1,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(5/2), x)","F",0
2,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(3/2), x)","F",0
3,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c)), x)","F",0
4,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/sqrt(b*sec(d*x + c)), x)","F",0
5,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c))^(3/2), x)","F",0
6,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c))^(5/2), x)","F",0
7,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^2, x)","F",0
8,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c), x)","F",0
9,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3), x)","F",0
10,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*cos(d*x + c), x)","F",0
11,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*cos(d*x + c)^2, x)","F",0
12,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c)^2, x)","F",0
13,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c), x)","F",0
14,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3), x)","F",0
15,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c), x)","F",0
16,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c)^2, x)","F",0
17,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(2/3), x)","F",0
18,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(2/3), x)","F",0
19,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c))^(2/3), x)","F",0
20,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(2/3), x)","F",0
21,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(2/3), x)","F",0
22,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
23,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
24,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c))^(4/3), x)","F",0
25,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
26,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
27,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c)^m, x)","F",0
28,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m, x)","F",0
29,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
30,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(1/3), x)","F",0
31,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(2/3), x)","F",0
32,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(4/3), x)","F",0
33,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
34,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^2, x)","F",0
35,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c), x)","F",0
36,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n, x)","F",0
37,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*cos(d*x + c), x)","F",0
38,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*cos(d*x + c)^2, x)","F",0
39,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^(3/2), x)","F",0
40,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
41,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sqrt(sec(d*x + c)), x)","F",0
42,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(3/2), x)","F",0
43,1,214,0,1.114466," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{45 \, {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 45 \, {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(45 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 290 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 130 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 400 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 350 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 190 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 195 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 195 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(45*(A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 45*(A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(45*A*a*tan(1/2*d*x + 1/2*c)^9 + 45*B*a*tan(1/2*d*x + 1/2*c)^9 - 290*A*a*tan(1/2*d*x + 1/2*c)^7 - 130*B*a*tan(1/2*d*x + 1/2*c)^7 + 400*A*a*tan(1/2*d*x + 1/2*c)^5 + 464*B*a*tan(1/2*d*x + 1/2*c)^5 - 350*A*a*tan(1/2*d*x + 1/2*c)^3 - 190*B*a*tan(1/2*d*x + 1/2*c)^3 + 195*A*a*tan(1/2*d*x + 1/2*c) + 195*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
44,1,188,0,0.257528," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, A a + 3 \, B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, A a + 3 \, B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 28 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 49 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 52 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 31 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 39 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*A*a + 3*B*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*A*a + 3*B*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(12*A*a*tan(1/2*d*x + 1/2*c)^7 + 9*B*a*tan(1/2*d*x + 1/2*c)^7 - 28*A*a*tan(1/2*d*x + 1/2*c)^5 - 49*B*a*tan(1/2*d*x + 1/2*c)^5 + 52*A*a*tan(1/2*d*x + 1/2*c)^3 + 31*B*a*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*tan(1/2*d*x + 1/2*c) - 39*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
45,1,154,0,0.989761," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*A*a*tan(1/2*d*x + 1/2*c)^5 + 3*B*a*tan(1/2*d*x + 1/2*c)^5 - 12*A*a*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*tan(1/2*d*x + 1/2*c)^3 + 9*A*a*tan(1/2*d*x + 1/2*c) + 9*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
46,1,124,0,0.278420," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(2 \, A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((2*A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*A*a*tan(1/2*d*x + 1/2*c)^3 + B*a*tan(1/2*d*x + 1/2*c)^3 - 2*A*a*tan(1/2*d*x + 1/2*c) - 3*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
47,1,84,0,1.410753," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} A a + {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"((d*x + c)*A*a + (A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*B*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
48,1,79,0,2.347261," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{B a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - B a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(A a + B a\right)} {\left(d x + c\right)} + \frac{2 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(B*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - B*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (A*a + B*a)*(d*x + c) + 2*A*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
49,1,93,0,0.226135," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(A a + 2 \, B a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((A*a + 2*B*a)*(d*x + c) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 3*A*a*tan(1/2*d*x + 1/2*c) + 2*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
50,1,124,0,0.308082," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(A a + B a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*a + B*a)*(d*x + c) + 2*(3*A*a*tan(1/2*d*x + 1/2*c)^5 + 3*B*a*tan(1/2*d*x + 1/2*c)^5 + 4*A*a*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*tan(1/2*d*x + 1/2*c)^3 + 9*A*a*tan(1/2*d*x + 1/2*c) + 9*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
51,1,156,0,0.474790," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, B a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 49 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 28 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 52 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 39 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*B*a)*(d*x + c) + 2*(9*A*a*tan(1/2*d*x + 1/2*c)^7 + 12*B*a*tan(1/2*d*x + 1/2*c)^7 + 49*A*a*tan(1/2*d*x + 1/2*c)^5 + 28*B*a*tan(1/2*d*x + 1/2*c)^5 + 31*A*a*tan(1/2*d*x + 1/2*c)^3 + 52*B*a*tan(1/2*d*x + 1/2*c)^3 + 39*A*a*tan(1/2*d*x + 1/2*c) + 36*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
52,1,184,0,0.259770," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{45 \, {\left(A a + B a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(45 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 130 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 290 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 190 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 350 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 195 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 195 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(45*(A*a + B*a)*(d*x + c) + 2*(45*A*a*tan(1/2*d*x + 1/2*c)^9 + 45*B*a*tan(1/2*d*x + 1/2*c)^9 + 130*A*a*tan(1/2*d*x + 1/2*c)^7 + 290*B*a*tan(1/2*d*x + 1/2*c)^7 + 464*A*a*tan(1/2*d*x + 1/2*c)^5 + 400*B*a*tan(1/2*d*x + 1/2*c)^5 + 190*A*a*tan(1/2*d*x + 1/2*c)^3 + 350*B*a*tan(1/2*d*x + 1/2*c)^3 + 195*A*a*tan(1/2*d*x + 1/2*c) + 195*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
53,1,246,0,0.729017," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(7 \, A a^{2} + 6 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(7 \, A a^{2} + 6 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(105 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 90 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 490 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 420 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 800 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 864 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 790 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 540 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 375 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 390 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(7*A*a^2 + 6*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(7*A*a^2 + 6*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(105*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 90*B*a^2*tan(1/2*d*x + 1/2*c)^9 - 490*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 420*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 800*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 864*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 790*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 540*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 375*A*a^2*tan(1/2*d*x + 1/2*c) + 390*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
54,1,212,0,0.320635," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(8 \, A a^{2} + 7 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, A a^{2} + 7 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 88 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 77 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 136 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 83 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(8*A*a^2 + 7*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*A*a^2 + 7*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(24*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 21*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 88*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 77*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 136*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 83*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*tan(1/2*d*x + 1/2*c) - 75*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
55,1,178,0,0.627135," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a^{2} + 2 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a^{2} + 2 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(3*A*a^2 + 2*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a^2 + 2*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(9*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 24*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 16*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^2*tan(1/2*d*x + 1/2*c) + 18*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
56,1,154,0,0.490537," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} A a^{2} + {\left(4 \, A a^{2} + 3 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(4 \, A a^{2} + 3 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*A*a^2 + (4*A*a^2 + 3*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (4*A*a^2 + 3*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 2*A*a^2*tan(1/2*d*x + 1/2*c) - 5*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
57,1,157,0,0.962481," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(2 \, A a^{2} + B a^{2}\right)} {\left(d x + c\right)} + {\left(A a^{2} + 2 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a^{2} + 2 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((2*A*a^2 + B*a^2)*(d*x + c) + (A*a^2 + 2*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a^2 + 2*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a^2*tan(1/2*d*x + 1/2*c)^3 - B*a^2*tan(1/2*d*x + 1/2*c)^3 - A*a^2*tan(1/2*d*x + 1/2*c) - B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
58,1,145,0,0.282518," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{2 \, B a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, B a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(3 \, A a^{2} + 4 \, B a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*B*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*B*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (3*A*a^2 + 4*B*a^2)*(d*x + c) + 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^2*tan(1/2*d*x + 1/2*c) + 2*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
59,1,142,0,0.546660," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(2 \, A a^{2} + 3 \, B a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*A*a^2 + 3*B*a^2)*(d*x + c) + 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 16*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 18*A*a^2*tan(1/2*d*x + 1/2*c) + 15*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
60,1,176,0,0.292674," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(7 \, A a^{2} + 8 \, B a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(21 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 77 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 88 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 83 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 136 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 75 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(7*A*a^2 + 8*B*a^2)*(d*x + c) + 2*(21*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 24*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 77*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 88*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 83*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 136*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 75*A*a^2*tan(1/2*d*x + 1/2*c) + 72*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
61,1,210,0,0.329754," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(6 \, A a^{2} + 7 \, B a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(90 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 105 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 420 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 490 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 864 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 540 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 790 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 390 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 375 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(6*A*a^2 + 7*B*a^2)*(d*x + c) + 2*(90*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 105*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 420*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 490*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 864*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 540*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 790*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 390*A*a^2*tan(1/2*d*x + 1/2*c) + 375*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
62,1,280,0,1.454788," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(26 \, A a^{3} + 23 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(26 \, A a^{3} + 23 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(390 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 345 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 2210 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1955 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5148 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4554 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5988 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5814 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4190 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3165 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1530 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(26*A*a^3 + 23*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(26*A*a^3 + 23*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(390*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 345*B*a^3*tan(1/2*d*x + 1/2*c)^11 - 2210*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 1955*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 5148*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 4554*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 5988*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 5814*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 4190*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 3165*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 1530*A*a^3*tan(1/2*d*x + 1/2*c) - 1575*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
63,1,246,0,0.767425," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(15 \, A a^{3} + 13 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(15 \, A a^{3} + 13 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(225 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 195 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1050 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 910 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1920 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1664 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1830 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1330 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 735 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 765 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(15*A*a^3 + 13*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(15*A*a^3 + 13*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(225*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 195*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 1050*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 910*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 1920*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1664*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 1830*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 1330*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 735*A*a^3*tan(1/2*d*x + 1/2*c) + 765*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
64,1,212,0,0.371857," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, A a^{3} + 3 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, A a^{3} + 3 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(60 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 45 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 220 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 165 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 292 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 219 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 132 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 147 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(15*(4*A*a^3 + 3*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*A*a^3 + 3*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(60*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 45*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 220*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 165*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 292*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 219*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 132*A*a^3*tan(1/2*d*x + 1/2*c) - 147*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
65,1,189,0,0.766579," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} A a^{3} + 3 \, {\left(7 \, A a^{3} + 5 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(7 \, A a^{3} + 5 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*A*a^3 + 3*(7*A*a^3 + 5*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(7*A*a^3 + 5*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 36*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 21*A*a^3*tan(1/2*d*x + 1/2*c) + 33*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
66,1,192,0,0.505113," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{4 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(3 \, A a^{3} + B a^{3}\right)} {\left(d x + c\right)} + {\left(6 \, A a^{3} + 7 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(6 \, A a^{3} + 7 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(3*A*a^3 + B*a^3)*(d*x + c) + (6*A*a^3 + 7*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (6*A*a^3 + 7*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 2*A*a^3*tan(1/2*d*x + 1/2*c) - 7*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
67,1,192,0,0.337113," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - {\left(7 \, A a^{3} + 6 \, B a^{3}\right)} {\left(d x + c\right)} - 2 \, {\left(A a^{3} + 3 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(A a^{3} + 3 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(5 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*B*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (7*A*a^3 + 6*B*a^3)*(d*x + c) - 2*(A*a^3 + 3*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(A*a^3 + 3*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(5*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 7*A*a^3*tan(1/2*d*x + 1/2*c) + 2*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
68,1,180,0,1.865191," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{6 \, B a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, B a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(5 \, A a^{3} + 7 \, B a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*B*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*B*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(5*A*a^3 + 7*B*a^3)*(d*x + c) + 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 33*A*a^3*tan(1/2*d*x + 1/2*c) + 21*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
69,1,176,0,0.321532," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, A a^{3} + 4 \, B a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(45 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 220 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 219 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 292 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 147 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 132 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(15*(3*A*a^3 + 4*B*a^3)*(d*x + c) + 2*(45*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 165*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 220*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 219*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 292*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 147*A*a^3*tan(1/2*d*x + 1/2*c) + 132*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
70,1,210,0,0.625649," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(13 \, A a^{3} + 15 \, B a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(195 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 225 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 910 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1050 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1664 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1920 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1330 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1830 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 765 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 735 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(13*A*a^3 + 15*B*a^3)*(d*x + c) + 2*(195*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 225*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 910*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 1050*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 1664*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1920*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 1330*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 1830*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 765*A*a^3*tan(1/2*d*x + 1/2*c) + 735*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
