)*a*b^3 + 240*B*b^4 + 48*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)^4 + 10*((5*A + 6*C)*a^4 + 24*B*a^3*b + 36*A*a^2*b^2)*cos(d*x + c)^3 + 32*(2*B*a^4 + 2*(4*A + 5*C)*a^3*b + 15*B*a^2*b^2 + 10*A*a*b^3)*cos(d*x + c)^2 + 15*((5*A + 6*C)*a^4 + 24*B*a^3*b + 12*(3*A + 4*C)*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
896,1,354,0,0.880078," ","integrate(cos(d*x+c)^7*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(5 \, B a^{4} + 4 \, {\left(5 \, A + 6 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 8 \, {\left(3 \, A + 4 \, C\right)} a b^{3} + 8 \, B b^{4}\right)} d x + {\left(240 \, A a^{4} \cos\left(d x + c\right)^{6} + 280 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{5} + 128 \, {\left(6 \, A + 7 \, C\right)} a^{4} + 3584 \, B a^{3} b + 1344 \, {\left(4 \, A + 5 \, C\right)} a^{2} b^{2} + 4480 \, B a b^{3} + 560 \, {\left(2 \, A + 3 \, C\right)} b^{4} + 48 \, {\left({\left(6 \, A + 7 \, C\right)} a^{4} + 28 \, B a^{3} b + 42 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left(5 \, B a^{4} + 4 \, {\left(5 \, A + 6 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(4 \, {\left(6 \, A + 7 \, C\right)} a^{4} + 112 \, B a^{3} b + 42 \, {\left(4 \, A + 5 \, C\right)} a^{2} b^{2} + 140 \, B a b^{3} + 35 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} + 105 \, {\left(5 \, B a^{4} + 4 \, {\left(5 \, A + 6 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 8 \, {\left(3 \, A + 4 \, C\right)} a b^{3} + 8 \, B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(105*(5*B*a^4 + 4*(5*A + 6*C)*a^3*b + 36*B*a^2*b^2 + 8*(3*A + 4*C)*a*b^3 + 8*B*b^4)*d*x + (240*A*a^4*cos(d*x + c)^6 + 280*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)^5 + 128*(6*A + 7*C)*a^4 + 3584*B*a^3*b + 1344*(4*A + 5*C)*a^2*b^2 + 4480*B*a*b^3 + 560*(2*A + 3*C)*b^4 + 48*((6*A + 7*C)*a^4 + 28*B*a^3*b + 42*A*a^2*b^2)*cos(d*x + c)^4 + 70*(5*B*a^4 + 4*(5*A + 6*C)*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3)*cos(d*x + c)^3 + 16*(4*(6*A + 7*C)*a^4 + 112*B*a^3*b + 42*(4*A + 5*C)*a^2*b^2 + 140*B*a*b^3 + 35*A*b^4)*cos(d*x + c)^2 + 105*(5*B*a^4 + 4*(5*A + 6*C)*a^3*b + 36*B*a^2*b^2 + 8*(3*A + 4*C)*a*b^3 + 8*B*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
897,1,268,0,0.867661," ","integrate((a+b*sec(d*x+c))^3*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""fricas"")","-\frac{48 \, {\left(C a^{5} - B a^{4} b\right)} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(24 \, C a^{4} b - 32 \, B a^{3} b^{2} - 8 \, C a^{2} b^{3} - 16 \, B a b^{4} - 3 \, C b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(24 \, C a^{4} b - 32 \, B a^{3} b^{2} - 8 \, C a^{2} b^{3} - 16 \, B a b^{4} - 3 \, C b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(6 \, C b^{5} - 16 \, {\left(3 \, C a^{3} b^{2} - 9 \, B a^{2} b^{3} - 3 \, C a b^{4} - B b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, C a^{2} b^{3} + 16 \, B a b^{4} + 3 \, C b^{5}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, C a b^{4} + B b^{5}\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*(C*a^5 - B*a^4*b)*d*x*cos(d*x + c)^4 + 3*(24*C*a^4*b - 32*B*a^3*b^2 - 8*C*a^2*b^3 - 16*B*a*b^4 - 3*C*b^5)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(24*C*a^4*b - 32*B*a^3*b^2 - 8*C*a^2*b^3 - 16*B*a*b^4 - 3*C*b^5)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 2*(6*C*b^5 - 16*(3*C*a^3*b^2 - 9*B*a^2*b^3 - 3*C*a*b^4 - B*b^5)*cos(d*x + c)^3 + 3*(8*C*a^2*b^3 + 16*B*a*b^4 + 3*C*b^5)*cos(d*x + c)^2 + 8*(3*C*a*b^4 + B*b^5)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
898,1,199,0,0.709125," ","integrate((a+b*sec(d*x+c))^2*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""fricas"")","-\frac{12 \, {\left(C a^{4} - B a^{3} b\right)} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, C a^{3} b - 6 \, B a^{2} b^{2} - 2 \, C a b^{3} - B b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, C a^{3} b - 6 \, B a^{2} b^{2} - 2 \, C a b^{3} - B b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, C b^{4} + 2 \, {\left(9 \, B a b^{3} + 2 \, C b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a b^{3} + B 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*(C*a^4 - B*a^3*b)*d*x*cos(d*x + c)^3 + 3*(4*C*a^3*b - 6*B*a^2*b^2 - 2*C*a*b^3 - B*b^4)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(4*C*a^3*b - 6*B*a^2*b^2 - 2*C*a*b^3 - B*b^4)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - 2*(2*C*b^4 + 2*(9*B*a*b^3 + 2*C*b^4)*cos(d*x + c)^2 + 3*(2*C*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
899,1,154,0,0.491106," ","integrate((a+b*sec(d*x+c))*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""fricas"")","-\frac{4 \, {\left(C a^{3} - B a^{2} b\right)} d x \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{2} b - 4 \, B a b^{2} - C b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, C a^{2} b - 4 \, B a b^{2} - C b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C b^{3} + 2 \, {\left(C a b^{2} + B 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*(C*a^3 - B*a^2*b)*d*x*cos(d*x + c)^2 + (2*C*a^2*b - 4*B*a*b^2 - C*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*C*a^2*b - 4*B*a*b^2 - C*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(C*b^3 + 2*(C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
900,1,817,0,28.022321," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(C a^{4} - B a^{3} b + A a^{2} b^{2}\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 \, C a^{5} - 2 \, B a^{4} b + {\left(2 \, A - C\right)} a^{3} b^{2} + B a^{2} b^{3} - {\left(2 \, A + C\right)} a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, C a^{5} - 2 \, B a^{4} b + {\left(2 \, A - C\right)} a^{3} b^{2} + B a^{2} b^{3} - {\left(2 \, A + C\right)} a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{2} b^{3} - 2 \, C b^{5} + 2 \, {\left(3 \, C a^{4} b - 3 \, B a^{3} b^{2} + {\left(3 \, A - C\right)} a^{2} b^{3} + 3 \, B a b^{4} - {\left(3 \, A + 2 \, C\right)} b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} - C a b^{4} + B 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(C a^{4} - B a^{3} b + A a^{2} 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) \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, C a^{5} - 2 \, B a^{4} b + {\left(2 \, A - C\right)} a^{3} b^{2} + B a^{2} b^{3} - {\left(2 \, A + C\right)} a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, C a^{5} - 2 \, B a^{4} b + {\left(2 \, A - C\right)} a^{3} b^{2} + B a^{2} b^{3} - {\left(2 \, A + C\right)} a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{2} b^{3} - 2 \, C b^{5} + 2 \, {\left(3 \, C a^{4} b - 3 \, B a^{3} b^{2} + {\left(3 \, A - C\right)} a^{2} b^{3} + 3 \, B a b^{4} - {\left(3 \, A + 2 \, C\right)} b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} - C a b^{4} + B 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*(C*a^4 - B*a^3*b + A*a^2*b^2)*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*C*a^5 - 2*B*a^4*b + (2*A - C)*a^3*b^2 + B*a^2*b^3 - (2*A + C)*a*b^4 + B*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(2*C*a^5 - 2*B*a^4*b + (2*A - C)*a^3*b^2 + B*a^2*b^3 - (2*A + C)*a*b^4 + B*b^5)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*C*a^2*b^3 - 2*C*b^5 + 2*(3*C*a^4*b - 3*B*a^3*b^2 + (3*A - C)*a^2*b^3 + 3*B*a*b^4 - (3*A + 2*C)*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - B*a^2*b^3 - C*a*b^4 + B*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*(C*a^4 - B*a^3*b + A*a^2*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)))*cos(d*x + c)^3 - 3*(2*C*a^5 - 2*B*a^4*b + (2*A - C)*a^3*b^2 + B*a^2*b^3 - (2*A + C)*a*b^4 + B*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(2*C*a^5 - 2*B*a^4*b + (2*A - C)*a^3*b^2 + B*a^2*b^3 - (2*A + C)*a*b^4 + B*b^5)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*C*a^2*b^3 - 2*C*b^5 + 2*(3*C*a^4*b - 3*B*a^3*b^2 + (3*A - C)*a^2*b^3 + 3*B*a*b^4 - (3*A + 2*C)*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - B*a^2*b^3 - C*a*b^4 + B*b^5)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d*cos(d*x + c)^3)]","A",0
901,1,657,0,14.945856," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{3} - B a^{2} b + A a b^{2}\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 \, C a^{4} - 2 \, B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} + 2 \, B a b^{3} - {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, C a^{4} - 2 \, B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} + 2 \, B a b^{3} - {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{2} b^{2} - C b^{4} - 2 \, {\left(C a^{3} b - B a^{2} b^{2} - C a b^{3} + B 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(C a^{3} - B a^{2} b + A 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) \cos\left(d x + c\right)^{2} - {\left(2 \, C a^{4} - 2 \, B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} + 2 \, B a b^{3} - {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{4} - 2 \, B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} + 2 \, B a b^{3} - {\left(2 \, A + C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{2} b^{2} - C b^{4} - 2 \, {\left(C a^{3} b - B a^{2} b^{2} - C a b^{3} + B 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*(C*a^3 - B*a^2*b + A*a*b^2)*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*C*a^4 - 2*B*a^3*b + (2*A - C)*a^2*b^2 + 2*B*a*b^3 - (2*A + C)*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*C*a^4 - 2*B*a^3*b + (2*A - C)*a^2*b^2 + 2*B*a*b^3 - (2*A + C)*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(C*a^2*b^2 - C*b^4 - 2*(C*a^3*b - B*a^2*b^2 - C*a*b^3 + B*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*(C*a^3 - B*a^2*b + A*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)))*cos(d*x + c)^2 - (2*C*a^4 - 2*B*a^3*b + (2*A - C)*a^2*b^2 + 2*B*a*b^3 - (2*A + C)*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (2*C*a^4 - 2*B*a^3*b + (2*A - C)*a^2*b^2 + 2*B*a*b^3 - (2*A + C)*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(C*a^2*b^2 - C*b^4 - 2*(C*a^3*b - B*a^2*b^2 - C*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d*cos(d*x + c)^2)]","B",0
902,1,482,0,6.520892," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(C a^{2} - B a b + A b^{2}\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(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{2} b - C 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(C a^{2} - 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) \cos\left(d x + c\right) - {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{2} b - C 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*((C*a^2 - B*a*b + A*b^2)*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)) - (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) + (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d*cos(d*x + c)), 1/2*(2*(C*a^2 - 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)))*cos(d*x + c) - (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) + (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d*cos(d*x + c))]","B",0
903,1,372,0,3.805718," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(A a^{2} b - A b^{3}\right)} d x + {\left(C a^{2} - 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) + {\left(C a^{3} - C a b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{3} - C a b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} b - a b^{3}\right)} d}, \frac{2 \, {\left(A a^{2} b - A b^{3}\right)} d x - 2 \, {\left(C a^{2} - 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(C a^{3} - C a b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{3} - C a b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} b - a b^{3}\right)} d}\right]"," ",0,"[1/2*(2*(A*a^2*b - A*b^3)*d*x + (C*a^2 - 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)) + (C*a^3 - C*a*b^2)*log(sin(d*x + c) + 1) - (C*a^3 - C*a*b^2)*log(-sin(d*x + c) + 1))/((a^3*b - a*b^3)*d), 1/2*(2*(A*a^2*b - A*b^3)*d*x - 2*(C*a^2 - 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))) + (C*a^3 - C*a*b^2)*log(sin(d*x + c) + 1) - (C*a^3 - C*a*b^2)*log(-sin(d*x + c) + 1))/((a^3*b - a*b^3)*d)]","A",0
904,1,336,0,1.400915," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} d x + {\left(C a^{2} - 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(C a^{2} - 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 + (C*a^2 - 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 + (C*a^2 - 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
905,1,454,0,0.589699," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left({\left(A + 2 \, C\right)} a^{4} - 2 \, B a^{3} b + {\left(A - 2 \, C\right)} a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} d x + {\left(C a^{2} b - 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({\left(A + 2 \, C\right)} a^{4} - 2 \, B a^{3} b + {\left(A - 2 \, C\right)} a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} d x - 2 \, {\left(C a^{2} b - 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 + 2*C)*a^4 - 2*B*a^3*b + (A - 2*C)*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*d*x + (C*a^2*b - 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 + 2*C)*a^4 - 2*B*a^3*b + (A - 2*C)*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*d*x - 2*(C*a^2*b - 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
906,1,599,0,0.543366," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{5} - {\left(A + 2 \, C\right)} a^{4} b + B a^{3} b^{2} - {\left(A - 2 \, C\right)} a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} d x + 3 \, {\left(C a^{2} b^{2} - 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(2 \, {\left(2 \, A + 3 \, C\right)} a^{5} - 6 \, B a^{4} b + 2 \, {\left(A - 3 \, C\right)} 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} - {\left(A + 2 \, C\right)} a^{4} b + B a^{3} b^{2} - {\left(A - 2 \, C\right)} a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} d x + 6 \, {\left(C a^{2} b^{2} - 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(2 \, {\left(2 \, A + 3 \, C\right)} a^{5} - 6 \, B a^{4} b + 2 \, {\left(A - 3 \, C\right)} 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 + 2*C)*a^4*b + B*a^3*b^2 - (A - 2*C)*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*d*x + 3*(C*a^2*b^2 - 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)) + (2*(2*A + 3*C)*a^5 - 6*B*a^4*b + 2*(A - 3*C)*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 + 2*C)*a^4*b + B*a^3*b^2 - (A - 2*C)*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*d*x + 6*(C*a^2*b^2 - 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))) + (2*(2*A + 3*C)*a^5 - 6*B*a^4*b + 2*(A - 3*C)*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
907,1,765,0,1.080978," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{6} - 4 \, B a^{5} b + {\left(A + 4 \, C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + 4 \, {\left(A - 2 \, C\right)} a^{2} b^{4} + 8 \, B a b^{5} - 8 \, A b^{6}\right)} d x + 12 \, {\left(C a^{2} b^{3} - 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} - 8 \, {\left(2 \, A + 3 \, C\right)} a^{5} b + 8 \, B a^{4} b^{2} - 8 \, {\left(A - 3 \, C\right)} 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({\left(3 \, A + 4 \, C\right)} a^{6} - 4 \, B a^{5} b + {\left(A - 4 \, C\right)} 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({\left(3 \, A + 4 \, C\right)} a^{6} - 4 \, B a^{5} b + {\left(A + 4 \, C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + 4 \, {\left(A - 2 \, C\right)} a^{2} b^{4} + 8 \, B a b^{5} - 8 \, A b^{6}\right)} d x - 24 \, {\left(C a^{2} b^{3} - 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} - 8 \, {\left(2 \, A + 3 \, C\right)} a^{5} b + 8 \, B a^{4} b^{2} - 8 \, {\left(A - 3 \, C\right)} 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({\left(3 \, A + 4 \, C\right)} a^{6} - 4 \, B a^{5} b + {\left(A - 4 \, C\right)} 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 + 4*C)*a^6 - 4*B*a^5*b + (A + 4*C)*a^4*b^2 - 4*B*a^3*b^3 + 4*(A - 2*C)*a^2*b^4 + 8*B*a*b^5 - 8*A*b^6)*d*x + 12*(C*a^2*b^3 - 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 - 8*(2*A + 3*C)*a^5*b + 8*B*a^4*b^2 - 8*(A - 3*C)*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 + 4*C)*a^6 - 4*B*a^5*b + (A - 4*C)*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 + 4*C)*a^6 - 4*B*a^5*b + (A + 4*C)*a^4*b^2 - 4*B*a^3*b^3 + 4*(A - 2*C)*a^2*b^4 + 8*B*a*b^5 - 8*A*b^6)*d*x - 24*(C*a^2*b^3 - 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 - 8*(2*A + 3*C)*a^5*b + 8*B*a^4*b^2 - 8*(A - 3*C)*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 + 4*C)*a^6 - 4*B*a^5*b + (A - 4*C)*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
908,1,1835,0,102.066126," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{6 \, {\left({\left(4 \, C a^{7} - 3 \, B a^{6} b + {\left(2 \, A - 5 \, C\right)} a^{5} b^{2} + 4 \, B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, C a^{6} b - 3 \, B a^{5} b^{2} + {\left(2 \, A - 5 \, C\right)} a^{4} b^{3} + 4 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)^{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) - 3 \, {\left({\left(8 \, C a^{8} - 6 \, B a^{7} b + 2 \, {\left(2 \, A - 7 \, C\right)} a^{6} b^{2} + 11 \, B a^{5} b^{3} - 4 \, {\left(2 \, A - C\right)} a^{4} b^{4} - 4 \, B a^{3} b^{5} + 2 \, {\left(2 \, A + C\right)} a^{2} b^{6} - B a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, C a^{7} b - 6 \, B a^{6} b^{2} + 2 \, {\left(2 \, A - 7 \, C\right)} a^{5} b^{3} + 11 \, B a^{4} b^{4} - 4 \, {\left(2 \, A - C\right)} a^{3} b^{5} - 4 \, B a^{2} b^{6} + 2 \, {\left(2 \, A + C\right)} a b^{7} - B b^{8}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(8 \, C a^{8} - 6 \, B a^{7} b + 2 \, {\left(2 \, A - 7 \, C\right)} a^{6} b^{2} + 11 \, B a^{5} b^{3} - 4 \, {\left(2 \, A - C\right)} a^{4} b^{4} - 4 \, B a^{3} b^{5} + 2 \, {\left(2 \, A + C\right)} a^{2} b^{6} - B a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, C a^{7} b - 6 \, B a^{6} b^{2} + 2 \, {\left(2 \, A - 7 \, C\right)} a^{5} b^{3} + 11 \, B a^{4} b^{4} - 4 \, {\left(2 \, A - C\right)} a^{3} b^{5} - 4 \, B a^{2} b^{6} + 2 \, {\left(2 \, A + C\right)} a b^{7} - B b^{8}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{4} b^{4} - 4 \, C a^{2} b^{6} + 2 \, C b^{8} + 2 \, {\left(12 \, C a^{7} b - 9 \, B a^{6} b^{2} + {\left(6 \, A - 19 \, C\right)} a^{5} b^{3} + 15 \, B a^{4} b^{4} - {\left(9 \, A - 5 \, C\right)} a^{3} b^{5} - 6 \, B a^{2} b^{6} + {\left(3 \, A + 2 \, C\right)} a b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, C a^{6} b^{2} - 9 \, B a^{5} b^{3} + 2 \, {\left(3 \, A - 10 \, C\right)} a^{4} b^{4} + 18 \, B a^{3} b^{5} - 4 \, {\left(3 \, A - C\right)} a^{2} b^{6} - 9 \, B a b^{7} + 2 \, {\left(3 \, A + 2 \, C\right)} b^{8}\right)} \cos\left(d x + c\right)^{2} - {\left(4 \, C a^{5} b^{3} - 3 \, B a^{4} b^{4} - 8 \, C a^{3} b^{5} + 6 \, B a^{2} b^{6} + 4 \, C a b^{7} - 3 \, B b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3}\right)}}, \frac{12 \, {\left({\left(4 \, C a^{7} - 3 \, B a^{6} b + {\left(2 \, A - 5 \, C\right)} a^{5} b^{2} + 4 \, B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, C a^{6} b - 3 \, B a^{5} b^{2} + {\left(2 \, A - 5 \, C\right)} a^{4} b^{3} + 4 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)^{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) - 3 \, {\left({\left(8 \, C a^{8} - 6 \, B a^{7} b + 2 \, {\left(2 \, A - 7 \, C\right)} a^{6} b^{2} + 11 \, B a^{5} b^{3} - 4 \, {\left(2 \, A - C\right)} a^{4} b^{4} - 4 \, B a^{3} b^{5} + 2 \, {\left(2 \, A + C\right)} a^{2} b^{6} - B a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, C a^{7} b - 6 \, B a^{6} b^{2} + 2 \, {\left(2 \, A - 7 \, C\right)} a^{5} b^{3} + 11 \, B a^{4} b^{4} - 4 \, {\left(2 \, A - C\right)} a^{3} b^{5} - 4 \, B a^{2} b^{6} + 2 \, {\left(2 \, A + C\right)} a b^{7} - B b^{8}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(8 \, C a^{8} - 6 \, B a^{7} b + 2 \, {\left(2 \, A - 7 \, C\right)} a^{6} b^{2} + 11 \, B a^{5} b^{3} - 4 \, {\left(2 \, A - C\right)} a^{4} b^{4} - 4 \, B a^{3} b^{5} + 2 \, {\left(2 \, A + C\right)} a^{2} b^{6} - B a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, C a^{7} b - 6 \, B a^{6} b^{2} + 2 \, {\left(2 \, A - 7 \, C\right)} a^{5} b^{3} + 11 \, B a^{4} b^{4} - 4 \, {\left(2 \, A - C\right)} a^{3} b^{5} - 4 \, B a^{2} b^{6} + 2 \, {\left(2 \, A + C\right)} a b^{7} - B b^{8}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{4} b^{4} - 4 \, C a^{2} b^{6} + 2 \, C b^{8} + 2 \, {\left(12 \, C a^{7} b - 9 \, B a^{6} b^{2} + {\left(6 \, A - 19 \, C\right)} a^{5} b^{3} + 15 \, B a^{4} b^{4} - {\left(9 \, A - 5 \, C\right)} a^{3} b^{5} - 6 \, B a^{2} b^{6} + {\left(3 \, A + 2 \, C\right)} a b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, C a^{6} b^{2} - 9 \, B a^{5} b^{3} + 2 \, {\left(3 \, A - 10 \, C\right)} a^{4} b^{4} + 18 \, B a^{3} b^{5} - 4 \, {\left(3 \, A - C\right)} a^{2} b^{6} - 9 \, B a b^{7} + 2 \, {\left(3 \, A + 2 \, C\right)} b^{8}\right)} \cos\left(d x + c\right)^{2} - {\left(4 \, C a^{5} b^{3} - 3 \, B a^{4} b^{4} - 8 \, C a^{3} b^{5} + 6 \, B a^{2} b^{6} + 4 \, C a b^{7} - 3 \, B b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/12*(6*((4*C*a^7 - 3*B*a^6*b + (2*A - 5*C)*a^5*b^2 + 4*B*a^4*b^3 - 3*A*a^3*b^4)*cos(d*x + c)^4 + (4*C*a^6*b - 3*B*a^5*b^2 + (2*A - 5*C)*a^4*b^3 + 4*B*a^3*b^4 - 3*A*a^2*b^5)*cos(d*x + c)^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)) - 3*((8*C*a^8 - 6*B*a^7*b + 2*(2*A - 7*C)*a^6*b^2 + 11*B*a^5*b^3 - 4*(2*A - C)*a^4*b^4 - 4*B*a^3*b^5 + 2*(2*A + C)*a^2*b^6 - B*a*b^7)*cos(d*x + c)^4 + (8*C*a^7*b - 6*B*a^6*b^2 + 2*(2*A - 7*C)*a^5*b^3 + 11*B*a^4*b^4 - 4*(2*A - C)*a^3*b^5 - 4*B*a^2*b^6 + 2*(2*A + C)*a*b^7 - B*b^8)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) + 3*((8*C*a^8 - 6*B*a^7*b + 2*(2*A - 7*C)*a^6*b^2 + 11*B*a^5*b^3 - 4*(2*A - C)*a^4*b^4 - 4*B*a^3*b^5 + 2*(2*A + C)*a^2*b^6 - B*a*b^7)*cos(d*x + c)^4 + (8*C*a^7*b - 6*B*a^6*b^2 + 2*(2*A - 7*C)*a^5*b^3 + 11*B*a^4*b^4 - 4*(2*A - C)*a^3*b^5 - 4*B*a^2*b^6 + 2*(2*A + C)*a*b^7 - B*b^8)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) + 2*(2*C*a^4*b^4 - 4*C*a^2*b^6 + 2*C*b^8 + 2*(12*C*a^7*b - 9*B*a^6*b^2 + (6*A - 19*C)*a^5*b^3 + 15*B*a^4*b^4 - (9*A - 5*C)*a^3*b^5 - 6*B*a^2*b^6 + (3*A + 2*C)*a*b^7)*cos(d*x + c)^3 + (12*C*a^6*b^2 - 9*B*a^5*b^3 + 2*(3*A - 10*C)*a^4*b^4 + 18*B*a^3*b^5 - 4*(3*A - C)*a^2*b^6 - 9*B*a*b^7 + 2*(3*A + 2*C)*b^8)*cos(d*x + c)^2 - (4*C*a^5*b^3 - 3*B*a^4*b^4 - 8*C*a^3*b^5 + 6*B*a^2*b^6 + 4*C*a*b^7 - 3*B*b^8)*cos(d*x + c))*sin(d*x + c))/((a^5*b^5 - 2*a^3*b^7 + a*b^9)*d*cos(d*x + c)^4 + (a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c)^3), 1/12*(12*((4*C*a^7 - 3*B*a^6*b + (2*A - 5*C)*a^5*b^2 + 4*B*a^4*b^3 - 3*A*a^3*b^4)*cos(d*x + c)^4 + (4*C*a^6*b - 3*B*a^5*b^2 + (2*A - 5*C)*a^4*b^3 + 4*B*a^3*b^4 - 3*A*a^2*b^5)*cos(d*x + c)^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))) - 3*((8*C*a^8 - 6*B*a^7*b + 2*(2*A - 7*C)*a^6*b^2 + 11*B*a^5*b^3 - 4*(2*A - C)*a^4*b^4 - 4*B*a^3*b^5 + 2*(2*A + C)*a^2*b^6 - B*a*b^7)*cos(d*x + c)^4 + (8*C*a^7*b - 6*B*a^6*b^2 + 2*(2*A - 7*C)*a^5*b^3 + 11*B*a^4*b^4 - 4*(2*A - C)*a^3*b^5 - 4*B*a^2*b^6 + 2*(2*A + C)*a*b^7 - B*b^8)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) + 3*((8*C*a^8 - 6*B*a^7*b + 2*(2*A - 7*C)*a^6*b^2 + 11*B*a^5*b^3 - 4*(2*A - C)*a^4*b^4 - 4*B*a^3*b^5 + 2*(2*A + C)*a^2*b^6 - B*a*b^7)*cos(d*x + c)^4 + (8*C*a^7*b - 6*B*a^6*b^2 + 2*(2*A - 7*C)*a^5*b^3 + 11*B*a^4*b^4 - 4*(2*A - C)*a^3*b^5 - 4*B*a^2*b^6 + 2*(2*A + C)*a*b^7 - B*b^8)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) + 2*(2*C*a^4*b^4 - 4*C*a^2*b^6 + 2*C*b^8 + 2*(12*C*a^7*b - 9*B*a^6*b^2 + (6*A - 19*C)*a^5*b^3 + 15*B*a^4*b^4 - (9*A - 5*C)*a^3*b^5 - 6*B*a^2*b^6 + (3*A + 2*C)*a*b^7)*cos(d*x + c)^3 + (12*C*a^6*b^2 - 9*B*a^5*b^3 + 2*(3*A - 10*C)*a^4*b^4 + 18*B*a^3*b^5 - 4*(3*A - C)*a^2*b^6 - 9*B*a*b^7 + 2*(3*A + 2*C)*b^8)*cos(d*x + c)^2 - (4*C*a^5*b^3 - 3*B*a^4*b^4 - 8*C*a^3*b^5 + 6*B*a^2*b^6 + 4*C*a*b^7 - 3*B*b^8)*cos(d*x + c))*sin(d*x + c))/((a^5*b^5 - 2*a^3*b^7 + a*b^9)*d*cos(d*x + c)^4 + (a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c)^3)]","B",0
909,1,1505,0,74.679238," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(3 \, C a^{6} - 2 \, B a^{5} b + {\left(A - 4 \, C\right)} a^{4} b^{2} + 3 \, B a^{3} b^{3} - 2 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, C a^{5} b - 2 \, B a^{4} b^{2} + {\left(A - 4 \, C\right)} a^{3} b^{3} + 3 \, B a^{2} b^{4} - 2 \, A a b^{5}\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 \, C a^{7} - 4 \, B a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + {\left(2 \, A + C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - 4 \, {\left(A - C\right)} a^{2} b^{5} - 4 \, B a b^{6} + {\left(2 \, A + C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(6 \, C a^{7} - 4 \, B a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + {\left(2 \, A + C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - 4 \, {\left(A - C\right)} a^{2} b^{5} - 4 \, B a b^{6} + {\left(2 \, A + C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7} - 2 \, {\left(3 \, C a^{6} b - 2 \, B a^{5} b^{2} + {\left(A - 5 \, C\right)} a^{4} b^{3} + 3 \, B a^{3} b^{4} - {\left(A - 2 \, C\right)} a^{2} b^{5} - B a b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} - 6 \, C a^{3} b^{4} + 4 \, B a^{2} b^{5} + 3 \, C a b^{6} - 2 \, B 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 \, C a^{6} - 2 \, B a^{5} b + {\left(A - 4 \, C\right)} a^{4} b^{2} + 3 \, B a^{3} b^{3} - 2 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, C a^{5} b - 2 \, B a^{4} b^{2} + {\left(A - 4 \, C\right)} a^{3} b^{3} + 3 \, B a^{2} b^{4} - 2 \, A a b^{5}\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 \, C a^{7} - 4 \, B a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + {\left(2 \, A + C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - 4 \, {\left(A - C\right)} a^{2} b^{5} - 4 \, B a b^{6} + {\left(2 \, A + C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(6 \, C a^{7} - 4 \, B a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + {\left(2 \, A + C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - 4 \, {\left(A - C\right)} a^{2} b^{5} - 4 \, B a b^{6} + {\left(2 \, A + C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7} - 2 \, {\left(3 \, C a^{6} b - 2 \, B a^{5} b^{2} + {\left(A - 5 \, C\right)} a^{4} b^{3} + 3 \, B a^{3} b^{4} - {\left(A - 2 \, C\right)} a^{2} b^{5} - B a b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} - 6 \, C a^{3} b^{4} + 4 \, B a^{2} b^{5} + 3 \, C a b^{6} - 2 \, B 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*C*a^6 - 2*B*a^5*b + (A - 4*C)*a^4*b^2 + 3*B*a^3*b^3 - 2*A*a^2*b^4)*cos(d*x + c)^3 + (3*C*a^5*b - 2*B*a^4*b^2 + (A - 4*C)*a^3*b^3 + 3*B*a^2*b^4 - 2*A*a*b^5)*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*C*a^7 - 4*B*a^6*b + (2*A - 11*C)*a^5*b^2 + 8*B*a^4*b^3 - 4*(A - C)*a^3*b^4 - 4*B*a^2*b^5 + (2*A + C)*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b - 4*B*a^5*b^2 + (2*A - 11*C)*a^4*b^3 + 8*B*a^3*b^4 - 4*(A - C)*a^2*b^5 - 4*B*a*b^6 + (2*A + C)*b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((6*C*a^7 - 4*B*a^6*b + (2*A - 11*C)*a^5*b^2 + 8*B*a^4*b^3 - 4*(A - C)*a^3*b^4 - 4*B*a^2*b^5 + (2*A + C)*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b - 4*B*a^5*b^2 + (2*A - 11*C)*a^4*b^3 + 8*B*a^3*b^4 - 4*(A - C)*a^2*b^5 - 4*B*a*b^6 + (2*A + C)*b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7 - 2*(3*C*a^6*b - 2*B*a^5*b^2 + (A - 5*C)*a^4*b^3 + 3*B*a^3*b^4 - (A - 2*C)*a^2*b^5 - B*a*b^6)*cos(d*x + c)^2 - (3*C*a^5*b^2 - 2*B*a^4*b^3 - 6*C*a^3*b^4 + 4*B*a^2*b^5 + 3*C*a*b^6 - 2*B*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*C*a^6 - 2*B*a^5*b + (A - 4*C)*a^4*b^2 + 3*B*a^3*b^3 - 2*A*a^2*b^4)*cos(d*x + c)^3 + (3*C*a^5*b - 2*B*a^4*b^2 + (A - 4*C)*a^3*b^3 + 3*B*a^2*b^4 - 2*A*a*b^5)*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*C*a^7 - 4*B*a^6*b + (2*A - 11*C)*a^5*b^2 + 8*B*a^4*b^3 - 4*(A - C)*a^3*b^4 - 4*B*a^2*b^5 + (2*A + C)*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b - 4*B*a^5*b^2 + (2*A - 11*C)*a^4*b^3 + 8*B*a^3*b^4 - 4*(A - C)*a^2*b^5 - 4*B*a*b^6 + (2*A + C)*b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((6*C*a^7 - 4*B*a^6*b + (2*A - 11*C)*a^5*b^2 + 8*B*a^4*b^3 - 4*(A - C)*a^3*b^4 - 4*B*a^2*b^5 + (2*A + C)*a*b^6)*cos(d*x + c)^3 + (6*C*a^6*b - 4*B*a^5*b^2 + (2*A - 11*C)*a^4*b^3 + 8*B*a^3*b^4 - 4*(A - C)*a^2*b^5 - 4*B*a*b^6 + (2*A + C)*b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7 - 2*(3*C*a^6*b - 2*B*a^5*b^2 + (A - 5*C)*a^4*b^3 + 3*B*a^3*b^4 - (A - 2*C)*a^2*b^5 - B*a*b^6)*cos(d*x + c)^2 - (3*C*a^5*b^2 - 2*B*a^4*b^3 - 6*C*a^3*b^4 + 4*B*a^2*b^5 + 3*C*a*b^6 - 2*B*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
910,1,1156,0,33.888520," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, C a^{5} - B a^{4} b - 3 \, C a^{3} b^{2} + 2 \, B a^{2} b^{3} - A a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{4} b - B a^{3} b^{2} - 3 \, C a^{2} b^{3} + 2 \, B a b^{4} - 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({\left(2 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(2 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C b^{6} + {\left(2 \, C a^{5} b - B a^{4} b^{2} + {\left(A - 3 \, C\right)} a^{3} b^{3} + B a^{2} b^{4} - {\left(A - C\right)} 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 \, C a^{5} - B a^{4} b - 3 \, C a^{3} b^{2} + 2 \, B a^{2} b^{3} - A a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{4} b - B a^{3} b^{2} - 3 \, C a^{2} b^{3} + 2 \, B a b^{4} - 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({\left(2 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(2 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C b^{6} + {\left(2 \, C a^{5} b - B a^{4} b^{2} + {\left(A - 3 \, C\right)} a^{3} b^{3} + B a^{2} b^{4} - {\left(A - C\right)} 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*C*a^5 - B*a^4*b - 3*C*a^3*b^2 + 2*B*a^2*b^3 - A*a*b^4)*cos(d*x + c)^2 + (2*C*a^4*b - B*a^3*b^2 - 3*C*a^2*b^3 + 2*B*a*b^4 - 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*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + (2*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((2*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + (2*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(C*a^4*b^2 - 2*C*a^2*b^4 + C*b^6 + (2*C*a^5*b - B*a^4*b^2 + (A - 3*C)*a^3*b^3 + B*a^2*b^4 - (A - C)*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*C*a^5 - B*a^4*b - 3*C*a^3*b^2 + 2*B*a^2*b^3 - A*a*b^4)*cos(d*x + c)^2 + (2*C*a^4*b - B*a^3*b^2 - 3*C*a^2*b^3 + 2*B*a*b^4 - 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*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + (2*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((2*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + (2*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(C*a^4*b^2 - 2*C*a^2*b^4 + C*b^6 + (2*C*a^5*b - B*a^4*b^2 + (A - 3*C)*a^3*b^3 + B*a^2*b^4 - (A - C)*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
911,1,728,0,9.135376," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(C a^{3} b - {\left(A + 2 \, C\right)} a b^{3} + B b^{4} + {\left(C a^{4} - {\left(A + 2 \, C\right)} a^{2} b^{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) + {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{4} b - B a^{3} b^{2} + {\left(A - C\right)} a^{2} b^{3} + B a b^{4} - A b^{5}\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(C a^{3} b - {\left(A + 2 \, C\right)} a b^{3} + B b^{4} + {\left(C a^{4} - {\left(A + 2 \, C\right)} a^{2} b^{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(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5} + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{4} b - B a^{3} b^{2} + {\left(A - C\right)} a^{2} b^{3} + B a b^{4} - A b^{5}\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*((C*a^3*b - (A + 2*C)*a*b^3 + B*b^4 + (C*a^4 - (A + 2*C)*a^2*b^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)) + (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) - (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(C*a^4*b - B*a^3*b^2 + (A - C)*a^2*b^3 + B*a*b^4 - A*b^5)*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*(C*a^3*b - (A + 2*C)*a*b^3 + B*b^4 + (C*a^4 - (A + 2*C)*a^2*b^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))) - (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) + (C*a^4*b - 2*C*a^2*b^3 + C*b^5 + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(C*a^4*b - B*a^3*b^2 + (A - C)*a^2*b^3 + B*a*b^4 - A*b^5)*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
912,1,593,0,0.734664," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(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 - {\left(2 \, A + C\right)} a^{2} b^{2} + A b^{4} + {\left(B a^{4} - {\left(2 \, A + C\right)} 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(C a^{5} - B a^{4} b + {\left(A - C\right)} 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 - {\left(2 \, A + C\right)} a^{2} b^{2} + A b^{4} + {\left(B a^{4} - {\left(2 \, A + C\right)} 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(C a^{5} - B a^{4} b + {\left(A - C\right)} 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 + C)*a^2*b^2 + A*b^4 + (B*a^4 - (2*A + C)*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*(C*a^5 - B*a^4*b + (A - C)*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 + C)*a^2*b^2 + A*b^4 + (B*a^4 - (2*A + C)*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))) + (C*a^5 - B*a^4*b + (A - C)*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
913,1,826,0,1.131373," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""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(C a^{4} b - 2 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3} + B a b^{4} - 2 \, A b^{5} + {\left(C a^{5} - 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({\left(A - C\right)} a^{5} b + B a^{4} b^{2} - {\left(3 \, A - C\right)} 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(C a^{4} b - 2 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3} + B a b^{4} - 2 \, A b^{5} + {\left(C a^{5} - 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({\left(A - C\right)} a^{5} b + B a^{4} b^{2} - {\left(3 \, A - C\right)} 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 - (C*a^4*b - 2*B*a^3*b^2 + 3*A*a^2*b^3 + B*a*b^4 - 2*A*b^5 + (C*a^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 - C)*a^5*b + B*a^4*b^2 - (3*A - C)*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 + (C*a^4*b - 2*B*a^3*b^2 + 3*A*a^2*b^3 + B*a*b^4 - 2*A*b^5 + (C*a^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 - C)*a^5*b + B*a^4*b^2 - (3*A - C)*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