71,1,244,0,0.400465," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(23 \, A a^{3} + 26 \, B a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(345 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 390 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1955 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2210 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4554 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5148 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5814 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5988 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4190 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1530 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(23*A*a^3 + 26*B*a^3)*(d*x + c) + 2*(345*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 390*B*a^3*tan(1/2*d*x + 1/2*c)^11 + 1955*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 2210*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 4554*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 5148*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 5814*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 5988*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 3165*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 4190*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 1575*A*a^3*tan(1/2*d*x + 1/2*c) + 1530*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
72,1,280,0,0.782093," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{105 \, {\left(8 \, A a^{4} + 7 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(8 \, A a^{4} + 7 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(840 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 735 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 4760 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4165 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 11088 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9702 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13488 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 11802 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9320 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7355 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3000 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3105 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(105*(8*A*a^4 + 7*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(8*A*a^4 + 7*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(840*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 735*B*a^4*tan(1/2*d*x + 1/2*c)^11 - 4760*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 4165*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 11088*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 9702*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 13488*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 11802*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 9320*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 7355*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 3000*A*a^4*tan(1/2*d*x + 1/2*c) - 3105*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
73,1,246,0,2.219236," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{105 \, {\left(5 \, A a^{4} + 4 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(5 \, A a^{4} + 4 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(525 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 420 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1960 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4480 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3584 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3950 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3160 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1395 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1500 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(105*(5*A*a^4 + 4*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(5*A*a^4 + 4*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(525*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 420*B*a^4*tan(1/2*d*x + 1/2*c)^9 - 2450*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 1960*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 4480*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 3584*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 3950*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 3160*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 1395*A*a^4*tan(1/2*d*x + 1/2*c) + 1500*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
74,1,223,0,0.633606," ","integrate((a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} A a^{4} + 3 \, {\left(48 \, A a^{4} + 35 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(48 \, A a^{4} + 35 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 424 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 385 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 520 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 511 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 216 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 279 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)*A*a^4 + 3*(48*A*a^4 + 35*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(48*A*a^4 + 35*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 105*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 424*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 385*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 520*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 511*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 216*A*a^4*tan(1/2*d*x + 1/2*c) - 279*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
75,1,227,0,0.804071," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 6 \, {\left(4 \, A a^{4} + B a^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(13 \, A a^{4} + 12 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(13 \, A a^{4} + 12 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 76 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 54 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 6*(4*A*a^4 + B*a^4)*(d*x + c) + 3*(13*A*a^4 + 12*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(13*A*a^4 + 12*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(21*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 30*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 48*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 76*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 27*A*a^4*tan(1/2*d*x + 1/2*c) + 54*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
76,1,230,0,0.318799," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(13 \, A a^{4} + 8 \, B a^{4}\right)} {\left(d x + c\right)} + {\left(8 \, A a^{4} + 13 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(8 \, A a^{4} + 13 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(5 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 7 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((13*A*a^4 + 8*B*a^4)*(d*x + c) + (8*A*a^4 + 13*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (8*A*a^4 + 13*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(5*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 5*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 7*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 7*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 11*A*a^4*tan(1/2*d*x + 1/2*c) + 11*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","A",0
77,1,226,0,0.580150," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{12 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(12 \, A a^{4} + 13 \, B a^{4}\right)} {\left(d x + c\right)} - 6 \, {\left(A a^{4} + 4 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 6 \, {\left(A a^{4} + 4 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(30 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 76 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 54 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(12*B*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(12*A*a^4 + 13*B*a^4)*(d*x + c) - 6*(A*a^4 + 4*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 6*(A*a^4 + 4*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(30*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 21*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 76*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 48*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 54*A*a^4*tan(1/2*d*x + 1/2*c) + 27*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
78,1,214,0,0.333651," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{24 \, B a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, B a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(35 \, A a^{4} + 48 \, B a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 385 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 424 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 511 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 520 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 279 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 216 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*B*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*B*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(35*A*a^4 + 48*B*a^4)*(d*x + c) + 2*(105*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 120*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 385*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 424*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 511*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 520*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 279*A*a^4*tan(1/2*d*x + 1/2*c) + 216*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
79,1,210,0,0.642931," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{105 \, {\left(4 \, A a^{4} + 5 \, B a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(420 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 525 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1960 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2450 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3584 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4480 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3950 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1500 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1395 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(105*(4*A*a^4 + 5*B*a^4)*(d*x + c) + 2*(420*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 525*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 1960*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 2450*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 3584*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 4480*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 3160*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 3950*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 1500*A*a^4*tan(1/2*d*x + 1/2*c) + 1395*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
80,1,244,0,0.930728," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{105 \, {\left(7 \, A a^{4} + 8 \, B a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(735 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 840 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 4165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4760 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 9702 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11088 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11802 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 13488 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7355 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9320 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3000 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(105*(7*A*a^4 + 8*B*a^4)*(d*x + c) + 2*(735*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 840*B*a^4*tan(1/2*d*x + 1/2*c)^11 + 4165*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 4760*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 9702*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 11088*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 11802*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 13488*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 7355*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 9320*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 3105*A*a^4*tan(1/2*d*x + 1/2*c) + 3000*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
81,1,278,0,0.416550," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{105 \, {\left(44 \, A a^{4} + 49 \, B a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(4620 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5145 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 30800 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 34300 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 87164 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 97069 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 135168 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 150528 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 126084 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 134099 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 58800 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 73220 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 22260 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21735 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(44*A*a^4 + 49*B*a^4)*(d*x + c) + 2*(4620*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 5145*B*a^4*tan(1/2*d*x + 1/2*c)^13 + 30800*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 34300*B*a^4*tan(1/2*d*x + 1/2*c)^11 + 87164*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 97069*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 135168*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 150528*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 126084*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 134099*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 58800*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 73220*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 22260*A*a^4*tan(1/2*d*x + 1/2*c) + 21735*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","A",0
82,1,182,0,0.799388," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{9 \, {\left(A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{9 \, {\left(A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a}}{6 \, d}"," ",0,"1/6*(9*(A - B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - 9*(A - B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 6*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a + 2*(9*A*tan(1/2*d*x + 1/2*c)^5 - 15*B*tan(1/2*d*x + 1/2*c)^5 - 12*A*tan(1/2*d*x + 1/2*c)^3 + 16*B*tan(1/2*d*x + 1/2*c)^3 + 3*A*tan(1/2*d*x + 1/2*c) - 9*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
83,1,156,0,0.298548," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, A - 3 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(2 \, A - 3 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a}}{2 \, d}"," ",0,"-1/2*((2*A - 3*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (2*A - 3*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a + 2*(2*A*tan(1/2*d*x + 1/2*c)^3 - 3*B*tan(1/2*d*x + 1/2*c)^3 - 2*A*tan(1/2*d*x + 1/2*c) + B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a))/d","A",0
84,1,109,0,0.790142," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a}}{d}"," ",0,"((A - B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (A - B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a - 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
85,1,70,0,0.242204," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} + \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"(B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a + (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a)/d","A",0
86,1,44,0,0.290414," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} A}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"((d*x + c)*A/a - (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a)/d","A",0
87,1,79,0,0.231035," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(d x + c\right)} {\left(A - B\right)}}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a}}{d}"," ",0,"-((d*x + c)*(A - B)/a - (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a - 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
88,1,123,0,0.215581," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} {\left(3 \, A - 2 \, B\right)}}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((d*x + c)*(3*A - 2*B)/a - 2*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a - 2*(3*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 + A*tan(1/2*d*x + 1/2*c) - 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
89,1,151,0,2.816105," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{9 \, {\left(d x + c\right)} {\left(A - B\right)}}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(9*(d*x + c)*(A - B)/a - 6*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a - 2*(15*A*tan(1/2*d*x + 1/2*c)^5 - 9*B*tan(1/2*d*x + 1/2*c)^5 + 16*A*tan(1/2*d*x + 1/2*c)^3 - 12*B*tan(1/2*d*x + 1/2*c)^3 + 9*A*tan(1/2*d*x + 1/2*c) - 3*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
90,1,226,0,1.572519," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(7 \, A - 10 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(7 \, A - 10 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(7*A - 10*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(7*A - 10*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 2*(15*A*tan(1/2*d*x + 1/2*c)^5 - 30*B*tan(1/2*d*x + 1/2*c)^5 - 24*A*tan(1/2*d*x + 1/2*c)^3 + 40*B*tan(1/2*d*x + 1/2*c)^3 + 9*A*tan(1/2*d*x + 1/2*c) - 18*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + 21*A*a^4*tan(1/2*d*x + 1/2*c) - 27*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
91,1,198,0,0.286772," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(4 \, A - 7 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(4 \, A - 7 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(4*A - 7*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(4*A - 7*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 6*(2*A*tan(1/2*d*x + 1/2*c)^3 - 5*B*tan(1/2*d*x + 1/2*c)^3 - 2*A*tan(1/2*d*x + 1/2*c) + 3*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^4*tan(1/2*d*x + 1/2*c) - 21*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
92,1,151,0,0.293904," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(A - 2 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, {\left(A - 2 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(A - 2*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*(A - 2*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 12*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*A*a^4*tan(1/2*d*x + 1/2*c) - 15*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
93,1,112,0,0.496373," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*tan(1/2*d*x + 1/2*c) - 9*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
94,1,60,0,0.263413," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{6 \, a^{2} d}"," ",0,"-1/6*(A*tan(1/2*d*x + 1/2*c)^3 - B*tan(1/2*d*x + 1/2*c)^3 - 3*A*tan(1/2*d*x + 1/2*c) - 3*B*tan(1/2*d*x + 1/2*c))/(a^2*d)","A",0
95,1,85,0,0.215753," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} A}{a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*A/a^2 + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*A*a^4*tan(1/2*d*x + 1/2*c) + 3*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
96,1,121,0,0.251914," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(d x + c\right)} {\left(2 \, A - B\right)}}{a^{2}} - \frac{12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*(2*A - B)/a^2 - 12*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^4*tan(1/2*d*x + 1/2*c) + 9*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
97,1,164,0,0.257729," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)} {\left(7 \, A - 4 \, B\right)}}{a^{2}} - \frac{6 \, {\left(5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*(7*A - 4*B)/a^2 - 6*(5*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 + 3*A*tan(1/2*d*x + 1/2*c) - 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 - 21*A*a^4*tan(1/2*d*x + 1/2*c) + 15*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
98,1,192,0,0.262965," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} {\left(10 \, A - 7 \, B\right)}}{a^{2}} - \frac{2 \, {\left(30 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(d*x + c)*(10*A - 7*B)/a^2 - 2*(30*A*tan(1/2*d*x + 1/2*c)^5 - 15*B*tan(1/2*d*x + 1/2*c)^5 + 40*A*tan(1/2*d*x + 1/2*c)^3 - 24*B*tan(1/2*d*x + 1/2*c)^3 + 18*A*tan(1/2*d*x + 1/2*c) - 9*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 - 27*A*a^4*tan(1/2*d*x + 1/2*c) + 21*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
99,1,233,0,0.348127," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(6 \, A - 13 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{30 \, {\left(6 \, A - 13 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{60 \, {\left(2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 465 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(6*A - 13*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 30*(6*A - 13*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 60*(2*A*tan(1/2*d*x + 1/2*c)^3 - 7*B*tan(1/2*d*x + 1/2*c)^3 - 2*A*tan(1/2*d*x + 1/2*c) + 5*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 30*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*A*a^12*tan(1/2*d*x + 1/2*c) - 465*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
100,1,186,0,0.305883," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(A - 3 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, {\left(A - 3 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{120 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(A - 3*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*(A - 3*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - 120*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) - 255*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
101,1,147,0,0.672805," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 10*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^12*tan(1/2*d*x + 1/2*c) - 105*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
102,1,75,0,1.010208," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"-1/60*(3*A*tan(1/2*d*x + 1/2*c)^5 - 3*B*tan(1/2*d*x + 1/2*c)^5 - 10*B*tan(1/2*d*x + 1/2*c)^3 - 15*A*tan(1/2*d*x + 1/2*c) - 15*B*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
103,1,75,0,1.908403," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"1/60*(3*A*tan(1/2*d*x + 1/2*c)^5 - 3*B*tan(1/2*d*x + 1/2*c)^5 - 10*A*tan(1/2*d*x + 1/2*c)^3 + 15*A*tan(1/2*d*x + 1/2*c) + 15*B*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
104,1,121,0,0.647865," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} A}{a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*A/a^3 - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 10*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) - 15*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
105,1,157,0,1.524505," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(d x + c\right)} {\left(3 \, A - B\right)}}{a^{3}} - \frac{120 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(60*(d*x + c)*(3*A - B)/a^3 - 120*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 30*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*A*a^12*tan(1/2*d*x + 1/2*c) - 105*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
106,1,200,0,0.472013," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(d x + c\right)} {\left(13 \, A - 6 \, B\right)}}{a^{3}} - \frac{60 \, {\left(7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(d*x + c)*(13*A - 6*B)/a^3 - 60*(7*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 + 5*A*tan(1/2*d*x + 1/2*c) - 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 40*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*A*a^12*tan(1/2*d*x + 1/2*c) - 255*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
107,1,228,0,0.306010," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(d x + c\right)} {\left(23 \, A - 13 \, B\right)}}{a^{3}} - \frac{20 \, {\left(51 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 76 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 50 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 735 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 465 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(d*x + c)*(23*A - 13*B)/a^3 - 20*(51*A*tan(1/2*d*x + 1/2*c)^5 - 21*B*tan(1/2*d*x + 1/2*c)^5 + 76*A*tan(1/2*d*x + 1/2*c)^3 - 36*B*tan(1/2*d*x + 1/2*c)^3 + 33*A*tan(1/2*d*x + 1/2*c) - 15*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 50*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 40*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 735*A*a^12*tan(1/2*d*x + 1/2*c) - 465*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
108,1,267,0,0.865891," ","integrate(sec(d*x+c)^6*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{420 \, {\left(8 \, A - 21 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{420 \, {\left(8 \, A - 21 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{840 \, {\left(2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 147 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 189 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 805 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1365 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5145 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 11655 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(420*(8*A - 21*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 420*(8*A - 21*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 840*(2*A*tan(1/2*d*x + 1/2*c)^3 - 9*B*tan(1/2*d*x + 1/2*c)^3 - 2*A*tan(1/2*d*x + 1/2*c) + 7*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 147*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 189*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 805*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 1365*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 5145*A*a^24*tan(1/2*d*x + 1/2*c) - 11655*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
109,1,220,0,1.331384," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(A - 4 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{840 \, {\left(A - 4 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{1680 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 147 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 805 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5145 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*(A - 4*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 840*(A - 4*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - 1680*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 147*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 805*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 1575*A*a^24*tan(1/2*d*x + 1/2*c) - 5145*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
110,1,181,0,0.578163," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{840 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 63 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 385 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 840*B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 63*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 105*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 385*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^24*tan(1/2*d*x + 1/2*c) - 1575*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
111,1,117,0,0.317870," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"-1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 - 15*B*tan(1/2*d*x + 1/2*c)^7 + 21*A*tan(1/2*d*x + 1/2*c)^5 - 63*B*tan(1/2*d*x + 1/2*c)^5 - 35*A*tan(1/2*d*x + 1/2*c)^3 - 105*B*tan(1/2*d*x + 1/2*c)^3 - 105*A*tan(1/2*d*x + 1/2*c) - 105*B*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
112,1,117,0,0.302917," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 - 15*B*tan(1/2*d*x + 1/2*c)^7 - 21*A*tan(1/2*d*x + 1/2*c)^5 - 21*B*tan(1/2*d*x + 1/2*c)^5 - 35*A*tan(1/2*d*x + 1/2*c)^3 + 35*B*tan(1/2*d*x + 1/2*c)^3 + 105*A*tan(1/2*d*x + 1/2*c) + 105*B*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
113,1,117,0,0.280777," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 63 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"-1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 - 15*B*tan(1/2*d*x + 1/2*c)^7 - 63*A*tan(1/2*d*x + 1/2*c)^5 + 21*B*tan(1/2*d*x + 1/2*c)^5 + 105*A*tan(1/2*d*x + 1/2*c)^3 + 35*B*tan(1/2*d*x + 1/2*c)^3 - 105*A*tan(1/2*d*x + 1/2*c) - 105*B*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
114,1,154,0,0.288123," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(d x + c\right)} A}{a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*(d*x + c)*A/a^4 + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 - 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 63*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*B*a^24*tan(1/2*d*x + 1/2*c)^3 - 1575*A*a^24*tan(1/2*d*x + 1/2*c) + 105*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
115,1,190,0,0.697619," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{840 \, {\left(d x + c\right)} {\left(4 \, A - B\right)}}{a^{4}} - \frac{1680 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 147 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 805 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 385 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5145 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1575 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(840*(d*x + c)*(4*A - B)/a^4 - 1680*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 - 147*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 805*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 385*B*a^24*tan(1/2*d*x + 1/2*c)^3 - 5145*A*a^24*tan(1/2*d*x + 1/2*c) + 1575*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
116,1,233,0,0.282228," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(d x + c\right)} {\left(21 \, A - 8 \, B\right)}}{a^{4}} - \frac{840 \, {\left(9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 189 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 147 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1365 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 805 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 11655 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5145 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(420*(d*x + c)*(21*A - 8*B)/a^4 - 840*(9*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 + 7*A*tan(1/2*d*x + 1/2*c) - 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 - 189*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 147*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 1365*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 805*B*a^24*tan(1/2*d*x + 1/2*c)^3 - 11655*A*a^24*tan(1/2*d*x + 1/2*c) + 5145*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
117,1,261,0,0.340098," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{420 \, {\left(d x + c\right)} {\left(44 \, A - 21 \, B\right)}}{a^{4}} - \frac{280 \, {\left(78 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 124 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 54 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 231 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 189 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2065 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1365 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21945 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11655 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(420*(d*x + c)*(44*A - 21*B)/a^4 - 280*(78*A*tan(1/2*d*x + 1/2*c)^5 - 27*B*tan(1/2*d*x + 1/2*c)^5 + 124*A*tan(1/2*d*x + 1/2*c)^3 - 48*B*tan(1/2*d*x + 1/2*c)^3 + 54*A*tan(1/2*d*x + 1/2*c) - 21*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 - 231*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 189*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 2065*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 1365*B*a^24*tan(1/2*d*x + 1/2*c)^3 - 21945*A*a^24*tan(1/2*d*x + 1/2*c) + 11655*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
118,1,268,0,2.279270," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(315 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 315 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(630 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 420 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(756 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 882 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(522 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 324 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(81 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 107 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"2/315*(315*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 315*sqrt(2)*B*a^5*sgn(cos(d*x + c)) - (630*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 420*sqrt(2)*B*a^5*sgn(cos(d*x + c)) - (756*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 882*sqrt(2)*B*a^5*sgn(cos(d*x + c)) - (522*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 324*sqrt(2)*B*a^5*sgn(cos(d*x + c)) - (81*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 107*sqrt(2)*B*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
119,1,222,0,14.355140," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(175 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 105 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(119 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 147 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(49 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 27 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-2/105*(105*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 105*sqrt(2)*B*a^4*sgn(cos(d*x + c)) - (175*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 105*sqrt(2)*B*a^4*sgn(cos(d*x + c)) - (119*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 147*sqrt(2)*B*a^4*sgn(cos(d*x + c)) - (49*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 27*sqrt(2)*B*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
120,1,176,0,1.163782," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \sqrt{2} A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 15 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(20 \, \sqrt{2} A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 10 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(5 \, \sqrt{2} A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{15 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"2/15*(15*sqrt(2)*A*a^3*sgn(cos(d*x + c)) + 15*sqrt(2)*B*a^3*sgn(cos(d*x + c)) - (20*sqrt(2)*A*a^3*sgn(cos(d*x + c)) + 10*sqrt(2)*B*a^3*sgn(cos(d*x + c)) - (5*sqrt(2)*A*a^3*sgn(cos(d*x + c)) + 7*sqrt(2)*B*a^3*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
121,1,129,0,0.987558," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + \sqrt{2} B a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"-2/3*(3*sqrt(2)*A*a^2*sgn(cos(d*x + c)) + 3*sqrt(2)*B*a^2*sgn(cos(d*x + c)) - (3*sqrt(2)*A*a^2*sgn(cos(d*x + c)) + sqrt(2)*B*a^2*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","B",0
122,1,193,0,1.446962," ","integrate((a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} B a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + \frac{A \sqrt{-a} a \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}}}{d}"," ",0,"-(2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*B*a*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + A*sqrt(-a)*a*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a))/d","B",0
123,1,336,0,5.765040," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}}}{2 \, d}"," ",0,"-1/2*((A*sqrt(-a)*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (A*sqrt(-a)*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a*sgn(cos(d*x + c)) - sqrt(2)*A*sqrt(-a)*a^2*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2))/d","B",0
124,1,630,0,1.576908," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(3 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(3 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) - \frac{4 \, \sqrt{2} {\left(5 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 17 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((3*A*sqrt(-a)*sgn(cos(d*x + c)) + 4*B*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (3*A*sqrt(-a)*sgn(cos(d*x + c)) + 4*B*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) - 4*sqrt(2)*(5*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a*sgn(cos(d*x + c)) - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 17*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 4*B*sqrt(-a)*a^4*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
125,1,889,0,4.965693," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, {\left(5 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(5 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(63 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 30 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 369 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 66 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1638 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 756 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1074 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 732 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 171 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 138 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 13 \, \sqrt{2} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6 \, \sqrt{2} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(3*(5*A*sqrt(-a)*sgn(cos(d*x + c)) + 6*B*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(5*A*sqrt(-a)*sgn(cos(d*x + c)) + 6*B*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(63*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a*sgn(cos(d*x + c)) - 30*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a*sgn(cos(d*x + c)) - 369*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 66*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 1638*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 756*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 1074*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 732*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 171*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 138*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 13*sqrt(2)*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 6*sqrt(2)*B*sqrt(-a)*a^6*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
126,1,1080,0,1.811263," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{15 \, {\left(7 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 15 \, {\left(7 \, A \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8 \, B \sqrt{-a} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) - \frac{4 \, \sqrt{2} {\left(279 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 504 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 285 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5976 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4605 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 31320 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 37281 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 90168 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 35643 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 66024 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9175 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 16904 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1311 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1992 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 43 \, A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 104 \, B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(15*(7*A*sqrt(-a)*sgn(cos(d*x + c)) + 8*B*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 15*(7*A*sqrt(-a)*sgn(cos(d*x + c)) + 8*B*sqrt(-a)*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) - 4*sqrt(2)*(279*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a*sgn(cos(d*x + c)) - 504*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a*sgn(cos(d*x + c)) + 285*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 5976*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 4605*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 31320*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 37281*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 90168*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 35643*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 66024*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 9175*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 16904*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 1311*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 1992*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 43*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 104*B*sqrt(-a)*a^8*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
127,1,258,0,2.093575," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{4 \, {\left({\left({\left({\left(2 \, \sqrt{2} {\left(57 \, A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 47 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \sqrt{2} {\left(57 \, A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 47 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 819 \, \sqrt{2} {\left(A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \sqrt{2} {\left(7 \, A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, \sqrt{2} {\left(A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/315*((((2*sqrt(2)*(57*A*a^6*sgn(cos(d*x + c)) + 47*B*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 9*sqrt(2)*(57*A*a^6*sgn(cos(d*x + c)) + 47*B*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 819*sqrt(2)*(A*a^6*sgn(cos(d*x + c)) + B*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 105*sqrt(2)*(7*A*a^6*sgn(cos(d*x + c)) + 5*B*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 315*sqrt(2)*(A*a^6*sgn(cos(d*x + c)) + B*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
128,1,215,0,1.551838," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{4 \, {\left({\left({\left(2 \, \sqrt{2} {\left(21 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, \sqrt{2} {\left(21 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 19 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 \, \sqrt{2} {\left(3 \, A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \sqrt{2} {\left(A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/105*(((2*sqrt(2)*(21*A*a^5*sgn(cos(d*x + c)) + 19*B*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 7*sqrt(2)*(21*A*a^5*sgn(cos(d*x + c)) + 19*B*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 70*sqrt(2)*(3*A*a^5*sgn(cos(d*x + c)) + 2*B*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 105*sqrt(2)*(A*a^5*sgn(cos(d*x + c)) + B*a^5*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
129,1,170,0,2.068528," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{4 \, {\left({\left(2 \, \sqrt{2} {\left(5 \, A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5 \, \sqrt{2} {\left(5 \, A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \sqrt{2} {\left(A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{15 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"4/15*((2*sqrt(2)*(5*A*a^4*sgn(cos(d*x + c)) + 3*B*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 5*sqrt(2)*(5*A*a^4*sgn(cos(d*x + c)) + 3*B*a^4*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)*(A*a^4*sgn(cos(d*x + c)) + B*a^4*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
130,1,263,0,6.971183," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, A \sqrt{-a} a^{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} + \frac{2 \, {\left(3 \, \sqrt{2} A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3 \, \sqrt{2} A a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4 \, \sqrt{2} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{3 \, d}"," ",0,"-1/3*(3*A*sqrt(-a)*a^2*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) + 2*(3*sqrt(2)*A*a^3*sgn(cos(d*x + c)) + 6*sqrt(2)*B*a^3*sgn(cos(d*x + c)) - (3*sqrt(2)*A*a^3*sgn(cos(d*x + c)) + 4*sqrt(2)*B*a^3*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
131,1,406,0,1.596599," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} B a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + {\left(3 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(3 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}}}{2 \, d}"," ",0,"-1/2*(4*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*B*a^2*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + (3*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (3*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) - sqrt(2)*A*sqrt(-a)*a^3*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2))/d","B",0
132,1,639,0,1.868462," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(7 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(7 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(7 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 95 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 53 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 5 \, A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4 \, B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((7*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 12*B*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (7*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 12*B*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(7*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 95*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 53*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 5*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 4*B*sqrt(-a)*a^5*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
133,1,897,0,1.929545," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, {\left(11 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 14 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(11 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 14 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(33 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 42 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 303 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 822 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2394 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3780 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1806 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2508 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 309 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 498 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 19 \, \sqrt{2} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 30 \, \sqrt{2} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(3*(11*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 14*B*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(11*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 14*B*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(33*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 42*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 303*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 822*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 2394*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 3780*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 1806*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 2508*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 309*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 498*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 19*sqrt(2)*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 30*sqrt(2)*B*sqrt(-a)*a^7*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
134,1,1088,0,8.925346," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, {\left(75 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 88 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(75 \, A \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 88 \, B \sqrt{-a} a \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(225 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 264 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6261 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4008 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 35925 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 33960 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 127449 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 131784 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 101667 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 108312 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 26079 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 29432 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3303 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3384 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 147 \, A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 152 \, B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(3*(75*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 88*B*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(75*A*sqrt(-a)*a*sgn(cos(d*x + c)) + 88*B*sqrt(-a)*a*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(225*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 264*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^2*sgn(cos(d*x + c)) - 6261*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 4008*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 35925*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 33960*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 127449*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 131784*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 101667*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 108312*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 26079*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 29432*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 3303*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 3384*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 147*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 152*B*sqrt(-a)*a^9*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