914,1,1102,0,0.610893," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(A + 2 \, C\right)} a^{7} - 4 \, B a^{6} b + 4 \, {\left(A - C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{6} b - 4 \, B a^{5} b^{2} + 4 \, {\left(A - C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} d x + {\left(2 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} + {\left(4 \, A - C\right)} a^{2} b^{4} + 2 \, B a b^{5} - 3 \, A b^{6} + {\left(2 \, C a^{5} b - 3 \, B a^{4} b^{2} + {\left(4 \, A - C\right)} 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 - 2 \, {\left(2 \, A - C\right)} a^{5} b^{2} - 6 \, B a^{4} b^{3} + 2 \, {\left(5 \, A - C\right)} 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({\left(A + 2 \, C\right)} a^{7} - 4 \, B a^{6} b + 4 \, {\left(A - C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{6} b - 4 \, B a^{5} b^{2} + 4 \, {\left(A - C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} d x - 2 \, {\left(2 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} + {\left(4 \, A - C\right)} a^{2} b^{4} + 2 \, B a b^{5} - 3 \, A b^{6} + {\left(2 \, C a^{5} b - 3 \, B a^{4} b^{2} + {\left(4 \, A - C\right)} 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 - 2 \, {\left(2 \, A - C\right)} a^{5} b^{2} - 6 \, B a^{4} b^{3} + 2 \, {\left(5 \, A - C\right)} 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 + 2*C)*a^7 - 4*B*a^6*b + 4*(A - C)*a^5*b^2 + 8*B*a^4*b^3 - (11*A - 2*C)*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*d*x*cos(d*x + c) + ((A + 2*C)*a^6*b - 4*B*a^5*b^2 + 4*(A - C)*a^4*b^3 + 8*B*a^3*b^4 - (11*A - 2*C)*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*d*x + (2*C*a^4*b^2 - 3*B*a^3*b^3 + (4*A - C)*a^2*b^4 + 2*B*a*b^5 - 3*A*b^6 + (2*C*a^5*b - 3*B*a^4*b^2 + (4*A - C)*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 - 2*(2*A - C)*a^5*b^2 - 6*B*a^4*b^3 + 2*(5*A - C)*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 + 2*C)*a^7 - 4*B*a^6*b + 4*(A - C)*a^5*b^2 + 8*B*a^4*b^3 - (11*A - 2*C)*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*d*x*cos(d*x + c) + ((A + 2*C)*a^6*b - 4*B*a^5*b^2 + 4*(A - C)*a^4*b^3 + 8*B*a^3*b^4 - (11*A - 2*C)*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*d*x - 2*(2*C*a^4*b^2 - 3*B*a^3*b^3 + (4*A - C)*a^2*b^4 + 2*B*a*b^5 - 3*A*b^6 + (2*C*a^5*b - 3*B*a^4*b^2 + (4*A - C)*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 - 2*(2*A - C)*a^5*b^2 - 6*B*a^4*b^3 + 2*(5*A - C)*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
915,1,1347,0,0.675928," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{8} - 2 \, {\left(A + 2 \, C\right)} a^{7} b + 4 \, B a^{6} b^{2} - 4 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - 11 \, B a^{4} b^{4} + 2 \, {\left(7 \, A - 2 \, C\right)} 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 \, {\left(A + 2 \, C\right)} a^{6} b^{2} + 4 \, B a^{5} b^{3} - 4 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - 11 \, B a^{3} b^{5} + 2 \, {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 6 \, B a b^{7} - 8 \, A b^{8}\right)} d x + 3 \, {\left(3 \, C a^{4} b^{3} - 4 \, B a^{3} b^{4} + {\left(5 \, A - 2 \, C\right)} a^{2} b^{5} + 3 \, B a b^{6} - 4 \, A b^{7} + {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A - 2 \, C\right)} 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(2 \, {\left(2 \, A + 3 \, C\right)} a^{7} b - 12 \, B a^{6} b^{2} + 2 \, {\left(5 \, A - 9 \, C\right)} a^{5} b^{3} + 30 \, B a^{4} b^{4} - 2 \, {\left(19 \, A - 6 \, C\right)} 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(2 \, {\left(2 \, A + 3 \, C\right)} a^{8} - 9 \, B a^{7} b + 4 \, {\left(A - 3 \, C\right)} a^{6} b^{2} + 18 \, B a^{5} b^{3} - 2 \, {\left(10 \, A - 3 \, C\right)} 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 \, {\left(A + 2 \, C\right)} a^{7} b + 4 \, B a^{6} b^{2} - 4 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - 11 \, B a^{4} b^{4} + 2 \, {\left(7 \, A - 2 \, C\right)} 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 \, {\left(A + 2 \, C\right)} a^{6} b^{2} + 4 \, B a^{5} b^{3} - 4 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - 11 \, B a^{3} b^{5} + 2 \, {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 6 \, B a b^{7} - 8 \, A b^{8}\right)} d x + 6 \, {\left(3 \, C a^{4} b^{3} - 4 \, B a^{3} b^{4} + {\left(5 \, A - 2 \, C\right)} a^{2} b^{5} + 3 \, B a b^{6} - 4 \, A b^{7} + {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A - 2 \, C\right)} 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(2 \, {\left(2 \, A + 3 \, C\right)} a^{7} b - 12 \, B a^{6} b^{2} + 2 \, {\left(5 \, A - 9 \, C\right)} a^{5} b^{3} + 30 \, B a^{4} b^{4} - 2 \, {\left(19 \, A - 6 \, C\right)} 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(2 \, {\left(2 \, A + 3 \, C\right)} a^{8} - 9 \, B a^{7} b + 4 \, {\left(A - 3 \, C\right)} a^{6} b^{2} + 18 \, B a^{5} b^{3} - 2 \, {\left(10 \, A - 3 \, C\right)} 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 + 2*C)*a^7*b + 4*B*a^6*b^2 - 4*(A - 2*C)*a^5*b^3 - 11*B*a^4*b^4 + 2*(7*A - 2*C)*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 + 2*C)*a^6*b^2 + 4*B*a^5*b^3 - 4*(A - 2*C)*a^4*b^4 - 11*B*a^3*b^5 + 2*(7*A - 2*C)*a^2*b^6 + 6*B*a*b^7 - 8*A*b^8)*d*x + 3*(3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A - 2*C)*a^2*b^5 + 3*B*a*b^6 - 4*A*b^7 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A - 2*C)*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)) + (2*(2*A + 3*C)*a^7*b - 12*B*a^6*b^2 + 2*(5*A - 9*C)*a^5*b^3 + 30*B*a^4*b^4 - 2*(19*A - 6*C)*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 + (2*(2*A + 3*C)*a^8 - 9*B*a^7*b + 4*(A - 3*C)*a^6*b^2 + 18*B*a^5*b^3 - 2*(10*A - 3*C)*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 + 2*C)*a^7*b + 4*B*a^6*b^2 - 4*(A - 2*C)*a^5*b^3 - 11*B*a^4*b^4 + 2*(7*A - 2*C)*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 + 2*C)*a^6*b^2 + 4*B*a^5*b^3 - 4*(A - 2*C)*a^4*b^4 - 11*B*a^3*b^5 + 2*(7*A - 2*C)*a^2*b^6 + 6*B*a*b^7 - 8*A*b^8)*d*x + 6*(3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A - 2*C)*a^2*b^5 + 3*B*a*b^6 - 4*A*b^7 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A - 2*C)*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))) + (2*(2*A + 3*C)*a^7*b - 12*B*a^6*b^2 + 2*(5*A - 9*C)*a^5*b^3 + 30*B*a^4*b^4 - 2*(19*A - 6*C)*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 + (2*(2*A + 3*C)*a^8 - 9*B*a^7*b + 4*(A - 3*C)*a^6*b^2 + 18*B*a^5*b^3 - 2*(10*A - 3*C)*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
916,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
917,1,2217,0,157.851533," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(6 \, C a^{8} - 2 \, B a^{7} b - 15 \, C a^{6} b^{2} + 5 \, B a^{5} b^{3} + {\left(A + 12 \, C\right)} a^{4} b^{4} - 6 \, B a^{3} b^{5} + 2 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, C a^{7} b - 2 \, B a^{6} b^{2} - 15 \, C a^{5} b^{3} + 5 \, B a^{4} b^{4} + {\left(A + 12 \, C\right)} a^{3} b^{5} - 6 \, B a^{2} b^{6} + 2 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{6} b^{2} - 2 \, B a^{5} b^{3} - 15 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + {\left(A + 12 \, C\right)} a^{2} b^{6} - 6 \, B a b^{7} + 2 \, 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({\left(3 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(3 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{6} b^{3} - 6 \, C a^{4} b^{5} + 6 \, C a^{2} b^{7} - 2 \, C b^{9} + {\left(6 \, C a^{8} b - 2 \, B a^{7} b^{2} - 17 \, C a^{6} b^{3} + 7 \, B a^{5} b^{4} - {\left(3 \, A - 13 \, C\right)} a^{4} b^{5} - 5 \, B a^{3} b^{6} + {\left(3 \, A - 2 \, C\right)} a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} + {\left(A - 25 \, C\right)} a^{5} b^{4} + 9 \, B a^{4} b^{5} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} - 6 \, B a^{2} b^{7} + 4 \, {\left(A - C\right)} 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 \, C a^{8} - 2 \, B a^{7} b - 15 \, C a^{6} b^{2} + 5 \, B a^{5} b^{3} + {\left(A + 12 \, C\right)} a^{4} b^{4} - 6 \, B a^{3} b^{5} + 2 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, C a^{7} b - 2 \, B a^{6} b^{2} - 15 \, C a^{5} b^{3} + 5 \, B a^{4} b^{4} + {\left(A + 12 \, C\right)} a^{3} b^{5} - 6 \, B a^{2} b^{6} + 2 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{6} b^{2} - 2 \, B a^{5} b^{3} - 15 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + {\left(A + 12 \, C\right)} a^{2} b^{6} - 6 \, B a b^{7} + 2 \, 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({\left(3 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(3 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{6} b^{3} - 6 \, C a^{4} b^{5} + 6 \, C a^{2} b^{7} - 2 \, C b^{9} + {\left(6 \, C a^{8} b - 2 \, B a^{7} b^{2} - 17 \, C a^{6} b^{3} + 7 \, B a^{5} b^{4} - {\left(3 \, A - 13 \, C\right)} a^{4} b^{5} - 5 \, B a^{3} b^{6} + {\left(3 \, A - 2 \, C\right)} a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} + {\left(A - 25 \, C\right)} a^{5} b^{4} + 9 \, B a^{4} b^{5} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} - 6 \, B a^{2} b^{7} + 4 \, {\left(A - C\right)} 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*C*a^8 - 2*B*a^7*b - 15*C*a^6*b^2 + 5*B*a^5*b^3 + (A + 12*C)*a^4*b^4 - 6*B*a^3*b^5 + 2*A*a^2*b^6)*cos(d*x + c)^3 + 2*(6*C*a^7*b - 2*B*a^6*b^2 - 15*C*a^5*b^3 + 5*B*a^4*b^4 + (A + 12*C)*a^3*b^5 - 6*B*a^2*b^6 + 2*A*a*b^7)*cos(d*x + c)^2 + (6*C*a^6*b^2 - 2*B*a^5*b^3 - 15*C*a^4*b^4 + 5*B*a^3*b^5 + (A + 12*C)*a^2*b^6 - 6*B*a*b^7 + 2*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*((3*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*cos(d*x + c)^3 + 2*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*cos(d*x + c)^2 + (3*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) + 2*((3*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*cos(d*x + c)^3 + 2*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*cos(d*x + c)^2 + (3*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(2*C*a^6*b^3 - 6*C*a^4*b^5 + 6*C*a^2*b^7 - 2*C*b^9 + (6*C*a^8*b - 2*B*a^7*b^2 - 17*C*a^6*b^3 + 7*B*a^5*b^4 - (3*A - 13*C)*a^4*b^5 - 5*B*a^3*b^6 + (3*A - 2*C)*a^2*b^7)*cos(d*x + c)^2 + (9*C*a^7*b^2 - 3*B*a^6*b^3 + (A - 25*C)*a^5*b^4 + 9*B*a^4*b^5 - 5*(A - 4*C)*a^3*b^6 - 6*B*a^2*b^7 + 4*(A - C)*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*C*a^8 - 2*B*a^7*b - 15*C*a^6*b^2 + 5*B*a^5*b^3 + (A + 12*C)*a^4*b^4 - 6*B*a^3*b^5 + 2*A*a^2*b^6)*cos(d*x + c)^3 + 2*(6*C*a^7*b - 2*B*a^6*b^2 - 15*C*a^5*b^3 + 5*B*a^4*b^4 + (A + 12*C)*a^3*b^5 - 6*B*a^2*b^6 + 2*A*a*b^7)*cos(d*x + c)^2 + (6*C*a^6*b^2 - 2*B*a^5*b^3 - 15*C*a^4*b^4 + 5*B*a^3*b^5 + (A + 12*C)*a^2*b^6 - 6*B*a*b^7 + 2*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))) - ((3*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*cos(d*x + c)^3 + 2*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*cos(d*x + c)^2 + (3*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((3*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*cos(d*x + c)^3 + 2*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*cos(d*x + c)^2 + (3*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (2*C*a^6*b^3 - 6*C*a^4*b^5 + 6*C*a^2*b^7 - 2*C*b^9 + (6*C*a^8*b - 2*B*a^7*b^2 - 17*C*a^6*b^3 + 7*B*a^5*b^4 - (3*A - 13*C)*a^4*b^5 - 5*B*a^3*b^6 + (3*A - 2*C)*a^2*b^7)*cos(d*x + c)^2 + (9*C*a^7*b^2 - 3*B*a^6*b^3 + (A - 25*C)*a^5*b^4 + 9*B*a^4*b^5 - 5*(A - 4*C)*a^3*b^6 - 6*B*a^2*b^7 + 4*(A - C)*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
918,1,1501,0,32.691972," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} - B a^{2} b^{5} + 3 \, {\left(A + 2 \, C\right)} a b^{6} - 2 \, B b^{7} + {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} - B a^{4} b^{3} + 3 \, {\left(A + 2 \, C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} - B a^{3} b^{4} + 3 \, {\left(A + 2 \, C\right)} a^{2} b^{5} - 2 \, B 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(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, C a^{6} b^{2} - B a^{5} b^{3} - {\left(A + 9 \, C\right)} a^{4} b^{4} + 5 \, B a^{3} b^{5} - {\left(A - 6 \, C\right)} a^{2} b^{6} - 4 \, B a b^{7} + 2 \, A b^{8} + {\left(2 \, C a^{7} b - {\left(2 \, A + 7 \, C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} + {\left(A + 5 \, C\right)} a^{3} b^{5} - 3 \, B a^{2} b^{6} + A a b^{7}\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 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} - B a^{2} b^{5} + 3 \, {\left(A + 2 \, C\right)} a b^{6} - 2 \, B b^{7} + {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} - B a^{4} b^{3} + 3 \, {\left(A + 2 \, C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} - B a^{3} b^{4} + 3 \, {\left(A + 2 \, C\right)} a^{2} b^{5} - 2 \, B 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(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8} + {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(3 \, C a^{6} b^{2} - B a^{5} b^{3} - {\left(A + 9 \, C\right)} a^{4} b^{4} + 5 \, B a^{3} b^{5} - {\left(A - 6 \, C\right)} a^{2} b^{6} - 4 \, B a b^{7} + 2 \, A b^{8} + {\left(2 \, C a^{7} b - {\left(2 \, A + 7 \, C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} + {\left(A + 5 \, C\right)} a^{3} b^{5} - 3 \, B a^{2} b^{6} + A a b^{7}\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*C*a^5*b^2 - 5*C*a^3*b^4 - B*a^2*b^5 + 3*(A + 2*C)*a*b^6 - 2*B*b^7 + (2*C*a^7 - 5*C*a^5*b^2 - B*a^4*b^3 + 3*(A + 2*C)*a^3*b^4 - 2*B*a^2*b^5)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 - B*a^3*b^4 + 3*(A + 2*C)*a^2*b^5 - 2*B*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*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + 2*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(3*C*a^6*b^2 - B*a^5*b^3 - (A + 9*C)*a^4*b^4 + 5*B*a^3*b^5 - (A - 6*C)*a^2*b^6 - 4*B*a*b^7 + 2*A*b^8 + (2*C*a^7*b - (2*A + 7*C)*a^5*b^3 + 3*B*a^4*b^4 + (A + 5*C)*a^3*b^5 - 3*B*a^2*b^6 + A*a*b^7)*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*C*a^5*b^2 - 5*C*a^3*b^4 - B*a^2*b^5 + 3*(A + 2*C)*a*b^6 - 2*B*b^7 + (2*C*a^7 - 5*C*a^5*b^2 - B*a^4*b^3 + 3*(A + 2*C)*a^3*b^4 - 2*B*a^2*b^5)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 - B*a^3*b^4 + 3*(A + 2*C)*a^2*b^5 - 2*B*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))) - (C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + (C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8 + (C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*cos(d*x + c)^2 + 2*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (3*C*a^6*b^2 - B*a^5*b^3 - (A + 9*C)*a^4*b^4 + 5*B*a^3*b^5 - (A - 6*C)*a^2*b^6 - 4*B*a*b^7 + 2*A*b^8 + (2*C*a^7*b - (2*A + 7*C)*a^5*b^3 + 3*B*a^4*b^4 + (A + 5*C)*a^3*b^5 - 3*B*a^2*b^6 + A*a*b^7)*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
919,1,848,0,0.590952," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, A + C\right)} a^{2} b^{2} - 3 \, B a b^{3} + {\left(A + 2 \, C\right)} b^{4} + {\left({\left(2 \, A + C\right)} a^{4} - 3 \, B a^{3} b + {\left(A + 2 \, C\right)} a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, A + C\right)} a^{3} b - 3 \, B a^{2} b^{2} + {\left(A + 2 \, C\right)} 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(C a^{5} + B a^{4} b - {\left(3 \, A + 5 \, C\right)} a^{3} b^{2} + B a^{2} b^{3} + {\left(3 \, A + 4 \, C\right)} a b^{4} - 2 \, B b^{5} + {\left(2 \, B a^{5} - {\left(4 \, A + 3 \, C\right)} a^{4} b - B a^{3} b^{2} + {\left(5 \, A + 3 \, C\right)} 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({\left(2 \, A + C\right)} a^{2} b^{2} - 3 \, B a b^{3} + {\left(A + 2 \, C\right)} b^{4} + {\left({\left(2 \, A + C\right)} a^{4} - 3 \, B a^{3} b + {\left(A + 2 \, C\right)} a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, A + C\right)} a^{3} b - 3 \, B a^{2} b^{2} + {\left(A + 2 \, C\right)} 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(C a^{5} + B a^{4} b - {\left(3 \, A + 5 \, C\right)} a^{3} b^{2} + B a^{2} b^{3} + {\left(3 \, A + 4 \, C\right)} a b^{4} - 2 \, B b^{5} + {\left(2 \, B a^{5} - {\left(4 \, A + 3 \, C\right)} a^{4} b - B a^{3} b^{2} + {\left(5 \, A + 3 \, C\right)} 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 + C)*a^2*b^2 - 3*B*a*b^3 + (A + 2*C)*b^4 + ((2*A + C)*a^4 - 3*B*a^3*b + (A + 2*C)*a^2*b^2)*cos(d*x + c)^2 + 2*((2*A + C)*a^3*b - 3*B*a^2*b^2 + (A + 2*C)*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*(C*a^5 + B*a^4*b - (3*A + 5*C)*a^3*b^2 + B*a^2*b^3 + (3*A + 4*C)*a*b^4 - 2*B*b^5 + (2*B*a^5 - (4*A + 3*C)*a^4*b - B*a^3*b^2 + (5*A + 3*C)*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 + C)*a^2*b^2 - 3*B*a*b^3 + (A + 2*C)*b^4 + ((2*A + C)*a^4 - 3*B*a^3*b + (A + 2*C)*a^2*b^2)*cos(d*x + c)^2 + 2*((2*A + C)*a^3*b - 3*B*a^2*b^2 + (A + 2*C)*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))) + (C*a^5 + B*a^4*b - (3*A + 5*C)*a^3*b^2 + B*a^2*b^3 + (3*A + 4*C)*a*b^4 - 2*B*b^5 + (2*B*a^5 - (4*A + 3*C)*a^4*b - B*a^3*b^2 + (5*A + 3*C)*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
920,1,1237,0,0.636231," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(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} - 3 \, {\left(2 \, A + C\right)} a^{4} b^{3} + B a^{3} b^{4} + 5 \, A a^{2} b^{5} - 2 \, A b^{7} + {\left(2 \, B a^{7} - 3 \, {\left(2 \, A + C\right)} 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 - 3 \, {\left(2 \, A + C\right)} 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(C a^{7} b - 3 \, B a^{6} b^{2} + {\left(5 \, A + C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} - {\left(7 \, A + 2 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7} + {\left(2 \, C a^{8} - 4 \, B a^{7} b + {\left(6 \, A - C\right)} a^{6} b^{2} + 5 \, B a^{5} b^{3} - {\left(9 \, A + C\right)} 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} - 3 \, {\left(2 \, A + C\right)} a^{4} b^{3} + B a^{3} b^{4} + 5 \, A a^{2} b^{5} - 2 \, A b^{7} + {\left(2 \, B a^{7} - 3 \, {\left(2 \, A + C\right)} 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 - 3 \, {\left(2 \, A + C\right)} 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(C a^{7} b - 3 \, B a^{6} b^{2} + {\left(5 \, A + C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} - {\left(7 \, A + 2 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7} + {\left(2 \, C a^{8} - 4 \, B a^{7} b + {\left(6 \, A - C\right)} a^{6} b^{2} + 5 \, B a^{5} b^{3} - {\left(9 \, A + C\right)} 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 - 3*(2*A + C)*a^4*b^3 + B*a^3*b^4 + 5*A*a^2*b^5 - 2*A*b^7 + (2*B*a^7 - 3*(2*A + C)*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 - 3*(2*A + C)*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*(C*a^7*b - 3*B*a^6*b^2 + (5*A + C)*a^5*b^3 + 3*B*a^4*b^4 - (7*A + 2*C)*a^3*b^5 + 2*A*a*b^7 + (2*C*a^8 - 4*B*a^7*b + (6*A - C)*a^6*b^2 + 5*B*a^5*b^3 - (9*A + C)*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 - 3*(2*A + C)*a^4*b^3 + B*a^3*b^4 + 5*A*a^2*b^5 - 2*A*b^7 + (2*B*a^7 - 3*(2*A + C)*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 - 3*(2*A + C)*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))) + (C*a^7*b - 3*B*a^6*b^2 + (5*A + C)*a^5*b^3 + 3*B*a^4*b^4 - (7*A + 2*C)*a^3*b^5 + 2*A*a*b^7 + (2*C*a^8 - 4*B*a^7*b + (6*A - C)*a^6*b^2 + 5*B*a^5*b^3 - (9*A + C)*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
921,1,1680,0,0.705644," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""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(2 \, C a^{6} b^{2} - 6 \, B a^{5} b^{3} + {\left(12 \, A + C\right)} 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(2 \, C a^{8} - 6 \, B a^{7} b + {\left(12 \, A + C\right)} 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(2 \, C a^{7} b - 6 \, B a^{6} b^{2} + {\left(12 \, A + C\right)} 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({\left(2 \, A - 3 \, C\right)} a^{7} b^{2} + 5 \, B a^{6} b^{3} - {\left(13 \, A - 3 \, C\right)} 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 \, {\left(A - C\right)} a^{8} b + 6 \, B a^{7} b^{2} - 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} - 9 \, B a^{5} b^{4} + {\left(25 \, A - C\right)} 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(2 \, C a^{6} b^{2} - 6 \, B a^{5} b^{3} + {\left(12 \, A + C\right)} 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(2 \, C a^{8} - 6 \, B a^{7} b + {\left(12 \, A + C\right)} 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(2 \, C a^{7} b - 6 \, B a^{6} b^{2} + {\left(12 \, A + C\right)} 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({\left(2 \, A - 3 \, C\right)} a^{7} b^{2} + 5 \, B a^{6} b^{3} - {\left(13 \, A - 3 \, C\right)} 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 \, {\left(A - C\right)} a^{8} b + 6 \, B a^{7} b^{2} - 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} - 9 \, B a^{5} b^{4} + {\left(25 \, A - C\right)} 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 + (2*C*a^6*b^2 - 6*B*a^5*b^3 + (12*A + C)*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 + (2*C*a^8 - 6*B*a^7*b + (12*A + C)*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*(2*C*a^7*b - 6*B*a^6*b^2 + (12*A + C)*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 - 3*C)*a^7*b^2 + 5*B*a^6*b^3 - (13*A - 3*C)*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 - C)*a^8*b + 6*B*a^7*b^2 - 5*(4*A - C)*a^6*b^3 - 9*B*a^5*b^4 + (25*A - C)*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 + (2*C*a^6*b^2 - 6*B*a^5*b^3 + (12*A + C)*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 + (2*C*a^8 - 6*B*a^7*b + (12*A + C)*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*(2*C*a^7*b - 6*B*a^6*b^2 + (12*A + C)*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 - 3*C)*a^7*b^2 + 5*B*a^6*b^3 - (13*A - 3*C)*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 - C)*a^8*b + 6*B*a^7*b^2 - 5*(4*A - C)*a^6*b^3 - 9*B*a^5*b^4 + (25*A - C)*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
922,1,2127,0,0.764727," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(A + 2 \, C\right)} a^{10} - 6 \, B a^{9} b + 3 \, {\left(3 \, A - 2 \, C\right)} a^{8} b^{2} + 18 \, B a^{7} b^{3} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{6} b^{4} - 18 \, B a^{5} b^{5} + {\left(35 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{9} b - 6 \, B a^{8} b^{2} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{7} b^{3} + 18 \, B a^{6} b^{4} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{5} b^{5} - 18 \, B a^{4} b^{6} + {\left(35 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{8} b^{2} - 6 \, B a^{7} b^{3} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{6} b^{4} + 18 \, B a^{5} b^{5} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{4} b^{6} - 18 \, B a^{3} b^{7} + {\left(35 \, A - 2 \, C\right)} a^{2} b^{8} + 6 \, B a b^{9} - 12 \, A b^{10}\right)} d x + {\left(6 \, C a^{6} b^{3} - 12 \, B a^{5} b^{4} + 5 \, {\left(4 \, A - C\right)} a^{4} b^{5} + 15 \, B a^{3} b^{6} - {\left(29 \, A - 2 \, C\right)} a^{2} b^{7} - 6 \, B a b^{8} + 12 \, A b^{9} + {\left(6 \, C a^{8} b - 12 \, B a^{7} b^{2} + 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} + 15 \, B a^{5} b^{4} - {\left(29 \, A - 2 \, C\right)} 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(6 \, C a^{7} b^{2} - 12 \, B a^{6} b^{3} + 5 \, {\left(4 \, A - C\right)} a^{5} b^{4} + 15 \, B a^{4} b^{5} - {\left(29 \, A - 2 \, C\right)} 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} - {\left(6 \, A - 5 \, C\right)} a^{7} b^{3} - 13 \, B a^{6} b^{4} + {\left(27 \, A - 7 \, C\right)} a^{5} b^{5} + 17 \, B a^{4} b^{6} - {\left(33 \, A - 2 \, C\right)} 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 - {\left(11 \, A - 6 \, C\right)} a^{8} b^{2} - 20 \, B a^{7} b^{3} + {\left(43 \, A - 9 \, C\right)} a^{6} b^{4} + 25 \, B a^{5} b^{5} - {\left(50 \, A - 3 \, C\right)} 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({\left(A + 2 \, C\right)} a^{10} - 6 \, B a^{9} b + 3 \, {\left(3 \, A - 2 \, C\right)} a^{8} b^{2} + 18 \, B a^{7} b^{3} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{6} b^{4} - 18 \, B a^{5} b^{5} + {\left(35 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{9} b - 6 \, B a^{8} b^{2} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{7} b^{3} + 18 \, B a^{6} b^{4} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{5} b^{5} - 18 \, B a^{4} b^{6} + {\left(35 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{8} b^{2} - 6 \, B a^{7} b^{3} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{6} b^{4} + 18 \, B a^{5} b^{5} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{4} b^{6} - 18 \, B a^{3} b^{7} + {\left(35 \, A - 2 \, C\right)} a^{2} b^{8} + 6 \, B a b^{9} - 12 \, A b^{10}\right)} d x - {\left(6 \, C a^{6} b^{3} - 12 \, B a^{5} b^{4} + 5 \, {\left(4 \, A - C\right)} a^{4} b^{5} + 15 \, B a^{3} b^{6} - {\left(29 \, A - 2 \, C\right)} a^{2} b^{7} - 6 \, B a b^{8} + 12 \, A b^{9} + {\left(6 \, C a^{8} b - 12 \, B a^{7} b^{2} + 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} + 15 \, B a^{5} b^{4} - {\left(29 \, A - 2 \, C\right)} 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(6 \, C a^{7} b^{2} - 12 \, B a^{6} b^{3} + 5 \, {\left(4 \, A - C\right)} a^{5} b^{4} + 15 \, B a^{4} b^{5} - {\left(29 \, A - 2 \, C\right)} 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} - {\left(6 \, A - 5 \, C\right)} a^{7} b^{3} - 13 \, B a^{6} b^{4} + {\left(27 \, A - 7 \, C\right)} a^{5} b^{5} + 17 \, B a^{4} b^{6} - {\left(33 \, A - 2 \, C\right)} 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 - {\left(11 \, A - 6 \, C\right)} a^{8} b^{2} - 20 \, B a^{7} b^{3} + {\left(43 \, A - 9 \, C\right)} a^{6} b^{4} + 25 \, B a^{5} b^{5} - {\left(50 \, A - 3 \, C\right)} 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 + 2*C)*a^10 - 6*B*a^9*b + 3*(3*A - 2*C)*a^8*b^2 + 18*B*a^7*b^3 - 3*(11*A - 2*C)*a^6*b^4 - 18*B*a^5*b^5 + (35*A - 2*C)*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 + 2*C)*a^9*b - 6*B*a^8*b^2 + 3*(3*A - 2*C)*a^7*b^3 + 18*B*a^6*b^4 - 3*(11*A - 2*C)*a^5*b^5 - 18*B*a^4*b^6 + (35*A - 2*C)*a^3*b^7 + 6*B*a^2*b^8 - 12*A*a*b^9)*d*x*cos(d*x + c) + 2*((A + 2*C)*a^8*b^2 - 6*B*a^7*b^3 + 3*(3*A - 2*C)*a^6*b^4 + 18*B*a^5*b^5 - 3*(11*A - 2*C)*a^4*b^6 - 18*B*a^3*b^7 + (35*A - 2*C)*a^2*b^8 + 6*B*a*b^9 - 12*A*b^10)*d*x + (6*C*a^6*b^3 - 12*B*a^5*b^4 + 5*(4*A - C)*a^4*b^5 + 15*B*a^3*b^6 - (29*A - 2*C)*a^2*b^7 - 6*B*a*b^8 + 12*A*b^9 + (6*C*a^8*b - 12*B*a^7*b^2 + 5*(4*A - C)*a^6*b^3 + 15*B*a^5*b^4 - (29*A - 2*C)*a^4*b^5 - 6*B*a^3*b^6 + 12*A*a^2*b^7)*cos(d*x + c)^2 + 2*(6*C*a^7*b^2 - 12*B*a^6*b^3 + 5*(4*A - C)*a^5*b^4 + 15*B*a^4*b^5 - (29*A - 2*C)*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 - 5*C)*a^7*b^3 - 13*B*a^6*b^4 + (27*A - 7*C)*a^5*b^5 + 17*B*a^4*b^6 - (33*A - 2*C)*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 - 6*C)*a^8*b^2 - 20*B*a^7*b^3 + (43*A - 9*C)*a^6*b^4 + 25*B*a^5*b^5 - (50*A - 3*C)*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 + 2*C)*a^10 - 6*B*a^9*b + 3*(3*A - 2*C)*a^8*b^2 + 18*B*a^7*b^3 - 3*(11*A - 2*C)*a^6*b^4 - 18*B*a^5*b^5 + (35*A - 2*C)*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 + 2*C)*a^9*b - 6*B*a^8*b^2 + 3*(3*A - 2*C)*a^7*b^3 + 18*B*a^6*b^4 - 3*(11*A - 2*C)*a^5*b^5 - 18*B*a^4*b^6 + (35*A - 2*C)*a^3*b^7 + 6*B*a^2*b^8 - 12*A*a*b^9)*d*x*cos(d*x + c) + ((A + 2*C)*a^8*b^2 - 6*B*a^7*b^3 + 3*(3*A - 2*C)*a^6*b^4 + 18*B*a^5*b^5 - 3*(11*A - 2*C)*a^4*b^6 - 18*B*a^3*b^7 + (35*A - 2*C)*a^2*b^8 + 6*B*a*b^9 - 12*A*b^10)*d*x - (6*C*a^6*b^3 - 12*B*a^5*b^4 + 5*(4*A - C)*a^4*b^5 + 15*B*a^3*b^6 - (29*A - 2*C)*a^2*b^7 - 6*B*a*b^8 + 12*A*b^9 + (6*C*a^8*b - 12*B*a^7*b^2 + 5*(4*A - C)*a^6*b^3 + 15*B*a^5*b^4 - (29*A - 2*C)*a^4*b^5 - 6*B*a^3*b^6 + 12*A*a^2*b^7)*cos(d*x + c)^2 + 2*(6*C*a^7*b^2 - 12*B*a^6*b^3 + 5*(4*A - C)*a^5*b^4 + 15*B*a^4*b^5 - (29*A - 2*C)*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 - 5*C)*a^7*b^3 - 13*B*a^6*b^4 + (27*A - 7*C)*a^5*b^5 + 17*B*a^4*b^6 - (33*A - 2*C)*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 - 6*C)*a^8*b^2 - 20*B*a^7*b^3 + (43*A - 9*C)*a^6*b^4 + 25*B*a^5*b^5 - (50*A - 3*C)*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
923,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
924,1,2466,0,161.421449," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, C a^{7} b^{3} - 7 \, C a^{5} b^{5} - {\left(A - 8 \, C\right)} a^{3} b^{7} + 3 \, B a^{2} b^{8} - 4 \, {\left(A + 2 \, C\right)} a b^{9} + 2 \, B b^{10} + {\left(2 \, C a^{10} - 7 \, C a^{8} b^{2} - {\left(A - 8 \, C\right)} a^{6} b^{4} + 3 \, B a^{5} b^{5} - 4 \, {\left(A + 2 \, C\right)} a^{4} b^{6} + 2 \, B a^{3} b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{9} b - 7 \, C a^{7} b^{3} - {\left(A - 8 \, C\right)} a^{5} b^{5} + 3 \, B a^{4} b^{6} - 4 \, {\left(A + 2 \, C\right)} a^{3} b^{7} + 2 \, B a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{8} b^{2} - 7 \, C a^{6} b^{4} - {\left(A - 8 \, C\right)} a^{4} b^{6} + 3 \, B a^{3} b^{7} - 4 \, {\left(A + 2 \, C\right)} a^{2} b^{8} + 2 \, B 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(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11} + {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, {\left(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11} + {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(11 \, C a^{8} b^{3} - 2 \, B a^{7} b^{4} - {\left(A + 43 \, C\right)} a^{6} b^{5} + 7 \, B a^{5} b^{6} + {\left(11 \, A + 68 \, C\right)} a^{4} b^{7} - 23 \, B a^{3} b^{8} - 4 \, {\left(A + 9 \, C\right)} a^{2} b^{9} + 18 \, B a b^{10} - 6 \, A b^{11} + {\left(6 \, C a^{10} b - 23 \, C a^{8} b^{3} - 4 \, B a^{7} b^{4} + {\left(13 \, A + 43 \, C\right)} a^{6} b^{5} - 7 \, B a^{5} b^{6} - {\left(11 \, A + 26 \, C\right)} a^{4} b^{7} + 11 \, B a^{3} b^{8} - 2 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, C a^{9} b^{2} - {\left(A + 20 \, C\right)} a^{7} b^{4} - B a^{6} b^{5} + 5 \, {\left(2 \, A + 7 \, C\right)} a^{5} b^{6} - 8 \, B a^{4} b^{7} - {\left(7 \, A + 20 \, C\right)} a^{3} b^{8} + 9 \, B a^{2} b^{9} - 2 \, A a b^{10}\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 \, C a^{7} b^{3} - 7 \, C a^{5} b^{5} - {\left(A - 8 \, C\right)} a^{3} b^{7} + 3 \, B a^{2} b^{8} - 4 \, {\left(A + 2 \, C\right)} a b^{9} + 2 \, B b^{10} + {\left(2 \, C a^{10} - 7 \, C a^{8} b^{2} - {\left(A - 8 \, C\right)} a^{6} b^{4} + 3 \, B a^{5} b^{5} - 4 \, {\left(A + 2 \, C\right)} a^{4} b^{6} + 2 \, B a^{3} b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{9} b - 7 \, C a^{7} b^{3} - {\left(A - 8 \, C\right)} a^{5} b^{5} + 3 \, B a^{4} b^{6} - 4 \, {\left(A + 2 \, C\right)} a^{3} b^{7} + 2 \, B a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{8} b^{2} - 7 \, C a^{6} b^{4} - {\left(A - 8 \, C\right)} a^{4} b^{6} + 3 \, B a^{3} b^{7} - 4 \, {\left(A + 2 \, C\right)} a^{2} b^{8} + 2 \, B 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(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11} + {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11} + {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(11 \, C a^{8} b^{3} - 2 \, B a^{7} b^{4} - {\left(A + 43 \, C\right)} a^{6} b^{5} + 7 \, B a^{5} b^{6} + {\left(11 \, A + 68 \, C\right)} a^{4} b^{7} - 23 \, B a^{3} b^{8} - 4 \, {\left(A + 9 \, C\right)} a^{2} b^{9} + 18 \, B a b^{10} - 6 \, A b^{11} + {\left(6 \, C a^{10} b - 23 \, C a^{8} b^{3} - 4 \, B a^{7} b^{4} + {\left(13 \, A + 43 \, C\right)} a^{6} b^{5} - 7 \, B a^{5} b^{6} - {\left(11 \, A + 26 \, C\right)} a^{4} b^{7} + 11 \, B a^{3} b^{8} - 2 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, C a^{9} b^{2} - {\left(A + 20 \, C\right)} a^{7} b^{4} - B a^{6} b^{5} + 5 \, {\left(2 \, A + 7 \, C\right)} a^{5} b^{6} - 8 \, B a^{4} b^{7} - {\left(7 \, A + 20 \, C\right)} a^{3} b^{8} + 9 \, B a^{2} b^{9} - 2 \, A a b^{10}\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*C*a^7*b^3 - 7*C*a^5*b^5 - (A - 8*C)*a^3*b^7 + 3*B*a^2*b^8 - 4*(A + 2*C)*a*b^9 + 2*B*b^10 + (2*C*a^10 - 7*C*a^8*b^2 - (A - 8*C)*a^6*b^4 + 3*B*a^5*b^5 - 4*(A + 2*C)*a^4*b^6 + 2*B*a^3*b^7)*cos(d*x + c)^3 + 3*(2*C*a^9*b - 7*C*a^7*b^3 - (A - 8*C)*a^5*b^5 + 3*B*a^4*b^6 - 4*(A + 2*C)*a^3*b^7 + 2*B*a^2*b^8)*cos(d*x + c)^2 + 3*(2*C*a^8*b^2 - 7*C*a^6*b^4 - (A - 8*C)*a^4*b^6 + 3*B*a^3*b^7 - 4*(A + 2*C)*a^2*b^8 + 2*B*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*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11 + (C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*cos(d*x + c)^3 + 3*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*cos(d*x + c)^2 + 3*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*cos(d*x + c))*log(sin(d*x + c) + 1) + 6*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11 + (C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*cos(d*x + c)^3 + 3*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*cos(d*x + c)^2 + 3*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(11*C*a^8*b^3 - 2*B*a^7*b^4 - (A + 43*C)*a^6*b^5 + 7*B*a^5*b^6 + (11*A + 68*C)*a^4*b^7 - 23*B*a^3*b^8 - 4*(A + 9*C)*a^2*b^9 + 18*B*a*b^10 - 6*A*b^11 + (6*C*a^10*b - 23*C*a^8*b^3 - 4*B*a^7*b^4 + (13*A + 43*C)*a^6*b^5 - 7*B*a^5*b^6 - (11*A + 26*C)*a^4*b^7 + 11*B*a^3*b^8 - 2*A*a^2*b^9)*cos(d*x + c)^2 + 3*(5*C*a^9*b^2 - (A + 20*C)*a^7*b^4 - B*a^6*b^5 + 5*(2*A + 7*C)*a^5*b^6 - 8*B*a^4*b^7 - (7*A + 20*C)*a^3*b^8 + 9*B*a^2*b^9 - 2*A*a*b^10)*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*C*a^7*b^3 - 7*C*a^5*b^5 - (A - 8*C)*a^3*b^7 + 3*B*a^2*b^8 - 4*(A + 2*C)*a*b^9 + 2*B*b^10 + (2*C*a^10 - 7*C*a^8*b^2 - (A - 8*C)*a^6*b^4 + 3*B*a^5*b^5 - 4*(A + 2*C)*a^4*b^6 + 2*B*a^3*b^7)*cos(d*x + c)^3 + 3*(2*C*a^9*b - 7*C*a^7*b^3 - (A - 8*C)*a^5*b^5 + 3*B*a^4*b^6 - 4*(A + 2*C)*a^3*b^7 + 2*B*a^2*b^8)*cos(d*x + c)^2 + 3*(2*C*a^8*b^2 - 7*C*a^6*b^4 - (A - 8*C)*a^4*b^6 + 3*B*a^3*b^7 - 4*(A + 2*C)*a^2*b^8 + 2*B*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*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11 + (C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*cos(d*x + c)^3 + 3*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*cos(d*x + c)^2 + 3*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*cos(d*x + c))*log(sin(d*x + c) + 1) + 3*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11 + (C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*cos(d*x + c)^3 + 3*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*cos(d*x + c)^2 + 3*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (11*C*a^8*b^3 - 2*B*a^7*b^4 - (A + 43*C)*a^6*b^5 + 7*B*a^5*b^6 + (11*A + 68*C)*a^4*b^7 - 23*B*a^3*b^8 - 4*(A + 9*C)*a^2*b^9 + 18*B*a*b^10 - 6*A*b^11 + (6*C*a^10*b - 23*C*a^8*b^3 - 4*B*a^7*b^4 + (13*A + 43*C)*a^6*b^5 - 7*B*a^5*b^6 - (11*A + 26*C)*a^4*b^7 + 11*B*a^3*b^8 - 2*A*a^2*b^9)*cos(d*x + c)^2 + 3*(5*C*a^9*b^2 - (A + 20*C)*a^7*b^4 - B*a^6*b^5 + 5*(2*A + 7*C)*a^5*b^6 - 8*B*a^4*b^7 - (7*A + 20*C)*a^3*b^8 + 9*B*a^2*b^9 - 2*A*a*b^10)*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
925,1,1420,0,0.645038," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{3} b^{3} - {\left(4 \, A + 3 \, C\right)} a^{2} b^{4} + 4 \, B a b^{5} - {\left(A + 2 \, C\right)} b^{6} + {\left(B a^{6} - {\left(4 \, A + 3 \, C\right)} a^{5} b + 4 \, B a^{4} b^{2} - {\left(A + 2 \, C\right)} a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{5} b - {\left(4 \, A + 3 \, C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} - {\left(A + 2 \, C\right)} a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{4} b^{2} - {\left(4 \, A + 3 \, C\right)} a^{3} b^{3} + 4 \, B a^{2} b^{4} - {\left(A + 2 \, C\right)} 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 \, C a^{7} + B a^{6} b + {\left(2 \, A - 7 \, C\right)} a^{5} b^{2} - 11 \, B a^{4} b^{3} + {\left(11 \, A + 23 \, C\right)} a^{3} b^{4} + 4 \, B a^{2} b^{5} - {\left(13 \, A + 18 \, C\right)} a b^{6} + 6 \, B b^{7} + {\left(2 \, {\left(3 \, A + 2 \, C\right)} a^{7} - 13 \, B a^{6} b + {\left(4 \, A + 7 \, C\right)} a^{5} b^{2} + 11 \, B a^{4} b^{3} - 11 \, {\left(A + C\right)} 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} + {\left(2 \, A + C\right)} a^{6} b - 10 \, B a^{5} b^{2} + {\left(7 \, A + 8 \, C\right)} a^{4} b^{3} + 7 \, B a^{3} b^{4} - {\left(10 \, A + 9 \, C\right)} 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} - {\left(4 \, A + 3 \, C\right)} a^{2} b^{4} + 4 \, B a b^{5} - {\left(A + 2 \, C\right)} b^{6} + {\left(B a^{6} - {\left(4 \, A + 3 \, C\right)} a^{5} b + 4 \, B a^{4} b^{2} - {\left(A + 2 \, C\right)} a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{5} b - {\left(4 \, A + 3 \, C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} - {\left(A + 2 \, C\right)} a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{4} b^{2} - {\left(4 \, A + 3 \, C\right)} a^{3} b^{3} + 4 \, B a^{2} b^{4} - {\left(A + 2 \, C\right)} 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 \, C a^{7} + B a^{6} b + {\left(2 \, A - 7 \, C\right)} a^{5} b^{2} - 11 \, B a^{4} b^{3} + {\left(11 \, A + 23 \, C\right)} a^{3} b^{4} + 4 \, B a^{2} b^{5} - {\left(13 \, A + 18 \, C\right)} a b^{6} + 6 \, B b^{7} + {\left(2 \, {\left(3 \, A + 2 \, C\right)} a^{7} - 13 \, B a^{6} b + {\left(4 \, A + 7 \, C\right)} a^{5} b^{2} + 11 \, B a^{4} b^{3} - 11 \, {\left(A + C\right)} 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} + {\left(2 \, A + C\right)} a^{6} b - 10 \, B a^{5} b^{2} + {\left(7 \, A + 8 \, C\right)} a^{4} b^{3} + 7 \, B a^{3} b^{4} - {\left(10 \, A + 9 \, C\right)} 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 + 3*C)*a^2*b^4 + 4*B*a*b^5 - (A + 2*C)*b^6 + (B*a^6 - (4*A + 3*C)*a^5*b + 4*B*a^4*b^2 - (A + 2*C)*a^3*b^3)*cos(d*x + c)^3 + 3*(B*a^5*b - (4*A + 3*C)*a^4*b^2 + 4*B*a^3*b^3 - (A + 2*C)*a^2*b^4)*cos(d*x + c)^2 + 3*(B*a^4*b^2 - (4*A + 3*C)*a^3*b^3 + 4*B*a^2*b^4 - (A + 2*C)*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*C*a^7 + B*a^6*b + (2*A - 7*C)*a^5*b^2 - 11*B*a^4*b^3 + (11*A + 23*C)*a^3*b^4 + 4*B*a^2*b^5 - (13*A + 18*C)*a*b^6 + 6*B*b^7 + (2*(3*A + 2*C)*a^7 - 13*B*a^6*b + (4*A + 7*C)*a^5*b^2 + 11*B*a^4*b^3 - 11*(A + C)*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 + C)*a^6*b - 10*B*a^5*b^2 + (7*A + 8*C)*a^4*b^3 + 7*B*a^3*b^4 - (10*A + 9*C)*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 + 3*C)*a^2*b^4 + 4*B*a*b^5 - (A + 2*C)*b^6 + (B*a^6 - (4*A + 3*C)*a^5*b + 4*B*a^4*b^2 - (A + 2*C)*a^3*b^3)*cos(d*x + c)^3 + 3*(B*a^5*b - (4*A + 3*C)*a^4*b^2 + 4*B*a^3*b^3 - (A + 2*C)*a^2*b^4)*cos(d*x + c)^2 + 3*(B*a^4*b^2 - (4*A + 3*C)*a^3*b^3 + 4*B*a^2*b^4 - (A + 2*C)*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*C*a^7 + B*a^6*b + (2*A - 7*C)*a^5*b^2 - 11*B*a^4*b^3 + (11*A + 23*C)*a^3*b^4 + 4*B*a^2*b^5 - (13*A + 18*C)*a*b^6 + 6*B*b^7 + (2*(3*A + 2*C)*a^7 - 13*B*a^6*b + (4*A + 7*C)*a^5*b^2 + 11*B*a^4*b^3 - 11*(A + C)*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 + C)*a^6*b - 10*B*a^5*b^2 + (7*A + 8*C)*a^4*b^3 + 7*B*a^3*b^4 - (10*A + 9*C)*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
926,1,1414,0,0.618096," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(2 \, A + C\right)} a^{3} b^{3} - 4 \, B a^{2} b^{4} + {\left(3 \, A + 4 \, C\right)} a b^{5} - B b^{6} + {\left({\left(2 \, A + C\right)} a^{6} - 4 \, B a^{5} b + {\left(3 \, A + 4 \, C\right)} a^{4} b^{2} - B a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(2 \, A + C\right)} a^{5} b - 4 \, B a^{4} b^{2} + {\left(3 \, A + 4 \, C\right)} a^{3} b^{3} - B a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + {\left(3 \, A + 4 \, C\right)} 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(C a^{6} b + 2 \, B a^{5} b^{2} - 11 \, {\left(A + C\right)} a^{4} b^{3} + 11 \, B a^{3} b^{4} + {\left(7 \, A + 4 \, C\right)} a^{2} b^{5} - 13 \, B a b^{6} + 2 \, {\left(2 \, A + 3 \, C\right)} b^{7} + {\left(6 \, B a^{7} - {\left(18 \, A + 13 \, C\right)} a^{6} b + 4 \, B a^{5} b^{2} + {\left(23 \, A + 11 \, C\right)} a^{4} b^{3} - 11 \, B a^{3} b^{4} - {\left(7 \, A - 2 \, C\right)} a^{2} b^{5} + B a b^{6} + 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{7} + 2 \, B a^{6} b - {\left(9 \, A + 10 \, C\right)} a^{5} b^{2} + 7 \, B a^{4} b^{3} + {\left(8 \, A + 7 \, C\right)} a^{3} b^{4} - 10 \, B a^{2} b^{5} + {\left(A + 2 \, C\right)} 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({\left(2 \, A + C\right)} a^{3} b^{3} - 4 \, B a^{2} b^{4} + {\left(3 \, A + 4 \, C\right)} a b^{5} - B b^{6} + {\left({\left(2 \, A + C\right)} a^{6} - 4 \, B a^{5} b + {\left(3 \, A + 4 \, C\right)} a^{4} b^{2} - B a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(2 \, A + C\right)} a^{5} b - 4 \, B a^{4} b^{2} + {\left(3 \, A + 4 \, C\right)} a^{3} b^{3} - B a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + {\left(3 \, A + 4 \, C\right)} 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(C a^{6} b + 2 \, B a^{5} b^{2} - 11 \, {\left(A + C\right)} a^{4} b^{3} + 11 \, B a^{3} b^{4} + {\left(7 \, A + 4 \, C\right)} a^{2} b^{5} - 13 \, B a b^{6} + 2 \, {\left(2 \, A + 3 \, C\right)} b^{7} + {\left(6 \, B a^{7} - {\left(18 \, A + 13 \, C\right)} a^{6} b + 4 \, B a^{5} b^{2} + {\left(23 \, A + 11 \, C\right)} a^{4} b^{3} - 11 \, B a^{3} b^{4} - {\left(7 \, A - 2 \, C\right)} a^{2} b^{5} + B a b^{6} + 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{7} + 2 \, B a^{6} b - {\left(9 \, A + 10 \, C\right)} a^{5} b^{2} + 7 \, B a^{4} b^{3} + {\left(8 \, A + 7 \, C\right)} a^{3} b^{4} - 10 \, B a^{2} b^{5} + {\left(A + 2 \, C\right)} 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 + C)*a^3*b^3 - 4*B*a^2*b^4 + (3*A + 4*C)*a*b^5 - B*b^6 + ((2*A + C)*a^6 - 4*B*a^5*b + (3*A + 4*C)*a^4*b^2 - B*a^3*b^3)*cos(d*x + c)^3 + 3*((2*A + C)*a^5*b - 4*B*a^4*b^2 + (3*A + 4*C)*a^3*b^3 - B*a^2*b^4)*cos(d*x + c)^2 + 3*((2*A + C)*a^4*b^2 - 4*B*a^3*b^3 + (3*A + 4*C)*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*(C*a^6*b + 2*B*a^5*b^2 - 11*(A + C)*a^4*b^3 + 11*B*a^3*b^4 + (7*A + 4*C)*a^2*b^5 - 13*B*a*b^6 + 2*(2*A + 3*C)*b^7 + (6*B*a^7 - (18*A + 13*C)*a^6*b + 4*B*a^5*b^2 + (23*A + 11*C)*a^4*b^3 - 11*B*a^3*b^4 - (7*A - 2*C)*a^2*b^5 + B*a*b^6 + 2*A*b^7)*cos(d*x + c)^2 + 3*(C*a^7 + 2*B*a^6*b - (9*A + 10*C)*a^5*b^2 + 7*B*a^4*b^3 + (8*A + 7*C)*a^3*b^4 - 10*B*a^2*b^5 + (A + 2*C)*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 + C)*a^3*b^3 - 4*B*a^2*b^4 + (3*A + 4*C)*a*b^5 - B*b^6 + ((2*A + C)*a^6 - 4*B*a^5*b + (3*A + 4*C)*a^4*b^2 - B*a^3*b^3)*cos(d*x + c)^3 + 3*((2*A + C)*a^5*b - 4*B*a^4*b^2 + (3*A + 4*C)*a^3*b^3 - B*a^2*b^4)*cos(d*x + c)^2 + 3*((2*A + C)*a^4*b^2 - 4*B*a^3*b^3 + (3*A + 4*C)*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))) + (C*a^6*b + 2*B*a^5*b^2 - 11*(A + C)*a^4*b^3 + 11*B*a^3*b^4 + (7*A + 4*C)*a^2*b^5 - 13*B*a*b^6 + 2*(2*A + 3*C)*b^7 + (6*B*a^7 - (18*A + 13*C)*a^6*b + 4*B*a^5*b^2 + (23*A + 11*C)*a^4*b^3 - 11*B*a^3*b^4 - (7*A - 2*C)*a^2*b^5 + B*a*b^6 + 2*A*b^7)*cos(d*x + c)^2 + 3*(C*a^7 + 2*B*a^6*b - (9*A + 10*C)*a^5*b^2 + 7*B*a^4*b^3 + (8*A + 7*C)*a^3*b^4 - 10*B*a^2*b^5 + (A + 2*C)*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
927,1,2056,0,0.718819," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(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} - 4 \, {\left(2 \, A + C\right)} a^{6} b^{4} + 3 \, B a^{5} b^{5} + {\left(8 \, A - C\right)} a^{4} b^{6} - 7 \, A a^{2} b^{8} + 2 \, A b^{10} + {\left(2 \, B a^{10} - 4 \, {\left(2 \, A + C\right)} a^{9} b + 3 \, B a^{8} b^{2} + {\left(8 \, A - C\right)} 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 - 4 \, {\left(2 \, A + C\right)} a^{8} b^{2} + 3 \, B a^{7} b^{3} + {\left(8 \, A - C\right)} 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} - 4 \, {\left(2 \, A + C\right)} a^{7} b^{3} + 3 \, B a^{6} b^{4} + {\left(8 \, A - C\right)} 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(2 \, C a^{9} b^{2} - 11 \, B a^{8} b^{3} + {\left(26 \, A + 11 \, C\right)} a^{7} b^{4} + 7 \, B a^{6} b^{5} - {\left(43 \, A + 13 \, C\right)} a^{5} b^{6} + 4 \, B a^{4} b^{7} + 23 \, A a^{3} b^{8} - 6 \, A a b^{10} + {\left(6 \, C a^{11} - 18 \, B a^{10} b + 4 \, {\left(9 \, A + C\right)} a^{9} b^{2} + 23 \, B a^{8} b^{3} - {\left(68 \, A + 11 \, C\right)} a^{7} b^{4} - 7 \, B a^{6} b^{5} + {\left(43 \, A + C\right)} 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(2 \, C a^{10} b - 9 \, B a^{9} b^{2} + {\left(20 \, A + 7 \, C\right)} a^{8} b^{3} + 8 \, B a^{7} b^{4} - 5 \, {\left(7 \, A + 2 \, C\right)} a^{6} b^{5} + B a^{5} b^{6} + {\left(20 \, A + C\right)} 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} - 4 \, {\left(2 \, A + C\right)} a^{6} b^{4} + 3 \, B a^{5} b^{5} + {\left(8 \, A - C\right)} a^{4} b^{6} - 7 \, A a^{2} b^{8} + 2 \, A b^{10} + {\left(2 \, B a^{10} - 4 \, {\left(2 \, A + C\right)} a^{9} b + 3 \, B a^{8} b^{2} + {\left(8 \, A - C\right)} 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 - 4 \, {\left(2 \, A + C\right)} a^{8} b^{2} + 3 \, B a^{7} b^{3} + {\left(8 \, A - C\right)} 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} - 4 \, {\left(2 \, A + C\right)} a^{7} b^{3} + 3 \, B a^{6} b^{4} + {\left(8 \, A - C\right)} 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(2 \, C a^{9} b^{2} - 11 \, B a^{8} b^{3} + {\left(26 \, A + 11 \, C\right)} a^{7} b^{4} + 7 \, B a^{6} b^{5} - {\left(43 \, A + 13 \, C\right)} a^{5} b^{6} + 4 \, B a^{4} b^{7} + 23 \, A a^{3} b^{8} - 6 \, A a b^{10} + {\left(6 \, C a^{11} - 18 \, B a^{10} b + 4 \, {\left(9 \, A + C\right)} a^{9} b^{2} + 23 \, B a^{8} b^{3} - {\left(68 \, A + 11 \, C\right)} a^{7} b^{4} - 7 \, B a^{6} b^{5} + {\left(43 \, A + C\right)} 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(2 \, C a^{10} b - 9 \, B a^{9} b^{2} + {\left(20 \, A + 7 \, C\right)} a^{8} b^{3} + 8 \, B a^{7} b^{4} - 5 \, {\left(7 \, A + 2 \, C\right)} a^{6} b^{5} + B a^{5} b^{6} + {\left(20 \, A + C\right)} 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 - 4*(2*A + C)*a^6*b^4 + 3*B*a^5*b^5 + (8*A - C)*a^4*b^6 - 7*A*a^2*b^8 + 2*A*b^10 + (2*B*a^10 - 4*(2*A + C)*a^9*b + 3*B*a^8*b^2 + (8*A - C)*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 - 4*(2*A + C)*a^8*b^2 + 3*B*a^7*b^3 + (8*A - C)*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 - 4*(2*A + C)*a^7*b^3 + 3*B*a^6*b^4 + (8*A - C)*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*(2*C*a^9*b^2 - 11*B*a^8*b^3 + (26*A + 11*C)*a^7*b^4 + 7*B*a^6*b^5 - (43*A + 13*C)*a^5*b^6 + 4*B*a^4*b^7 + 23*A*a^3*b^8 - 6*A*a*b^10 + (6*C*a^11 - 18*B*a^10*b + 4*(9*A + C)*a^9*b^2 + 23*B*a^8*b^3 - (68*A + 11*C)*a^7*b^4 - 7*B*a^6*b^5 + (43*A + C)*a^5*b^6 + 2*B*a^4*b^7 - 11*A*a^3*b^8)*cos(d*x + c)^2 + 3*(2*C*a^10*b - 9*B*a^9*b^2 + (20*A + 7*C)*a^8*b^3 + 8*B*a^7*b^4 - 5*(7*A + 2*C)*a^6*b^5 + B*a^5*b^6 + (20*A + C)*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 - 4*(2*A + C)*a^6*b^4 + 3*B*a^5*b^5 + (8*A - C)*a^4*b^6 - 7*A*a^2*b^8 + 2*A*b^10 + (2*B*a^10 - 4*(2*A + C)*a^9*b + 3*B*a^8*b^2 + (8*A - C)*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 - 4*(2*A + C)*a^8*b^2 + 3*B*a^7*b^3 + (8*A - C)*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 - 4*(2*A + C)*a^7*b^3 + 3*B*a^6*b^4 + (8*A - C)*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))) + (2*C*a^9*b^2 - 11*B*a^8*b^3 + (26*A + 11*C)*a^7*b^4 + 7*B*a^6*b^5 - (43*A + 13*C)*a^5*b^6 + 4*B*a^4*b^7 + 23*A*a^3*b^8 - 6*A*a*b^10 + (6*C*a^11 - 18*B*a^10*b + 4*(9*A + C)*a^9*b^2 + 23*B*a^8*b^3 - (68*A + 11*C)*a^7*b^4 - 7*B*a^6*b^5 + (43*A + C)*a^5*b^6 + 2*B*a^4*b^7 - 11*A*a^3*b^8)*cos(d*x + c)^2 + 3*(2*C*a^10*b - 9*B*a^9*b^2 + (20*A + 7*C)*a^8*b^3 + 8*B*a^7*b^4 - 5*(7*A + 2*C)*a^6*b^5 + B*a^5*b^6 + (20*A + C)*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
928,1,2766,0,0.907374," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""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(2 \, C a^{8} b^{3} - 8 \, B a^{7} b^{4} + {\left(20 \, A + 3 \, C\right)} 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(2 \, C a^{11} - 8 \, B a^{10} b + {\left(20 \, A + 3 \, C\right)} 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(2 \, C a^{10} b - 8 \, B a^{9} b^{2} + {\left(20 \, A + 3 \, C\right)} 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(2 \, C a^{9} b^{2} - 8 \, B a^{8} b^{3} + {\left(20 \, A + 3 \, C\right)} 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({\left(6 \, A - 11 \, C\right)} a^{9} b^{3} + 26 \, B a^{8} b^{4} - {\left(71 \, A - 7 \, C\right)} a^{7} b^{5} - 43 \, B a^{6} b^{6} + {\left(133 \, A + 4 \, C\right)} 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 \, {\left(A - C\right)} a^{11} b + 36 \, B a^{10} b^{2} - {\left(132 \, A - 23 \, C\right)} a^{9} b^{3} - 68 \, B a^{8} b^{4} + {\left(239 \, A - 7 \, C\right)} a^{7} b^{5} + 43 \, B a^{6} b^{6} - {\left(169 \, A - 2 \, C\right)} 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(3 \, {\left(2 \, A - 3 \, C\right)} a^{10} b^{2} + 20 \, B a^{9} b^{3} - {\left(59 \, A - 8 \, C\right)} a^{8} b^{4} - 35 \, B a^{7} b^{5} + {\left(110 \, A + C\right)} 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(2 \, C a^{8} b^{3} - 8 \, B a^{7} b^{4} + {\left(20 \, A + 3 \, C\right)} 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(2 \, C a^{11} - 8 \, B a^{10} b + {\left(20 \, A + 3 \, C\right)} 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(2 \, C a^{10} b - 8 \, B a^{9} b^{2} + {\left(20 \, A + 3 \, C\right)} 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(2 \, C a^{9} b^{2} - 8 \, B a^{8} b^{3} + {\left(20 \, A + 3 \, C\right)} 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({\left(6 \, A - 11 \, C\right)} a^{9} b^{3} + 26 \, B a^{8} b^{4} - {\left(71 \, A - 7 \, C\right)} a^{7} b^{5} - 43 \, B a^{6} b^{6} + {\left(133 \, A + 4 \, C\right)} 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 \, {\left(A - C\right)} a^{11} b + 36 \, B a^{10} b^{2} - {\left(132 \, A - 23 \, C\right)} a^{9} b^{3} - 68 \, B a^{8} b^{4} + {\left(239 \, A - 7 \, C\right)} a^{7} b^{5} + 43 \, B a^{6} b^{6} - {\left(169 \, A - 2 \, C\right)} 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(3 \, {\left(2 \, A - 3 \, C\right)} a^{10} b^{2} + 20 \, B a^{9} b^{3} - {\left(59 \, A - 8 \, C\right)} a^{8} b^{4} - 35 \, B a^{7} b^{5} + {\left(110 \, A + C\right)} 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*(2*C*a^8*b^3 - 8*B*a^7*b^4 + (20*A + 3*C)*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 + (2*C*a^11 - 8*B*a^10*b + (20*A + 3*C)*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*(2*C*a^10*b - 8*B*a^9*b^2 + (20*A + 3*C)*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*(2*C*a^9*b^2 - 8*B*a^8*b^3 + (20*A + 3*C)*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 - 11*C)*a^9*b^3 + 26*B*a^8*b^4 - (71*A - 7*C)*a^7*b^5 - 43*B*a^6*b^6 + (133*A + 4*C)*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 - C)*a^11*b + 36*B*a^10*b^2 - (132*A - 23*C)*a^9*b^3 - 68*B*a^8*b^4 + (239*A - 7*C)*a^7*b^5 + 43*B*a^6*b^6 - (169*A - 2*C)*a^5*b^7 - 11*B*a^4*b^8 + 44*A*a^3*b^9)*cos(d*x + c)^2 + 3*(3*(2*A - 3*C)*a^10*b^2 + 20*B*a^9*b^3 - (59*A - 8*C)*a^8*b^4 - 35*B*a^7*b^5 + (110*A + C)*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*(2*C*a^8*b^3 - 8*B*a^7*b^4 + (20*A + 3*C)*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 + (2*C*a^11 - 8*B*a^10*b + (20*A + 3*C)*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*(2*C*a^10*b - 8*B*a^9*b^2 + (20*A + 3*C)*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*(2*C*a^9*b^2 - 8*B*a^8*b^3 + (20*A + 3*C)*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 - 11*C)*a^9*b^3 + 26*B*a^8*b^4 - (71*A - 7*C)*a^7*b^5 - 43*B*a^6*b^6 + (133*A + 4*C)*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 - C)*a^11*b + 36*B*a^10*b^2 - (132*A - 23*C)*a^9*b^3 - 68*B*a^8*b^4 + (239*A - 7*C)*a^7*b^5 + 43*B*a^6*b^6 - (169*A - 2*C)*a^5*b^7 - 11*B*a^4*b^8 + 44*A*a^3*b^9)*cos(d*x + c)^2 + 3*(3*(2*A - 3*C)*a^10*b^2 + 20*B*a^9*b^3 - (59*A - 8*C)*a^8*b^4 - 35*B*a^7*b^5 + (110*A + C)*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
929,1,3454,0,1.074486," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{6 \, {\left({\left(A + 2 \, C\right)} a^{13} - 8 \, B a^{12} b + 8 \, {\left(2 \, A - C\right)} a^{11} b^{2} + 32 \, B a^{10} b^{3} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{9} b^{4} - 48 \, B a^{8} b^{5} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{7} b^{6} + 32 \, B a^{6} b^{7} - {\left(79 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{12} b - 8 \, B a^{11} b^{2} + 8 \, {\left(2 \, A - C\right)} a^{10} b^{3} + 32 \, B a^{9} b^{4} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{8} b^{5} - 48 \, B a^{7} b^{6} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{6} b^{7} + 32 \, B a^{5} b^{8} - {\left(79 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{11} b^{2} - 8 \, B a^{10} b^{3} + 8 \, {\left(2 \, A - C\right)} a^{9} b^{4} + 32 \, B a^{8} b^{5} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{7} b^{6} - 48 \, B a^{6} b^{7} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{5} b^{8} + 32 \, B a^{4} b^{9} - {\left(79 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{10} b^{3} - 8 \, B a^{9} b^{4} + 8 \, {\left(2 \, A - C\right)} a^{8} b^{5} + 32 \, B a^{7} b^{6} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{6} b^{7} - 48 \, B a^{5} b^{8} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{4} b^{9} + 32 \, B a^{3} b^{10} - {\left(79 \, A - 2 \, C\right)} a^{2} b^{11} - 8 \, B a b^{12} + 20 \, A b^{13}\right)} d x + 3 \, {\left(8 \, C a^{8} b^{4} - 20 \, B a^{7} b^{5} + 8 \, {\left(5 \, A - C\right)} a^{6} b^{6} + 35 \, B a^{5} b^{7} - 7 \, {\left(12 \, A - C\right)} a^{4} b^{8} - 28 \, B a^{3} b^{9} + {\left(69 \, A - 2 \, C\right)} a^{2} b^{10} + 8 \, B a b^{11} - 20 \, A b^{12} + {\left(8 \, C a^{11} b - 20 \, B a^{10} b^{2} + 8 \, {\left(5 \, A - C\right)} a^{9} b^{3} + 35 \, B a^{8} b^{4} - 7 \, {\left(12 \, A - C\right)} a^{7} b^{5} - 28 \, B a^{6} b^{6} + {\left(69 \, A - 2 \, C\right)} 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(8 \, C a^{10} b^{2} - 20 \, B a^{9} b^{3} + 8 \, {\left(5 \, A - C\right)} a^{8} b^{4} + 35 \, B a^{7} b^{5} - 7 \, {\left(12 \, A - C\right)} a^{6} b^{6} - 28 \, B a^{5} b^{7} + {\left(69 \, A - 2 \, C\right)} 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(8 \, C a^{9} b^{3} - 20 \, B a^{8} b^{4} + 8 \, {\left(5 \, A - C\right)} a^{7} b^{5} + 35 \, B a^{6} b^{6} - 7 \, {\left(12 \, A - C\right)} a^{5} b^{7} - 28 \, B a^{4} b^{8} + {\left(69 \, A - 2 \, C\right)} 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} - 2 \, {\left(12 \, A - 13 \, C\right)} a^{9} b^{4} - 71 \, B a^{8} b^{5} + {\left(170 \, A - 43 \, C\right)} a^{7} b^{6} + 133 \, B a^{6} b^{7} - {\left(313 \, A - 23 \, C\right)} a^{5} b^{8} - 92 \, B a^{4} b^{9} + {\left(227 \, A - 6 \, C\right)} 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 - 9 \, {\left(7 \, A - 4 \, C\right)} a^{11} b^{2} - 132 \, B a^{10} b^{3} + 2 \, {\left(171 \, A - 34 \, C\right)} a^{9} b^{4} + 239 \, B a^{8} b^{5} - {\left(590 \, A - 43 \, C\right)} a^{7} b^{6} - 169 \, B a^{6} b^{7} + {\left(421 \, A - 11 \, C\right)} 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} - {\left(23 \, A - 20 \, C\right)} a^{10} b^{3} - 59 \, B a^{9} b^{4} + {\left(146 \, A - 35 \, C\right)} a^{8} b^{5} + 110 \, B a^{7} b^{6} - {\left(263 \, A - 20 \, C\right)} a^{6} b^{7} - 77 \, B a^{5} b^{8} + 5 \, {\left(38 \, A - C\right)} 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({\left(A + 2 \, C\right)} a^{13} - 8 \, B a^{12} b + 8 \, {\left(2 \, A - C\right)} a^{11} b^{2} + 32 \, B a^{10} b^{3} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{9} b^{4} - 48 \, B a^{8} b^{5} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{7} b^{6} + 32 \, B a^{6} b^{7} - {\left(79 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{12} b - 8 \, B a^{11} b^{2} + 8 \, {\left(2 \, A - C\right)} a^{10} b^{3} + 32 \, B a^{9} b^{4} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{8} b^{5} - 48 \, B a^{7} b^{6} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{6} b^{7} + 32 \, B a^{5} b^{8} - {\left(79 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{11} b^{2} - 8 \, B a^{10} b^{3} + 8 \, {\left(2 \, A - C\right)} a^{9} b^{4} + 32 \, B a^{8} b^{5} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{7} b^{6} - 48 \, B a^{6} b^{7} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{5} b^{8} + 32 \, B a^{4} b^{9} - {\left(79 \, A - 2 \, C\right)} 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({\left(A + 2 \, C\right)} a^{10} b^{3} - 8 \, B a^{9} b^{4} + 8 \, {\left(2 \, A - C\right)} a^{8} b^{5} + 32 \, B a^{7} b^{6} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{6} b^{7} - 48 \, B a^{5} b^{8} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{4} b^{9} + 32 \, B a^{3} b^{10} - {\left(79 \, A - 2 \, C\right)} a^{2} b^{11} - 8 \, B a b^{12} + 20 \, A b^{13}\right)} d x - 3 \, {\left(8 \, C a^{8} b^{4} - 20 \, B a^{7} b^{5} + 8 \, {\left(5 \, A - C\right)} a^{6} b^{6} + 35 \, B a^{5} b^{7} - 7 \, {\left(12 \, A - C\right)} a^{4} b^{8} - 28 \, B a^{3} b^{9} + {\left(69 \, A - 2 \, C\right)} a^{2} b^{10} + 8 \, B a b^{11} - 20 \, A b^{12} + {\left(8 \, C a^{11} b - 20 \, B a^{10} b^{2} + 8 \, {\left(5 \, A - C\right)} a^{9} b^{3} + 35 \, B a^{8} b^{4} - 7 \, {\left(12 \, A - C\right)} a^{7} b^{5} - 28 \, B a^{6} b^{6} + {\left(69 \, A - 2 \, C\right)} 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(8 \, C a^{10} b^{2} - 20 \, B a^{9} b^{3} + 8 \, {\left(5 \, A - C\right)} a^{8} b^{4} + 35 \, B a^{7} b^{5} - 7 \, {\left(12 \, A - C\right)} a^{6} b^{6} - 28 \, B a^{5} b^{7} + {\left(69 \, A - 2 \, C\right)} 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(8 \, C a^{9} b^{3} - 20 \, B a^{8} b^{4} + 8 \, {\left(5 \, A - C\right)} a^{7} b^{5} + 35 \, B a^{6} b^{6} - 7 \, {\left(12 \, A - C\right)} a^{5} b^{7} - 28 \, B a^{4} b^{8} + {\left(69 \, A - 2 \, C\right)} 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} - 2 \, {\left(12 \, A - 13 \, C\right)} a^{9} b^{4} - 71 \, B a^{8} b^{5} + {\left(170 \, A - 43 \, C\right)} a^{7} b^{6} + 133 \, B a^{6} b^{7} - {\left(313 \, A - 23 \, C\right)} a^{5} b^{8} - 92 \, B a^{4} b^{9} + {\left(227 \, A - 6 \, C\right)} 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 - 9 \, {\left(7 \, A - 4 \, C\right)} a^{11} b^{2} - 132 \, B a^{10} b^{3} + 2 \, {\left(171 \, A - 34 \, C\right)} a^{9} b^{4} + 239 \, B a^{8} b^{5} - {\left(590 \, A - 43 \, C\right)} a^{7} b^{6} - 169 \, B a^{6} b^{7} + {\left(421 \, A - 11 \, C\right)} 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} - {\left(23 \, A - 20 \, C\right)} a^{10} b^{3} - 59 \, B a^{9} b^{4} + {\left(146 \, A - 35 \, C\right)} a^{8} b^{5} + 110 \, B a^{7} b^{6} - {\left(263 \, A - 20 \, C\right)} a^{6} b^{7} - 77 \, B a^{5} b^{8} + 5 \, {\left(38 \, A - C\right)} 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 + 2*C)*a^13 - 8*B*a^12*b + 8*(2*A - C)*a^11*b^2 + 32*B*a^10*b^3 - 2*(37*A - 6*C)*a^9*b^4 - 48*B*a^8*b^5 + 4*(29*A - 2*C)*a^7*b^6 + 32*B*a^6*b^7 - (79*A - 2*C)*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 + 2*C)*a^12*b - 8*B*a^11*b^2 + 8*(2*A - C)*a^10*b^3 + 32*B*a^9*b^4 - 2*(37*A - 6*C)*a^8*b^5 - 48*B*a^7*b^6 + 4*(29*A - 2*C)*a^6*b^7 + 32*B*a^5*b^8 - (79*A - 2*C)*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 + 2*C)*a^11*b^2 - 8*B*a^10*b^3 + 8*(2*A - C)*a^9*b^4 + 32*B*a^8*b^5 - 2*(37*A - 6*C)*a^7*b^6 - 48*B*a^6*b^7 + 4*(29*A - 2*C)*a^5*b^8 + 32*B*a^4*b^9 - (79*A - 2*C)*a^3*b^10 - 8*B*a^2*b^11 + 20*A*a*b^12)*d*x*cos(d*x + c) + 6*((A + 2*C)*a^10*b^3 - 8*B*a^9*b^4 + 8*(2*A - C)*a^8*b^5 + 32*B*a^7*b^6 - 2*(37*A - 6*C)*a^6*b^7 - 48*B*a^5*b^8 + 4*(29*A - 2*C)*a^4*b^9 + 32*B*a^3*b^10 - (79*A - 2*C)*a^2*b^11 - 8*B*a*b^12 + 20*A*b^13)*d*x + 3*(8*C*a^8*b^4 - 20*B*a^7*b^5 + 8*(5*A - C)*a^6*b^6 + 35*B*a^5*b^7 - 7*(12*A - C)*a^4*b^8 - 28*B*a^3*b^9 + (69*A - 2*C)*a^2*b^10 + 8*B*a*b^11 - 20*A*b^12 + (8*C*a^11*b - 20*B*a^10*b^2 + 8*(5*A - C)*a^9*b^3 + 35*B*a^8*b^4 - 7*(12*A - C)*a^7*b^5 - 28*B*a^6*b^6 + (69*A - 2*C)*a^5*b^7 + 8*B*a^4*b^8 - 20*A*a^3*b^9)*cos(d*x + c)^3 + 3*(8*C*a^10*b^2 - 20*B*a^9*b^3 + 8*(5*A - C)*a^8*b^4 + 35*B*a^7*b^5 - 7*(12*A - C)*a^6*b^6 - 28*B*a^5*b^7 + (69*A - 2*C)*a^4*b^8 + 8*B*a^3*b^9 - 20*A*a^2*b^10)*cos(d*x + c)^2 + 3*(8*C*a^9*b^3 - 20*B*a^8*b^4 + 8*(5*A - C)*a^7*b^5 + 35*B*a^6*b^6 - 7*(12*A - C)*a^5*b^7 - 28*B*a^4*b^8 + (69*A - 2*C)*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 - 2*(12*A - 13*C)*a^9*b^4 - 71*B*a^8*b^5 + (170*A - 43*C)*a^7*b^6 + 133*B*a^6*b^7 - (313*A - 23*C)*a^5*b^8 - 92*B*a^4*b^9 + (227*A - 6*C)*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 - 9*(7*A - 4*C)*a^11*b^2 - 132*B*a^10*b^3 + 2*(171*A - 34*C)*a^9*b^4 + 239*B*a^8*b^5 - (590*A - 43*C)*a^7*b^6 - 169*B*a^6*b^7 + (421*A - 11*C)*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 - 20*C)*a^10*b^3 - 59*B*a^9*b^4 + (146*A - 35*C)*a^8*b^5 + 110*B*a^7*b^6 - (263*A - 20*C)*a^6*b^7 - 77*B*a^5*b^8 + 5*(38*A - C)*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 + 2*C)*a^13 - 8*B*a^12*b + 8*(2*A - C)*a^11*b^2 + 32*B*a^10*b^3 - 2*(37*A - 6*C)*a^9*b^4 - 48*B*a^8*b^5 + 4*(29*A - 2*C)*a^7*b^6 + 32*B*a^6*b^7 - (79*A - 2*C)*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 + 2*C)*a^12*b - 8*B*a^11*b^2 + 8*(2*A - C)*a^10*b^3 + 32*B*a^9*b^4 - 2*(37*A - 6*C)*a^8*b^5 - 48*B*a^7*b^6 + 4*(29*A - 2*C)*a^6*b^7 + 32*B*a^5*b^8 - (79*A - 2*C)*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 + 2*C)*a^11*b^2 - 8*B*a^10*b^3 + 8*(2*A - C)*a^9*b^4 + 32*B*a^8*b^5 - 2*(37*A - 6*C)*a^7*b^6 - 48*B*a^6*b^7 + 4*(29*A - 2*C)*a^5*b^8 + 32*B*a^4*b^9 - (79*A - 2*C)*a^3*b^10 - 8*B*a^2*b^11 + 20*A*a*b^12)*d*x*cos(d*x + c) + 3*((A + 2*C)*a^10*b^3 - 8*B*a^9*b^4 + 8*(2*A - C)*a^8*b^5 + 32*B*a^7*b^6 - 2*(37*A - 6*C)*a^6*b^7 - 48*B*a^5*b^8 + 4*(29*A - 2*C)*a^4*b^9 + 32*B*a^3*b^10 - (79*A - 2*C)*a^2*b^11 - 8*B*a*b^12 + 20*A*b^13)*d*x - 3*(8*C*a^8*b^4 - 20*B*a^7*b^5 + 8*(5*A - C)*a^6*b^6 + 35*B*a^5*b^7 - 7*(12*A - C)*a^4*b^8 - 28*B*a^3*b^9 + (69*A - 2*C)*a^2*b^10 + 8*B*a*b^11 - 20*A*b^12 + (8*C*a^11*b - 20*B*a^10*b^2 + 8*(5*A - C)*a^9*b^3 + 35*B*a^8*b^4 - 7*(12*A - C)*a^7*b^5 - 28*B*a^6*b^6 + (69*A - 2*C)*a^5*b^7 + 8*B*a^4*b^8 - 20*A*a^3*b^9)*cos(d*x + c)^3 + 3*(8*C*a^10*b^2 - 20*B*a^9*b^3 + 8*(5*A - C)*a^8*b^4 + 35*B*a^7*b^5 - 7*(12*A - C)*a^6*b^6 - 28*B*a^5*b^7 + (69*A - 2*C)*a^4*b^8 + 8*B*a^3*b^9 - 20*A*a^2*b^10)*cos(d*x + c)^2 + 3*(8*C*a^9*b^3 - 20*B*a^8*b^4 + 8*(5*A - C)*a^7*b^5 + 35*B*a^6*b^6 - 7*(12*A - C)*a^5*b^7 - 28*B*a^4*b^8 + (69*A - 2*C)*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 - 2*(12*A - 13*C)*a^9*b^4 - 71*B*a^8*b^5 + (170*A - 43*C)*a^7*b^6 + 133*B*a^6*b^7 - (313*A - 23*C)*a^5*b^8 - 92*B*a^4*b^9 + (227*A - 6*C)*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 - 9*(7*A - 4*C)*a^11*b^2 - 132*B*a^10*b^3 + 2*(171*A - 34*C)*a^9*b^4 + 239*B*a^8*b^5 - (590*A - 43*C)*a^7*b^6 - 169*B*a^6*b^7 + (421*A - 11*C)*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 - 20*C)*a^10*b^3 - 59*B*a^9*b^4 + (146*A - 35*C)*a^8*b^5 + 110*B*a^7*b^6 - (263*A - 20*C)*a^6*b^7 - 77*B*a^5*b^8 + 5*(38*A - C)*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
930,1,45,0,0.490055," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(C a - B b\right)} d x - C b \log\left(\sin\left(d x + c\right) + 1\right) + C b \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, d}"," ",0,"-1/2*(2*(C*a - B*b)*d*x - C*b*log(sin(d*x + c) + 1) + C*b*log(-sin(d*x + c) + 1))/d","A",0
931,1,285,0,0.535363," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} d x + {\left(2 \, C a b - B 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^{3} - a b^{2}\right)} d}, -\frac{{\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} d x - {\left(2 \, C a b - B 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^{3} - a b^{2}\right)} d}\right]"," ",0,"[-1/2*(2*(C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*d*x + (2*C*a*b - B*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)))/((a^3 - a*b^2)*d), -((C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*d*x - (2*C*a*b - B*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^3 - a*b^2)*d)]","A",0
932,1,714,0,0.609389," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(C a^{6} - B a^{5} b - 2 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + C a^{2} b^{4} - B a b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{5} b - B a^{4} b^{2} - 2 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + C a b^{5} - B b^{6}\right)} d x - {\left(3 \, C a^{3} b^{2} - 2 \, B a^{2} b^{3} - C a b^{4} + B b^{5} + {\left(3 \, C a^{4} b - 2 \, B a^{3} b^{2} - C a^{2} b^{3} + B 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(2 \, C a^{4} b^{2} - B a^{3} b^{3} - 2 \, C a^{2} b^{4} + B a b^{5}\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(C a^{6} - B a^{5} b - 2 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + C a^{2} b^{4} - B a b^{5}\right)} d x \cos\left(d x + c\right) + {\left(C a^{5} b - B a^{4} b^{2} - 2 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + C a b^{5} - B b^{6}\right)} d x - {\left(3 \, C a^{3} b^{2} - 2 \, B a^{2} b^{3} - C a b^{4} + B b^{5} + {\left(3 \, C a^{4} b - 2 \, B a^{3} b^{2} - C a^{2} b^{3} + B 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(2 \, C a^{4} b^{2} - B a^{3} b^{3} - 2 \, C a^{2} b^{4} + B a b^{5}\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*(C*a^6 - B*a^5*b - 2*C*a^4*b^2 + 2*B*a^3*b^3 + C*a^2*b^4 - B*a*b^5)*d*x*cos(d*x + c) + 2*(C*a^5*b - B*a^4*b^2 - 2*C*a^3*b^3 + 2*B*a^2*b^4 + C*a*b^5 - B*b^6)*d*x - (3*C*a^3*b^2 - 2*B*a^2*b^3 - C*a*b^4 + B*b^5 + (3*C*a^4*b - 2*B*a^3*b^2 - C*a^2*b^3 + B*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*(2*C*a^4*b^2 - B*a^3*b^3 - 2*C*a^2*b^4 + B*a*b^5)*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), -((C*a^6 - B*a^5*b - 2*C*a^4*b^2 + 2*B*a^3*b^3 + C*a^2*b^4 - B*a*b^5)*d*x*cos(d*x + c) + (C*a^5*b - B*a^4*b^2 - 2*C*a^3*b^3 + 2*B*a^2*b^4 + C*a*b^5 - B*b^6)*d*x - (3*C*a^3*b^2 - 2*B*a^2*b^3 - C*a*b^4 + B*b^5 + (3*C*a^4*b - 2*B*a^3*b^2 - C*a^2*b^3 + B*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*C*a^4*b^2 - B*a^3*b^3 - 2*C*a^2*b^4 + B*a*b^5)*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
933,1,1443,0,0.736792," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(C a^{9} - B a^{8} b - 3 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - C a^{3} b^{6} + B a^{2} b^{7}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(C a^{8} b - B a^{7} b^{2} - 3 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - C a^{2} b^{7} + B a b^{8}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(C a^{7} b^{2} - B a^{6} b^{3} - 3 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - C a b^{8} + B b^{9}\right)} d x + {\left(8 \, C a^{5} b^{3} - 6 \, B a^{4} b^{4} - 4 \, C a^{3} b^{5} + 5 \, B a^{2} b^{6} + 2 \, C a b^{7} - 2 \, B b^{8} + {\left(8 \, C a^{7} b - 6 \, B a^{6} b^{2} - 4 \, C a^{5} b^{3} + 5 \, B a^{4} b^{4} + 2 \, C a^{3} b^{5} - 2 \, B a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, C a^{6} b^{2} - 6 \, B a^{5} b^{3} - 4 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 2 \, C a^{2} b^{6} - 2 \, B 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(8 \, C a^{6} b^{3} - 5 \, B a^{5} b^{4} - 10 \, C a^{4} b^{5} + 7 \, B a^{3} b^{6} + 2 \, C a^{2} b^{7} - 2 \, B a b^{8} + {\left(10 \, C a^{7} b^{2} - 6 \, B a^{6} b^{3} - 14 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 4 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7}\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(C a^{9} - B a^{8} b - 3 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - C a^{3} b^{6} + B a^{2} b^{7}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(C a^{8} b - B a^{7} b^{2} - 3 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - C a^{2} b^{7} + B a b^{8}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{7} b^{2} - B a^{6} b^{3} - 3 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - C a b^{8} + B b^{9}\right)} d x - {\left(8 \, C a^{5} b^{3} - 6 \, B a^{4} b^{4} - 4 \, C a^{3} b^{5} + 5 \, B a^{2} b^{6} + 2 \, C a b^{7} - 2 \, B b^{8} + {\left(8 \, C a^{7} b - 6 \, B a^{6} b^{2} - 4 \, C a^{5} b^{3} + 5 \, B a^{4} b^{4} + 2 \, C a^{3} b^{5} - 2 \, B a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, C a^{6} b^{2} - 6 \, B a^{5} b^{3} - 4 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 2 \, C a^{2} b^{6} - 2 \, B 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(8 \, C a^{6} b^{3} - 5 \, B a^{5} b^{4} - 10 \, C a^{4} b^{5} + 7 \, B a^{3} b^{6} + 2 \, C a^{2} b^{7} - 2 \, B a b^{8} + {\left(10 \, C a^{7} b^{2} - 6 \, B a^{6} b^{3} - 14 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 4 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7}\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*(C*a^9 - B*a^8*b - 3*C*a^7*b^2 + 3*B*a^6*b^3 + 3*C*a^5*b^4 - 3*B*a^4*b^5 - C*a^3*b^6 + B*a^2*b^7)*d*x*cos(d*x + c)^2 + 8*(C*a^8*b - B*a^7*b^2 - 3*C*a^6*b^3 + 3*B*a^5*b^4 + 3*C*a^4*b^5 - 3*B*a^3*b^6 - C*a^2*b^7 + B*a*b^8)*d*x*cos(d*x + c) + 4*(C*a^7*b^2 - B*a^6*b^3 - 3*C*a^5*b^4 + 3*B*a^4*b^5 + 3*C*a^3*b^6 - 3*B*a^2*b^7 - C*a*b^8 + B*b^9)*d*x + (8*C*a^5*b^3 - 6*B*a^4*b^4 - 4*C*a^3*b^5 + 5*B*a^2*b^6 + 2*C*a*b^7 - 2*B*b^8 + (8*C*a^7*b - 6*B*a^6*b^2 - 4*C*a^5*b^3 + 5*B*a^4*b^4 + 2*C*a^3*b^5 - 2*B*a^2*b^6)*cos(d*x + c)^2 + 2*(8*C*a^6*b^2 - 6*B*a^5*b^3 - 4*C*a^4*b^4 + 5*B*a^3*b^5 + 2*C*a^2*b^6 - 2*B*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*(8*C*a^6*b^3 - 5*B*a^5*b^4 - 10*C*a^4*b^5 + 7*B*a^3*b^6 + 2*C*a^2*b^7 - 2*B*a*b^8 + (10*C*a^7*b^2 - 6*B*a^6*b^3 - 14*C*a^5*b^4 + 9*B*a^4*b^5 + 4*C*a^3*b^6 - 3*B*a^2*b^7)*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*(C*a^9 - B*a^8*b - 3*C*a^7*b^2 + 3*B*a^6*b^3 + 3*C*a^5*b^4 - 3*B*a^4*b^5 - C*a^3*b^6 + B*a^2*b^7)*d*x*cos(d*x + c)^2 + 4*(C*a^8*b - B*a^7*b^2 - 3*C*a^6*b^3 + 3*B*a^5*b^4 + 3*C*a^4*b^5 - 3*B*a^3*b^6 - C*a^2*b^7 + B*a*b^8)*d*x*cos(d*x + c) + 2*(C*a^7*b^2 - B*a^6*b^3 - 3*C*a^5*b^4 + 3*B*a^4*b^5 + 3*C*a^3*b^6 - 3*B*a^2*b^7 - C*a*b^8 + B*b^9)*d*x - (8*C*a^5*b^3 - 6*B*a^4*b^4 - 4*C*a^3*b^5 + 5*B*a^2*b^6 + 2*C*a*b^7 - 2*B*b^8 + (8*C*a^7*b - 6*B*a^6*b^2 - 4*C*a^5*b^3 + 5*B*a^4*b^4 + 2*C*a^3*b^5 - 2*B*a^2*b^6)*cos(d*x + c)^2 + 2*(8*C*a^6*b^2 - 6*B*a^5*b^3 - 4*C*a^4*b^4 + 5*B*a^3*b^5 + 2*C*a^2*b^6 - 2*B*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))) + (8*C*a^6*b^3 - 5*B*a^5*b^4 - 10*C*a^4*b^5 + 7*B*a^3*b^6 + 2*C*a^2*b^7 - 2*B*a*b^8 + (10*C*a^7*b^2 - 6*B*a^6*b^3 - 14*C*a^5*b^4 + 9*B*a^4*b^5 + 4*C*a^3*b^6 - 3*B*a^2*b^7)*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