135,1,306,0,2.272819," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{8 \, {\left({\left({\left({\left(4 \, {\left(2 \, \sqrt{2} {\left(143 \, A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 125 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 11 \, \sqrt{2} {\left(143 \, A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 125 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 99 \, \sqrt{2} {\left(143 \, A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 125 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 231 \, \sqrt{2} {\left(69 \, A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 65 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1155 \, \sqrt{2} {\left(9 \, A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3465 \, \sqrt{2} {\left(A a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{3465 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{5} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/3465*((((4*(2*sqrt(2)*(143*A*a^8*sgn(cos(d*x + c)) + 125*B*a^8*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 11*sqrt(2)*(143*A*a^8*sgn(cos(d*x + c)) + 125*B*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 99*sqrt(2)*(143*A*a^8*sgn(cos(d*x + c)) + 125*B*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 231*sqrt(2)*(69*A*a^8*sgn(cos(d*x + c)) + 65*B*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 1155*sqrt(2)*(9*A*a^8*sgn(cos(d*x + c)) + 7*B*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 3465*sqrt(2)*(A*a^8*sgn(cos(d*x + c)) + B*a^8*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^5*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
136,1,261,0,2.063941," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{8 \, {\left({\left({\left(4 \, {\left(2 \, \sqrt{2} {\left(15 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \sqrt{2} {\left(15 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 63 \, \sqrt{2} {\left(15 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 13 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 210 \, \sqrt{2} {\left(4 \, A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 3 \, B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, \sqrt{2} {\left(A a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{4} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/315*(((4*(2*sqrt(2)*(15*A*a^7*sgn(cos(d*x + c)) + 13*B*a^7*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 9*sqrt(2)*(15*A*a^7*sgn(cos(d*x + c)) + 13*B*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 63*sqrt(2)*(15*A*a^7*sgn(cos(d*x + c)) + 13*B*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 210*sqrt(2)*(4*A*a^7*sgn(cos(d*x + c)) + 3*B*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 315*sqrt(2)*(A*a^7*sgn(cos(d*x + c)) + B*a^7*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^4*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
137,1,216,0,1.776396," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{8 \, {\left({\left(4 \, {\left(2 \, \sqrt{2} {\left(7 \, A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, \sqrt{2} {\left(7 \, A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, \sqrt{2} {\left(7 \, A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5 \, B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \sqrt{2} {\left(A a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + B a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{105 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} d}"," ",0,"8/105*((4*(2*sqrt(2)*(7*A*a^6*sgn(cos(d*x + c)) + 5*B*a^6*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2 - 7*sqrt(2)*(7*A*a^6*sgn(cos(d*x + c)) + 5*B*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 + 35*sqrt(2)*(7*A*a^6*sgn(cos(d*x + c)) + 5*B*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)^2 - 105*sqrt(2)*(A*a^6*sgn(cos(d*x + c)) + B*a^6*sgn(cos(d*x + c))))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*d)","A",0
138,1,309,0,1.960657," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{15 \, A \sqrt{-a} a^{3} \log\left(\frac{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}{{\left| 2 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 4 \, \sqrt{2} {\left| a \right|} - 6 \, a \right|}}\right) \mathrm{sgn}\left(\cos\left(d x + c\right)\right)}{{\left| a \right|}} - \frac{2 \, {\left(45 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 60 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(80 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 80 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(35 \, \sqrt{2} A a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 32 \, \sqrt{2} B a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{15 \, d}"," ",0,"-1/15*(15*A*sqrt(-a)*a^3*log(abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 4*sqrt(2)*abs(a) - 6*a)/abs(2*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 4*sqrt(2)*abs(a) - 6*a))*sgn(cos(d*x + c))/abs(a) - 2*(45*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 60*sqrt(2)*B*a^5*sgn(cos(d*x + c)) - (80*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 80*sqrt(2)*B*a^5*sgn(cos(d*x + c)) - (35*sqrt(2)*A*a^5*sgn(cos(d*x + c)) + 32*sqrt(2)*B*a^5*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","B",0
139,1,480,0,1.962298," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, {\left(5 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(5 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 2 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(3 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 9 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - {\left(3 \, \sqrt{2} A a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 7 \, \sqrt{2} B a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{12 \, {\left(3 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - \sqrt{2} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}}}{6 \, d}"," ",0,"-1/6*(3*(5*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(5*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 2*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(3*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 9*sqrt(2)*B*a^4*sgn(cos(d*x + c)) - (3*sqrt(2)*A*a^4*sgn(cos(d*x + c)) + 7*sqrt(2)*B*a^4*sgn(cos(d*x + c)))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) + 12*(3*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) - sqrt(2)*A*sqrt(-a)*a^4*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2))/d","B",0
140,1,709,0,2.069167," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{16 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} B a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} + {\left(19 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 20 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - {\left(19 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 20 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 171 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 89 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 9 \, A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4 \, B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(16*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*B*a^3*sgn(cos(d*x + c))*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 - a) + (19*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 20*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - (19*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 20*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 171*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 89*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 9*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 4*B*sqrt(-a)*a^6*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
141,1,905,0,2.481582," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, {\left(25 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 38 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(25 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 38 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(75 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 114 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1125 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 1710 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6174 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6804 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4314 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 4284 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 807 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 858 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 49 \, \sqrt{2} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 54 \, \sqrt{2} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(3*(25*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 38*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(25*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 38*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(75*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 114*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 1125*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 1710*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 6174*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 6804*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 4314*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 4284*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 807*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 858*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 49*sqrt(2)*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 54*sqrt(2)*B*sqrt(-a)*a^8*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3)/d","B",0
142,1,1096,0,2.863913," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, {\left(163 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 200 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 3 \, {\left(163 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 200 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, \sqrt{2} {\left(489 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 600 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 10269 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 12600 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 69885 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 103992 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 259233 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 339864 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 209979 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 262920 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 55511 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 73640 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 6687 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 8808 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 299 \, A \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 392 \, B \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(3*(163*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 200*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 3*(163*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 200*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*sqrt(2)*(489*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 600*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 10269*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 12600*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 69885*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 103992*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 259233*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 339864*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 209979*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 262920*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 55511*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 73640*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 6687*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 8808*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 299*A*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 392*B*sqrt(-a)*a^10*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^4)/d","B",0
143,1,1377,0,4.182609," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{15 \, {\left(283 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 326 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right) - 15 \, {\left(283 \, A \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 326 \, B \sqrt{-a} a^{2} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right) + \frac{4 \, {\left(4245 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} A \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4890 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{18} B \sqrt{-a} a^{3} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 114615 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} A \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 132030 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{16} B \sqrt{-a} a^{4} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1298820 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 1319880 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{-a} a^{5} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6176700 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 6888120 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B \sqrt{-a} a^{6} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 16394598 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 18352620 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} a^{7} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 14042770 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 15746180 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a^{8} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 4791060 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 5497320 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{9} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 860300 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 959320 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{10} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 75885 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) + 84810 \, \sqrt{2} {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{11} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2671 \, \sqrt{2} A \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right) - 2990 \, \sqrt{2} B \sqrt{-a} a^{12} \mathrm{sgn}\left(\cos\left(d x + c\right)\right)\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{5}}}{3840 \, d}"," ",0,"-1/3840*(15*(283*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 326*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3))) - 15*(283*A*sqrt(-a)*a^2*sgn(cos(d*x + c)) + 326*B*sqrt(-a)*a^2*sgn(cos(d*x + c)))*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3))) + 4*(4245*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*A*sqrt(-a)*a^3*sgn(cos(d*x + c)) + 4890*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^18*B*sqrt(-a)*a^3*sgn(cos(d*x + c)) - 114615*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*A*sqrt(-a)*a^4*sgn(cos(d*x + c)) - 132030*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^16*B*sqrt(-a)*a^4*sgn(cos(d*x + c)) + 1298820*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(-a)*a^5*sgn(cos(d*x + c)) + 1319880*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(-a)*a^5*sgn(cos(d*x + c)) - 6176700*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*sqrt(-a)*a^6*sgn(cos(d*x + c)) - 6888120*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*sqrt(-a)*a^6*sgn(cos(d*x + c)) + 16394598*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a)*a^7*sgn(cos(d*x + c)) + 18352620*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a)*a^7*sgn(cos(d*x + c)) - 14042770*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a^8*sgn(cos(d*x + c)) - 15746180*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a^8*sgn(cos(d*x + c)) + 4791060*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^9*sgn(cos(d*x + c)) + 5497320*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^9*sgn(cos(d*x + c)) - 860300*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^10*sgn(cos(d*x + c)) - 959320*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^10*sgn(cos(d*x + c)) + 75885*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^11*sgn(cos(d*x + c)) + 84810*sqrt(2)*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^11*sgn(cos(d*x + c)) - 2671*sqrt(2)*A*sqrt(-a)*a^12*sgn(cos(d*x + c)) - 2990*sqrt(2)*B*sqrt(-a)*a^12*sgn(cos(d*x + c)))/((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^5)/d","B",0
144,1,287,0,2.350137," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{105 \, \sqrt{2} {\left(A - B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\frac{105 \, \sqrt{2} A a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - {\left({\left(\frac{\sqrt{2} {\left(119 \, A a^{3} - 92 \, B a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{7 \, \sqrt{2} {\left(37 \, A a^{3} - 16 \, B a^{3}\right)}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{35 \, \sqrt{2} {\left(7 \, A a^{3} - 4 \, B a^{3}\right)}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{3} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{105 \, d}"," ",0,"-1/105*(105*sqrt(2)*(A - B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(105*sqrt(2)*A*a^3/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - ((sqrt(2)*(119*A*a^3 - 92*B*a^3)*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 7*sqrt(2)*(37*A*a^3 - 16*B*a^3)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2 + 35*sqrt(2)*(7*A*a^3 - 4*B*a^3)/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^3*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
145,1,271,0,2.684106," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(\sqrt{2} A - \sqrt{2} B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left({\left(10 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 20 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - {\left(10 \, \sqrt{2} A a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 17 \, \sqrt{2} B a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{15 \, \sqrt{2} B a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{15 \, d}"," ",0,"1/15*(15*(sqrt(2)*A - sqrt(2)*B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*((10*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 20*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - (10*sqrt(2)*A*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 17*sqrt(2)*B*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)*B*a^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
146,1,186,0,2.136573," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} {\left(A - B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{2 \, {\left(\frac{\sqrt{2} {\left(3 \, A a - 2 \, B a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, \sqrt{2} A a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{3 \, d}"," ",0,"-1/3*(3*sqrt(2)*(A - B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 2*(sqrt(2)*(3*A*a - 2*B*a)*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*sqrt(2)*A*a/sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
147,1,144,0,1.984755," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(\sqrt{2} A - \sqrt{2} B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{d}"," ",0,"(2*sqrt(2)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*B*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (sqrt(2)*A - sqrt(2)*B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
148,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.14index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
149,1,393,0,6.625380," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(A - B\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(A - 2 \, B\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left(A - 2 \, B\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} - A \sqrt{-a} a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{2 \, d}"," ",0,"1/2*(sqrt(2)*(A - B)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (A - 2*B)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (A - 2*B)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a) - A*sqrt(-a)*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
150,1,649,0,6.152057," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{4 \, \sqrt{2} {\left(A - B\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(7 \, A - 4 \, B\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left(7 \, A - 4 \, B\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(17 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} - 57 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a + 19 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{2} - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{2} - 3 \, A \sqrt{-a} a^{3} + 4 \, B \sqrt{-a} a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"-1/8*(4*sqrt(2)*(A - B)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (7*A - 4*B)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (7*A - 4*B)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(17*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a) - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a) - 57*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a + 19*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^2 - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^2 - 3*A*sqrt(-a)*a^3 + 4*B*sqrt(-a)*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
151,1,846,0,2.248435," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{24 \, \sqrt{2} {\left(A - B\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{3 \, {\left(9 \, A - 14 \, B\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, {\left(9 \, A - 14 \, B\right)} \log\left({\left| {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{4 \, \sqrt{2} {\left(165 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{-a} - 102 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{-a} - 1323 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A \sqrt{-a} a + 954 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B \sqrt{-a} a + 3906 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{-a} a^{2} - 2268 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{-a} a^{2} - 2118 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A \sqrt{-a} a^{3} + 1044 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B \sqrt{-a} a^{3} + 393 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{-a} a^{4} - 222 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B \sqrt{-a} a^{4} - 31 \, A \sqrt{-a} a^{5} + 18 \, B \sqrt{-a} a^{5}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{48 \, d}"," ",0,"1/48*(24*sqrt(2)*(A - B)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 3*(9*A - 14*B)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 3*(9*A - 14*B)*log(abs((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 4*sqrt(2)*(165*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(-a) - 102*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(-a) - 1323*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*sqrt(-a)*a + 954*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*sqrt(-a)*a + 3906*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(-a)*a^2 - 2268*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(-a)*a^2 - 2118*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*sqrt(-a)*a^3 + 1044*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*sqrt(-a)*a^3 + 393*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(-a)*a^4 - 222*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*sqrt(-a)*a^4 - 31*A*sqrt(-a)*a^5 + 18*B*sqrt(-a)*a^5)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
152,1,312,0,6.953232," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{15 \, \sqrt{2} {\left(11 \, A - 15 \, B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left({\left({\left(\frac{15 \, \sqrt{2} {\left(A a^{3} - B a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(245 \, A a^{3} - 381 \, B a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, \sqrt{2} {\left(73 \, A a^{3} - 105 \, B a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{15 \, \sqrt{2} {\left(9 \, A a^{3} - 17 \, B a^{3}\right)}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}}{60 \, d}"," ",0,"1/60*(15*sqrt(2)*(11*A - 15*B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (((15*sqrt(2)*(A*a^3 - B*a^3)*tan(1/2*d*x + 1/2*c)^2/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(245*A*a^3 - 381*B*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*(73*A*a^3 - 105*B*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 15*sqrt(2)*(9*A*a^3 - 17*B*a^3)/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)^2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/d","A",0