934,1,2408,0,1.064192," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^5,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(C a^{12} - B a^{11} b - 4 \, C a^{10} b^{2} + 4 \, B a^{9} b^{3} + 6 \, C a^{8} b^{4} - 6 \, B a^{7} b^{5} - 4 \, C a^{6} b^{6} + 4 \, B a^{5} b^{7} + C a^{4} b^{8} - B a^{3} b^{9}\right)} d x \cos\left(d x + c\right)^{3} + 36 \, {\left(C a^{11} b - B a^{10} b^{2} - 4 \, C a^{9} b^{3} + 4 \, B a^{8} b^{4} + 6 \, C a^{7} b^{5} - 6 \, B a^{6} b^{6} - 4 \, C a^{5} b^{7} + 4 \, B a^{4} b^{8} + C a^{3} b^{9} - B a^{2} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 36 \, {\left(C a^{10} b^{2} - B a^{9} b^{3} - 4 \, C a^{8} b^{4} + 4 \, B a^{7} b^{5} + 6 \, C a^{6} b^{6} - 6 \, B a^{5} b^{7} - 4 \, C a^{4} b^{8} + 4 \, B a^{3} b^{9} + C a^{2} b^{10} - B a b^{11}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(C a^{9} b^{3} - B a^{8} b^{4} - 4 \, C a^{7} b^{5} + 4 \, B a^{6} b^{6} + 6 \, C a^{5} b^{7} - 6 \, B a^{4} b^{8} - 4 \, C a^{3} b^{9} + 4 \, B a^{2} b^{10} + C a b^{11} - B b^{12}\right)} d x + 3 \, {\left(10 \, C a^{7} b^{4} - 8 \, B a^{6} b^{5} - 5 \, C a^{5} b^{6} + 8 \, B a^{4} b^{7} + 7 \, C a^{3} b^{8} - 7 \, B a^{2} b^{9} - 2 \, C a b^{10} + 2 \, B b^{11} + {\left(10 \, C a^{10} b - 8 \, B a^{9} b^{2} - 5 \, C a^{8} b^{3} + 8 \, B a^{7} b^{4} + 7 \, C a^{6} b^{5} - 7 \, B a^{5} b^{6} - 2 \, C a^{4} b^{7} + 2 \, B a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(10 \, C a^{9} b^{2} - 8 \, B a^{8} b^{3} - 5 \, C a^{7} b^{4} + 8 \, B a^{6} b^{5} + 7 \, C a^{5} b^{6} - 7 \, B a^{4} b^{7} - 2 \, C a^{3} b^{8} + 2 \, B a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(10 \, C a^{8} b^{3} - 8 \, B a^{7} b^{4} - 5 \, C a^{6} b^{5} + 8 \, B a^{5} b^{6} + 7 \, C a^{4} b^{7} - 7 \, B a^{3} b^{8} - 2 \, C a^{2} b^{9} + 2 \, B 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(37 \, C a^{8} b^{4} - 26 \, B a^{7} b^{5} - 50 \, C a^{6} b^{6} + 43 \, B a^{5} b^{7} + 19 \, C a^{4} b^{8} - 23 \, B a^{3} b^{9} - 6 \, C a^{2} b^{10} + 6 \, B a b^{11} + {\left(54 \, C a^{10} b^{2} - 36 \, B a^{9} b^{3} - 91 \, C a^{8} b^{4} + 68 \, B a^{7} b^{5} + 50 \, C a^{6} b^{6} - 43 \, B a^{5} b^{7} - 13 \, C a^{4} b^{8} + 11 \, B a^{3} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(29 \, C a^{9} b^{3} - 20 \, B a^{8} b^{4} - 43 \, C a^{7} b^{5} + 35 \, B a^{6} b^{6} + 19 \, C a^{5} b^{7} - 20 \, B a^{4} b^{8} - 5 \, C a^{3} b^{9} + 5 \, B a^{2} b^{10}\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(C a^{12} - B a^{11} b - 4 \, C a^{10} b^{2} + 4 \, B a^{9} b^{3} + 6 \, C a^{8} b^{4} - 6 \, B a^{7} b^{5} - 4 \, C a^{6} b^{6} + 4 \, B a^{5} b^{7} + C a^{4} b^{8} - B a^{3} b^{9}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(C a^{11} b - B a^{10} b^{2} - 4 \, C a^{9} b^{3} + 4 \, B a^{8} b^{4} + 6 \, C a^{7} b^{5} - 6 \, B a^{6} b^{6} - 4 \, C a^{5} b^{7} + 4 \, B a^{4} b^{8} + C a^{3} b^{9} - B a^{2} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(C a^{10} b^{2} - B a^{9} b^{3} - 4 \, C a^{8} b^{4} + 4 \, B a^{7} b^{5} + 6 \, C a^{6} b^{6} - 6 \, B a^{5} b^{7} - 4 \, C a^{4} b^{8} + 4 \, B a^{3} b^{9} + C a^{2} b^{10} - B a b^{11}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(C a^{9} b^{3} - B a^{8} b^{4} - 4 \, C a^{7} b^{5} + 4 \, B a^{6} b^{6} + 6 \, C a^{5} b^{7} - 6 \, B a^{4} b^{8} - 4 \, C a^{3} b^{9} + 4 \, B a^{2} b^{10} + C a b^{11} - B b^{12}\right)} d x - 3 \, {\left(10 \, C a^{7} b^{4} - 8 \, B a^{6} b^{5} - 5 \, C a^{5} b^{6} + 8 \, B a^{4} b^{7} + 7 \, C a^{3} b^{8} - 7 \, B a^{2} b^{9} - 2 \, C a b^{10} + 2 \, B b^{11} + {\left(10 \, C a^{10} b - 8 \, B a^{9} b^{2} - 5 \, C a^{8} b^{3} + 8 \, B a^{7} b^{4} + 7 \, C a^{6} b^{5} - 7 \, B a^{5} b^{6} - 2 \, C a^{4} b^{7} + 2 \, B a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(10 \, C a^{9} b^{2} - 8 \, B a^{8} b^{3} - 5 \, C a^{7} b^{4} + 8 \, B a^{6} b^{5} + 7 \, C a^{5} b^{6} - 7 \, B a^{4} b^{7} - 2 \, C a^{3} b^{8} + 2 \, B a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(10 \, C a^{8} b^{3} - 8 \, B a^{7} b^{4} - 5 \, C a^{6} b^{5} + 8 \, B a^{5} b^{6} + 7 \, C a^{4} b^{7} - 7 \, B a^{3} b^{8} - 2 \, C a^{2} b^{9} + 2 \, B 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(37 \, C a^{8} b^{4} - 26 \, B a^{7} b^{5} - 50 \, C a^{6} b^{6} + 43 \, B a^{5} b^{7} + 19 \, C a^{4} b^{8} - 23 \, B a^{3} b^{9} - 6 \, C a^{2} b^{10} + 6 \, B a b^{11} + {\left(54 \, C a^{10} b^{2} - 36 \, B a^{9} b^{3} - 91 \, C a^{8} b^{4} + 68 \, B a^{7} b^{5} + 50 \, C a^{6} b^{6} - 43 \, B a^{5} b^{7} - 13 \, C a^{4} b^{8} + 11 \, B a^{3} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(29 \, C a^{9} b^{3} - 20 \, B a^{8} b^{4} - 43 \, C a^{7} b^{5} + 35 \, B a^{6} b^{6} + 19 \, C a^{5} b^{7} - 20 \, B a^{4} b^{8} - 5 \, C a^{3} b^{9} + 5 \, B a^{2} b^{10}\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*(C*a^12 - B*a^11*b - 4*C*a^10*b^2 + 4*B*a^9*b^3 + 6*C*a^8*b^4 - 6*B*a^7*b^5 - 4*C*a^6*b^6 + 4*B*a^5*b^7 + C*a^4*b^8 - B*a^3*b^9)*d*x*cos(d*x + c)^3 + 36*(C*a^11*b - B*a^10*b^2 - 4*C*a^9*b^3 + 4*B*a^8*b^4 + 6*C*a^7*b^5 - 6*B*a^6*b^6 - 4*C*a^5*b^7 + 4*B*a^4*b^8 + C*a^3*b^9 - B*a^2*b^10)*d*x*cos(d*x + c)^2 + 36*(C*a^10*b^2 - B*a^9*b^3 - 4*C*a^8*b^4 + 4*B*a^7*b^5 + 6*C*a^6*b^6 - 6*B*a^5*b^7 - 4*C*a^4*b^8 + 4*B*a^3*b^9 + C*a^2*b^10 - B*a*b^11)*d*x*cos(d*x + c) + 12*(C*a^9*b^3 - B*a^8*b^4 - 4*C*a^7*b^5 + 4*B*a^6*b^6 + 6*C*a^5*b^7 - 6*B*a^4*b^8 - 4*C*a^3*b^9 + 4*B*a^2*b^10 + C*a*b^11 - B*b^12)*d*x + 3*(10*C*a^7*b^4 - 8*B*a^6*b^5 - 5*C*a^5*b^6 + 8*B*a^4*b^7 + 7*C*a^3*b^8 - 7*B*a^2*b^9 - 2*C*a*b^10 + 2*B*b^11 + (10*C*a^10*b - 8*B*a^9*b^2 - 5*C*a^8*b^3 + 8*B*a^7*b^4 + 7*C*a^6*b^5 - 7*B*a^5*b^6 - 2*C*a^4*b^7 + 2*B*a^3*b^8)*cos(d*x + c)^3 + 3*(10*C*a^9*b^2 - 8*B*a^8*b^3 - 5*C*a^7*b^4 + 8*B*a^6*b^5 + 7*C*a^5*b^6 - 7*B*a^4*b^7 - 2*C*a^3*b^8 + 2*B*a^2*b^9)*cos(d*x + c)^2 + 3*(10*C*a^8*b^3 - 8*B*a^7*b^4 - 5*C*a^6*b^5 + 8*B*a^5*b^6 + 7*C*a^4*b^7 - 7*B*a^3*b^8 - 2*C*a^2*b^9 + 2*B*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*(37*C*a^8*b^4 - 26*B*a^7*b^5 - 50*C*a^6*b^6 + 43*B*a^5*b^7 + 19*C*a^4*b^8 - 23*B*a^3*b^9 - 6*C*a^2*b^10 + 6*B*a*b^11 + (54*C*a^10*b^2 - 36*B*a^9*b^3 - 91*C*a^8*b^4 + 68*B*a^7*b^5 + 50*C*a^6*b^6 - 43*B*a^5*b^7 - 13*C*a^4*b^8 + 11*B*a^3*b^9)*cos(d*x + c)^2 + 3*(29*C*a^9*b^3 - 20*B*a^8*b^4 - 43*C*a^7*b^5 + 35*B*a^6*b^6 + 19*C*a^5*b^7 - 20*B*a^4*b^8 - 5*C*a^3*b^9 + 5*B*a^2*b^10)*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*(C*a^12 - B*a^11*b - 4*C*a^10*b^2 + 4*B*a^9*b^3 + 6*C*a^8*b^4 - 6*B*a^7*b^5 - 4*C*a^6*b^6 + 4*B*a^5*b^7 + C*a^4*b^8 - B*a^3*b^9)*d*x*cos(d*x + c)^3 + 18*(C*a^11*b - B*a^10*b^2 - 4*C*a^9*b^3 + 4*B*a^8*b^4 + 6*C*a^7*b^5 - 6*B*a^6*b^6 - 4*C*a^5*b^7 + 4*B*a^4*b^8 + C*a^3*b^9 - B*a^2*b^10)*d*x*cos(d*x + c)^2 + 18*(C*a^10*b^2 - B*a^9*b^3 - 4*C*a^8*b^4 + 4*B*a^7*b^5 + 6*C*a^6*b^6 - 6*B*a^5*b^7 - 4*C*a^4*b^8 + 4*B*a^3*b^9 + C*a^2*b^10 - B*a*b^11)*d*x*cos(d*x + c) + 6*(C*a^9*b^3 - B*a^8*b^4 - 4*C*a^7*b^5 + 4*B*a^6*b^6 + 6*C*a^5*b^7 - 6*B*a^4*b^8 - 4*C*a^3*b^9 + 4*B*a^2*b^10 + C*a*b^11 - B*b^12)*d*x - 3*(10*C*a^7*b^4 - 8*B*a^6*b^5 - 5*C*a^5*b^6 + 8*B*a^4*b^7 + 7*C*a^3*b^8 - 7*B*a^2*b^9 - 2*C*a*b^10 + 2*B*b^11 + (10*C*a^10*b - 8*B*a^9*b^2 - 5*C*a^8*b^3 + 8*B*a^7*b^4 + 7*C*a^6*b^5 - 7*B*a^5*b^6 - 2*C*a^4*b^7 + 2*B*a^3*b^8)*cos(d*x + c)^3 + 3*(10*C*a^9*b^2 - 8*B*a^8*b^3 - 5*C*a^7*b^4 + 8*B*a^6*b^5 + 7*C*a^5*b^6 - 7*B*a^4*b^7 - 2*C*a^3*b^8 + 2*B*a^2*b^9)*cos(d*x + c)^2 + 3*(10*C*a^8*b^3 - 8*B*a^7*b^4 - 5*C*a^6*b^5 + 8*B*a^5*b^6 + 7*C*a^4*b^7 - 7*B*a^3*b^8 - 2*C*a^2*b^9 + 2*B*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))) + (37*C*a^8*b^4 - 26*B*a^7*b^5 - 50*C*a^6*b^6 + 43*B*a^5*b^7 + 19*C*a^4*b^8 - 23*B*a^3*b^9 - 6*C*a^2*b^10 + 6*B*a*b^11 + (54*C*a^10*b^2 - 36*B*a^9*b^3 - 91*C*a^8*b^4 + 68*B*a^7*b^5 + 50*C*a^6*b^6 - 43*B*a^5*b^7 - 13*C*a^4*b^8 + 11*B*a^3*b^9)*cos(d*x + c)^2 + 3*(29*C*a^9*b^3 - 20*B*a^8*b^4 - 43*C*a^7*b^5 + 35*B*a^6*b^6 + 19*C*a^5*b^7 - 20*B*a^4*b^8 - 5*C*a^3*b^9 + 5*B*a^2*b^10)*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
935,0,0,0,0.562806," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{5} + 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((C*sec(d*x + c)^5 + B*sec(d*x + c)^4 + A*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
936,0,0,0,0.522274," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + B*sec(d*x + c)^3 + A*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
937,0,0,0,0.472035," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + B*sec(d*x + c)^2 + A*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
938,0,0,0,0.898669," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a), x)","F",0
939,0,0,0,1.312383," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
940,0,0,0,2.180093," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
941,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
942,0,0,0,1.911911," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{6} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^6 + (C*a + 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
943,0,0,0,0.746029," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{5} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^5 + (C*a + 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
944,0,0,0,0.634239," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{4} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^4 + (C*a + 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
945,0,0,0,26.777215," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
946,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
947,0,0,0,2.173009," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^2*sec(d*x + c)^3 + (C*a + 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
948,0,0,0,2.970790," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3*sec(d*x + c)^3 + (C*a + 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
949,0,0,0,86.977189," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^4*sec(d*x + c)^3 + (C*a + 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), x)","F",0
950,0,0,0,0.574023," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{6} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{5} + A a^{2} \sec\left(d x + c\right)^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^6 + (2*C*a*b + B*b^2)*sec(d*x + c)^5 + A*a^2*sec(d*x + c)^2 + (C*a^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
951,0,0,0,0.530557," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{5} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{4} + A a^{2} \sec\left(d x + c\right) + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^5 + (2*C*a*b + B*b^2)*sec(d*x + c)^4 + A*a^2*sec(d*x + c) + (C*a^2 + 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
952,0,0,0,0.932295," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
953,0,0,0,1.398894," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right) + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)*sec(d*x + c)^3 + A*a^2*cos(d*x + c) + (C*a^2 + 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
954,0,0,0,2.250018," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \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(C a^{2} + 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((C*b^2*cos(d*x + c)^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^2*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^2 + (C*a^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
955,0,0,0,79.247832," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \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(C a^{2} + 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((C*b^2*cos(d*x + c)^3*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^3 + (C*a^2 + 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
956,0,0,0,4.739750," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \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(C a^{2} + 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((C*b^2*cos(d*x + c)^4*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^4*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^4 + (C*a^2 + 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
957,0,0,0,96.906299," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \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(C a^{2} + 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}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^5*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^5*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^5 + (C*a^2 + 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), x)","F",0
958,0,0,0,0.603782," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{5} + 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((C*sec(d*x + c)^5 + B*sec(d*x + c)^4 + A*sec(d*x + c)^3)/sqrt(b*sec(d*x + c) + a), x)","F",0
959,0,0,0,0.548869," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + B*sec(d*x + c)^3 + A*sec(d*x + c)^2)/sqrt(b*sec(d*x + c) + a), x)","F",0
960,0,0,0,0.591600," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + B*sec(d*x + c)^2 + A*sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
961,0,0,0,27.864238," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/sqrt(b*sec(d*x + c) + a), x)","F",0
962,0,0,0,50.016784," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
963,0,0,0,2.115163," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
964,0,0,0,0.531482," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{5} + 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((C*sec(d*x + c)^5 + 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
965,0,0,0,0.522950," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + 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
966,0,0,0,0.486578," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + 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
967,0,0,0,24.114895," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*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
968,0,0,0,1.366870," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
969,0,0,0,2.316755," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
970,0,0,0,0.692670," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{5} + 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((C*sec(d*x + c)^5 + 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
971,0,0,0,0.732855," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{4} + 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((C*sec(d*x + c)^4 + 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
972,0,0,0,0.567977," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{3} + 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((C*sec(d*x + c)^3 + 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
973,0,0,0,23.535144," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{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((C*sec(d*x + c)^2 + 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
974,0,0,0,1.472991," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
975,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
976,0,0,0,1.741577," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)*sqrt(b*sec(d*x + c) + a), x)","F",0
977,0,0,0,2.143472," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right) - C a + B b\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*sec(d*x + c) - C*a + B*b)*sqrt(b*sec(d*x + c) + a), x)","F",0
978,-1,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
979,0,0,0,67.952905," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \sec\left(d x + c\right) - C a + B b\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((C*b*sec(d*x + c) - C*a + B*b)*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
980,0,0,0,51.964487," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \sec\left(d x + c\right) - C a + B b\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((C*b*sec(d*x + c) - C*a + B*b)*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
981,0,0,0,0.455762," ","integrate(sec(d*x+c)^(5/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{5} + {\left(C a + B b\right)} \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{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^5 + (C*a + B*b)*sec(d*x + c)^4 + A*a*sec(d*x + c)^2 + (B*a + A*b)*sec(d*x + c)^3)*sqrt(sec(d*x + c)), x)","F",0
982,0,0,0,0.461961," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{4} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^4 + (C*a + 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
983,0,0,0,0.457615," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
984,0,0,0,0.455187," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
985,0,0,0,0.457175," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
986,0,0,0,0.462254," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
987,0,0,0,0.468169," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
988,0,0,0,0.494525," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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{9}{2}}}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^3 + (C*a + B*b)*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))/sec(d*x + c)^(9/2), x)","F",0
989,0,0,0,0.530349," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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{11}{2}}}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^3 + (C*a + B*b)*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))/sec(d*x + c)^(11/2), x)","F",0
990,0,0,0,0.520140," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{5} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{4} + A a^{2} \sec\left(d x + c\right) + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^5 + (2*C*a*b + B*b^2)*sec(d*x + c)^4 + A*a^2*sec(d*x + c) + (C*a^2 + 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
991,0,0,0,0.506468," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
992,0,0,0,0.515931," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
993,0,0,0,0.485387," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
994,0,0,0,0.485845," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
995,0,0,0,0.546412," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
996,0,0,0,0.496009," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
997,0,0,0,0.487012," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, 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((C*b^3*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*sec(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
998,0,0,0,0.601971," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, 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((C*b^3*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*sec(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
999,0,0,0,0.560025," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, 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((C*b^3*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*sec(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1000,0,0,0,0.694638," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, 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((C*b^3*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*sec(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1001,0,0,0,0.561015," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, 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((C*b^3*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*sec(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1002,0,0,0,0.531402," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, 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((C*b^3*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*sec(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1003,0,0,0,0.576595," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, 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((C*b^3*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*sec(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1004,0,0,0,0.566637," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \sec\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, 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)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^4*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*sec(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*sec(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
1005,0,0,0,1.115159," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \sec\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, 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)}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^4*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*sec(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*sec(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*sec(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
1006,0,0,0,0.548424," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \sec\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, 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)}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^4*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*sec(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*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)^(3/2), x)","F",0
1007,0,0,0,0.518181," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \sec\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, 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)}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b^4*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*sec(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*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)^(5/2), x)","F",0
1008,0,0,0,0.594967," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \sec\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, 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)}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b^4*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*sec(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*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)^(7/2), x)","F",0
1009,0,0,0,0.619458," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \sec\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, 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)}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b^4*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*sec(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*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)^(9/2), x)","F",0
1010,0,0,0,0.589482," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \sec\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, 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)}{\sec\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*b^4*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*sec(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*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)^(11/2), x)","F",0
1011,0,0,0,0.546499," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \sec\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, 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)}{\sec\left(d x + c\right)^{\frac{13}{2}}}, x\right)"," ",0,"integral((C*b^4*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*sec(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*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)^(13/2), x)","F",0
1012,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1013,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1014,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1015,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1016,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1017,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1018,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1019,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1020,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1021,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1022,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1023,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1024,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1025,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1026,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1027,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1028,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1029,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1030,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1031,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1032,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1033,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1034,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1035,0,0,0,1.662618," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
1036,0,0,0,1.406113," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
1037,0,0,0,0.954892," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
1038,-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)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1039,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1040,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1041,0,0,0,10.530529," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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{3}{2}}}, x\right)"," ",0,"integral((C*b*sec(d*x + c)^3 + (C*a + 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)^(3/2), x)","F",0
1042,0,0,0,2.959540," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
1043,0,0,0,1.268289," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
1044,0,0,0,1.200876," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
1045,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1046,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1047,0,0,0,14.084454," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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{3}{2}}}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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)^(3/2), x)","F",0
1048,0,0,0,8.462829," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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{5}{2}}}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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)^(5/2), x)","F",0
1049,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1050,0,0,0,1.180839," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
1051,0,0,0,0.993764," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
1052,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1053,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1054,0,0,0,4.116537," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
1055,0,0,0,1.236194," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
1056,0,0,0,0.955067," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
1057,0,0,0,0.986930," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right)^{5} + a \sec\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b*sec(d*x + c)^5 + a*sec(d*x + c)^4), x)","F",0
1058,-1,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1059,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1060,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1061,0,0,0,0.629702," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{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((C*sec(d*x + c)^2 + 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
1062,0,0,0,0.886385," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{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((C*sec(d*x + c)^2 + 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
1063,0,0,0,0.622433," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{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((C*sec(d*x + c)^2 + 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
1064,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1065,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1066,0,0,0,2.213836," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{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((C*sec(d*x + c)^2 + 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
1067,0,0,0,1.229656," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{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((C*sec(d*x + c)^2 + 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
1068,0,0,0,2.596800," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{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((C*sec(d*x + c)^2 + 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
1069,0,0,0,0.847821," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{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((C*sec(d*x + c)^2 + 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
1070,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1071,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1072,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1073,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1074,0,0,0,1.860270," ","integrate((a+b*sec(d*x+c))^m*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)*(b*sec(d*x + c) + a)^m, x)","F",0
1075,0,0,0,0.644247," ","integrate(cos(d*x+c)^(9/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^4*sec(d*x + c)^2 + A*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
1076,0,0,0,0.968179," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^3*sec(d*x + c)^2 + A*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
1077,0,0,0,0.657963," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2*sec(d*x + c)^2 + A*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
1078,0,0,0,0.560783," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)*sec(d*x + c)^2 + A*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1079,0,0,0,1.045209," ","integrate(cos(d*x+c)^(1/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c)), x)","F",0
1080,0,0,0,0.670028," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)/sqrt(cos(d*x + c)), x)","F",0
1081,0,0,0,0.664885," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)/cos(d*x + c)^(3/2), x)","F",0
1082,0,0,0,0.811738," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)/cos(d*x + c)^(5/2), x)","F",0
1083,0,0,0,0.579713," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + A a \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^4*sec(d*x + c)^3 + C*a*cos(d*x + c)^4*sec(d*x + c)^2 + A*a*cos(d*x + c)^4*sec(d*x + c) + A*a*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
1084,0,0,0,0.607598," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + A 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((C*a*cos(d*x + c)^3*sec(d*x + c)^3 + C*a*cos(d*x + c)^3*sec(d*x + c)^2 + A*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
1085,0,0,0,0.575441," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A 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((C*a*cos(d*x + c)^2*sec(d*x + c)^3 + C*a*cos(d*x + c)^2*sec(d*x + c)^2 + A*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
1086,0,0,0,0.677435," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + C a \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + A 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((C*a*cos(d*x + c)*sec(d*x + c)^3 + C*a*cos(d*x + c)*sec(d*x + c)^2 + A*a*cos(d*x + c)*sec(d*x + c) + A*a*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1087,0,0,0,0.717850," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \sec\left(d x + c\right)^{3} + C a \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right) + A a\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a*sec(d*x + c)^3 + C*a*sec(d*x + c)^2 + A*a*sec(d*x + c) + A*a)*sqrt(cos(d*x + c)), x)","F",0
1088,0,0,0,0.648482," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + C a \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right) + A a}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a*sec(d*x + c)^3 + C*a*sec(d*x + c)^2 + A*a*sec(d*x + c) + A*a)/sqrt(cos(d*x + c)), x)","F",0
1089,0,0,0,0.684808," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + C a \sec\left(d x + c\right)^{2} + A a \sec\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a*sec(d*x + c)^3 + C*a*sec(d*x + c)^2 + A*a*sec(d*x + c) + A*a)/cos(d*x + c)^(3/2), x)","F",0
1090,0,0,0,0.618463," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right) + A a^{2} \cos\left(d x + c\right)^{5}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^5*sec(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^5*sec(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^5*sec(d*x + c)^2 + 2*A*a^2*cos(d*x + c)^5*sec(d*x + c) + A*a^2*cos(d*x + c)^5)*sqrt(cos(d*x + c)), x)","F",0
1091,0,0,0,0.655397," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 2 \, A 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((C*a^2*cos(d*x + c)^4*sec(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^4*sec(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^4*sec(d*x + c)^2 + 2*A*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
1092,0,0,0,0.490788," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 2 \, A 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((C*a^2*cos(d*x + c)^3*sec(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3*sec(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^3*sec(d*x + c)^2 + 2*A*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
1093,0,0,0,0.565402," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 2 \, A 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((C*a^2*cos(d*x + c)^2*sec(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^2*sec(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2*sec(d*x + c)^2 + 2*A*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
1094,0,0,0,0.578388," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 2 \, A 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((C*a^2*cos(d*x + c)*sec(d*x + c)^4 + 2*C*a^2*cos(d*x + c)*sec(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)*sec(d*x + c)^2 + 2*A*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
1095,0,0,0,0.491572," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \sec\left(d x + c\right) + A a^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + 2*C*a^2*sec(d*x + c)^3 + (A + C)*a^2*sec(d*x + c)^2 + 2*A*a^2*sec(d*x + c) + A*a^2)*sqrt(cos(d*x + c)), x)","F",0
1096,0,0,0,0.495487," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \sec\left(d x + c\right) + A a^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + 2*C*a^2*sec(d*x + c)^3 + (A + C)*a^2*sec(d*x + c)^2 + 2*A*a^2*sec(d*x + c) + A*a^2)/sqrt(cos(d*x + c)), x)","F",0
1097,0,0,0,0.657229," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + 2 \, C a^{2} \sec\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \sec\left(d x + c\right)^{2} + 2 \, A a^{2} \sec\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a^2*sec(d*x + c)^4 + 2*C*a^2*sec(d*x + c)^3 + (A + C)*a^2*sec(d*x + c)^2 + 2*A*a^2*sec(d*x + c) + A*a^2)/cos(d*x + c)^(3/2), x)","F",0
1098,0,0,0,0.553012," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)^{6}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^6*sec(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^6*sec(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^6*sec(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^6*sec(d*x + c)^2 + 3*A*a^3*cos(d*x + c)^6*sec(d*x + c) + A*a^3*cos(d*x + c)^6)*sqrt(cos(d*x + c)), x)","F",0
1099,0,0,0,0.526103," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)^{5}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5*sec(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^5*sec(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^5*sec(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^5*sec(d*x + c)^2 + 3*A*a^3*cos(d*x + c)^5*sec(d*x + c) + A*a^3*cos(d*x + c)^5)*sqrt(cos(d*x + c)), x)","F",0