153,1,296,0,2.365552," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(\frac{3 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a} - \frac{2 \, {\left(15 \, \sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 23 \, \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{27 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{3 \, {\left(7 \, \sqrt{2} A - 11 \, \sqrt{2} B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{12 \, d}"," ",0,"1/12*(((3*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a - 2*(15*sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 23*sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a)*tan(1/2*d*x + 1/2*c)^2 + 27*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a)*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 3*(7*sqrt(2)*A - 11*sqrt(2)*B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
154,1,190,0,2.500898," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(\frac{\sqrt{2} {\left(A a^{2} - B a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(A a^{2} - 9 \, B a^{2}\right)}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{\sqrt{2} {\left(3 \, A - 7 \, B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{4 \, d}"," ",0,"-1/4*((sqrt(2)*(A*a^2 - B*a^2)*tan(1/2*d*x + 1/2*c)^2/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(A*a^2 - 9*B*a^2)/(a^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(2)*(3*A - 7*B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
155,1,154,0,1.942013," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(\sqrt{2} A + 3 \, \sqrt{2} B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{{\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}}}{4 \, d}"," ",0,"1/4*((sqrt(2)*A + 3*sqrt(2)*B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - (sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3)/d","B",0
156,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.13index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
157,1,453,0,13.188304," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(9 \, A - 5 \, B\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{4 \, {\left(3 \, A - 2 \, B\right)} \log\left(\frac{{\left| -17179869184 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 34359738368 \, \sqrt{2} {\left| a \right|} + 51539607552 \, a \right|}}{{\left| -17179869184 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 34359738368 \, \sqrt{2} {\left| a \right|} + 51539607552 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{16 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A - A a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"1/8*(sqrt(2)*(9*A - 5*B)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 4*(3*A - 2*B)*log(abs(-17179869184*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 34359738368*sqrt(2)*abs(a) + 51539607552*a)/abs(-17179869184*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 34359738368*sqrt(2)*abs(a) + 51539607552*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 16*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A - A*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
158,1,673,0,3.180441," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} {\left(13 \, A - 9 \, B\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{{\left(19 \, A - 12 \, B\right)} \log\left(\frac{{\left| 147573952589676412928 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 295147905179352825856 \, \sqrt{2} {\left| a \right|} - 442721857769029238784 \, a \right|}}{{\left| 147573952589676412928 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 295147905179352825856 \, \sqrt{2} {\left| a \right|} - 442721857769029238784 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{2 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{4 \, \sqrt{2} {\left(29 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B - 133 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B a + 55 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{2} - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B a^{2} - 7 \, A a^{3} + 4 \, B a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{8 \, d}"," ",0,"-1/8*(sqrt(2)*(13*A - 9*B)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + (19*A - 12*B)*log(abs(147573952589676412928*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 295147905179352825856*sqrt(2)*abs(a) - 442721857769029238784*a)/abs(147573952589676412928*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 295147905179352825856*sqrt(2)*abs(a) - 442721857769029238784*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 2*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 4*sqrt(2)*(29*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B - 133*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*a + 55*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^2 - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*a^2 - 7*A*a^3 + 4*B*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
159,1,851,0,3.342567," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} {\left(17 \, A - 13 \, B\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{3 \, {\left(47 \, A - 38 \, B\right)} \log\left(\frac{{\left| -1947111321950560360698936123457536 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 3894222643901120721397872246915072 \, \sqrt{2} {\left| a \right|} + 5841333965851681082096808370372608 \, a \right|}}{{\left| -1947111321950560360698936123457536 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 3894222643901120721397872246915072 \, \sqrt{2} {\left| a \right|} + 5841333965851681082096808370372608 \, a \right|}}\right)}{\sqrt{-a} {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{12 \, {\left(\sqrt{2} A a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{4 \, \sqrt{2} {\left(339 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A - 174 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B - 3165 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A a + 1842 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B a + 9198 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A a^{2} - 5292 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B a^{2} - 4938 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a^{3} + 2820 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B a^{3} + 975 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{4} - 582 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B a^{4} - 73 \, A a^{5} + 42 \, B a^{5}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{3} \sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{48 \, d}"," ",0,"1/48*(6*sqrt(2)*(17*A - 13*B)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 3*(47*A - 38*B)*log(abs(-1947111321950560360698936123457536*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 3894222643901120721397872246915072*sqrt(2)*abs(a) + 5841333965851681082096808370372608*a)/abs(-1947111321950560360698936123457536*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 3894222643901120721397872246915072*sqrt(2)*abs(a) + 5841333965851681082096808370372608*a))/(sqrt(-a)*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 12*(sqrt(2)*A*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^3 - 4*sqrt(2)*(339*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A - 174*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B - 3165*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*a + 1842*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*a + 9198*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*a^2 - 5292*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*a^2 - 4938*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a^3 + 2820*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*a^3 + 975*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^4 - 582*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*a^4 - 73*A*a^5 + 42*B*a^5)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^3*sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
160,1,311,0,3.395005," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(3 \, {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{2} {\left(15 \, A a^{5} - 23 \, B a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{4 \, \sqrt{2} {\left(75 \, A a^{5} - 167 \, B a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{3 \, \sqrt{2} {\left(83 \, A a^{5} - 155 \, B a^{5}\right)}}{a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{3 \, \sqrt{2} {\left(75 \, A - 163 \, B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{96 \, d}"," ",0,"1/96*(((3*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*(15*A*a^5 - 23*B*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 - 4*sqrt(2)*(75*A*a^5 - 167*B*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)^2 + 3*sqrt(2)*(83*A*a^5 - 155*B*a^5)/(a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - a)*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)) - 3*sqrt(2)*(75*A - 163*B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
161,1,289,0,6.393646," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(\frac{2 \, {\left(\sqrt{2} A a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - \sqrt{2} B a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{9 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 17 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{11 \, \sqrt{2} A a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) - 83 \, \sqrt{2} B a^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{{\left(19 \, \sqrt{2} A - 75 \, \sqrt{2} B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"-1/32*(((2*(sqrt(2)*A*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - sqrt(2)*B*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))*tan(1/2*d*x + 1/2*c)^2/a^8 + (9*sqrt(2)*A*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 17*sqrt(2)*B*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^8)*tan(1/2*d*x + 1/2*c)^2 - (11*sqrt(2)*A*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1) - 83*sqrt(2)*B*a^6*sgn(tan(1/2*d*x + 1/2*c)^2 - 1))/a^8)*tan(1/2*d*x + 1/2*c)/sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a) - (19*sqrt(2)*A - 75*sqrt(2)*B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
162,1,191,0,13.491875," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{\sqrt{2} {\left(3 \, A a^{5} - 11 \, B a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{\sqrt{2} {\left(5 \, A + 19 \, B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"-1/32*(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + sqrt(2)*(3*A*a^5 - 11*B*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) - sqrt(2)*(5*A + 19*B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
163,1,191,0,7.466169," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(5 \, A a^{5} + 3 \, B a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(3 \, A + 5 \, B\right)} \log\left({\left| -\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{32 \, d}"," ",0,"1/32*(sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(5*A*a^5 + 3*B*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(3*A + 5*B)*log(abs(-sqrt(-a)*tan(1/2*d*x + 1/2*c) + sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
164,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos(d*t_nostep+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableWarning, assuming -2*a+a is positive. Hint: run assume to make assumptions on a variableDiscontinuities at zeroes of cos(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Evaluation time: 1.36index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
165,1,499,0,4.674091," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(21 \, A a^{5} - 13 \, B a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(115 \, A - 43 \, B\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{32 \, {\left(5 \, A - 2 \, B\right)} \log\left(\frac{{\left| -562949953421312 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 1125899906842624 \, \sqrt{2} {\left| a \right|} + 1688849860263936 \, a \right|}}{{\left| -562949953421312 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 1125899906842624 \, \sqrt{2} {\left| a \right|} + 1688849860263936 \, a \right|}}\right)}{\sqrt{-a} a {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{128 \, \sqrt{2} {\left(3 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A - A a\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{64 \, d}"," ",0,"1/64*(2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(21*A*a^5 - 13*B*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(115*A - 43*B)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 32*(5*A - 2*B)*log(abs(-562949953421312*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 1125899906842624*sqrt(2)*abs(a) + 1688849860263936*a)/abs(-562949953421312*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 1125899906842624*sqrt(2)*abs(a) + 1688849860263936*a))/(sqrt(-a)*a*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 128*sqrt(2)*(3*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A - A*a)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
166,1,720,0,4.667126," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{\sqrt{2} {\left(29 \, A a^{5} - 21 \, B a^{5}\right)}}{a^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(219 \, A - 115 \, B\right)} \log\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} + \frac{8 \, {\left(39 \, A - 20 \, B\right)} \log\left(\frac{{\left| 309485009821345068724781056 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - 618970019642690137449562112 \, \sqrt{2} {\left| a \right|} - 928455029464035206174343168 \, a \right|}}{{\left| 309485009821345068724781056 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 618970019642690137449562112 \, \sqrt{2} {\left| a \right|} - 928455029464035206174343168 \, a \right|}}\right)}{\sqrt{-a} a {\left| a \right|} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} - \frac{32 \, \sqrt{2} {\left(41 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A - 12 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B - 209 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a + 76 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B a + 91 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{2} - 36 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B a^{2} - 11 \, A a^{3} + 4 \, B a^{3}\right)}}{{\left({\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{-a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{-a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2} \sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{64 \, d}"," ",0,"-1/64*(2*sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*d*x + 1/2*c)^2/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - sqrt(2)*(29*A*a^5 - 21*B*a^5)/(a^8*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))*tan(1/2*d*x + 1/2*c) + sqrt(2)*(219*A - 115*B)*log((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) + 8*(39*A - 20*B)*log(abs(309485009821345068724781056*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - 618970019642690137449562112*sqrt(2)*abs(a) - 928455029464035206174343168*a)/abs(309485009821345068724781056*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 618970019642690137449562112*sqrt(2)*abs(a) - 928455029464035206174343168*a))/(sqrt(-a)*a*abs(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)) - 32*sqrt(2)*(41*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A - 12*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B - 209*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a + 76*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*a + 91*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^2 - 36*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*a^2 - 11*A*a^3 + 4*B*a^3)/(((sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(-a)*tan(1/2*d*x + 1/2*c) - sqrt(-a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2*sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","B",0
167,1,166,0,1.125754," ","integrate((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(A {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}\right)} + \frac{{\left(\sqrt{2} A \sqrt{a} \arctan\left(-i\right) - A \sqrt{a} \arctan\left(-\frac{1}{2} i \, \sqrt{2}\right)\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{a}\right)}}{d}"," ",0,"-2*(A*(sqrt(2)*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c)))) + (sqrt(2)*A*sqrt(a)*arctan(-I) - A*sqrt(a)*arctan(-1/2*I*sqrt(2)))*sgn(tan(1/2*d*x + 1/2*c))/a)/d","C",0
168,1,238,0,1.146633," ","integrate(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{{\left(-2 i \, \sqrt{2} A \arctan\left(-i\right) + 3 i \, A \arctan\left(-\frac{1}{2} i \, \sqrt{2}\right) + \sqrt{2} A\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\sqrt{-a}} + \frac{2 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{3 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{d}"," ",0,"-((-2*I*sqrt(2)*A*arctan(-I) + 3*I*A*arctan(-1/2*I*sqrt(2)) + sqrt(2)*A)*sgn(tan(1/2*d*x + 1/2*c))/sqrt(-a) + 2*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 3*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A/((a*tan(1/2*d*x + 1/2*c)^2 + a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))))/d","C",0
169,1,265,0,4.070861," ","integrate(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{{\left(-8 i \, \sqrt{2} A \arctan\left(-i\right) + 11 i \, A \arctan\left(-\frac{1}{2} i \, \sqrt{2}\right) + 7 \, \sqrt{2} A\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\sqrt{-a}} + \frac{8 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{11 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} {\left(3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{3}{2}} A + 10 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A a\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{4 \, d}"," ",0,"-1/4*((-8*I*sqrt(2)*A*arctan(-I) + 11*I*A*arctan(-1/2*I*sqrt(2)) + 7*sqrt(2)*A)*sgn(tan(1/2*d*x + 1/2*c))/sqrt(-a) + 8*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 11*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - sqrt(2)*(3*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(3/2)*A + 10*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A*a)/((a*tan(1/2*d*x + 1/2*c)^2 + a)^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))))/d","C",0
170,1,290,0,4.361294," ","integrate(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{{\left(-48 i \, \sqrt{2} A \arctan\left(-i\right) + 69 i \, A \arctan\left(-\frac{1}{2} i \, \sqrt{2}\right) + 49 \, \sqrt{2} A\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{\sqrt{-a}} + \frac{48 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{69 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} {\left(21 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{5}{2}} A + 80 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{3}{2}} A a + 108 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A a^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{24 \, d}"," ",0,"-1/24*((-48*I*sqrt(2)*A*arctan(-I) + 69*I*A*arctan(-1/2*I*sqrt(2)) + 49*sqrt(2)*A)*sgn(tan(1/2*d*x + 1/2*c))/sqrt(-a) + 48*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 69*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - sqrt(2)*(21*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(5/2)*A + 80*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(3/2)*A*a + 108*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A*a^2)/((a*tan(1/2*d*x + 1/2*c)^2 + a)^3*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))))/d","C",0
171,1,196,0,1.148116," ","integrate((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{4 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(3*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 4*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^2))/d","A",0
172,1,261,0,2.211715," ","integrate(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{7 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{10 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{3 \, \sqrt{2} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{3}{2}} A + 4 \, \sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A a}{{\left({\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} + 3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a + 2 \, a^{2}\right)} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{2 \, d}"," ",0,"-1/2*(7*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 10*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - (3*sqrt(2)*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(3/2)*A + 4*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A*a)/(((a*tan(1/2*d*x + 1/2*c)^2 - a)^2 + 3*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a + 2*a^2)*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))))/d","B",0
173,1,295,0,1.453801," ","integrate(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{22 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{31 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} {\left(7 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{3}{2}} A + 18 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A a\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{2 \, \sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{4 \, d}"," ",0,"-1/4*(22*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 31*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - sqrt(2)*(7*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(3/2)*A + 18*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A*a)/((a*tan(1/2*d*x + 1/2*c)^2 + a)^2*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^2))/d","A",0
174,1,320,0,1.529447," ","integrate(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{180 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{255 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{12 \, \sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{\sqrt{2} {\left(63 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{5}{2}} A + 272 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{3}{2}} A a + 324 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A a^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{3} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{24 \, d}"," ",0,"-1/24*(180*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 255*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 12*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A/(a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^2) - sqrt(2)*(63*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(5/2)*A + 272*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(3/2)*A*a + 324*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A*a^2)/((a*tan(1/2*d*x + 1/2*c)^2 + a)^3*a*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))))/d","A",0
175,1,222,0,1.365094," ","integrate((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{23 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{32 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} {\left(9 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{3}{2}} A + 7 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A a\right)}}{a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{16 \, d}"," ",0,"-1/16*(23*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 32*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - sqrt(2)*(9*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(3/2)*A + 7*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A*a)/(a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^4))/d","A",0
176,1,295,0,1.468809," ","integrate(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{79 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{112 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{16 \, \sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} {\left(17 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{3}{2}} A + 15 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A a\right)}}{a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{16 \, d}"," ",0,"-1/16*(79*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 112*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 16*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A/((a*tan(1/2*d*x + 1/2*c)^2 + a)*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - sqrt(2)*(17*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(3/2)*A + 15*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A*a)/(a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^4))/d","A",0
177,1,308,0,2.918144," ","integrate(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{167 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{236 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} {\left(69 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{7}{2}} A + 315 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{5}{2}} A a + 444 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{3}{2}} A a^{2} + 196 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A a^{3}\right)}}{{\left({\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{2} + 3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)} a + 2 \, a^{2}\right)}^{2} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{16 \, d}"," ",0,"-1/16*(167*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 236*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - sqrt(2)*(69*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(7/2)*A + 315*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(5/2)*A*a + 444*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(3/2)*A*a^2 + 196*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A*a^3)/(((a*tan(1/2*d*x + 1/2*c)^2 - a)^2 + 3*(a*tan(1/2*d*x + 1/2*c)^2 - a)*a + 2*a^2)^2*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))))/d","A",0
178,1,346,0,1.936226," ","integrate(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{861 \, \sqrt{2} A \arctan\left(\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{\sqrt{a}}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{1218 \, A \arctan\left(\frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a}}{2 \, \sqrt{a}}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{2 \, \sqrt{2} {\left(129 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{5}{2}} A + 560 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{3}{2}} A a + 636 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A a^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{3} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{3 \, \sqrt{2} {\left(33 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a\right)}^{\frac{3}{2}} A + 31 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a} A a\right)}}{a^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{48 \, d}"," ",0,"-1/48*(861*sqrt(2)*A*arctan(sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 1218*A*arctan(1/2*sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)/sqrt(a))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 2*sqrt(2)*(129*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(5/2)*A + 560*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(3/2)*A*a + 636*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A*a^2)/((a*tan(1/2*d*x + 1/2*c)^2 + a)^3*a^2*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))) - 3*sqrt(2)*(33*(a*tan(1/2*d*x + 1/2*c)^2 - a)^(3/2)*A + 31*sqrt(a*tan(1/2*d*x + 1/2*c)^2 - a)*A*a)/(a^4*sgn(tan(1/2*d*x + 1/2*c)^2 - 1)*sgn(tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^4))/d","A",0
179,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
180,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
181,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
182,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
183,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
184,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
185,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
186,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
187,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
188,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
189,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
190,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
191,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
192,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(9/2), x)","F",0
193,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
194,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
195,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
196,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
197,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(5/2), x)","F",0
198,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(7/2), x)","F",0
199,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(9/2), x)","F",0
200,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(11/2), x)","F",0
201,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a), x)","F",0
202,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
203,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
204,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
205,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
206,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
207,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
208,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
209,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^2, x)","F",0
210,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
211,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
212,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
213,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
214,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
215,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
216,0,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(9/2)/(a*sec(d*x + c) + a)^3, x)","F",0
217,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^3, x)","F",0
218,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^3, x)","F",0
219,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
220,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
221,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
222,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
223,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
224,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
225,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
226,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
227,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
228,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
229,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
230,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
231,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2), x)","F",0
232,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
233,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
234,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
235,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
236,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
237,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
238,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(9/2), x)","F",0
239,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2), x)","F",0
240,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
241,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
242,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
243,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
244,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(5/2), x)","F",0
245,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(7/2), x)","F",0
246,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(9/2), x)","F",0
247,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(11/2), x)","F",0
248,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
249,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
250,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
251,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
252,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
253,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
254,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
255,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
256,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
257,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
258,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^(3/2), x)","F",0
259,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
260,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
261,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2)), x)","F",0
262,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
263,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
264,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
265,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^(5/2), x)","F",0
266,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
267,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
268,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
269,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(2/3), x)","F",0
270,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
271,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(4/3), x)","F",0
272,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(4/3), x)","F",0
273,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(1/3), x)","F",0
274,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(2/3), x)","F",0
275,0,0,0,0.000000," ","integrate((c*sec(f*x+e))^n*(a+a*sec(f*x+e))^m*(A+B*sec(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sec\left(f x + e\right) + A\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m} \left(c \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sec(f*x + e) + A)*(a*sec(f*x + e) + a)^m*(c*sec(f*x + e))^n, x)","F",0
276,0,0,0,0.000000," ","integrate(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{-n - 1}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1), x)","F",0
277,1,304,0,0.300263," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, A a + 3 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, A a + 3 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*A*a + 3*B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*A*a + 3*B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(12*A*a*tan(1/2*d*x + 1/2*c)^7 - 24*B*a*tan(1/2*d*x + 1/2*c)^7 - 24*A*b*tan(1/2*d*x + 1/2*c)^7 + 15*B*b*tan(1/2*d*x + 1/2*c)^7 - 12*A*a*tan(1/2*d*x + 1/2*c)^5 + 40*B*a*tan(1/2*d*x + 1/2*c)^5 + 40*A*b*tan(1/2*d*x + 1/2*c)^5 + 9*B*b*tan(1/2*d*x + 1/2*c)^5 - 12*A*a*tan(1/2*d*x + 1/2*c)^3 - 40*B*a*tan(1/2*d*x + 1/2*c)^3 - 40*A*b*tan(1/2*d*x + 1/2*c)^3 + 9*B*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*a*tan(1/2*d*x + 1/2*c) + 24*B*a*tan(1/2*d*x + 1/2*c) + 24*A*b*tan(1/2*d*x + 1/2*c) + 15*B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
278,1,210,0,0.271776," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(B a + A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(B a + A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a + A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a + A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a*tan(1/2*d*x + 1/2*c)^5 - 3*B*a*tan(1/2*d*x + 1/2*c)^5 - 3*A*b*tan(1/2*d*x + 1/2*c)^5 + 6*B*b*tan(1/2*d*x + 1/2*c)^5 - 12*A*a*tan(1/2*d*x + 1/2*c)^3 - 4*B*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a*tan(1/2*d*x + 1/2*c) + 3*B*a*tan(1/2*d*x + 1/2*c) + 3*A*b*tan(1/2*d*x + 1/2*c) + 6*B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
279,1,153,0,0.235386," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(2 \, A a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, A a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((2*A*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*A*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*B*a*tan(1/2*d*x + 1/2*c)^3 + 2*A*b*tan(1/2*d*x + 1/2*c)^3 - B*b*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c) - 2*A*b*tan(1/2*d*x + 1/2*c) - B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
280,1,84,0,0.258471," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} A a + {\left(B a + A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a + A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"((d*x + c)*A*a + (B*a + A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a + A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*B*b*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
281,1,79,0,0.467478," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{B b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - B b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(B a + A b\right)} {\left(d x + c\right)} + \frac{2 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(B*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - B*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (B*a + A*b)*(d*x + c) + 2*A*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
282,1,121,0,0.223469," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(A a + 2 \, B b\right)} {\left(d x + c\right)} - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((A*a + 2*B*b)*(d*x + c) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 - 2*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - 2*B*a*tan(1/2*d*x + 1/2*c) - 2*A*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
283,1,180,0,0.786163," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(B a + A b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a + A*b)*(d*x + c) + 2*(6*A*a*tan(1/2*d*x + 1/2*c)^5 - 3*B*a*tan(1/2*d*x + 1/2*c)^5 - 3*A*b*tan(1/2*d*x + 1/2*c)^5 + 6*B*b*tan(1/2*d*x + 1/2*c)^5 + 4*A*a*tan(1/2*d*x + 1/2*c)^3 + 12*B*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a*tan(1/2*d*x + 1/2*c) + 3*B*a*tan(1/2*d*x + 1/2*c) + 3*A*b*tan(1/2*d*x + 1/2*c) + 6*B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
284,1,272,0,0.237245," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, B b\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*B*b)*(d*x + c) - 2*(15*A*a*tan(1/2*d*x + 1/2*c)^7 - 24*B*a*tan(1/2*d*x + 1/2*c)^7 - 24*A*b*tan(1/2*d*x + 1/2*c)^7 + 12*B*b*tan(1/2*d*x + 1/2*c)^7 - 9*A*a*tan(1/2*d*x + 1/2*c)^5 - 40*B*a*tan(1/2*d*x + 1/2*c)^5 - 40*A*b*tan(1/2*d*x + 1/2*c)^5 + 12*B*b*tan(1/2*d*x + 1/2*c)^5 + 9*A*a*tan(1/2*d*x + 1/2*c)^3 - 40*B*a*tan(1/2*d*x + 1/2*c)^3 - 40*A*b*tan(1/2*d*x + 1/2*c)^3 - 12*B*b*tan(1/2*d*x + 1/2*c)^3 - 15*A*a*tan(1/2*d*x + 1/2*c) - 24*B*a*tan(1/2*d*x + 1/2*c) - 24*A*b*tan(1/2*d*x + 1/2*c) - 12*B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
285,1,528,0,0.331214," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, A a^{2} + 6 \, B a b + 3 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, A a^{2} + 6 \, B a b + 3 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 150 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 75 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 640 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 160 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 400 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 800 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 464 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 640 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 150 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*A*a^2 + 6*B*a*b + 3*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*A*a^2 + 6*B*a*b + 3*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(60*A*a^2*tan(1/2*d*x + 1/2*c)^9 - 120*B*a^2*tan(1/2*d*x + 1/2*c)^9 - 240*A*a*b*tan(1/2*d*x + 1/2*c)^9 + 150*B*a*b*tan(1/2*d*x + 1/2*c)^9 + 75*A*b^2*tan(1/2*d*x + 1/2*c)^9 - 120*B*b^2*tan(1/2*d*x + 1/2*c)^9 - 120*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 320*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 640*A*a*b*tan(1/2*d*x + 1/2*c)^7 - 60*B*a*b*tan(1/2*d*x + 1/2*c)^7 - 30*A*b^2*tan(1/2*d*x + 1/2*c)^7 + 160*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 400*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 800*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 464*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 120*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 320*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 640*A*a*b*tan(1/2*d*x + 1/2*c)^3 + 60*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 30*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 160*B*b^2*tan(1/2*d*x + 1/2*c)^3 - 60*A*a^2*tan(1/2*d*x + 1/2*c) - 120*B*a^2*tan(1/2*d*x + 1/2*c) - 240*A*a*b*tan(1/2*d*x + 1/2*c) - 150*B*a*b*tan(1/2*d*x + 1/2*c) - 75*A*b^2*tan(1/2*d*x + 1/2*c) - 120*B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
286,1,478,0,0.288765," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, B a^{2} + 8 \, A a b + 3 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, B a^{2} + 8 \, A a b + 3 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*B*a^2 + 8*A*a*b + 3*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*B*a^2 + 8*A*a*b + 3*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(24*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 12*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 24*A*a*b*tan(1/2*d*x + 1/2*c)^7 + 48*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 24*A*b^2*tan(1/2*d*x + 1/2*c)^7 - 15*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 24*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 80*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 40*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 9*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*A*a*b*tan(1/2*d*x + 1/2*c)^3 + 80*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 40*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 9*B*b^2*tan(1/2*d*x + 1/2*c)^3 - 24*A*a^2*tan(1/2*d*x + 1/2*c) - 12*B*a^2*tan(1/2*d*x + 1/2*c) - 24*A*a*b*tan(1/2*d*x + 1/2*c) - 48*B*a*b*tan(1/2*d*x + 1/2*c) - 24*A*b^2*tan(1/2*d*x + 1/2*c) - 15*B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
287,1,294,0,0.434675," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(2 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*A*a^2 + 2*B*a*b + A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a^2 + 2*B*a*b + A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*B*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 4*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^2*tan(1/2*d*x + 1/2*c) + 12*A*a*b*tan(1/2*d*x + 1/2*c) + 6*B*a*b*tan(1/2*d*x + 1/2*c) + 3*A*b^2*tan(1/2*d*x + 1/2*c) + 6*B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
288,1,192,0,0.291933," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} A a^{2} + {\left(2 \, B a^{2} + 4 \, A a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, B a^{2} + 4 \, A a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(4 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*A*a^2 + (2*B*a^2 + 4*A*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*B*a^2 + 4*A*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(4*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^2*tan(1/2*d*x + 1/2*c)^3 - B*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b*tan(1/2*d*x + 1/2*c) - 2*A*b^2*tan(1/2*d*x + 1/2*c) - B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
289,1,154,0,0.276496," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(B a^{2} + 2 \, A a b\right)} {\left(d x + c\right)} + {\left(2 \, B a b + A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, B a b + A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((B*a^2 + 2*A*a*b)*(d*x + c) + (2*B*a*b + A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*B*a*b + A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a^2*tan(1/2*d*x + 1/2*c)^3 - B*b^2*tan(1/2*d*x + 1/2*c)^3 - A*a^2*tan(1/2*d*x + 1/2*c) - B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
290,1,178,0,0.454498," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{2 \, B b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, B b^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*B*b^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*B*b^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (A*a^2 + 4*B*a*b + 2*A*b^2)*(d*x + c) - 2*(A*a^2*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 4*A*a*b*tan(1/2*d*x + 1/2*c)^3 - A*a^2*tan(1/2*d*x + 1/2*c) - 2*B*a^2*tan(1/2*d*x + 1/2*c) - 4*A*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
291,1,254,0,0.493108," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(B a^{2} + 2 \, A a b + 2 \, B b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a^2 + 2*A*a*b + 2*B*b^2)*(d*x + c) + 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) + 6*A*a*b*tan(1/2*d*x + 1/2*c) + 12*B*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
292,1,437,0,0.255418," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a^{2} + 8 \, B a b + 4 \, A b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^2 + 8*B*a*b + 4*A*b^2)*(d*x + c) - 2*(15*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*A*a*b*tan(1/2*d*x + 1/2*c)^7 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 40*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 80*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*B*b^2*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^2*tan(1/2*d*x + 1/2*c) - 24*B*a^2*tan(1/2*d*x + 1/2*c) - 48*A*a*b*tan(1/2*d*x + 1/2*c) - 24*B*a*b*tan(1/2*d*x + 1/2*c) - 12*A*b^2*tan(1/2*d*x + 1/2*c) - 24*B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
293,1,487,0,0.639766," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{2} + 6 \, A a b + 4 \, B b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 150 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 640 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 640 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a^2 + 6*A*a*b + 4*B*b^2)*(d*x + c) + 2*(120*A*a^2*tan(1/2*d*x + 1/2*c)^9 - 75*B*a^2*tan(1/2*d*x + 1/2*c)^9 - 150*A*a*b*tan(1/2*d*x + 1/2*c)^9 + 240*B*a*b*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*B*b^2*tan(1/2*d*x + 1/2*c)^9 + 160*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 30*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 60*A*a*b*tan(1/2*d*x + 1/2*c)^7 + 640*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 320*A*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*B*b^2*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 400*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 160*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 60*A*a*b*tan(1/2*d*x + 1/2*c)^3 + 640*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 320*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^2*tan(1/2*d*x + 1/2*c) + 75*B*a^2*tan(1/2*d*x + 1/2*c) + 150*A*a*b*tan(1/2*d*x + 1/2*c) + 240*B*a*b*tan(1/2*d*x + 1/2*c) + 120*A*b^2*tan(1/2*d*x + 1/2*c) + 60*B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
294,1,722,0,0.816887," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, B a^{3} + 12 \, A a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, B a^{3} + 12 \, A a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 480 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 90 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 480 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 90 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*B*a^3 + 12*A*a^2*b + 9*B*a*b^2 + 3*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*B*a^3 + 12*A*a^2*b + 9*B*a*b^2 + 3*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 60*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 180*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 225*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 75*A*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*B*b^3*tan(1/2*d*x + 1/2*c)^9 - 480*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 120*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 360*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 90*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 30*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 160*B*b^3*tan(1/2*d*x + 1/2*c)^7 + 720*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1200*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 464*B*b^3*tan(1/2*d*x + 1/2*c)^5 - 480*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 120*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 360*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 90*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 30*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 160*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^3*tan(1/2*d*x + 1/2*c) + 60*B*a^3*tan(1/2*d*x + 1/2*c) + 180*A*a^2*b*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b*tan(1/2*d*x + 1/2*c) + 360*A*a*b^2*tan(1/2*d*x + 1/2*c) + 225*B*a*b^2*tan(1/2*d*x + 1/2*c) + 75*A*b^3*tan(1/2*d*x + 1/2*c) + 120*B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
295,1,586,0,0.701896," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(8 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 3 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 3 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 216 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 120 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 216 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(8*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 3*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 3*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(24*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 72*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 15*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 72*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 216*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 120*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 40*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 9*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 216*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 40*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 9*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*B*a^3*tan(1/2*d*x + 1/2*c) - 72*A*a^2*b*tan(1/2*d*x + 1/2*c) - 36*B*a^2*b*tan(1/2*d*x + 1/2*c) - 36*A*a*b^2*tan(1/2*d*x + 1/2*c) - 72*B*a*b^2*tan(1/2*d*x + 1/2*c) - 24*A*b^3*tan(1/2*d*x + 1/2*c) - 15*B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
296,1,336,0,0.653014," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} A a^{3} + 3 \, {\left(2 \, B a^{3} + 6 \, A a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, B a^{3} + 6 \, A a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*A*a^3 + 3*(2*B*a^3 + 6*A*a^2*b + 3*B*a*b^2 + A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*B*a^3 + 6*A*a^2*b + 3*B*a*b^2 + A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(18*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 9*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*B*b^3*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 18*B*a^2*b*tan(1/2*d*x + 1/2*c) + 18*A*a*b^2*tan(1/2*d*x + 1/2*c) + 9*B*a*b^2*tan(1/2*d*x + 1/2*c) + 3*A*b^3*tan(1/2*d*x + 1/2*c) + 6*B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