1100,0,0,0,0.548492," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^4*sec(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4*sec(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^4*sec(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^4*sec(d*x + c)^2 + 3*A*a^3*cos(d*x + c)^4*sec(d*x + c) + A*a^3*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
1101,0,0,0,0.695172," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^3*sec(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^3*sec(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3*sec(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^3*sec(d*x + c)^2 + 3*A*a^3*cos(d*x + c)^3*sec(d*x + c) + A*a^3*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
1102,0,0,0,0.520020," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^2*sec(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^2*sec(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^2*sec(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2*sec(d*x + c)^2 + 3*A*a^3*cos(d*x + c)^2*sec(d*x + c) + A*a^3*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
1103,0,0,0,0.553771," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)*sec(d*x + c)^5 + 3*C*a^3*cos(d*x + c)*sec(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)*sec(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)*sec(d*x + c)^2 + 3*A*a^3*cos(d*x + c)*sec(d*x + c) + A*a^3*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1104,0,0,0,0.517669," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)*sqrt(cos(d*x + c)), x)","F",0
1105,0,0,0,0.537754," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)/sqrt(cos(d*x + c)), x)","F",0
1106,0,0,0,0.650487," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + 3 \, C a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \sec\left(d x + c\right)^{2} + 3 \, A a^{3} \sec\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + 3*C*a^3*sec(d*x + c)^4 + (A + 3*C)*a^3*sec(d*x + c)^3 + (3*A + C)*a^3*sec(d*x + c)^2 + 3*A*a^3*sec(d*x + c) + A*a^3)/cos(d*x + c)^(3/2), x)","F",0
1107,0,0,0,0.605211," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^3*sec(d*x + c)^2 + A*cos(d*x + c)^3)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
1108,0,0,0,0.528793," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + A*cos(d*x + c)^2)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
1109,0,0,0,0.578461," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + A*cos(d*x + c))*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
1110,0,0,0,0.599399," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
1111,0,0,0,0.586123," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)*sec(d*x + c) + a*cos(d*x + c)), x)","F",0
1112,0,0,0,0.526069," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1113,0,0,0,0.543287," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1114,0,0,0,0.673780," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
1115,0,0,0,0.486718," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
1116,0,0,0,0.472638," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1117,0,0,0,0.540834," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1118,0,0,0,0.499566," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1119,0,0,0,0.538646," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1120,0,0,0,0.610480," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + A \cos\left(d x + c\right)^{2}\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((C*cos(d*x + c)^2*sec(d*x + c)^2 + A*cos(d*x + c)^2)*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
1121,0,0,0,0.533047," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
1122,0,0,0,0.552144," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1123,0,0,0,0.495602," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1124,0,0,0,0.547822," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1125,0,0,0,0.629702," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1126,0,0,0,0.542765," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + 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((C*sec(d*x + c)^2 + 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
1127,1,110,0,0.455815," ","integrate(cos(d*x+c)^(9/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A \cos\left(d x + c\right)^{4} + 40 \, A \cos\left(d x + c\right)^{3} + 3 \, {\left(16 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(16 \, A + 21 \, C\right)} \cos\left(d x + c\right) + 128 \, A + 168 \, C\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 + 40*A*cos(d*x + c)^3 + 3*(16*A + 21*C)*cos(d*x + c)^2 + 4*(16*A + 21*C)*cos(d*x + c) + 128*A + 168*C)*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
1128,1,92,0,0.463127," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, A \cos\left(d x + c\right)^{3} + 18 \, A \cos\left(d x + c\right)^{2} + {\left(24 \, A + 35 \, C\right)} \cos\left(d x + c\right) + 48 \, A + 70 \, C\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 + 18*A*cos(d*x + c)^2 + (24*A + 35*C)*cos(d*x + c) + 48*A + 70*C)*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
1129,1,76,0,0.460932," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A \cos\left(d x + c\right)^{2} + 4 \, A \cos\left(d x + c\right) + 8 \, A + 15 \, C\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*cos(d*x + c) + 8*A + 15*C)*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
1130,1,323,0,0.670520," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(A \cos\left(d x + c\right) + 2 \, 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(C \cos\left(d x + c\right) + C\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 \cos\left(d x + c\right) + 2 \, 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(C \cos\left(d x + c\right) + C\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*cos(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) + 3*(C*cos(d*x + c) + 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) + d), 1/3*(2*(A*cos(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) + 3*(C*cos(d*x + c) + 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) + d)]","A",0
1131,1,355,0,0.651824," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, A \cos\left(d x + c\right) + C\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(C \cos\left(d x + c\right)^{2} + C \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 \cos\left(d x + c\right) + C\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(C \cos\left(d x + c\right)^{2} + C \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*cos(d*x + c) + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (C*cos(d*x + c)^2 + C*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*cos(d*x + c) + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (C*cos(d*x + c)^2 + C*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
1132,1,391,0,0.659909," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, C \cos\left(d x + c\right) + 2 \, C\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(8 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 3 \, C\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(3 \, C \cos\left(d x + c\right) + 2 \, C\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(8 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 3 \, C\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*(3*C*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 3*C)*cos(d*x + c)^3 + (8*A + 3*C)*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*(3*C*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 3*C)*cos(d*x + c)^3 + (8*A + 3*C)*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
1133,1,427,0,0.597484," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(8 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 10 \, C \cos\left(d x + c\right) + 8 \, C\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(8 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, A + 5 \, C\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(8 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 10 \, C \cos\left(d x + c\right) + 8 \, C\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(8 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, A + 5 \, C\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*(8*A + 5*C)*cos(d*x + c)^2 + 10*C*cos(d*x + c) + 8*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 5*C)*cos(d*x + c)^4 + (8*A + 5*C)*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*(8*A + 5*C)*cos(d*x + c)^2 + 10*C*cos(d*x + c) + 8*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 5*C)*cos(d*x + c)^4 + (8*A + 5*C)*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
1134,1,461,0,0.663660," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 56 \, C \cos\left(d x + c\right) + 48 \, C\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(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(48 \, A + 35 \, C\right)} \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(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 56 \, C \cos\left(d x + c\right) + 48 \, C\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(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(48 \, A + 35 \, C\right)} \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*(48*A + 35*C)*cos(d*x + c)^3 + 2*(48*A + 35*C)*cos(d*x + c)^2 + 56*C*cos(d*x + c) + 48*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((48*A + 35*C)*cos(d*x + c)^5 + (48*A + 35*C)*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*(48*A + 35*C)*cos(d*x + c)^3 + 2*(48*A + 35*C)*cos(d*x + c)^2 + 56*C*cos(d*x + c) + 48*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((48*A + 35*C)*cos(d*x + c)^5 + (48*A + 35*C)*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
1135,1,136,0,0.499783," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, A a \cos\left(d x + c\right)^{5} + 245 \, A a \cos\left(d x + c\right)^{4} + 5 \, {\left(56 \, A + 33 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(112 \, A + 143 \, C\right)} a \cos\left(d x + c\right)^{2} + 4 \, {\left(112 \, A + 143 \, C\right)} a \cos\left(d x + c\right) + 8 \, {\left(112 \, A + 143 \, C\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)}{1155 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/1155*(105*A*a*cos(d*x + c)^5 + 245*A*a*cos(d*x + c)^4 + 5*(56*A + 33*C)*a*cos(d*x + c)^3 + 3*(112*A + 143*C)*a*cos(d*x + c)^2 + 4*(112*A + 143*C)*a*cos(d*x + c) + 8*(112*A + 143*C)*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
1136,1,117,0,0.585145," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A a \cos\left(d x + c\right)^{4} + 85 \, A a \cos\left(d x + c\right)^{3} + 3 \, {\left(34 \, A + 21 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(136 \, A + 189 \, C\right)} a \cos\left(d x + c\right) + 2 \, {\left(136 \, A + 189 \, C\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 + 85*A*a*cos(d*x + c)^3 + 3*(34*A + 21*C)*a*cos(d*x + c)^2 + (136*A + 189*C)*a*cos(d*x + c) + 2*(136*A + 189*C)*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
1137,1,98,0,0.517671," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, A a \cos\left(d x + c\right)^{3} + 39 \, A a \cos\left(d x + c\right)^{2} + {\left(52 \, A + 35 \, C\right)} a \cos\left(d x + c\right) + {\left(104 \, A + 175 \, C\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 + 39*A*a*cos(d*x + c)^2 + (52*A + 35*C)*a*cos(d*x + c) + (104*A + 175*C)*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
1138,1,367,0,0.624503," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(A a \cos\left(d x + c\right)^{2} + 3 \, A a \cos\left(d x + c\right) + {\left(6 \, A + 5 \, C\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) + 5 \, {\left(C a \cos\left(d x + c\right) + C 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)}{10 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{2 \, {\left(A a \cos\left(d x + c\right)^{2} + 3 \, A a \cos\left(d x + c\right) + {\left(6 \, A + 5 \, C\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) + 5 \, {\left(C a \cos\left(d x + c\right) + C 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)}{5 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/10*(4*(A*a*cos(d*x + c)^2 + 3*A*a*cos(d*x + c) + (6*A + 5*C)*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 5*(C*a*cos(d*x + c) + C*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), 1/5*(2*(A*a*cos(d*x + c)^2 + 3*A*a*cos(d*x + c) + (6*A + 5*C)*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 5*(C*a*cos(d*x + c) + C*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
1139,1,393,0,0.520875," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, A a \cos\left(d x + c\right)^{2} + 10 \, A a \cos\left(d x + c\right) + 3 \, C 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) + 9 \, {\left(C a \cos\left(d x + c\right)^{2} + C 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)}{12 \, {\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)^{2} + 10 \, A a \cos\left(d x + c\right) + 3 \, C 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) + 9 \, {\left(C a \cos\left(d x + c\right)^{2} + C 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)}{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*cos(d*x + c)^2 + 10*A*a*cos(d*x + c) + 3*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 9*(C*a*cos(d*x + c)^2 + C*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)), 1/6*(2*(2*A*a*cos(d*x + c)^2 + 10*A*a*cos(d*x + c) + 3*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 9*(C*a*cos(d*x + c)^2 + C*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
1140,1,423,0,0.543098," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, A a \cos\left(d x + c\right)^{2} + 7 \, C a \cos\left(d x + c\right) + 2 \, C 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(8 \, A + 7 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(8 \, A + 7 \, C\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(8 \, A a \cos\left(d x + c\right)^{2} + 7 \, C a \cos\left(d x + c\right) + 2 \, C 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(8 \, A + 7 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(8 \, A + 7 \, C\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*(8*A*a*cos(d*x + c)^2 + 7*C*a*cos(d*x + c) + 2*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 7*C)*a*cos(d*x + c)^3 + (8*A + 7*C)*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*(8*A*a*cos(d*x + c)^2 + 7*C*a*cos(d*x + c) + 2*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 7*C)*a*cos(d*x + c)^3 + (8*A + 7*C)*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
1141,1,437,0,0.630410," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(8 \, A + 11 \, C\right)} a \cos\left(d x + c\right)^{2} + 22 \, C a \cos\left(d x + c\right) + 8 \, C 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(24 \, A + 11 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(24 \, A + 11 \, C\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(8 \, A + 11 \, C\right)} a \cos\left(d x + c\right)^{2} + 22 \, C a \cos\left(d x + c\right) + 8 \, C 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(24 \, A + 11 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(24 \, A + 11 \, C\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*(8*A + 11*C)*a*cos(d*x + c)^2 + 22*C*a*cos(d*x + c) + 8*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((24*A + 11*C)*a*cos(d*x + c)^4 + (24*A + 11*C)*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*(8*A + 11*C)*a*cos(d*x + c)^2 + 22*C*a*cos(d*x + c) + 8*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((24*A + 11*C)*a*cos(d*x + c)^4 + (24*A + 11*C)*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
1142,1,469,0,0.745802," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left({\left(112 \, A + 75 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(16 \, A + 25 \, C\right)} a \cos\left(d x + c\right)^{2} + 40 \, C a \cos\left(d x + c\right) + 16 \, C 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(112 \, A + 75 \, C\right)} a \cos\left(d x + c\right)^{5} + {\left(112 \, A + 75 \, C\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)}{256 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}, \frac{2 \, {\left({\left(112 \, A + 75 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(16 \, A + 25 \, C\right)} a \cos\left(d x + c\right)^{2} + 40 \, C a \cos\left(d x + c\right) + 16 \, C 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(112 \, A + 75 \, C\right)} a \cos\left(d x + c\right)^{5} + {\left(112 \, A + 75 \, C\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)}{128 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/256*(4*((112*A + 75*C)*a*cos(d*x + c)^3 + 2*(16*A + 25*C)*a*cos(d*x + c)^2 + 40*C*a*cos(d*x + c) + 16*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((112*A + 75*C)*a*cos(d*x + c)^5 + (112*A + 75*C)*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), 1/128*(2*((112*A + 75*C)*a*cos(d*x + c)^3 + 2*(16*A + 25*C)*a*cos(d*x + c)^2 + 40*C*a*cos(d*x + c) + 16*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((112*A + 75*C)*a*cos(d*x + c)^5 + (112*A + 75*C)*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
1143,1,509,0,0.694656," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(15 \, {\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{4} + 10 \, {\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 912 \, C a \cos\left(d x + c\right) + 384 \, C 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({\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{6} + {\left(176 \, A + 133 \, C\right)} a \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(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{4} + 10 \, {\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 912 \, C a \cos\left(d x + c\right) + 384 \, C 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({\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{6} + {\left(176 \, A + 133 \, C\right)} a \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*(176*A + 133*C)*a*cos(d*x + c)^4 + 10*(176*A + 133*C)*a*cos(d*x + c)^3 + 8*(80*A + 133*C)*a*cos(d*x + c)^2 + 912*C*a*cos(d*x + c) + 384*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((176*A + 133*C)*a*cos(d*x + c)^6 + (176*A + 133*C)*a*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*(176*A + 133*C)*a*cos(d*x + c)^4 + 10*(176*A + 133*C)*a*cos(d*x + c)^3 + 8*(80*A + 133*C)*a*cos(d*x + c)^2 + 912*C*a*cos(d*x + c) + 384*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((176*A + 133*C)*a*cos(d*x + c)^6 + (176*A + 133*C)*a*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
1144,1,168,0,0.554082," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, A a^{2} \cos\left(d x + c\right)^{6} + 11970 \, A a^{2} \cos\left(d x + c\right)^{5} + 35 \, {\left(523 \, A + 143 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(2092 \, A + 1859 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8368 \, A + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 4 \, {\left(8368 \, A + 10439 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(8368 \, A + 10439 \, C\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)}{45045 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/45045*(3465*A*a^2*cos(d*x + c)^6 + 11970*A*a^2*cos(d*x + c)^5 + 35*(523*A + 143*C)*a^2*cos(d*x + c)^4 + 10*(2092*A + 1859*C)*a^2*cos(d*x + c)^3 + 3*(8368*A + 10439*C)*a^2*cos(d*x + c)^2 + 4*(8368*A + 10439*C)*a^2*cos(d*x + c) + 8*(8368*A + 10439*C)*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
1145,1,146,0,0.517291," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, A a^{2} \cos\left(d x + c\right)^{5} + 224 \, A a^{2} \cos\left(d x + c\right)^{4} + {\left(355 \, A + 99 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 6 \, {\left(71 \, A + 66 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(568 \, A + 759 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(568 \, A + 759 \, C\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)}{693 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/693*(63*A*a^2*cos(d*x + c)^5 + 224*A*a^2*cos(d*x + c)^4 + (355*A + 99*C)*a^2*cos(d*x + c)^3 + 6*(71*A + 66*C)*a^2*cos(d*x + c)^2 + (568*A + 759*C)*a^2*cos(d*x + c) + 2*(568*A + 759*C)*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
1146,1,127,0,0.497598," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A a^{2} \cos\left(d x + c\right)^{4} + 130 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(73 \, A + 21 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(146 \, A + 147 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(584 \, A + 903 \, C\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 + 130*A*a^2*cos(d*x + c)^3 + 3*(73*A + 21*C)*a^2*cos(d*x + c)^2 + 2*(146*A + 147*C)*a^2*cos(d*x + c) + (584*A + 903*C)*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
1147,1,429,0,0.560987," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, A a^{2} \cos\left(d x + c\right)^{3} + 12 \, A a^{2} \cos\left(d x + c\right)^{2} + {\left(23 \, A + 7 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(23 \, A + 28 \, C\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) + 21 \, {\left(C a^{2} \cos\left(d x + c\right) + C 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)}{42 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{2 \, {\left(3 \, A a^{2} \cos\left(d x + c\right)^{3} + 12 \, A a^{2} \cos\left(d x + c\right)^{2} + {\left(23 \, A + 7 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(23 \, A + 28 \, C\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) + 21 \, {\left(C a^{2} \cos\left(d x + c\right) + C 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)}{21 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/42*(4*(3*A*a^2*cos(d*x + c)^3 + 12*A*a^2*cos(d*x + c)^2 + (23*A + 7*C)*a^2*cos(d*x + c) + 2*(23*A + 28*C)*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 21*(C*a^2*cos(d*x + c) + C*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), 1/21*(2*(3*A*a^2*cos(d*x + c)^3 + 12*A*a^2*cos(d*x + c)^2 + (23*A + 7*C)*a^2*cos(d*x + c) + 2*(23*A + 28*C)*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 21*(C*a^2*cos(d*x + c) + C*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
1148,1,453,0,0.495321," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 28 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(43 \, A + 15 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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) + 75 \, {\left(C a^{2} \cos\left(d x + c\right)^{2} + C 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)}{60 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{2 \, {\left(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 28 \, A a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(43 \, A + 15 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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) + 75 \, {\left(C a^{2} \cos\left(d x + c\right)^{2} + C 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)}{30 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/60*(4*(6*A*a^2*cos(d*x + c)^3 + 28*A*a^2*cos(d*x + c)^2 + 2*(43*A + 15*C)*a^2*cos(d*x + c) + 15*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 75*(C*a^2*cos(d*x + c)^2 + C*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)), 1/30*(2*(6*A*a^2*cos(d*x + c)^3 + 28*A*a^2*cos(d*x + c)^2 + 2*(43*A + 15*C)*a^2*cos(d*x + c) + 15*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 75*(C*a^2*cos(d*x + c)^2 + C*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
1149,1,473,0,0.564433," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, A a^{2} \cos\left(d x + c\right)^{3} + 64 \, A a^{2} \cos\left(d x + c\right)^{2} + 33 \, C a^{2} \cos\left(d x + c\right) + 6 \, C 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(8 \, A + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 19 \, C\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)}{48 \, {\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)^{3} + 64 \, A a^{2} \cos\left(d x + c\right)^{2} + 33 \, C a^{2} \cos\left(d x + c\right) + 6 \, C 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(8 \, A + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 19 \, C\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)}{24 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/48*(4*(8*A*a^2*cos(d*x + c)^3 + 64*A*a^2*cos(d*x + c)^2 + 33*C*a^2*cos(d*x + c) + 6*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 19*C)*a^2*cos(d*x + c)^3 + (8*A + 19*C)*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), 1/24*(2*(8*A*a^2*cos(d*x + c)^3 + 64*A*a^2*cos(d*x + c)^2 + 33*C*a^2*cos(d*x + c) + 6*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 19*C)*a^2*cos(d*x + c)^3 + (8*A + 19*C)*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
1150,1,485,0,0.618568," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(48 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 34 \, C a^{2} \cos\left(d x + c\right) + 8 \, C 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(8 \, A + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(8 \, A + 5 \, C\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(48 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 34 \, C a^{2} \cos\left(d x + c\right) + 8 \, C 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(8 \, A + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(8 \, A + 5 \, C\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*(48*A*a^2*cos(d*x + c)^3 + 3*(8*A + 25*C)*a^2*cos(d*x + c)^2 + 34*C*a^2*cos(d*x + c) + 8*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((8*A + 5*C)*a^2*cos(d*x + c)^4 + (8*A + 5*C)*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*(48*A*a^2*cos(d*x + c)^3 + 3*(8*A + 25*C)*a^2*cos(d*x + c)^2 + 34*C*a^2*cos(d*x + c) + 8*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((8*A + 5*C)*a^2*cos(d*x + c)^4 + (8*A + 5*C)*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
1151,1,497,0,0.738348," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(176 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 184 \, C a^{2} \cos\left(d x + c\right) + 48 \, C 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(304 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(304 \, A + 163 \, C\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(176 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 184 \, C a^{2} \cos\left(d x + c\right) + 48 \, C 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(304 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(304 \, A + 163 \, C\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*(176*A + 163*C)*a^2*cos(d*x + c)^3 + 2*(48*A + 163*C)*a^2*cos(d*x + c)^2 + 184*C*a^2*cos(d*x + c) + 48*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((304*A + 163*C)*a^2*cos(d*x + c)^5 + (304*A + 163*C)*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*(176*A + 163*C)*a^2*cos(d*x + c)^3 + 2*(48*A + 163*C)*a^2*cos(d*x + c)^2 + 184*C*a^2*cos(d*x + c) + 48*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((304*A + 163*C)*a^2*cos(d*x + c)^5 + (304*A + 163*C)*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
1152,1,537,0,0.782467," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(15 \, {\left(400 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(272 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 1392 \, C a^{2} \cos\left(d x + c\right) + 384 \, C 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(400 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(400 \, A + 283 \, C\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(400 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(272 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 1392 \, C a^{2} \cos\left(d x + c\right) + 384 \, C 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(400 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(400 \, A + 283 \, C\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*(400*A + 283*C)*a^2*cos(d*x + c)^4 + 10*(272*A + 283*C)*a^2*cos(d*x + c)^3 + 8*(80*A + 283*C)*a^2*cos(d*x + c)^2 + 1392*C*a^2*cos(d*x + c) + 384*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((400*A + 283*C)*a^2*cos(d*x + c)^6 + (400*A + 283*C)*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*(400*A + 283*C)*a^2*cos(d*x + c)^4 + 10*(272*A + 283*C)*a^2*cos(d*x + c)^3 + 8*(80*A + 283*C)*a^2*cos(d*x + c)^2 + 1392*C*a^2*cos(d*x + c) + 384*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((400*A + 283*C)*a^2*cos(d*x + c)^6 + (400*A + 283*C)*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
1153,1,577,0,0.660495," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 2 \, {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(184 \, A + 203 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 48 \, {\left(8 \, A + 29 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 896 \, C a^{2} \cos\left(d x + c\right) + 256 \, C 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(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{7} + {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{6}\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)}{6144 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}, \frac{2 \, {\left(3 \, {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 2 \, {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(184 \, A + 203 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 48 \, {\left(8 \, A + 29 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 896 \, C a^{2} \cos\left(d x + c\right) + 256 \, C 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(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{7} + {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{6}\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)}{3072 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}\right]"," ",0,"[1/6144*(4*(3*(1304*A + 1015*C)*a^2*cos(d*x + c)^5 + 2*(1304*A + 1015*C)*a^2*cos(d*x + c)^4 + 8*(184*A + 203*C)*a^2*cos(d*x + c)^3 + 48*(8*A + 29*C)*a^2*cos(d*x + c)^2 + 896*C*a^2*cos(d*x + c) + 256*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((1304*A + 1015*C)*a^2*cos(d*x + c)^7 + (1304*A + 1015*C)*a^2*cos(d*x + c)^6)*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)^7 + d*cos(d*x + c)^6), 1/3072*(2*(3*(1304*A + 1015*C)*a^2*cos(d*x + c)^5 + 2*(1304*A + 1015*C)*a^2*cos(d*x + c)^4 + 8*(184*A + 203*C)*a^2*cos(d*x + c)^3 + 48*(8*A + 29*C)*a^2*cos(d*x + c)^2 + 896*C*a^2*cos(d*x + c) + 256*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((1304*A + 1015*C)*a^2*cos(d*x + c)^7 + (1304*A + 1015*C)*a^2*cos(d*x + c)^6)*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)^7 + d*cos(d*x + c)^6)]","A",0
1154,1,384,0,0.520588," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)/(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 \, A \cos\left(d x + c\right)^{2} + {\left(31 \, A + 35 \, C\right)} \cos\left(d x + c\right) - 43 \, A - 35 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 \, A \cos\left(d x + c\right)^{2} + {\left(31 \, A + 35 \, C\right)} \cos\left(d x + c\right) - 43 \, A - 35 \, C\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*cos(d*x + c)^2 + (31*A + 35*C)*cos(d*x + c) - 43*A - 35*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 105*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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 + C)*a*cos(d*x + c) + (A + C)*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*cos(d*x + c)^2 + (31*A + 35*C)*cos(d*x + c) - 43*A - 35*C)*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
1155,1,352,0,0.509409," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, A \cos\left(d x + c\right)^{2} - A \cos\left(d x + c\right) + 13 \, A + 15 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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} - A \cos\left(d x + c\right) + 13 \, A + 15 \, C\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*cos(d*x + c) + 13*A + 15*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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 + C)*a*cos(d*x + c) + (A + C)*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*cos(d*x + c) + 13*A + 15*C)*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
1156,1,322,0,0.602928," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(A \cos\left(d x + c\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) + \frac{3 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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 + C)*a*cos(d*x + c) + (A + C)*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)*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
1157,1,489,0,0.577003," ","integrate((A+C*sec(d*x+c)^2)*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(C \cos\left(d x + c\right) + C\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{\sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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) + {\left(C \cos\left(d x + c\right) + C\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)}{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) + (C*cos(d*x + c) + 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)) + sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*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 + C)*a*cos(d*x + c) + (A + C)*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) + (C*cos(d*x + c) + 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) + a*d)]","A",0
1158,1,542,0,0.655003," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, C \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(C \cos\left(d x + c\right)^{2} + C \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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A + C\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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A + C\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 \, C \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(C \cos\left(d x + c\right)^{2} + C \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*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (C*cos(d*x + c)^2 + C*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 + C)*a*cos(d*x + c)^2 + (A + C)*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 + C)*a*cos(d*x + c)^2 + (A + C)*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*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (C*cos(d*x + c)^2 + C*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
1159,1,601,0,0.683762," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(C \cos\left(d x + c\right) - 2 \, C\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(8 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 7 \, C\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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A + C\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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A + C\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(C \cos\left(d x + c\right) - 2 \, C\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(8 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 7 \, C\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*(C*cos(d*x + c) - 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - ((8*A + 7*C)*cos(d*x + c)^3 + (8*A + 7*C)*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 + C)*a*cos(d*x + c)^3 + (A + C)*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 + C)*a*cos(d*x + c)^3 + (A + C)*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*(C*cos(d*x + c) - 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 7*C)*cos(d*x + c)^3 + (8*A + 7*C)*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
1160,1,638,0,0.705244," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(8 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} - 2 \, C \cos\left(d x + c\right) + 8 \, C\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(8 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, A + 9 \, C\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) + \frac{48 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A + C\right)} a \cos\left(d x + c\right)^{3}\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}}}{96 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}, -\frac{48 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A + C\right)} a \cos\left(d x + c\right)^{3}\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 \, {\left(8 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} - 2 \, C \cos\left(d x + c\right) + 8 \, C\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(8 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, A + 9 \, C\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(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/96*(4*(3*(8*A + 7*C)*cos(d*x + c)^2 - 2*C*cos(d*x + c) + 8*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 9*C)*cos(d*x + c)^4 + (8*A + 9*C)*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)) + 48*sqrt(2)*((A + C)*a*cos(d*x + c)^4 + (A + C)*a*cos(d*x + c)^3)*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)^4 + a*d*cos(d*x + c)^3), -1/48*(48*sqrt(2)*((A + C)*a*cos(d*x + c)^4 + (A + C)*a*cos(d*x + c)^3)*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*(8*A + 7*C)*cos(d*x + c)^2 - 2*C*cos(d*x + c) + 8*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 9*C)*cos(d*x + c)^4 + (8*A + 9*C)*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)))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)]","A",0
1161,1,468,0,0.676465," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{5 \, \sqrt{2} {\left({\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right) + 15 \, A + 7 \, C\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)^{3} - 4 \, A \cos\left(d x + c\right)^{2} + 4 \, {\left(9 \, A + 5 \, C\right)} \cos\left(d x + c\right) + 49 \, A + 25 \, C\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)}{40 \, {\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{5 \, \sqrt{2} {\left({\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right) + 15 \, A + 7 \, C\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)^{3} - 4 \, A \cos\left(d x + c\right)^{2} + 4 \, {\left(9 \, A + 5 \, C\right)} \cos\left(d x + c\right) + 49 \, A + 25 \, C\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)}{20 \, {\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,"[1/40*(5*sqrt(2)*((15*A + 7*C)*cos(d*x + c)^2 + 2*(15*A + 7*C)*cos(d*x + c) + 15*A + 7*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*(4*A*cos(d*x + c)^3 - 4*A*cos(d*x + c)^2 + 4*(9*A + 5*C)*cos(d*x + c) + 49*A + 25*C)*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), 1/20*(5*sqrt(2)*((15*A + 7*C)*cos(d*x + c)^2 + 2*(15*A + 7*C)*cos(d*x + c) + 15*A + 7*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*(4*A*cos(d*x + c)^3 - 4*A*cos(d*x + c)^2 + 4*(9*A + 5*C)*cos(d*x + c) + 49*A + 25*C)*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
1162,1,434,0,0.517920," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(11 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 11 \, A + 3 \, C\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 \, A \cos\left(d x + c\right) - 19 \, A - 3 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 11 \, A + 3 \, C\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 \, A \cos\left(d x + c\right) - 19 \, A - 3 \, C\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 + 3*C)*cos(d*x + c)^2 + 2*(11*A + 3*C)*cos(d*x + c) + 11*A + 3*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*(4*A*cos(d*x + c)^2 - 12*A*cos(d*x + c) - 19*A - 3*C)*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 + 3*C)*cos(d*x + c)^2 + 2*(11*A + 3*C)*cos(d*x + c) + 11*A + 3*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*(4*A*cos(d*x + c)^2 - 12*A*cos(d*x + c) - 19*A - 3*C)*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
1163,1,406,0,0.560294," ","integrate((A+C*sec(d*x+c)^2)*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 - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - C\right)} \cos\left(d x + c\right) + 7 \, A - C\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 + C\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 - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - C\right)} \cos\left(d x + c\right) + 7 \, A - C\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 + C\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 - C)*cos(d*x + c)^2 + 2*(7*A - C)*cos(d*x + c) + 7*A - 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*(4*A*cos(d*x + c) + 5*A + C)*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 - C)*cos(d*x + c)^2 + 2*(7*A - C)*cos(d*x + c) + 7*A - 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*(4*A*cos(d*x + c) + 5*A + C)*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
1164,1,600,0,0.683327," ","integrate((A+C*sec(d*x+c)^2)/(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 - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 5 \, C\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 + C\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(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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(3 \, A - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 5 \, C\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 + C\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(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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)*((3*A - 5*C)*cos(d*x + c)^2 + 2*(3*A - 5*C)*cos(d*x + c) + 3*A - 5*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 + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + 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)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/4*(sqrt(2)*((3*A - 5*C)*cos(d*x + c)^2 + 2*(3*A - 5*C)*cos(d*x + c) + 3*A - 5*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 + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + 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)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
1165,1,668,0,0.561235," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(A + 9 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(A + 9 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(A + 9 \, C\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 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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) + 6 \, {\left(C \cos\left(d x + c\right)^{3} + 2 \, C \cos\left(d x + c\right)^{2} + C \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(A + 9 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(A + 9 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(A + 9 \, C\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 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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) + 6 \, {\left(C \cos\left(d x + c\right)^{3} + 2 \, C \cos\left(d x + c\right)^{2} + C \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)*((A + 9*C)*cos(d*x + c)^3 + 2*(A + 9*C)*cos(d*x + c)^2 + (A + 9*C)*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*C)*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 6*(C*cos(d*x + c)^3 + 2*C*cos(d*x + c)^2 + C*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)*((A + 9*C)*cos(d*x + c)^3 + 2*(A + 9*C)*cos(d*x + c)^2 + (A + 9*C)*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*C)*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 6*(C*cos(d*x + c)^3 + 2*C*cos(d*x + c)^2 + C*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
1166,1,754,0,0.615534," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{2} {\left({\left(5 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(5 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(5 \, A + 13 \, C\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(2 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) - 2 \, C\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(8 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(8 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 19 \, C\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(5 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(5 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(5 \, A + 13 \, C\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(2 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) - 2 \, C\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(8 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(8 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 19 \, C\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)*((5*A + 13*C)*cos(d*x + c)^4 + 2*(5*A + 13*C)*cos(d*x + c)^3 + (5*A + 13*C)*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*((2*A + 7*C)*cos(d*x + c)^2 + 3*C*cos(d*x + c) - 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 19*C)*cos(d*x + c)^4 + 2*(8*A + 19*C)*cos(d*x + c)^3 + (8*A + 19*C)*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)*((5*A + 13*C)*cos(d*x + c)^4 + 2*(5*A + 13*C)*cos(d*x + c)^3 + (5*A + 13*C)*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*((2*A + 7*C)*cos(d*x + c)^2 + 3*C*cos(d*x + c) - 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 19*C)*cos(d*x + c)^4 + 2*(8*A + 19*C)*cos(d*x + c)^3 + (8*A + 19*C)*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
1167,1,564,0,0.710625," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left({\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right) + 283 \, A + 75 \, C\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 \, A \cos\left(d x + c\right)^{3} + 32 \, {\left(49 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(911 \, A + 255 \, C\right)} \cos\left(d x + c\right) + 2671 \, A + 735 \, C\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 + 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right) + 283 \, A + 75 \, C\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 \, A \cos\left(d x + c\right)^{3} + 32 \, {\left(49 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(911 \, A + 255 \, C\right)} \cos\left(d x + c\right) + 2671 \, A + 735 \, C\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 + 75*C)*cos(d*x + c)^3 + 3*(283*A + 75*C)*cos(d*x + c)^2 + 3*(283*A + 75*C)*cos(d*x + c) + 283*A + 75*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*(96*A*cos(d*x + c)^4 - 160*A*cos(d*x + c)^3 + 32*(49*A + 15*C)*cos(d*x + c)^2 + 5*(911*A + 255*C)*cos(d*x + c) + 2671*A + 735*C)*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 + 75*C)*cos(d*x + c)^3 + 3*(283*A + 75*C)*cos(d*x + c)^2 + 3*(283*A + 75*C)*cos(d*x + c) + 283*A + 75*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*(96*A*cos(d*x + c)^4 - 160*A*cos(d*x + c)^3 + 32*(49*A + 15*C)*cos(d*x + c)^2 + 5*(911*A + 255*C)*cos(d*x + c) + 2671*A + 735*C)*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
1168,1,530,0,0.590243," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right) + 163 \, A + 19 \, C\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} - 160 \, A \cos\left(d x + c\right)^{2} - {\left(503 \, A + 39 \, C\right)} \cos\left(d x + c\right) - 299 \, A - 27 \, C\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 + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right) + 163 \, A + 19 \, C\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} - 160 \, A \cos\left(d x + c\right)^{2} - {\left(503 \, A + 39 \, C\right)} \cos\left(d x + c\right) - 299 \, A - 27 \, C\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 + 19*C)*cos(d*x + c)^3 + 3*(163*A + 19*C)*cos(d*x + c)^2 + 3*(163*A + 19*C)*cos(d*x + c) + 163*A + 19*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*(32*A*cos(d*x + c)^3 - 160*A*cos(d*x + c)^2 - (503*A + 39*C)*cos(d*x + c) - 299*A - 27*C)*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 + 19*C)*cos(d*x + c)^3 + 3*(163*A + 19*C)*cos(d*x + c)^2 + 3*(163*A + 19*C)*cos(d*x + c) + 163*A + 19*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*(32*A*cos(d*x + c)^3 - 160*A*cos(d*x + c)^2 - (503*A + 39*C)*cos(d*x + c) - 299*A - 27*C)*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
1169,1,500,0,0.544264," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{5 \, \sqrt{2} {\left({\left(15 \, A - C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right) + 15 \, A - C\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} + 5 \, {\left(17 \, A + C\right)} \cos\left(d x + c\right) + 49 \, A + C\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{5 \, \sqrt{2} {\left({\left(15 \, A - C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right) + 15 \, A - C\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} + 5 \, {\left(17 \, A + C\right)} \cos\left(d x + c\right) + 49 \, A + C\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*(5*sqrt(2)*((15*A - C)*cos(d*x + c)^3 + 3*(15*A - C)*cos(d*x + c)^2 + 3*(15*A - C)*cos(d*x + c) + 15*A - 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*(32*A*cos(d*x + c)^2 + 5*(17*A + C)*cos(d*x + c) + 49*A + C)*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*(5*sqrt(2)*((15*A - C)*cos(d*x + c)^3 + 3*(15*A - C)*cos(d*x + c)^2 + 3*(15*A - C)*cos(d*x + c) + 15*A - 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*(32*A*cos(d*x + c)^2 + 5*(17*A + C)*cos(d*x + c) + 49*A + C)*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
1170,1,482,0,0.508875," ","integrate((A+C*sec(d*x+c)^2)/(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 + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 3 \, C\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 - 3 \, C\right)} \cos\left(d x + c\right) + 9 \, A - 7 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 3 \, C\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 - 3 \, C\right)} \cos\left(d x + c\right) + 9 \, A - 7 \, C\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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 3*C)*cos(d*x + c)^2 + 3*(19*A + 3*C)*cos(d*x + c) + 19*A + 3*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*((13*A - 3*C)*cos(d*x + c) + 9*A - 7*C)*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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 3*C)*cos(d*x + c)^2 + 3*(19*A + 3*C)*cos(d*x + c) + 19*A + 3*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*((13*A - 3*C)*cos(d*x + c) + 9*A - 7*C)*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
1171,1,716,0,0.630904," ","integrate((A+C*sec(d*x+c)^2)/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 - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 43 \, C\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 - 11 \, C\right)} \cos\left(d x + c\right) + A - 15 \, C\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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\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(5 \, A - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 43 \, C\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 - 11 \, C\right)} \cos\left(d x + c\right) + A - 15 \, C\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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\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)*((5*A - 43*C)*cos(d*x + c)^3 + 3*(5*A - 43*C)*cos(d*x + c)^2 + 3*(5*A - 43*C)*cos(d*x + c) + 5*A - 43*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*((5*A - 11*C)*cos(d*x + c) + A - 15*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 32*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 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)^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 - 43*C)*cos(d*x + c)^3 + 3*(5*A - 43*C)*cos(d*x + c)^2 + 3*(5*A - 43*C)*cos(d*x + c) + 5*A - 43*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*((5*A - 11*C)*cos(d*x + c) + A - 15*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 32*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 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)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
1172,1,800,0,0.561403," ","integrate((A+C*sec(d*x+c)^2)/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 + 115 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A + 115 \, C\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(3 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A + 55 \, C\right)} \cos\left(d x + c\right) + 16 \, C\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) + 80 \, {\left(C \cos\left(d x + c\right)^{4} + 3 \, C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + C \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(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A + 115 \, C\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(3 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A + 55 \, C\right)} \cos\left(d x + c\right) + 16 \, C\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) + 80 \, {\left(C \cos\left(d x + c\right)^{4} + 3 \, C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + C \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)*((3*A + 115*C)*cos(d*x + c)^4 + 3*(3*A + 115*C)*cos(d*x + c)^3 + 3*(3*A + 115*C)*cos(d*x + c)^2 + (3*A + 115*C)*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*((3*A + 35*C)*cos(d*x + c)^2 + (7*A + 55*C)*cos(d*x + c) + 16*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 80*(C*cos(d*x + c)^4 + 3*C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + C*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)*((3*A + 115*C)*cos(d*x + c)^4 + 3*(3*A + 115*C)*cos(d*x + c)^3 + 3*(3*A + 115*C)*cos(d*x + c)^2 + (3*A + 115*C)*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*((3*A + 35*C)*cos(d*x + c)^2 + (7*A + 55*C)*cos(d*x + c) + 16*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 80*(C*cos(d*x + c)^4 + 3*C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + C*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
1173,0,0,0,0.559838," ","integrate(cos(d*x+c)^(9/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^4*sec(d*x + c)^2 + B*cos(d*x + c)^4*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1174,0,0,0,0.472594," ","integrate(cos(d*x+c)^(7/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + B \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((C*cos(d*x + c)^3*sec(d*x + c)^2 + B*cos(d*x + c)^3*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1175,0,0,0,0.454743," ","integrate(cos(d*x+c)^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + B \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((C*cos(d*x + c)^2*sec(d*x + c)^2 + B*cos(d*x + c)^2*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1176,0,0,0,0.449754," ","integrate(cos(d*x+c)^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right) \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)*sec(d*x + c)^2 + B*cos(d*x + c)*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1177,0,0,0,0.465818," ","integrate(cos(d*x+c)^(1/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1178,0,0,0,0.515060," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
1179,0,0,0,0.477440," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
1180,0,0,0,0.564469," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^3*sec(d*x + c)^2 + B*cos(d*x + c)^3*sec(d*x + c) + A*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
1181,0,0,0,0.682459," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2*sec(d*x + c)^2 + B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
1182,0,0,0,0.590066," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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)}, x\right)"," ",0,"integral((C*cos(d*x + c)*sec(d*x + c)^2 + B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1183,0,0,0,0.583252," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c)), x)","F",0
1184,0,0,0,0.469502," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/sqrt(cos(d*x + c)), x)","F",0
1185,0,0,0,0.439518," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/cos(d*x + c)^(3/2), x)","F",0
1186,0,0,0,0.538889," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/cos(d*x + c)^(5/2), x)","F",0
1187,0,0,0,0.584498," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(B + C\right)} a \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + A a \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^4*sec(d*x + c)^3 + (B + C)*a*cos(d*x + c)^4*sec(d*x + c)^2 + (A + B)*a*cos(d*x + c)^4*sec(d*x + c) + A*a*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
1188,0,0,0,0.558067," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3*sec(d*x + c)^3 + (B + C)*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
1189,0,0,0,0.643361," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^2*sec(d*x + c)^3 + (B + C)*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
1190,0,0,0,0.696713," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)*sec(d*x + c)^3 + (B + C)*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
1191,0,0,0,0.631802," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*sec(d*x + c)^3 + (B + C)*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)*sqrt(cos(d*x + c)), x)","F",0
1192,0,0,0,0.546127," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*sec(d*x + c)^3 + (B + C)*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/sqrt(cos(d*x + c)), x)","F",0
1193,0,0,0,0.616252," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \sec\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*sec(d*x + c)^3 + (B + C)*a*sec(d*x + c)^2 + (A + B)*a*sec(d*x + c) + A*a)/cos(d*x + c)^(3/2), x)","F",0
1194,0,0,0,0.994887," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\right)} a^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right) + A a^{2} \cos\left(d x + c\right)^{5}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^5*sec(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^5*sec(d*x + c)^3 + (A + 2*B + C)*a^2*cos(d*x + c)^5*sec(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c)^5*sec(d*x + c) + A*a^2*cos(d*x + c)^5)*sqrt(cos(d*x + c)), x)","F",0
1195,0,0,0,0.467278," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4*sec(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^4*sec(d*x + c)^3 + (A + 2*B + C)*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
1196,0,0,0,0.466676," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^3*sec(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3*sec(d*x + c)^3 + (A + 2*B + C)*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
1197,0,0,0,0.467289," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^2*sec(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^2*sec(d*x + c)^3 + (A + 2*B + C)*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
1198,0,0,0,0.461950," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)*sec(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)*sec(d*x + c)^3 + (A + 2*B + C)*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
1199,0,0,0,0.461932," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*sec(d*x + c)^4 + (B + 2*C)*a^2*sec(d*x + c)^3 + (A + 2*B + C)*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
1200,0,0,0,0.445684," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*sec(d*x + c)^4 + (B + 2*C)*a^2*sec(d*x + c)^3 + (A + 2*B + C)*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
1201,0,0,0,0.468754," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \sec\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \sec\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*sec(d*x + c)^4 + (B + 2*C)*a^2*sec(d*x + c)^3 + (A + 2*B + C)*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
1202,0,0,0,0.913711," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\right)} a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)^{5}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5*sec(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^5*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^5*sec(d*x + c)^3 + (3*A + 3*B + C)*a^3*cos(d*x + c)^5*sec(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c)^5*sec(d*x + c) + A*a^3*cos(d*x + c)^5)*sqrt(cos(d*x + c)), x)","F",0
1203,0,0,0,0.485079," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\right)} a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^4*sec(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^4*sec(d*x + c)^3 + (3*A + 3*B + C)*a^3*cos(d*x + c)^4*sec(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c)^4*sec(d*x + c) + A*a^3*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
1204,0,0,0,0.584801," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\right)} a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^3*sec(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3*sec(d*x + c)^3 + (3*A + 3*B + C)*a^3*cos(d*x + c)^3*sec(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c)^3*sec(d*x + c) + A*a^3*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
1205,0,0,0,0.620484," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\right)} a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^2*sec(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^2*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^2*sec(d*x + c)^3 + (3*A + 3*B + C)*a^3*cos(d*x + c)^2*sec(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c)^2*sec(d*x + c) + A*a^3*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
1206,0,0,0,0.672815," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\right)} a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right) + A a^{3} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)*sec(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)*sec(d*x + c)^3 + (3*A + 3*B + C)*a^3*cos(d*x + c)*sec(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c)*sec(d*x + c) + A*a^3*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1207,0,0,0,0.789337," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + (B + 3*C)*a^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^3 + (3*A + 3*B + C)*a^3*sec(d*x + c)^2 + (3*A + B)*a^3*sec(d*x + c) + A*a^3)*sqrt(cos(d*x + c)), x)","F",0
1208,0,0,0,0.558173," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \sec\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \sec\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a^3*sec(d*x + c)^5 + (B + 3*C)*a^3*sec(d*x + c)^4 + (A + 3*B + 3*C)*a^3*sec(d*x + c)^3 + (3*A + 3*B + C)*a^3*sec(d*x + c)^2 + (3*A + B)*a^3*sec(d*x + c) + A*a^3)/sqrt(cos(d*x + c)), x)","F",0
1209,0,0,0,0.577115," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{4} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right)^{6} + {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right)^{5} + {\left(A + 4 \, B + 6 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, A + 3 \, B + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right)^{3} + {\left(6 \, A + 4 \, B + C\right)} a^{4} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right)^{2} + {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right) + A a^{4} \cos\left(d x + c\right)^{6}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^4*cos(d*x + c)^6*sec(d*x + c)^6 + (B + 4*C)*a^4*cos(d*x + c)^6*sec(d*x + c)^5 + (A + 4*B + 6*C)*a^4*cos(d*x + c)^6*sec(d*x + c)^4 + 2*(2*A + 3*B + 2*C)*a^4*cos(d*x + c)^6*sec(d*x + c)^3 + (6*A + 4*B + C)*a^4*cos(d*x + c)^6*sec(d*x + c)^2 + (4*A + B)*a^4*cos(d*x + c)^6*sec(d*x + c) + A*a^4*cos(d*x + c)^6)*sqrt(cos(d*x + c)), x)","F",0
1210,0,0,0,0.583433," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{4} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{6} + {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{5} + {\left(A + 4 \, B + 6 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, A + 3 \, B + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{3} + {\left(6 \, A + 4 \, B + C\right)} a^{4} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{2} + {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right) + A a^{4} \cos\left(d x + c\right)^{5}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^4*cos(d*x + c)^5*sec(d*x + c)^6 + (B + 4*C)*a^4*cos(d*x + c)^5*sec(d*x + c)^5 + (A + 4*B + 6*C)*a^4*cos(d*x + c)^5*sec(d*x + c)^4 + 2*(2*A + 3*B + 2*C)*a^4*cos(d*x + c)^5*sec(d*x + c)^3 + (6*A + 4*B + C)*a^4*cos(d*x + c)^5*sec(d*x + c)^2 + (4*A + B)*a^4*cos(d*x + c)^5*sec(d*x + c) + A*a^4*cos(d*x + c)^5)*sqrt(cos(d*x + c)), x)","F",0
1211,0,0,0,0.611988," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{6} + {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{5} + {\left(A + 4 \, B + 6 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, A + 3 \, B + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(6 \, A + 4 \, B + C\right)} a^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + A a^{4} \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^4*cos(d*x + c)^4*sec(d*x + c)^6 + (B + 4*C)*a^4*cos(d*x + c)^4*sec(d*x + c)^5 + (A + 4*B + 6*C)*a^4*cos(d*x + c)^4*sec(d*x + c)^4 + 2*(2*A + 3*B + 2*C)*a^4*cos(d*x + c)^4*sec(d*x + c)^3 + (6*A + 4*B + C)*a^4*cos(d*x + c)^4*sec(d*x + c)^2 + (4*A + B)*a^4*cos(d*x + c)^4*sec(d*x + c) + A*a^4*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
1212,0,0,0,0.576974," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{6} + {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{5} + {\left(A + 4 \, B + 6 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, A + 3 \, B + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(6 \, A + 4 \, B + C\right)} a^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A a^{4} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^4*cos(d*x + c)^3*sec(d*x + c)^6 + (B + 4*C)*a^4*cos(d*x + c)^3*sec(d*x + c)^5 + (A + 4*B + 6*C)*a^4*cos(d*x + c)^3*sec(d*x + c)^4 + 2*(2*A + 3*B + 2*C)*a^4*cos(d*x + c)^3*sec(d*x + c)^3 + (6*A + 4*B + C)*a^4*cos(d*x + c)^3*sec(d*x + c)^2 + (4*A + B)*a^4*cos(d*x + c)^3*sec(d*x + c) + A*a^4*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
1213,0,0,0,0.652208," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{6} + {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{5} + {\left(A + 4 \, B + 6 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, A + 3 \, B + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(6 \, A + 4 \, B + C\right)} a^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + A a^{4} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^4*cos(d*x + c)^2*sec(d*x + c)^6 + (B + 4*C)*a^4*cos(d*x + c)^2*sec(d*x + c)^5 + (A + 4*B + 6*C)*a^4*cos(d*x + c)^2*sec(d*x + c)^4 + 2*(2*A + 3*B + 2*C)*a^4*cos(d*x + c)^2*sec(d*x + c)^3 + (6*A + 4*B + C)*a^4*cos(d*x + c)^2*sec(d*x + c)^2 + (4*A + B)*a^4*cos(d*x + c)^2*sec(d*x + c) + A*a^4*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
1214,0,0,0,0.600019," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{4} \cos\left(d x + c\right) \sec\left(d x + c\right)^{6} + {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right) \sec\left(d x + c\right)^{5} + {\left(A + 4 \, B + 6 \, C\right)} a^{4} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, A + 3 \, B + 2 \, C\right)} a^{4} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(6 \, A + 4 \, B + C\right)} a^{4} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) \sec\left(d x + c\right) + A a^{4} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^4*cos(d*x + c)*sec(d*x + c)^6 + (B + 4*C)*a^4*cos(d*x + c)*sec(d*x + c)^5 + (A + 4*B + 6*C)*a^4*cos(d*x + c)*sec(d*x + c)^4 + 2*(2*A + 3*B + 2*C)*a^4*cos(d*x + c)*sec(d*x + c)^3 + (6*A + 4*B + C)*a^4*cos(d*x + c)*sec(d*x + c)^2 + (4*A + B)*a^4*cos(d*x + c)*sec(d*x + c) + A*a^4*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1215,0,0,0,0.630398," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{4} \sec\left(d x + c\right)^{6} + {\left(B + 4 \, C\right)} a^{4} \sec\left(d x + c\right)^{5} + {\left(A + 4 \, B + 6 \, C\right)} a^{4} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, A + 3 \, B + 2 \, C\right)} a^{4} \sec\left(d x + c\right)^{3} + {\left(6 \, A + 4 \, B + C\right)} a^{4} \sec\left(d x + c\right)^{2} + {\left(4 \, A + B\right)} a^{4} \sec\left(d x + c\right) + A a^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^4*sec(d*x + c)^6 + (B + 4*C)*a^4*sec(d*x + c)^5 + (A + 4*B + 6*C)*a^4*sec(d*x + c)^4 + 2*(2*A + 3*B + 2*C)*a^4*sec(d*x + c)^3 + (6*A + 4*B + C)*a^4*sec(d*x + c)^2 + (4*A + B)*a^4*sec(d*x + c) + A*a^4)*sqrt(cos(d*x + c)), x)","F",0
1216,0,0,0,0.546076," ","integrate((a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{4} \sec\left(d x + c\right)^{6} + {\left(B + 4 \, C\right)} a^{4} \sec\left(d x + c\right)^{5} + {\left(A + 4 \, B + 6 \, C\right)} a^{4} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, A + 3 \, B + 2 \, C\right)} a^{4} \sec\left(d x + c\right)^{3} + {\left(6 \, A + 4 \, B + C\right)} a^{4} \sec\left(d x + c\right)^{2} + {\left(4 \, A + B\right)} a^{4} \sec\left(d x + c\right) + A a^{4}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a^4*sec(d*x + c)^6 + (B + 4*C)*a^4*sec(d*x + c)^5 + (A + 4*B + 6*C)*a^4*sec(d*x + c)^4 + 2*(2*A + 3*B + 2*C)*a^4*sec(d*x + c)^3 + (6*A + 4*B + C)*a^4*sec(d*x + c)^2 + (4*A + B)*a^4*sec(d*x + c) + A*a^4)/sqrt(cos(d*x + c)), x)","F",0
1217,0,0,0,0.511441," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^3*sec(d*x + c)^2 + B*cos(d*x + c)^3*sec(d*x + c) + A*cos(d*x + c)^3)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
1218,0,0,0,0.582443," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
1219,0,0,0,0.514832," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
1220,0,0,0,0.583595," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
1221,0,0,0,0.544709," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) \sec\left(d x + c\right) + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
1222,0,0,0,0.493718," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \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((C*sec(d*x + c)^2 + 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
1223,0,0,0,0.534391," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \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((C*sec(d*x + c)^2 + 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
1224,0,0,0,0.542272," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{3}\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((C*cos(d*x + c)^3*sec(d*x + c)^2 + B*cos(d*x + c)^3*sec(d*x + c) + A*cos(d*x + c)^3)*sqrt(cos(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
1225,0,0,0,0.529180," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
1226,0,0,0,0.485582," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
1227,0,0,0,0.537095," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