297,1,241,0,0.382623," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{4 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} {\left(d x + c\right)} + {\left(6 \, B a^{2} b + 6 \, A a b^{2} + B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(6 \, B a^{2} b + 6 \, A a b^{2} + B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(B*a^3 + 3*A*a^2*b)*(d*x + c) + (6*B*a^2*b + 6*A*a*b^2 + B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (6*B*a^2*b + 6*A*a*b^2 + B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^3*tan(1/2*d*x + 1/2*c)^3 - B*b^3*tan(1/2*d*x + 1/2*c)^3 - 6*B*a*b^2*tan(1/2*d*x + 1/2*c) - 2*A*b^3*tan(1/2*d*x + 1/2*c) - B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
298,1,234,0,0.350029," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - {\left(A a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2}\right)} {\left(d x + c\right)} - 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*B*b^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (A*a^3 + 6*B*a^2*b + 6*A*a*b^2)*(d*x + c) - 2*(3*B*a*b^2 + A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(3*B*a*b^2 + A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - A*a^3*tan(1/2*d*x + 1/2*c) - 2*B*a^3*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
299,1,314,0,0.673711," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{6 \, B b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, B b^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(B a^{3} + 3 \, A a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*B*b^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*B*b^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(B*a^3 + 3*A*a^2*b + 6*B*a*b^2 + 2*A*b^3)*(d*x + c) + 2*(6*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*tan(1/2*d*x + 1/2*c) + 3*B*a^3*tan(1/2*d*x + 1/2*c) + 9*A*a^2*b*tan(1/2*d*x + 1/2*c) + 18*B*a^2*b*tan(1/2*d*x + 1/2*c) + 18*A*a*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
300,1,536,0,0.315965," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 8 \, B b^{3}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 120 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 216 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 216 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 8*B*b^3)*(d*x + c) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 72*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 120*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 216*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 120*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 216*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^3*tan(1/2*d*x + 1/2*c) - 24*B*a^3*tan(1/2*d*x + 1/2*c) - 72*A*a^2*b*tan(1/2*d*x + 1/2*c) - 36*B*a^2*b*tan(1/2*d*x + 1/2*c) - 36*A*a*b^2*tan(1/2*d*x + 1/2*c) - 72*B*a*b^2*tan(1/2*d*x + 1/2*c) - 24*A*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
301,1,672,0,0.341600," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a^3 + 9*A*a^2*b + 12*B*a*b^2 + 4*A*b^3)*(d*x + c) + 2*(120*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 75*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 225*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 180*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*B*b^3*tan(1/2*d*x + 1/2*c)^9 + 160*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 30*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 960*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 480*B*b^3*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1200*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 720*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 160*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 960*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 480*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^3*tan(1/2*d*x + 1/2*c) + 75*B*a^3*tan(1/2*d*x + 1/2*c) + 225*A*a^2*b*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b*tan(1/2*d*x + 1/2*c) + 360*A*a*b^2*tan(1/2*d*x + 1/2*c) + 180*B*a*b^2*tan(1/2*d*x + 1/2*c) + 60*A*b^3*tan(1/2*d*x + 1/2*c) + 120*B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
302,1,1186,0,2.277281," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(240 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 120 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 480 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 960 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1440 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 900 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 600 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 165 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1200 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1440 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3520 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5280 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1260 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 840 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2240 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 560 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 25 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2400 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5760 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8640 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4992 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1248 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5760 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8640 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4992 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1248 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 450 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1440 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3520 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5280 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1260 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 840 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2240 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 480 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1440 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 900 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 600 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 165 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(8*B*a^4 + 32*A*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*B*a^4 + 32*A*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(240*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 120*B*a^4*tan(1/2*d*x + 1/2*c)^11 - 480*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 960*B*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 1440*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 900*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 600*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 960*B*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 240*A*b^4*tan(1/2*d*x + 1/2*c)^11 - 165*B*b^4*tan(1/2*d*x + 1/2*c)^11 - 1200*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 360*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 1440*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 3520*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 5280*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 1260*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 840*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 2240*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 560*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 25*B*b^4*tan(1/2*d*x + 1/2*c)^9 + 2400*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 240*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 960*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 5760*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 8640*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 240*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 4992*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 1248*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 450*B*b^4*tan(1/2*d*x + 1/2*c)^7 - 2400*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 240*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 960*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 5760*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 8640*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 240*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 4992*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 1248*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 450*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 1200*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 360*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 1440*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 3520*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 5280*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 1260*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 840*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 2240*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 560*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 25*B*b^4*tan(1/2*d*x + 1/2*c)^3 - 240*A*a^4*tan(1/2*d*x + 1/2*c) - 120*B*a^4*tan(1/2*d*x + 1/2*c) - 480*A*a^3*b*tan(1/2*d*x + 1/2*c) - 960*B*a^3*b*tan(1/2*d*x + 1/2*c) - 1440*A*a^2*b^2*tan(1/2*d*x + 1/2*c) - 900*B*a^2*b^2*tan(1/2*d*x + 1/2*c) - 600*A*a*b^3*tan(1/2*d*x + 1/2*c) - 960*B*a*b^3*tan(1/2*d*x + 1/2*c) - 240*A*b^4*tan(1/2*d*x + 1/2*c) - 165*B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
303,1,850,0,1.081947," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(8 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 12 \, B a b^{3} + 3 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(8 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 12 \, B a b^{3} + 3 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 300 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 480 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1920 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1920 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1280 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2880 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1600 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 480 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1920 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1920 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1280 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 300 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(8*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 12*B*a*b^3 + 3*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(8*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 12*B*a*b^3 + 3*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 480*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 240*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 300*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 75*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 120*B*b^4*tan(1/2*d*x + 1/2*c)^9 - 480*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 1920*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 480*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 1920*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 1280*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 120*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 30*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 160*B*b^4*tan(1/2*d*x + 1/2*c)^7 + 720*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 2880*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 2400*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 1600*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 464*B*b^4*tan(1/2*d*x + 1/2*c)^5 - 480*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 1920*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 480*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 1920*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 1280*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 120*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 30*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 160*B*b^4*tan(1/2*d*x + 1/2*c)^3 + 120*B*a^4*tan(1/2*d*x + 1/2*c) + 480*A*a^3*b*tan(1/2*d*x + 1/2*c) + 240*B*a^3*b*tan(1/2*d*x + 1/2*c) + 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 480*A*a*b^3*tan(1/2*d*x + 1/2*c) + 300*B*a*b^3*tan(1/2*d*x + 1/2*c) + 75*A*b^4*tan(1/2*d*x + 1/2*c) + 120*B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
304,1,635,0,2.389362," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} A a^{4} + 3 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 3 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 3 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(96 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 144 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 288 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 432 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 432 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 144 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)*A*a^4 + 3*(8*B*a^4 + 32*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 3*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*B*a^4 + 32*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 3*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(96*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 144*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 48*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 96*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 24*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 15*B*b^4*tan(1/2*d*x + 1/2*c)^7 - 288*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 432*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 48*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 160*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 40*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 9*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 288*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 432*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 72*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 48*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 160*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 40*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 9*B*b^4*tan(1/2*d*x + 1/2*c)^3 - 96*B*a^3*b*tan(1/2*d*x + 1/2*c) - 144*A*a^2*b^2*tan(1/2*d*x + 1/2*c) - 72*B*a^2*b^2*tan(1/2*d*x + 1/2*c) - 48*A*a*b^3*tan(1/2*d*x + 1/2*c) - 96*B*a*b^3*tan(1/2*d*x + 1/2*c) - 24*A*b^4*tan(1/2*d*x + 1/2*c) - 15*B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
305,1,387,0,0.371552," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 6 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} {\left(d x + c\right)} + 3 \, {\left(8 \, B a^{3} b + 12 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(8 \, B a^{3} b + 12 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(36 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 6*(B*a^4 + 4*A*a^3*b)*(d*x + c) + 3*(8*B*a^3*b + 12*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(8*B*a^3*b + 12*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(36*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 24*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*B*b^4*tan(1/2*d*x + 1/2*c)^5 - 72*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 48*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*B*b^4*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 24*A*a*b^3*tan(1/2*d*x + 1/2*c) + 12*B*a*b^3*tan(1/2*d*x + 1/2*c) + 3*A*b^4*tan(1/2*d*x + 1/2*c) + 6*B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
306,1,528,0,2.107296," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(A a^{4} + 8 \, B a^{3} b + 12 \, A a^{2} b^{2}\right)} {\left(d x + c\right)} + {\left(12 \, B a^{2} b^{2} + 8 \, A a b^{3} + B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(12 \, B a^{2} b^{2} + 8 \, A a b^{3} + B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((A*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*(d*x + c) + (12*B*a^2*b^2 + 8*A*a*b^3 + B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (12*B*a^2*b^2 + 8*A*a*b^3 + B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(A*a^4*tan(1/2*d*x + 1/2*c)^7 - 2*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 8*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 8*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 2*A*b^4*tan(1/2*d*x + 1/2*c)^7 - B*b^4*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 2*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 8*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 8*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 2*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 8*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 8*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 3*B*b^4*tan(1/2*d*x + 1/2*c)^3 - A*a^4*tan(1/2*d*x + 1/2*c) - 2*B*a^4*tan(1/2*d*x + 1/2*c) - 8*A*a^3*b*tan(1/2*d*x + 1/2*c) - 8*B*a*b^3*tan(1/2*d*x + 1/2*c) - 2*A*b^4*tan(1/2*d*x + 1/2*c) - B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","B",0
307,1,371,0,1.858845," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{12 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(B a^{4} + 4 \, A a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(12*B*b^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(B*a^4 + 4*A*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3)*(d*x + c) - 6*(4*B*a*b^3 + A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 6*(4*B*a*b^3 + A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 24*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^4*tan(1/2*d*x + 1/2*c) + 3*B*a^4*tan(1/2*d*x + 1/2*c) + 12*A*a^3*b*tan(1/2*d*x + 1/2*c) + 24*B*a^3*b*tan(1/2*d*x + 1/2*c) + 36*A*a^2*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
308,1,603,0,0.421103," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{24 \, B b^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, B b^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(3 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*B*b^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*B*b^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(3*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*(d*x + c) - 2*(15*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 96*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 96*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 40*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^4*tan(1/2*d*x + 1/2*c) - 24*B*a^4*tan(1/2*d*x + 1/2*c) - 96*A*a^3*b*tan(1/2*d*x + 1/2*c) - 48*B*a^3*b*tan(1/2*d*x + 1/2*c) - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c) - 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c) - 96*A*a*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
309,1,791,0,0.324130," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 8 \, B b^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 300 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1280 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1920 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1920 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2880 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1280 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1920 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1920 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 300 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a^4 + 12*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 8*B*b^4)*(d*x + c) + 2*(120*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 75*B*a^4*tan(1/2*d*x + 1/2*c)^9 - 300*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 480*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 240*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 480*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 160*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 30*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 120*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 1280*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 1920*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 1920*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 480*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 1600*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 2400*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 2880*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 720*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 160*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 1280*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 1920*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 1920*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 480*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^4*tan(1/2*d*x + 1/2*c) + 75*B*a^4*tan(1/2*d*x + 1/2*c) + 300*A*a^3*b*tan(1/2*d*x + 1/2*c) + 480*B*a^3*b*tan(1/2*d*x + 1/2*c) + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 240*A*a*b^3*tan(1/2*d*x + 1/2*c) + 480*B*a*b^3*tan(1/2*d*x + 1/2*c) + 120*A*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
310,1,1127,0,3.048144," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(5 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1440 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 560 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 840 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5280 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1440 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1248 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8640 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1248 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8640 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2400 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 560 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 840 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5280 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1440 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1440 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*(d*x + c) - 2*(165*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 240*B*a^4*tan(1/2*d*x + 1/2*c)^11 - 960*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 600*B*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 1440*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 960*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 480*B*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^11 - 240*B*b^4*tan(1/2*d*x + 1/2*c)^11 - 25*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 560*B*a^4*tan(1/2*d*x + 1/2*c)^9 - 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 840*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 5280*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 1440*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 360*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 1200*B*b^4*tan(1/2*d*x + 1/2*c)^9 + 450*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 1248*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 240*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 8640*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 960*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 2400*B*b^4*tan(1/2*d*x + 1/2*c)^7 - 450*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 1248*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 240*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 8640*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 960*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 240*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 2400*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 25*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 560*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 840*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 5280*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 1440*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 360*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 1200*B*b^4*tan(1/2*d*x + 1/2*c)^3 - 165*A*a^4*tan(1/2*d*x + 1/2*c) - 240*B*a^4*tan(1/2*d*x + 1/2*c) - 960*A*a^3*b*tan(1/2*d*x + 1/2*c) - 600*B*a^3*b*tan(1/2*d*x + 1/2*c) - 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c) - 1440*B*a^2*b^2*tan(1/2*d*x + 1/2*c) - 960*A*a*b^3*tan(1/2*d*x + 1/2*c) - 480*B*a*b^3*tan(1/2*d*x + 1/2*c) - 120*A*b^4*tan(1/2*d*x + 1/2*c) - 240*B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