1228,0,0,0,0.590296," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
1229,0,0,0,0.505543," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
1230,0,0,0,0.506261," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
1231,0,0,0,0.499597," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
1232,0,0,0,0.558370," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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^{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((C*cos(d*x + c)^2*sec(d*x + c)^2 + B*cos(d*x + c)^2*sec(d*x + c) + A*cos(d*x + c)^2)*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
1233,0,0,0,0.557070," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
1234,0,0,0,0.471607," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
1235,0,0,0,0.563740," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
1236,0,0,0,0.590825," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
1237,0,0,0,0.547113," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
1238,0,0,0,0.538817," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*sec(d*x + c)^2 + 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
1239,0,0,0,0.612315," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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^{4} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \sec\left(d x + c\right) + a^{4}}, x\right)"," ",0,"integral((C*cos(d*x + c)*sec(d*x + c)^2 + B*cos(d*x + c)*sec(d*x + c) + A*cos(d*x + c))*sqrt(cos(d*x + c))/(a^4*sec(d*x + c)^4 + 4*a^4*sec(d*x + c)^3 + 6*a^4*sec(d*x + c)^2 + 4*a^4*sec(d*x + c) + a^4), x)","F",0
1240,0,0,0,0.492958," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{4} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \sec\left(d x + c\right) + a^{4}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^4*sec(d*x + c)^4 + 4*a^4*sec(d*x + c)^3 + 6*a^4*sec(d*x + c)^2 + 4*a^4*sec(d*x + c) + a^4), x)","F",0
1241,0,0,0,0.547090," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{4} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) \sec\left(d x + c\right) + a^{4} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^4*cos(d*x + c)*sec(d*x + c)^4 + 4*a^4*cos(d*x + c)*sec(d*x + c)^3 + 6*a^4*cos(d*x + c)*sec(d*x + c)^2 + 4*a^4*cos(d*x + c)*sec(d*x + c) + a^4*cos(d*x + c)), x)","F",0
1242,0,0,0,0.577903," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{4} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^4*cos(d*x + c)^2*sec(d*x + c)^4 + 4*a^4*cos(d*x + c)^2*sec(d*x + c)^3 + 6*a^4*cos(d*x + c)^2*sec(d*x + c)^2 + 4*a^4*cos(d*x + c)^2*sec(d*x + c) + a^4*cos(d*x + c)^2), x)","F",0
1243,0,0,0,0.514612," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{4} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^4*cos(d*x + c)^3*sec(d*x + c)^4 + 4*a^4*cos(d*x + c)^3*sec(d*x + c)^3 + 6*a^4*cos(d*x + c)^3*sec(d*x + c)^2 + 4*a^4*cos(d*x + c)^3*sec(d*x + c) + a^4*cos(d*x + c)^3), x)","F",0
1244,0,0,0,0.544249," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a^4*cos(d*x + c)^4*sec(d*x + c)^4 + 4*a^4*cos(d*x + c)^4*sec(d*x + c)^3 + 6*a^4*cos(d*x + c)^4*sec(d*x + c)^2 + 4*a^4*cos(d*x + c)^4*sec(d*x + c) + a^4*cos(d*x + c)^4), x)","F",0
1245,1,125,0,0.456963," ","integrate(cos(d*x+c)^(9/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""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} + 3 \, {\left(16 \, A + 18 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(16 \, A + 18 \, B + 21 \, C\right)} \cos\left(d x + c\right) + 128 \, A + 144 \, B + 168 \, C\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 + 3*(16*A + 18*B + 21*C)*cos(d*x + c)^2 + 4*(16*A + 18*B + 21*C)*cos(d*x + c) + 128*A + 144*B + 168*C)*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
1246,1,104,0,0.433239," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""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} + {\left(24 \, A + 28 \, B + 35 \, C\right)} \cos\left(d x + c\right) + 48 \, A + 56 \, B + 70 \, C\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 + (24*A + 28*B + 35*C)*cos(d*x + c) + 48*A + 56*B + 70*C)*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
1247,1,84,0,0.430397," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""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 + 15 \, C\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 + 15*C)*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
1248,1,329,0,0.595757," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\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(C \cos\left(d x + c\right) + C\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 \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(C \cos\left(d x + c\right) + C\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*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) + 3*(C*cos(d*x + c) + 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) + d), 1/3*(2*(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) + 3*(C*cos(d*x + c) + 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) + d)]","A",0
1249,1,371,0,0.543670," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, A \cos\left(d x + c\right) + C\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 \, B + C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B + C\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 \, {\left(2 \, A \cos\left(d x + c\right) + C\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 \, B + C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B + C\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*(2*A*cos(d*x + c) + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((2*B + C)*cos(d*x + c)^2 + (2*B + C)*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*cos(d*x + c) + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((2*B + C)*cos(d*x + c)^2 + (2*B + C)*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
1250,1,413,0,0.684395," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left({\left(4 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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(8 \, A + 4 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 4 \, B + 3 \, C\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 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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(8 \, A + 4 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 4 \, B + 3 \, C\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*B + 3*C)*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 4*B + 3*C)*cos(d*x + c)^3 + (8*A + 4*B + 3*C)*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*B + 3*C)*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 4*B + 3*C)*cos(d*x + c)^3 + (8*A + 4*B + 3*C)*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
1251,1,457,0,0.987590," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(8 \, A + 6 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 8 \, C\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(8 \, A + 6 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, A + 6 \, B + 5 \, C\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(8 \, A + 6 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 8 \, C\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(8 \, A + 6 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, A + 6 \, B + 5 \, C\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*(8*A + 6*B + 5*C)*cos(d*x + c)^2 + 2*(6*B + 5*C)*cos(d*x + c) + 8*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 6*B + 5*C)*cos(d*x + c)^4 + (8*A + 6*B + 5*C)*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*(8*A + 6*B + 5*C)*cos(d*x + c)^2 + 2*(6*B + 5*C)*cos(d*x + c) + 8*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 6*B + 5*C)*cos(d*x + c)^4 + (8*A + 6*B + 5*C)*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
1252,1,497,0,1.003969," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 48 \, C\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(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(48 \, A + 40 \, B + 35 \, C\right)} \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(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 48 \, C\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(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(48 \, A + 40 \, B + 35 \, C\right)} \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*(48*A + 40*B + 35*C)*cos(d*x + c)^3 + 2*(48*A + 40*B + 35*C)*cos(d*x + c)^2 + 8*(8*B + 7*C)*cos(d*x + c) + 48*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((48*A + 40*B + 35*C)*cos(d*x + c)^5 + (48*A + 40*B + 35*C)*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*(48*A + 40*B + 35*C)*cos(d*x + c)^3 + 2*(48*A + 40*B + 35*C)*cos(d*x + c)^2 + 8*(8*B + 7*C)*cos(d*x + c) + 48*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((48*A + 40*B + 35*C)*cos(d*x + c)^5 + (48*A + 40*B + 35*C)*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
1253,1,154,0,0.555753," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""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 + 99 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(336 \, A + 374 \, B + 429 \, C\right)} a \cos\left(d x + c\right)^{2} + 4 \, {\left(336 \, A + 374 \, B + 429 \, C\right)} a \cos\left(d x + c\right) + 8 \, {\left(336 \, A + 374 \, B + 429 \, C\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 + 99*C)*a*cos(d*x + c)^3 + 3*(336*A + 374*B + 429*C)*a*cos(d*x + c)^2 + 4*(336*A + 374*B + 429*C)*a*cos(d*x + c) + 8*(336*A + 374*B + 429*C)*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
1254,1,132,0,0.581374," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""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 + 21 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(136 \, A + 156 \, B + 189 \, C\right)} a \cos\left(d x + c\right) + 2 \, {\left(136 \, A + 156 \, B + 189 \, C\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 + 21*C)*a*cos(d*x + c)^2 + (136*A + 156*B + 189*C)*a*cos(d*x + c) + 2*(136*A + 156*B + 189*C)*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
1255,1,110,0,0.435073," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""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 + 35 \, C\right)} a \cos\left(d x + c\right) + {\left(104 \, A + 126 \, B + 175 \, C\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 + 35*C)*a*cos(d*x + c) + (104*A + 126*B + 175*C)*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
1256,1,385,0,0.605113," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\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 + 15 \, C\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(C a \cos\left(d x + c\right) + C 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)}{30 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \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 + 15 \, C\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(C a \cos\left(d x + c\right) + C 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)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/30*(4*(3*A*a*cos(d*x + c)^2 + (9*A + 5*B)*a*cos(d*x + c) + (18*A + 25*B + 15*C)*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*(C*a*cos(d*x + c) + C*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), 1/15*(2*(3*A*a*cos(d*x + c)^2 + (9*A + 5*B)*a*cos(d*x + c) + (18*A + 25*B + 15*C)*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*(C*a*cos(d*x + c) + C*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
1257,1,429,0,0.540118," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, A a \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A + 3 \, B\right)} a \cos\left(d x + c\right) + 3 \, C 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(2 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(2 \, B + 3 \, C\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)}{12 \, {\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)^{2} + 2 \, {\left(5 \, A + 3 \, B\right)} a \cos\left(d x + c\right) + 3 \, C 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(2 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(2 \, B + 3 \, C\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)}{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*cos(d*x + c)^2 + 2*(5*A + 3*B)*a*cos(d*x + c) + 3*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((2*B + 3*C)*a*cos(d*x + c)^2 + (2*B + 3*C)*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)), 1/6*(2*(2*A*a*cos(d*x + c)^2 + 2*(5*A + 3*B)*a*cos(d*x + c) + 3*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((2*B + 3*C)*a*cos(d*x + c)^2 + (2*B + 3*C)*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
1258,1,445,0,0.965181," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, A a \cos\left(d x + c\right)^{2} + {\left(4 \, B + 7 \, C\right)} a \cos\left(d x + c\right) + 2 \, C 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(8 \, A + 12 \, B + 7 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(8 \, A + 12 \, B + 7 \, C\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(8 \, A a \cos\left(d x + c\right)^{2} + {\left(4 \, B + 7 \, C\right)} a \cos\left(d x + c\right) + 2 \, C 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(8 \, A + 12 \, B + 7 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(8 \, A + 12 \, B + 7 \, C\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*(8*A*a*cos(d*x + c)^2 + (4*B + 7*C)*a*cos(d*x + c) + 2*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 12*B + 7*C)*a*cos(d*x + c)^3 + (8*A + 12*B + 7*C)*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*(8*A*a*cos(d*x + c)^2 + (4*B + 7*C)*a*cos(d*x + c) + 2*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A + 12*B + 7*C)*a*cos(d*x + c)^3 + (8*A + 12*B + 7*C)*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
1259,1,467,0,0.757267," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(8 \, A + 14 \, B + 11 \, C\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 11 \, C\right)} a \cos\left(d x + c\right) + 8 \, C 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(24 \, A + 14 \, B + 11 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(24 \, A + 14 \, B + 11 \, C\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(8 \, A + 14 \, B + 11 \, C\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 11 \, C\right)} a \cos\left(d x + c\right) + 8 \, C 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(24 \, A + 14 \, B + 11 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(24 \, A + 14 \, B + 11 \, C\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*(8*A + 14*B + 11*C)*a*cos(d*x + c)^2 + 2*(6*B + 11*C)*a*cos(d*x + c) + 8*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((24*A + 14*B + 11*C)*a*cos(d*x + c)^4 + (24*A + 14*B + 11*C)*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*(8*A + 14*B + 11*C)*a*cos(d*x + c)^2 + 2*(6*B + 11*C)*a*cos(d*x + c) + 8*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((24*A + 14*B + 11*C)*a*cos(d*x + c)^4 + (24*A + 14*B + 11*C)*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
1260,1,509,0,0.920361," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(112 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 15 \, C\right)} a \cos\left(d x + c\right) + 48 \, C 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(112 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{5} + {\left(112 \, A + 88 \, B + 75 \, C\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(112 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 15 \, C\right)} a \cos\left(d x + c\right) + 48 \, C 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(112 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{5} + {\left(112 \, A + 88 \, B + 75 \, C\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*(112*A + 88*B + 75*C)*a*cos(d*x + c)^3 + 2*(48*A + 88*B + 75*C)*a*cos(d*x + c)^2 + 8*(8*B + 15*C)*a*cos(d*x + c) + 48*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((112*A + 88*B + 75*C)*a*cos(d*x + c)^5 + (112*A + 88*B + 75*C)*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*(112*A + 88*B + 75*C)*a*cos(d*x + c)^3 + 2*(48*A + 88*B + 75*C)*a*cos(d*x + c)^2 + 8*(8*B + 15*C)*a*cos(d*x + c) + 48*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((112*A + 88*B + 75*C)*a*cos(d*x + c)^5 + (112*A + 88*B + 75*C)*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
1261,1,551,0,0.883501," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(15 \, {\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{4} + 10 \, {\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, B + 19 \, C\right)} a \cos\left(d x + c\right) + 384 \, C 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({\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{6} + {\left(176 \, A + 150 \, B + 133 \, C\right)} a \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(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{4} + 10 \, {\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, B + 19 \, C\right)} a \cos\left(d x + c\right) + 384 \, C 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({\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{6} + {\left(176 \, A + 150 \, B + 133 \, C\right)} a \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*(176*A + 150*B + 133*C)*a*cos(d*x + c)^4 + 10*(176*A + 150*B + 133*C)*a*cos(d*x + c)^3 + 8*(80*A + 150*B + 133*C)*a*cos(d*x + c)^2 + 48*(10*B + 19*C)*a*cos(d*x + c) + 384*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((176*A + 150*B + 133*C)*a*cos(d*x + c)^6 + (176*A + 150*B + 133*C)*a*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*(176*A + 150*B + 133*C)*a*cos(d*x + c)^4 + 10*(176*A + 150*B + 133*C)*a*cos(d*x + c)^3 + 8*(80*A + 150*B + 133*C)*a*cos(d*x + c)^2 + 48*(10*B + 19*C)*a*cos(d*x + c) + 384*C*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((176*A + 150*B + 133*C)*a*cos(d*x + c)^6 + (176*A + 150*B + 133*C)*a*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
1262,1,189,0,0.441124," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, A a^{2} \cos\left(d x + c\right)^{6} + 315 \, {\left(38 \, A + 13 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + 35 \, {\left(523 \, A + 416 \, B + 143 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(4184 \, A + 4615 \, B + 3718 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 4 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\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)}{45045 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/45045*(3465*A*a^2*cos(d*x + c)^6 + 315*(38*A + 13*B)*a^2*cos(d*x + c)^5 + 35*(523*A + 416*B + 143*C)*a^2*cos(d*x + c)^4 + 5*(4184*A + 4615*B + 3718*C)*a^2*cos(d*x + c)^3 + 3*(8368*A + 9230*B + 10439*C)*a^2*cos(d*x + c)^2 + 4*(8368*A + 9230*B + 10439*C)*a^2*cos(d*x + c) + 8*(8368*A + 9230*B + 10439*C)*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
1263,1,165,0,0.443481," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""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 + 99 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(710 \, A + 803 \, B + 660 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2840 \, A + 3212 \, B + 3795 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(2840 \, A + 3212 \, B + 3795 \, C\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 + 99*C)*a^2*cos(d*x + c)^3 + 3*(710*A + 803*B + 660*C)*a^2*cos(d*x + c)^2 + (2840*A + 3212*B + 3795*C)*a^2*cos(d*x + c) + 2*(2840*A + 3212*B + 3795*C)*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
1264,1,141,0,0.482611," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""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 + 21 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(292 \, A + 345 \, B + 294 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(584 \, A + 690 \, B + 903 \, C\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 + 21*C)*a^2*cos(d*x + c)^2 + (292*A + 345*B + 294*C)*a^2*cos(d*x + c) + (584*A + 690*B + 903*C)*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
1265,1,451,0,0.566654," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\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 + 35 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(230 \, A + 301 \, B + 280 \, C\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(C a^{2} \cos\left(d x + c\right) + C 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)}{210 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \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 + 35 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(230 \, A + 301 \, B + 280 \, C\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(C a^{2} \cos\left(d x + c\right) + C 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)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/210*(4*(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 + 35*C)*a^2*cos(d*x + c) + (230*A + 301*B + 280*C)*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 105*(C*a^2*cos(d*x + c) + C*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), 1/105*(2*(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 + 35*C)*a^2*cos(d*x + c) + (230*A + 301*B + 280*C)*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 105*(C*a^2*cos(d*x + c) + C*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
1266,1,495,0,0.552227," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(43 \, A + 40 \, B + 15 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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(2 \, B + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, B + 5 \, C\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)}{60 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{2 \, {\left(6 \, A a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(43 \, A + 40 \, B + 15 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, C 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(2 \, B + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, B + 5 \, C\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)}{30 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/60*(4*(6*A*a^2*cos(d*x + c)^3 + 2*(14*A + 5*B)*a^2*cos(d*x + c)^2 + 2*(43*A + 40*B + 15*C)*a^2*cos(d*x + c) + 15*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((2*B + 5*C)*a^2*cos(d*x + c)^2 + (2*B + 5*C)*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)), 1/30*(2*(6*A*a^2*cos(d*x + c)^3 + 2*(14*A + 5*B)*a^2*cos(d*x + c)^2 + 2*(43*A + 40*B + 15*C)*a^2*cos(d*x + c) + 15*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((2*B + 5*C)*a^2*cos(d*x + c)^2 + (2*B + 5*C)*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
1267,1,509,0,0.859980," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, A a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(8 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right) + 6 \, C 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(8 \, A + 20 \, B + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 20 \, B + 19 \, C\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)}{48 \, {\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)^{3} + 8 \, {\left(8 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right) + 6 \, C 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(8 \, A + 20 \, B + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 20 \, B + 19 \, C\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)}{24 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/48*(4*(8*A*a^2*cos(d*x + c)^3 + 8*(8*A + 3*B)*a^2*cos(d*x + c)^2 + 3*(4*B + 11*C)*a^2*cos(d*x + c) + 6*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 20*B + 19*C)*a^2*cos(d*x + c)^3 + (8*A + 20*B + 19*C)*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), 1/24*(2*(8*A*a^2*cos(d*x + c)^3 + 8*(8*A + 3*B)*a^2*cos(d*x + c)^2 + 3*(4*B + 11*C)*a^2*cos(d*x + c) + 6*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 20*B + 19*C)*a^2*cos(d*x + c)^3 + (8*A + 20*B + 19*C)*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
1268,1,515,0,0.805861," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(48 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 22 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 17 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, C 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(40 \, A + 38 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(40 \, A + 38 \, B + 25 \, C\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(48 \, A a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 22 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 17 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, C 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(40 \, A + 38 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(40 \, A + 38 \, B + 25 \, C\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*(48*A*a^2*cos(d*x + c)^3 + 3*(8*A + 22*B + 25*C)*a^2*cos(d*x + c)^2 + 2*(6*B + 17*C)*a^2*cos(d*x + c) + 8*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((40*A + 38*B + 25*C)*a^2*cos(d*x + c)^4 + (40*A + 38*B + 25*C)*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*(48*A*a^2*cos(d*x + c)^3 + 3*(8*A + 22*B + 25*C)*a^2*cos(d*x + c)^2 + 2*(6*B + 17*C)*a^2*cos(d*x + c) + 8*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((40*A + 38*B + 25*C)*a^2*cos(d*x + c)^4 + (40*A + 38*B + 25*C)*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
1269,1,533,0,0.947860," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(176 \, A + 200 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 136 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 23 \, C\right)} a^{2} \cos\left(d x + c\right) + 48 \, C 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(304 \, A + 200 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(304 \, A + 200 \, B + 163 \, C\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(176 \, A + 200 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 136 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, B + 23 \, C\right)} a^{2} \cos\left(d x + c\right) + 48 \, C 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(304 \, A + 200 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(304 \, A + 200 \, B + 163 \, C\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*(176*A + 200*B + 163*C)*a^2*cos(d*x + c)^3 + 2*(48*A + 136*B + 163*C)*a^2*cos(d*x + c)^2 + 8*(8*B + 23*C)*a^2*cos(d*x + c) + 48*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((304*A + 200*B + 163*C)*a^2*cos(d*x + c)^5 + (304*A + 200*B + 163*C)*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*(176*A + 200*B + 163*C)*a^2*cos(d*x + c)^3 + 2*(48*A + 136*B + 163*C)*a^2*cos(d*x + c)^2 + 8*(8*B + 23*C)*a^2*cos(d*x + c) + 48*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((304*A + 200*B + 163*C)*a^2*cos(d*x + c)^5 + (304*A + 200*B + 163*C)*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
1270,1,579,0,1.044060," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(15 \, {\left(400 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(272 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 230 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, B + 29 \, C\right)} a^{2} \cos\left(d x + c\right) + 384 \, C 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(400 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(400 \, A + 326 \, B + 283 \, C\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(400 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(272 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 230 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 48 \, {\left(10 \, B + 29 \, C\right)} a^{2} \cos\left(d x + c\right) + 384 \, C 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(400 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(400 \, A + 326 \, B + 283 \, C\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*(400*A + 326*B + 283*C)*a^2*cos(d*x + c)^4 + 10*(272*A + 326*B + 283*C)*a^2*cos(d*x + c)^3 + 8*(80*A + 230*B + 283*C)*a^2*cos(d*x + c)^2 + 48*(10*B + 29*C)*a^2*cos(d*x + c) + 384*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((400*A + 326*B + 283*C)*a^2*cos(d*x + c)^6 + (400*A + 326*B + 283*C)*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*(400*A + 326*B + 283*C)*a^2*cos(d*x + c)^4 + 10*(272*A + 326*B + 283*C)*a^2*cos(d*x + c)^3 + 8*(80*A + 230*B + 283*C)*a^2*cos(d*x + c)^2 + 48*(10*B + 29*C)*a^2*cos(d*x + c) + 384*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((400*A + 326*B + 283*C)*a^2*cos(d*x + c)^6 + (400*A + 326*B + 283*C)*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
1271,1,625,0,0.958032," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(15 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 10 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(920 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 48 \, {\left(40 \, A + 116 \, B + 145 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 128 \, {\left(12 \, B + 35 \, C\right)} a^{2} \cos\left(d x + c\right) + 1280 \, C 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(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{7} + {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{6}\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)}{30720 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}, \frac{2 \, {\left(15 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 10 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(920 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 48 \, {\left(40 \, A + 116 \, B + 145 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 128 \, {\left(12 \, B + 35 \, C\right)} a^{2} \cos\left(d x + c\right) + 1280 \, C 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(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{7} + {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{6}\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)}{15360 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}\right]"," ",0,"[1/30720*(4*(15*(1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^5 + 10*(1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^4 + 8*(920*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^3 + 48*(40*A + 116*B + 145*C)*a^2*cos(d*x + c)^2 + 128*(12*B + 35*C)*a^2*cos(d*x + c) + 1280*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^7 + (1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^6)*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)^7 + d*cos(d*x + c)^6), 1/15360*(2*(15*(1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^5 + 10*(1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^4 + 8*(920*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^3 + 48*(40*A + 116*B + 145*C)*a^2*cos(d*x + c)^2 + 128*(12*B + 35*C)*a^2*cos(d*x + c) + 1280*C*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 15*((1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^7 + (1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^6)*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)^7 + d*cos(d*x + c)^6)]","A",0
1272,1,416,0,0.503539," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""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 + 35 \, C\right)} \cos\left(d x + c\right) - 43 \, A + 91 \, B - 35 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + 35 \, C\right)} \cos\left(d x + c\right) - 43 \, A + 91 \, B - 35 \, C\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 + 35*C)*cos(d*x + c) - 43*A + 91*B - 35*C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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 + 35*C)*cos(d*x + c) - 43*A + 91*B - 35*C)*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
1273,1,378,0,0.534670," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""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 + 15 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + 15 \, C\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 + 15*C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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 + 15*C)*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
1274,1,340,0,0.513125," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C)*a*cos(d*x + c) + (A - B + C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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
1275,1,501,0,0.824302," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""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(C \cos\left(d x + c\right) + C\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{\sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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) + {\left(C \cos\left(d x + c\right) + C\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)}{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) + (C*cos(d*x + c) + 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)) + sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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) + (C*cos(d*x + c) + 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) + a*d)]","A",0
1276,1,580,0,0.670320," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, C \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 \, B - C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B - C\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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B + C\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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B + C\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 \, C \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 \, B - C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B - C\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*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*B - C)*cos(d*x + c)^2 + (2*B - C)*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 + C)*a*cos(d*x + c)^2 + (A - B + C)*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 + C)*a*cos(d*x + c)^2 + (A - B + C)*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*C*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*B - C)*cos(d*x + c)^2 + (2*B - C)*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
1277,1,636,0,0.818245," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left({\left(4 \, B - C\right)} \cos\left(d x + c\right) + 2 \, C\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(8 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A - 4 \, B + 7 \, C\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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B + C\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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B + C\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 \, B - C\right)} \cos\left(d x + c\right) + 2 \, C\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(8 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A - 4 \, B + 7 \, C\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*B - C)*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A - 4*B + 7*C)*cos(d*x + c)^3 + (8*A - 4*B + 7*C)*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 + C)*a*cos(d*x + c)^3 + (A - B + C)*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 + C)*a*cos(d*x + c)^3 + (A - B + C)*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*B - C)*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A - 4*B + 7*C)*cos(d*x + c)^3 + (8*A - 4*B + 7*C)*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
1278,1,680,0,0.925344," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, {\left(8 \, A - 2 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B - C\right)} \cos\left(d x + c\right) + 8 \, C\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(8 \, A - 14 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, A - 14 \, B + 9 \, C\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) + \frac{48 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{3}\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}}}{96 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}, -\frac{48 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{3}\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 \, {\left(8 \, A - 2 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B - C\right)} \cos\left(d x + c\right) + 8 \, C\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(8 \, A - 14 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, A - 14 \, B + 9 \, C\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(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/96*(4*(3*(8*A - 2*B + 7*C)*cos(d*x + c)^2 + 2*(6*B - C)*cos(d*x + c) + 8*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A - 14*B + 9*C)*cos(d*x + c)^4 + (8*A - 14*B + 9*C)*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)) + 48*sqrt(2)*((A - B + C)*a*cos(d*x + c)^4 + (A - B + C)*a*cos(d*x + c)^3)*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)^4 + a*d*cos(d*x + c)^3), -1/48*(48*sqrt(2)*((A - B + C)*a*cos(d*x + c)^4 + (A - B + C)*a*cos(d*x + c)^3)*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*(8*A - 2*B + 7*C)*cos(d*x + c)^2 + 2*(6*B - C)*cos(d*x + c) + 8*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A - 14*B + 9*C)*cos(d*x + c)^4 + (8*A - 14*B + 9*C)*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)))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)]","A",0
1279,1,553,0,1.122756," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, A 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 b \cos\left(d x + c\right) + B 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) + \frac{\sqrt{2} {\left({\left(A - B\right)} a^{2} - {\left(A - B\right)} a b + {\left({\left(A - B\right)} a^{2} - {\left(A - B\right)} a b\right)} \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}}}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{2 \, A 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) + \sqrt{2} {\left({\left(A - B\right)} a^{2} - {\left(A - B\right)} a b + {\left({\left(A - B\right)} a^{2} - {\left(A - B\right)} a b\right)} \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(B b \cos\left(d x + c\right) + B 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)}{a d \cos\left(d x + c\right) + a d}\right]"," ",0,"[1/2*(4*A*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (B*b*cos(d*x + c) + B*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)) + sqrt(2)*((A - B)*a^2 - (A - B)*a*b + ((A - B)*a^2 - (A - B)*a*b)*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) + a*d), (2*A*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^2 - (A - B)*a*b + ((A - B)*a^2 - (A - B)*a*b)*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)) + (B*b*cos(d*x + c) + B*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*cos(d*x + c) + a*d)]","A",0
1280,1,510,0,0.555615," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left({\left(15 \, A - 11 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A - 11 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 15 \, A - 11 \, B + 7 \, C\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 + 5 \, C\right)} \cos\left(d x + c\right) + 147 \, A - 95 \, B + 75 \, C\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 + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A - 11 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 15 \, A - 11 \, B + 7 \, C\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 + 5 \, C\right)} \cos\left(d x + c\right) + 147 \, A - 95 \, B + 75 \, C\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 + 7*C)*cos(d*x + c)^2 + 2*(15*A - 11*B + 7*C)*cos(d*x + c) + 15*A - 11*B + 7*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*(12*A*cos(d*x + c)^3 - 4*(3*A - 5*B)*cos(d*x + c)^2 + 12*(9*A - 5*B + 5*C)*cos(d*x + c) + 147*A - 95*B + 75*C)*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 + 7*C)*cos(d*x + c)^2 + 2*(15*A - 11*B + 7*C)*cos(d*x + c) + 15*A - 11*B + 7*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*(12*A*cos(d*x + c)^3 - 4*(3*A - 5*B)*cos(d*x + c)^2 + 12*(9*A - 5*B + 5*C)*cos(d*x + c) + 147*A - 95*B + 75*C)*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
1281,1,466,0,0.587893," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(11 \, A - 7 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A - 7 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 11 \, A - 7 \, B + 3 \, C\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 - 3 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A - 7 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 11 \, A - 7 \, B + 3 \, C\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 - 3 \, C\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 + 3*C)*cos(d*x + c)^2 + 2*(11*A - 7*B + 3*C)*cos(d*x + c) + 11*A - 7*B + 3*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*(4*A*cos(d*x + c)^2 - 12*(A - B)*cos(d*x + c) - 19*A + 15*B - 3*C)*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 + 3*C)*cos(d*x + c)^2 + 2*(11*A - 7*B + 3*C)*cos(d*x + c) + 11*A - 7*B + 3*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*(4*A*cos(d*x + c)^2 - 12*(A - B)*cos(d*x + c) - 19*A + 15*B - 3*C)*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
1282,1,430,0,0.523475," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(7 \, A - 3 \, B - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 3 \, B - C\right)} \cos\left(d x + c\right) + 7 \, A - 3 \, B - C\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 + C\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 - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 3 \, B - C\right)} \cos\left(d x + c\right) + 7 \, A - 3 \, B - C\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 + C\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 - C)*cos(d*x + c)^2 + 2*(7*A - 3*B - C)*cos(d*x + c) + 7*A - 3*B - 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*(4*A*cos(d*x + c) + 5*A - B + C)*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 - C)*cos(d*x + c)^2 + 2*(7*A - 3*B - C)*cos(d*x + c) + 7*A - 3*B - 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*(4*A*cos(d*x + c) + 5*A - B + C)*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
1283,1,612,0,0.541572," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A + B - 5 \, C\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 + C\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(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A + B - 5 \, C\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 + C\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(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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)*((3*A + B - 5*C)*cos(d*x + c)^2 + 2*(3*A + B - 5*C)*cos(d*x + c) + 3*A + B - 5*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 - B + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + 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)^2 + 2*a^2*d*cos(d*x + c) + a^2*d), -1/4*(sqrt(2)*((3*A + B - 5*C)*cos(d*x + c)^2 + 2*(3*A + B - 5*C)*cos(d*x + c) + 3*A + B - 5*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 - B + C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 4*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + 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)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)]","A",0
1284,1,728,0,0.809074," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(A - 5 \, B + 9 \, C\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 - B + 3 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B - 3 \, C\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(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(A - 5 \, B + 9 \, C\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 - B + 3 \, C\right)} \cos\left(d x + c\right) + 2 \, C\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 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B - 3 \, C\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)*((A - 5*B + 9*C)*cos(d*x + c)^3 + 2*(A - 5*B + 9*C)*cos(d*x + c)^2 + (A - 5*B + 9*C)*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 - B + 3*C)*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*((2*B - 3*C)*cos(d*x + c)^3 + 2*(2*B - 3*C)*cos(d*x + c)^2 + (2*B - 3*C)*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)*((A - 5*B + 9*C)*cos(d*x + c)^3 + 2*(A - 5*B + 9*C)*cos(d*x + c)^2 + (A - 5*B + 9*C)*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 - B + 3*C)*cos(d*x + c) + 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*((2*B - 3*C)*cos(d*x + c)^3 + 2*(2*B - 3*C)*cos(d*x + c)^2 + (2*B - 3*C)*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
1285,1,808,0,0.868425," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{2} {\left({\left(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(5 \, A - 9 \, B + 13 \, C\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(2 \, A - 6 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(4 \, B - 3 \, C\right)} \cos\left(d x + c\right) - 2 \, C\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(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A - 12 \, B + 19 \, C\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(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(5 \, A - 9 \, B + 13 \, C\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(2 \, A - 6 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(4 \, B - 3 \, C\right)} \cos\left(d x + c\right) - 2 \, C\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(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, A - 12 \, B + 19 \, C\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)*((5*A - 9*B + 13*C)*cos(d*x + c)^4 + 2*(5*A - 9*B + 13*C)*cos(d*x + c)^3 + (5*A - 9*B + 13*C)*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*((2*A - 6*B + 7*C)*cos(d*x + c)^2 - (4*B - 3*C)*cos(d*x + c) - 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A - 12*B + 19*C)*cos(d*x + c)^4 + 2*(8*A - 12*B + 19*C)*cos(d*x + c)^3 + (8*A - 12*B + 19*C)*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)*((5*A - 9*B + 13*C)*cos(d*x + c)^4 + 2*(5*A - 9*B + 13*C)*cos(d*x + c)^3 + (5*A - 9*B + 13*C)*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*((2*A - 6*B + 7*C)*cos(d*x + c)^2 - (4*B - 3*C)*cos(d*x + c) - 2*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + ((8*A - 12*B + 19*C)*cos(d*x + c)^4 + 2*(8*A - 12*B + 19*C)*cos(d*x + c)^3 + (8*A - 12*B + 19*C)*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
1286,1,614,0,0.474115," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left({\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right) + 283 \, A - 163 \, B + 75 \, C\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 + 15 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(911 \, A - 503 \, B + 255 \, C\right)} \cos\left(d x + c\right) + 2671 \, A - 1495 \, B + 735 \, C\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 + 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right) + 283 \, A - 163 \, B + 75 \, C\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 + 15 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(911 \, A - 503 \, B + 255 \, C\right)} \cos\left(d x + c\right) + 2671 \, A - 1495 \, B + 735 \, C\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 + 75*C)*cos(d*x + c)^3 + 3*(283*A - 163*B + 75*C)*cos(d*x + c)^2 + 3*(283*A - 163*B + 75*C)*cos(d*x + c) + 283*A - 163*B + 75*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*(96*A*cos(d*x + c)^4 - 160*(A - B)*cos(d*x + c)^3 + 32*(49*A - 25*B + 15*C)*cos(d*x + c)^2 + 5*(911*A - 503*B + 255*C)*cos(d*x + c) + 2671*A - 1495*B + 735*C)*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 + 75*C)*cos(d*x + c)^3 + 3*(283*A - 163*B + 75*C)*cos(d*x + c)^2 + 3*(283*A - 163*B + 75*C)*cos(d*x + c) + 283*A - 163*B + 75*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*(96*A*cos(d*x + c)^4 - 160*(A - B)*cos(d*x + c)^3 + 32*(49*A - 25*B + 15*C)*cos(d*x + c)^2 + 5*(911*A - 503*B + 255*C)*cos(d*x + c) + 2671*A - 1495*B + 735*C)*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
1287,1,578,0,0.478158," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left({\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 163 \, A - 75 \, B + 19 \, C\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 + 39 \, C\right)} \cos\left(d x + c\right) - 299 \, A + 147 \, B - 27 \, C\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 + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 163 \, A - 75 \, B + 19 \, C\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 + 39 \, C\right)} \cos\left(d x + c\right) - 299 \, A + 147 \, B - 27 \, C\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 + 19*C)*cos(d*x + c)^3 + 3*(163*A - 75*B + 19*C)*cos(d*x + c)^2 + 3*(163*A - 75*B + 19*C)*cos(d*x + c) + 163*A - 75*B + 19*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*(32*A*cos(d*x + c)^3 - 32*(5*A - 3*B)*cos(d*x + c)^2 - (503*A - 255*B + 39*C)*cos(d*x + c) - 299*A + 147*B - 27*C)*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 + 19*C)*cos(d*x + c)^3 + 3*(163*A - 75*B + 19*C)*cos(d*x + c)^2 + 3*(163*A - 75*B + 19*C)*cos(d*x + c) + 163*A - 75*B + 19*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*(32*A*cos(d*x + c)^3 - 32*(5*A - 3*B)*cos(d*x + c)^2 - (503*A - 255*B + 39*C)*cos(d*x + c) - 299*A + 147*B - 27*C)*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
1288,1,536,0,0.541924," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 75 \, A - 19 \, B - 5 \, C\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 + 5 \, C\right)} \cos\left(d x + c\right) + 49 \, A - 9 \, B + C\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 - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 75 \, A - 19 \, B - 5 \, C\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 + 5 \, C\right)} \cos\left(d x + c\right) + 49 \, A - 9 \, B + C\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 - 5*C)*cos(d*x + c)^3 + 3*(75*A - 19*B - 5*C)*cos(d*x + c)^2 + 3*(75*A - 19*B - 5*C)*cos(d*x + c) + 75*A - 19*B - 5*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*(32*A*cos(d*x + c)^2 + (85*A - 13*B + 5*C)*cos(d*x + c) + 49*A - 9*B + C)*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 - 5*C)*cos(d*x + c)^3 + 3*(75*A - 19*B - 5*C)*cos(d*x + c)^2 + 3*(75*A - 19*B - 5*C)*cos(d*x + c) + 75*A - 19*B - 5*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*(32*A*cos(d*x + c)^2 + (85*A - 13*B + 5*C)*cos(d*x + c) + 49*A - 9*B + C)*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
1289,1,518,0,0.560822," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B + 3 \, C\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 - 3 \, C\right)} \cos\left(d x + c\right) + 9 \, A - B - 7 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B + 3 \, C\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 - 3 \, C\right)} \cos\left(d x + c\right) + 9 \, A - B - 7 \, C\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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 5*B + 3*C)*cos(d*x + c)^2 + 3*(19*A + 5*B + 3*C)*cos(d*x + c) + 19*A + 5*B + 3*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*((13*A - 5*B - 3*C)*cos(d*x + c) + 9*A - B - 7*C)*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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 5*B + 3*C)*cos(d*x + c)^2 + 3*(19*A + 5*B + 3*C)*cos(d*x + c) + 19*A + 5*B + 3*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*((13*A - 5*B - 3*C)*cos(d*x + c) + 9*A - B - 7*C)*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
1290,1,752,0,0.883754," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left({\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B - 43 \, C\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 - 11 \, C\right)} \cos\left(d x + c\right) + A + 7 \, B - 15 \, C\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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\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(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B - 43 \, C\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 - 11 \, C\right)} \cos\left(d x + c\right) + A + 7 \, B - 15 \, C\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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\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)*((5*A + 3*B - 43*C)*cos(d*x + c)^3 + 3*(5*A + 3*B - 43*C)*cos(d*x + c)^2 + 3*(5*A + 3*B - 43*C)*cos(d*x + c) + 5*A + 3*B - 43*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*((5*A + 3*B - 11*C)*cos(d*x + c) + A + 7*B - 15*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 32*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 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)^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 - 43*C)*cos(d*x + c)^3 + 3*(5*A + 3*B - 43*C)*cos(d*x + c)^2 + 3*(5*A + 3*B - 43*C)*cos(d*x + c) + 5*A + 3*B - 43*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*((5*A + 3*B - 11*C)*cos(d*x + c) + A + 7*B - 15*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 32*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 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)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)]","A",0
1291,1,884,0,0.899137," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - 43 \, B + 115 \, C\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(3 \, A - 11 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 15 \, B + 55 \, C\right)} \cos\left(d x + c\right) + 16 \, C\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 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B - 5 \, C\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(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - 43 \, B + 115 \, C\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(3 \, A - 11 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 15 \, B + 55 \, C\right)} \cos\left(d x + c\right) + 16 \, C\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 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B - 5 \, C\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)*((3*A - 43*B + 115*C)*cos(d*x + c)^4 + 3*(3*A - 43*B + 115*C)*cos(d*x + c)^3 + 3*(3*A - 43*B + 115*C)*cos(d*x + c)^2 + (3*A - 43*B + 115*C)*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*((3*A - 11*B + 35*C)*cos(d*x + c)^2 + (7*A - 15*B + 55*C)*cos(d*x + c) + 16*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 16*((2*B - 5*C)*cos(d*x + c)^4 + 3*(2*B - 5*C)*cos(d*x + c)^3 + 3*(2*B - 5*C)*cos(d*x + c)^2 + (2*B - 5*C)*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)*((3*A - 43*B + 115*C)*cos(d*x + c)^4 + 3*(3*A - 43*B + 115*C)*cos(d*x + c)^3 + 3*(3*A - 43*B + 115*C)*cos(d*x + c)^2 + (3*A - 43*B + 115*C)*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*((3*A - 11*B + 35*C)*cos(d*x + c)^2 + (7*A - 15*B + 55*C)*cos(d*x + c) + 16*C)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 16*((2*B - 5*C)*cos(d*x + c)^4 + 3*(2*B - 5*C)*cos(d*x + c)^3 + 3*(2*B - 5*C)*cos(d*x + c)^2 + (2*B - 5*C)*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
1292,0,0,0,0.655120," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^4*sec(d*x + c)^3 + (C*a + 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(cos(d*x + c)), x)","F",0
1293,0,0,0,0.728624," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3*sec(d*x + c)^3 + (C*a + 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
1294,0,0,0,0.939318," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^2*sec(d*x + c)^3 + (C*a + 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
1295,0,0,0,0.715928," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)*sec(d*x + c)^3 + (C*a + 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
1296,0,0,0,0.880349," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
1297,0,0,0,0.718071," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
1298,0,0,0,1.380634," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*sec(d*x + c)^3 + (C*a + 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
1299,0,0,0,0.755918," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \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(C a^{2} + 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{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^4*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^4 + (C*a^2 + 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(cos(d*x + c)), x)","F",0
1300,0,0,0,0.656119," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \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(C a^{2} + 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((C*b^2*cos(d*x + c)^3*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^3 + (C*a^2 + 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
1301,0,0,0,0.824376," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \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(C a^{2} + 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((C*b^2*cos(d*x + c)^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^2*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^2 + (C*a^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
1302,0,0,0,0.720998," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right) + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)*sec(d*x + c)^3 + A*a^2*cos(d*x + c) + (C*a^2 + 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
1303,0,0,0,0.684093," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
1304,0,0,0,0.547342," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \sec\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*sec(d*x + c)^3 + A*a^2 + (C*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
1305,0,0,0,0.887869," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{4} + A a^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^5*sec(d*x + c)^4 + A*a^3*cos(d*x + c)^5 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^5*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*cos(d*x + c)^5*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c)^5*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1306,0,0,0,0.737051," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + A a^{3} \cos\left(d x + c\right)^{4} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^4*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4*sec(d*x + c)^4 + A*a^3*cos(d*x + c)^4 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^4*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*cos(d*x + c)^4*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c)^4*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1307,0,0,0,0.816439," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + A a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} 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((C*b^3*cos(d*x + c)^3*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^3*sec(d*x + c)^4 + A*a^3*cos(d*x + c)^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*cos(d*x + c)^3*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c)^3*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1308,0,0,0,0.892205," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + A a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} 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((C*b^3*cos(d*x + c)^2*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^2*sec(d*x + c)^4 + A*a^3*cos(d*x + c)^2 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^2*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*cos(d*x + c)^2*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c)^2*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1309,0,0,0,1.067209," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + A a^{3} \cos\left(d x + c\right) + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} 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((C*b^3*cos(d*x + c)*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)*sec(d*x + c)^4 + A*a^3*cos(d*x + c) + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*cos(d*x + c)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c)*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1310,0,0,0,0.746531," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, 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{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^3*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*sec(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1311,0,0,0,1.876436," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \sec\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \sec\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, 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{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^3*sec(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*sec(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*sec(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*sec(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*sec(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
1312,0,0,0,0.781724," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{5} + A a^{4} \cos\left(d x + c\right)^{5} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^5*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5*sec(d*x + c)^5 + A*a^4*cos(d*x + c)^5 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^5*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^5*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^5*sec(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c)^5*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1313,0,0,0,0.630090," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{5} + A a^{4} \cos\left(d x + c\right)^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^4*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^4*sec(d*x + c)^5 + A*a^4*cos(d*x + c)^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^4*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^4*sec(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c)^4*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1314,0,0,0,0.866576," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{5} + A a^{4} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} 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((C*b^4*cos(d*x + c)^3*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^3*sec(d*x + c)^5 + A*a^4*cos(d*x + c)^3 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^3*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^3*sec(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c)^3*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1315,0,0,0,0.683685," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{5} + A a^{4} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} 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((C*b^4*cos(d*x + c)^2*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^2*sec(d*x + c)^5 + A*a^4*cos(d*x + c)^2 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^2*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^2*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2*sec(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c)^2*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1316,0,0,0,0.830126," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right) \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{5} + A a^{4} \cos\left(d x + c\right) + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} 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((C*b^4*cos(d*x + c)*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)*sec(d*x + c)^5 + A*a^4*cos(d*x + c) + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)*sec(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c)*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1317,0,0,0,0.689235," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \sec\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \sec\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \sec\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \sec\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, 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)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^4*sec(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*sec(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*sec(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*sec(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*sec(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1318,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1319,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1320,0,0,0,151.493567," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
1321,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1322,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1323,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1324,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1325,0,0,0,171.929548," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
1326,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1327,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1328,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1329,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1330,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1331,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1332,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1333,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1334,0,0,0,0.938708," ","integrate(cos(d*x+c)^(9/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^4*sec(d*x + c)^2 + B*cos(d*x + c)^4*sec(d*x + c) + A*cos(d*x + c)^4)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1335,0,0,0,1.240940," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^3*sec(d*x + c)^2 + 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
1336,0,0,0,0.533573," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
1337,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1338,0,0,0,7.143048," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1339,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1340,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1341,0,0,0,1.106666," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^4*sec(d*x + c)^3 + (C*a + 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
1342,0,0,0,1.322552," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3*sec(d*x + c)^3 + (C*a + 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
1343,0,0,0,2.749232," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^2*sec(d*x + c)^3 + (C*a + 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
1344,0,0,0,4.642106," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b*cos(d*x + c)*sec(d*x + c)^3 + (C*a + 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)*sqrt(cos(d*x + c)), x)","F",0
1345,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1346,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1347,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1348,0,0,0,1.237340," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \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(C a^{2} + 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((C*b^2*cos(d*x + c)^5*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^5*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^5 + (C*a^2 + 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
1349,0,0,0,1.294257," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \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(C a^{2} + 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((C*b^2*cos(d*x + c)^4*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^4*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^4 + (C*a^2 + 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
1350,0,0,0,2.842812," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \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(C a^{2} + 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((C*b^2*cos(d*x + c)^3*sec(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3*sec(d*x + c)^3 + A*a^2*cos(d*x + c)^3 + (C*a^2 + 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
1351,-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)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1352,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1353,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1354,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1355,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1356,0,0,0,0.929365," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + B \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + A \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^3*sec(d*x + c)^2 + B*cos(d*x + c)^3*sec(d*x + c) + A*cos(d*x + c)^3)*sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
1357,0,0,0,0.548211," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
1358,0,0,0,1.096678," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
1359,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1360,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1361,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1362,0,0,0,2.901782," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""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
1363,0,0,0,0.787683," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
1364,0,0,0,1.567657," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
1365,0,0,0,0.558368," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*sec(d*x + c)^2 + 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
1366,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1367,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1368,0,0,0,1.205172," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2*sec(d*x + c)^2 + 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
1369,0,0,0,1.126532," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 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((C*cos(d*x + c)*sec(d*x + c)^2 + 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
1370,0,0,0,1.190375," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*sec(d*x + c)^2 + 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
1371,0,0,0,1.125070," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*sec(d*x + c)^2 + 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
1372,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1373,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