311,1,412,0,0.282428," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, B a^{3} - 2 \, A a^{2} b + B a b^{2} - A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{3 \, {\left(2 \, B a^{3} - 2 \, A a^{2} b + B a b^{2} - A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{12 \, {\left(B a^{4} - A a^{3} b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{4}} + \frac{2 \, {\left(6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*B*a^3 - 2*A*a^2*b + B*a*b^2 - A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 3*(2*B*a^3 - 2*A*a^2*b + B*a*b^2 - A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 12*(B*a^4 - A*a^3*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^4) + 2*(6*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*B*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 4*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^2*tan(1/2*d*x + 1/2*c) - 6*A*a*b*tan(1/2*d*x + 1/2*c) - 3*B*a*b*tan(1/2*d*x + 1/2*c) + 3*A*b^2*tan(1/2*d*x + 1/2*c) + 6*B*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*b^3))/d","B",0
312,1,269,0,0.618792," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, B a^{2} - 2 \, A a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} - \frac{{\left(2 \, B a^{2} - 2 \, A a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{4 \, {\left(B a^{3} - A a^{2} b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{3}} + \frac{2 \, {\left(2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*((2*B*a^2 - 2*A*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 - (2*B*a^2 - 2*A*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - 4*(B*a^3 - A*a^2*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^3) + 2*(2*B*a*tan(1/2*d*x + 1/2*c)^3 - 2*A*b*tan(1/2*d*x + 1/2*c)^3 + B*b*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c) + 2*A*b*tan(1/2*d*x + 1/2*c) + B*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^2))/d","B",0
313,1,176,0,0.628204," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(B a - A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{{\left(B a - A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}} + \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b} - \frac{2 \, {\left(B a^{2} - A a b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} b^{2}}}{d}"," ",0,"-((B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - (B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 + 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b) - 2*(B*a^2 - A*a*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*b^2))/d","A",0
314,1,127,0,1.330903," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b} + \frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} {\left(B a - A b\right)}}{\sqrt{-a^{2} + b^{2}} b}}{d}"," ",0,"(B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b - B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b + 2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*(B*a - A*b)/(sqrt(-a^2 + b^2)*b))/d","A",0
315,1,274,0,0.434271," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(\sqrt{-a^{2} + b^{2}} A {\left(a - 2 \, b\right)} {\left| -a + b \right|} + \sqrt{-a^{2} + b^{2}} B a {\left| -a + b \right|} - \sqrt{-a^{2} + b^{2}} A {\left| a \right|} {\left| -a + b \right|} + \sqrt{-a^{2} + b^{2}} B {\left| a \right|} {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{b + \sqrt{{\left(a + b\right)} {\left(a - b\right)} + b^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} a^{2} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} {\left| a \right|}} + \frac{{\left(A a + B a - 2 \, A b + A {\left| a \right|} - B {\left| a \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{b - \sqrt{{\left(a + b\right)} {\left(a - b\right)} + b^{2}}}{a - b}}}\right)\right)}}{a^{2} - b {\left| a \right|}}}{d}"," ",0,"((sqrt(-a^2 + b^2)*A*(a - 2*b)*abs(-a + b) + sqrt(-a^2 + b^2)*B*a*abs(-a + b) - sqrt(-a^2 + b^2)*A*abs(a)*abs(-a + b) + sqrt(-a^2 + b^2)*B*abs(a)*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b + sqrt((a + b)*(a - b) + b^2))/(a - b))))/((a^2 - 2*a*b + b^2)*a^2 + (a^2*b - 2*a*b^2 + b^3)*abs(a)) + (A*a + B*a - 2*A*b + A*abs(a) - B*abs(a))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(b - sqrt((a + b)*(a - b) + b^2))/(a - b))))/(a^2 - b*abs(a)))/d","B",0
316,1,141,0,0.922641," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(B a - A b\right)} {\left(d x + c\right)}}{a^{2}} + \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a} - \frac{2 \, {\left(B a b - A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{2}}}{d}"," ",0,"((B*a - A*b)*(d*x + c)/a^2 + 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a) - 2*(B*a*b - A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^2))/d","A",0
317,1,227,0,0.273410," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(A a^{2} - 2 \, B a b + 2 \, A b^{2}\right)} {\left(d x + c\right)}}{a^{3}} + \frac{4 \, {\left(B a b^{2} - A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{3}} - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*((A*a^2 - 2*B*a*b + 2*A*b^2)*(d*x + c)/a^3 + 4*(B*a*b^2 - A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^3) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 2*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - 2*B*a*tan(1/2*d*x + 1/2*c) + 2*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2))/d","A",0
318,1,360,0,0.305220," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(B a^{3} - A a^{2} b + 2 \, B a b^{2} - 2 \, A b^{3}\right)} {\left(d x + c\right)}}{a^{4}} - \frac{12 \, {\left(B a b^{3} - A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{4}} + \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a^3 - A*a^2*b + 2*B*a*b^2 - 2*A*b^3)*(d*x + c)/a^4 - 12*(B*a*b^3 - A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^4) + 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) - 3*A*a*b*tan(1/2*d*x + 1/2*c) - 6*B*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3))/d","B",0
319,1,642,0,0.300946," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, A a^{4} - 4 \, B a^{3} b + 4 \, A a^{2} b^{2} - 8 \, B a b^{3} + 8 \, A b^{4}\right)} {\left(d x + c\right)}}{a^{5}} + \frac{48 \, {\left(B a b^{4} - A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a^{5}} - \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^4 - 4*B*a^3*b + 4*A*a^2*b^2 - 8*B*a*b^3 + 8*A*b^4)*(d*x + c)/a^5 + 48*(B*a*b^4 - A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a^5) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 24*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 12*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 9*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 12*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 72*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^3*tan(1/2*d*x + 1/2*c) - 24*B*a^3*tan(1/2*d*x + 1/2*c) + 24*A*a^2*b*tan(1/2*d*x + 1/2*c) + 12*B*a^2*b*tan(1/2*d*x + 1/2*c) - 12*A*a*b^2*tan(1/2*d*x + 1/2*c) - 24*B*a*b^2*tan(1/2*d*x + 1/2*c) + 24*A*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^4))/d","B",0
320,1,384,0,0.339139," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(3 \, B a^{5} - 2 \, A a^{4} b - 4 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{4 \, {\left(B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{{\left(6 \, B a^{2} - 4 \, A a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{{\left(6 \, B a^{2} - 4 \, A a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{2 \, {\left(4 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{3}}}{2 \, d}"," ",0,"-1/2*(4*(3*B*a^5 - 2*A*a^4*b - 4*B*a^3*b^2 + 3*A*a^2*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - 4*(B*a^4*tan(1/2*d*x + 1/2*c) - A*a^3*b*tan(1/2*d*x + 1/2*c))/((a^2*b^3 - b^5)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - (6*B*a^2 - 4*A*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + (6*B*a^2 - 4*A*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 2*(4*B*a*tan(1/2*d*x + 1/2*c)^3 - 2*A*b*tan(1/2*d*x + 1/2*c)^3 + B*b*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*tan(1/2*d*x + 1/2*c) + 2*A*b*tan(1/2*d*x + 1/2*c) + B*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^3))/d","A",0
321,1,404,0,0.362922," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(2 \, B a^{4} - A a^{3} b - 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, {\left(2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} {\left(a^{2} b^{2} - b^{4}\right)}} - \frac{{\left(2 \, B a - A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{{\left(2 \, B a - A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}}}{d}"," ",0,"(2*(2*B*a^4 - A*a^3*b - 3*B*a^2*b^2 + 2*A*a*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^3 - b^5)*sqrt(-a^2 + b^2)) - 2*(2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + B*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^3*tan(1/2*d*x + 1/2*c) + A*a^2*b*tan(1/2*d*x + 1/2*c) - B*a^2*b*tan(1/2*d*x + 1/2*c) + B*a*b^2*tan(1/2*d*x + 1/2*c) + B*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)*(a^2*b^2 - b^4)) - (2*B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + (2*B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3)/d","B",0
322,1,231,0,0.306778," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(B a^{3} - 2 \, B a b^{2} + A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} + \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}} - \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b - b^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}}}{d}"," ",0,"-(2*(B*a^3 - 2*B*a*b^2 + A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^2*b^2 - b^4)*sqrt(-a^2 + b^2)) - B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 + B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 - 2*(B*a^2*tan(1/2*d*x + 1/2*c) - A*a*b*tan(1/2*d*x + 1/2*c))/((a^2*b - b^3)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)))/d","A",0
323,1,172,0,0.326372," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)} {\left(A a - B b\right)}}{{\left(a^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{2} - b^{2}\right)}}\right)}}{d}"," ",0,"-2*((pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))*(A*a - B*b)/((a^2 - b^2)*sqrt(-a^2 + b^2)) + (B*a*tan(1/2*d*x + 1/2*c) - A*b*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^2 - b^2)))/d","A",0
324,1,201,0,0.299689," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a^{3} - 2 \, A a^{2} b + A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{{\left(d x + c\right)} A}{a^{2}} + \frac{2 \, {\left(B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}}}{d}"," ",0,"(2*(B*a^3 - 2*A*a^2*b + A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - a^2*b^2)*sqrt(-a^2 + b^2)) + (d*x + c)*A/a^2 + 2*(B*a*b*tan(1/2*d*x + 1/2*c) - A*b^2*tan(1/2*d*x + 1/2*c))/((a^3 - a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)))/d","A",0
325,1,1107,0,0.488915," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(B a^{8} - 2 \, A a^{7} b - 3 \, B a^{7} b + 5 \, A a^{6} b^{2} - 2 \, B a^{6} b^{2} + 4 \, A a^{5} b^{3} + 5 \, B a^{5} b^{3} - 9 \, A a^{4} b^{4} + B a^{4} b^{4} - 2 \, A a^{3} b^{5} - 2 \, B a^{3} b^{5} + 4 \, A a^{2} b^{6} - B a^{3} {\left| -a^{5} + a^{3} b^{2} \right|} + 2 \, A a^{2} b {\left| -a^{5} + a^{3} b^{2} \right|} - B a^{2} b {\left| -a^{5} + a^{3} b^{2} \right|} + A a b^{2} {\left| -a^{5} + a^{3} b^{2} \right|} + B a b^{2} {\left| -a^{5} + a^{3} b^{2} \right|} - 2 \, A b^{3} {\left| -a^{5} + a^{3} b^{2} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{4} b - a^{2} b^{3} + \sqrt{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} + {\left(a^{4} b - a^{2} b^{3}\right)}^{2}}}{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}}}}\right)\right)}}{a^{4} b {\left| -a^{5} + a^{3} b^{2} \right|} - a^{2} b^{3} {\left| -a^{5} + a^{3} b^{2} \right|} + {\left(a^{5} - a^{3} b^{2}\right)}^{2}} - \frac{{\left({\left(2 \, a^{2} b + a b^{2} - 2 \, b^{3}\right)} \sqrt{-a^{2} + b^{2}} A {\left| -a^{5} + a^{3} b^{2} \right|} {\left| -a + b \right|} - {\left(a^{3} + a^{2} b - a b^{2}\right)} \sqrt{-a^{2} + b^{2}} B {\left| -a^{5} + a^{3} b^{2} \right|} {\left| -a + b \right|} + {\left(2 \, a^{7} b - 5 \, a^{6} b^{2} - 4 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 2 \, a^{3} b^{5} - 4 \, a^{2} b^{6}\right)} \sqrt{-a^{2} + b^{2}} A {\left| -a + b \right|} - {\left(a^{8} - 3 \, a^{7} b - 2 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + a^{4} b^{4} - 2 \, a^{3} b^{5}\right)} \sqrt{-a^{2} + b^{2}} B {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{4} b - a^{2} b^{3} - \sqrt{{\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} + {\left(a^{4} b - a^{2} b^{3}\right)}^{2}}}{a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{6} b - 2 \, a^{5} b^{2} + 2 \, a^{3} b^{4} - a^{2} b^{5}\right)} {\left| -a^{5} + a^{3} b^{2} \right|}} + \frac{2 \, {\left(A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{4} - a^{2} b^{2}\right)}}}{d}"," ",0,"((B*a^8 - 2*A*a^7*b - 3*B*a^7*b + 5*A*a^6*b^2 - 2*B*a^6*b^2 + 4*A*a^5*b^3 + 5*B*a^5*b^3 - 9*A*a^4*b^4 + B*a^4*b^4 - 2*A*a^3*b^5 - 2*B*a^3*b^5 + 4*A*a^2*b^6 - B*a^3*abs(-a^5 + a^3*b^2) + 2*A*a^2*b*abs(-a^5 + a^3*b^2) - B*a^2*b*abs(-a^5 + a^3*b^2) + A*a*b^2*abs(-a^5 + a^3*b^2) + B*a*b^2*abs(-a^5 + a^3*b^2) - 2*A*b^3*abs(-a^5 + a^3*b^2))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^4*b - a^2*b^3 + sqrt((a^5 + a^4*b - a^3*b^2 - a^2*b^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3) + (a^4*b - a^2*b^3)^2))/(a^5 - a^4*b - a^3*b^2 + a^2*b^3))))/(a^4*b*abs(-a^5 + a^3*b^2) - a^2*b^3*abs(-a^5 + a^3*b^2) + (a^5 - a^3*b^2)^2) - ((2*a^2*b + a*b^2 - 2*b^3)*sqrt(-a^2 + b^2)*A*abs(-a^5 + a^3*b^2)*abs(-a + b) - (a^3 + a^2*b - a*b^2)*sqrt(-a^2 + b^2)*B*abs(-a^5 + a^3*b^2)*abs(-a + b) + (2*a^7*b - 5*a^6*b^2 - 4*a^5*b^3 + 9*a^4*b^4 + 2*a^3*b^5 - 4*a^2*b^6)*sqrt(-a^2 + b^2)*A*abs(-a + b) - (a^8 - 3*a^7*b - 2*a^6*b^2 + 5*a^5*b^3 + a^4*b^4 - 2*a^3*b^5)*sqrt(-a^2 + b^2)*B*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^4*b - a^2*b^3 - sqrt((a^5 + a^4*b - a^3*b^2 - a^2*b^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3) + (a^4*b - a^2*b^3)^2))/(a^5 - a^4*b - a^3*b^2 + a^2*b^3))))/((a^5 - a^3*b^2)^2*(a^2 - 2*a*b + b^2) - (a^6*b - 2*a^5*b^2 + 2*a^3*b^4 - a^2*b^5)*abs(-a^5 + a^3*b^2)) + 2*(A*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^3*tan(1/2*d*x + 1/2*c)^3 - A*a^3*tan(1/2*d*x + 1/2*c) - A*a^2*b*tan(1/2*d*x + 1/2*c) + A*a*b^2*tan(1/2*d*x + 1/2*c) - B*a*b^2*tan(1/2*d*x + 1/2*c) + 2*A*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^4 - a^2*b^2)))/d","B",0
326,1,340,0,1.158688," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(3 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3} - 2 \, B a b^{4} + 3 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{4 \, {\left(B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} + \frac{{\left(A a^{2} - 4 \, B a b + 6 \, A b^{2}\right)} {\left(d x + c\right)}}{a^{4}} - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}}}{2 \, d}"," ",0,"1/2*(4*(3*B*a^3*b^2 - 4*A*a^2*b^3 - 2*B*a*b^4 + 3*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - a^4*b^2)*sqrt(-a^2 + b^2)) + 4*(B*a*b^3*tan(1/2*d*x + 1/2*c) - A*b^4*tan(1/2*d*x + 1/2*c))/((a^5 - a^3*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) + (A*a^2 - 4*B*a*b + 6*A*b^2)*(d*x + c)/a^4 - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 4*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - 2*B*a*tan(1/2*d*x + 1/2*c) + 4*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3))/d","A",0
327,1,473,0,3.261834," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(4 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4} - 3 \, B a b^{5} + 4 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{7} - a^{5} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{12 \, {\left(B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}} - \frac{3 \, {\left(B a^{3} - 2 \, A a^{2} b + 6 \, B a b^{2} - 8 \, A b^{3}\right)} {\left(d x + c\right)}}{a^{5}} - \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{4}}}{6 \, d}"," ",0,"-1/6*(12*(4*B*a^3*b^3 - 5*A*a^2*b^4 - 3*B*a*b^5 + 4*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^7 - a^5*b^2)*sqrt(-a^2 + b^2)) + 12*(B*a*b^4*tan(1/2*d*x + 1/2*c) - A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - a^4*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)) - 3*(B*a^3 - 2*A*a^2*b + 6*B*a*b^2 - 8*A*b^3)*(d*x + c)/a^5 - 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) - 6*A*a*b*tan(1/2*d*x + 1/2*c) - 12*B*a*b*tan(1/2*d*x + 1/2*c) + 18*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^4))/d","A",0
328,1,1391,0,0.498055," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(12 \, B a^{7} - 6 \, A a^{6} b - 29 \, B a^{5} b^{2} + 15 \, A a^{4} b^{3} + 20 \, B a^{3} b^{4} - 12 \, A a^{2} b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, {\left(12 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 67 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 29 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 26 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 13 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} - \frac{{\left(12 \, B a^{2} - 6 \, A a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{5}} + \frac{{\left(12 \, B a^{2} - 6 \, A a b + B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{5}}}{2 \, d}"," ",0,"-1/2*(2*(12*B*a^7 - 6*A*a^6*b - 29*B*a^5*b^2 + 15*A*a^4*b^3 + 20*B*a^3*b^4 - 12*A*a^2*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^5 - 2*a^2*b^7 + b^9)*sqrt(-a^2 + b^2)) - 2*(12*B*a^7*tan(1/2*d*x + 1/2*c)^7 - 6*A*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 17*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 16*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 2*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 2*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 13*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 4*A*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^7 - 2*A*b^7*tan(1/2*d*x + 1/2*c)^7 + B*b^7*tan(1/2*d*x + 1/2*c)^7 - 36*B*a^7*tan(1/2*d*x + 1/2*c)^5 + 18*A*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 67*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 35*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 29*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 16*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 26*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 10*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 5*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 4*A*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 2*A*b^7*tan(1/2*d*x + 1/2*c)^5 + 3*B*b^7*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^7*tan(1/2*d*x + 1/2*c)^3 - 18*A*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 9*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 67*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 35*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 16*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 26*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 10*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*A*a*b^6*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^7*tan(1/2*d*x + 1/2*c)^3 + 3*B*b^7*tan(1/2*d*x + 1/2*c)^3 - 12*B*a^7*tan(1/2*d*x + 1/2*c) + 6*A*a^6*b*tan(1/2*d*x + 1/2*c) - 18*B*a^6*b*tan(1/2*d*x + 1/2*c) + 9*A*a^5*b^2*tan(1/2*d*x + 1/2*c) + 17*B*a^5*b^2*tan(1/2*d*x + 1/2*c) - 9*A*a^4*b^3*tan(1/2*d*x + 1/2*c) + 33*B*a^4*b^3*tan(1/2*d*x + 1/2*c) - 16*A*a^3*b^4*tan(1/2*d*x + 1/2*c) + 2*B*a^3*b^4*tan(1/2*d*x + 1/2*c) - 2*A*a^2*b^5*tan(1/2*d*x + 1/2*c) - 13*B*a^2*b^5*tan(1/2*d*x + 1/2*c) + 4*A*a*b^6*tan(1/2*d*x + 1/2*c) - 4*B*a*b^6*tan(1/2*d*x + 1/2*c) + 2*A*b^7*tan(1/2*d*x + 1/2*c) + B*b^7*tan(1/2*d*x + 1/2*c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) - (12*B*a^2 - 6*A*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^5 + (12*B*a^2 - 6*A*a*b + B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^5)/d","B",0
329,1,581,0,0.458924," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(6 \, B a^{6} - 2 \, A a^{5} b - 15 \, B a^{4} b^{2} + 5 \, A a^{3} b^{3} + 12 \, B a^{2} b^{4} - 6 \, A a b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{4 \, B a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} - \frac{{\left(3 \, B a - A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{{\left(3 \, B a - A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b^{3}}}{d}"," ",0,"((6*B*a^6 - 2*A*a^5*b - 15*B*a^4*b^2 + 5*A*a^3*b^3 + 12*B*a^2*b^4 - 6*A*a*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(-a^2 + b^2)) - (4*B*a^6*tan(1/2*d*x + 1/2*c)^3 - 2*A*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 5*B*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 7*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 6*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^6*tan(1/2*d*x + 1/2*c) + 2*A*a^5*b*tan(1/2*d*x + 1/2*c) - 5*B*a^5*b*tan(1/2*d*x + 1/2*c) + 3*A*a^4*b^2*tan(1/2*d*x + 1/2*c) + 7*B*a^4*b^2*tan(1/2*d*x + 1/2*c) - 5*A*a^3*b^3*tan(1/2*d*x + 1/2*c) + 8*B*a^3*b^3*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^4*tan(1/2*d*x + 1/2*c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) - (3*B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + (3*B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^3))/d","B",0
330,1,486,0,0.479737," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, B a^{5} - 5 \, B a^{3} b^{2} - A a^{2} b^{3} + 6 \, B a b^{4} - 2 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{3}} + \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{3}} - \frac{2 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"-((2*B*a^5 - 5*B*a^3*b^2 - A*a^2*b^3 + 6*B*a*b^4 - 2*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(-a^2 + b^2)) - B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^3 + B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^3 - (2*B*a^5*tan(1/2*d*x + 1/2*c)^3 - 3*B*a^4*b*tan(1/2*d*x + 1/2*c)^3 + A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^5*tan(1/2*d*x + 1/2*c) - 3*B*a^4*b*tan(1/2*d*x + 1/2*c) + A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 5*B*a^3*b^2*tan(1/2*d*x + 1/2*c) - 3*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 6*B*a^2*b^3*tan(1/2*d*x + 1/2*c) - 4*A*a*b^4*tan(1/2*d*x + 1/2*c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
331,1,400,0,3.443472," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(B a^{2} - 3 \, A a b + 2 \, B b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"((B*a^2 - 3*A*a*b + 2*B*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) - (2*A*a^3*tan(1/2*d*x + 1/2*c)^3 - B*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 2*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*A*a^3*tan(1/2*d*x + 1/2*c) - B*a^3*tan(1/2*d*x + 1/2*c) - A*a^2*b*tan(1/2*d*x + 1/2*c) + 3*B*a^2*b*tan(1/2*d*x + 1/2*c) - A*a*b^2*tan(1/2*d*x + 1/2*c) + 4*B*a*b^2*tan(1/2*d*x + 1/2*c) - 2*A*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
332,1,399,0,0.377247," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, A a^{2} - 3 \, B a b + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"((2*A*a^2 - 3*B*a*b + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) - (2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + A*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^3*tan(1/2*d*x + 1/2*c) + 4*A*a^2*b*tan(1/2*d*x + 1/2*c) - B*a^2*b*tan(1/2*d*x + 1/2*c) + 3*A*a*b^2*tan(1/2*d*x + 1/2*c) - B*a*b^2*tan(1/2*d*x + 1/2*c) - A*b^3*tan(1/2*d*x + 1/2*c) - 2*B*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
333,1,457,0,0.373742," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, B a^{5} - 6 \, A a^{4} b + B a^{3} b^{2} + 5 \, A a^{2} b^{3} - 2 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{{\left(d x + c\right)} A}{a^{3}} + \frac{4 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{d}"," ",0,"((2*B*a^5 - 6*A*a^4*b + B*a^3*b^2 + 5*A*a^2*b^3 - 2*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(-a^2 + b^2)) + (d*x + c)*A/a^3 + (4*B*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 2*A*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^4*b*tan(1/2*d*x + 1/2*c) + 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - 3*B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + B*a^2*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a*b^4*tan(1/2*d*x + 1/2*c) - 2*A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
334,1,546,0,0.398636," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, B a^{5} b - 12 \, A a^{4} b^{2} - 5 \, B a^{3} b^{3} + 15 \, A a^{2} b^{4} + 2 \, B a b^{5} - 6 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{6 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} - \frac{{\left(B a - 3 \, A b\right)} {\left(d x + c\right)}}{a^{4}} - \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}}}{d}"," ",0,"-((6*B*a^5*b - 12*A*a^4*b^2 - 5*B*a^3*b^3 + 15*A*a^2*b^4 + 2*B*a*b^5 - 6*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(-a^2 + b^2)) + (6*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 3*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 5*A*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 2*B*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*A*b^6*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^4*b^2*tan(1/2*d*x + 1/2*c) + 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c) - 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c) + 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c) + 3*B*a^2*b^4*tan(1/2*d*x + 1/2*c) - 5*A*a*b^5*tan(1/2*d*x + 1/2*c) + 2*B*a*b^5*tan(1/2*d*x + 1/2*c) - 4*A*b^6*tan(1/2*d*x + 1/2*c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) - (B*a - 3*A*b)*(d*x + c)/a^4 - 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3))/d","A",0
335,1,2700,0,0.787333," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(a^{6} - a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} - 23 \, a^{2} b^{4} - 6 \, a b^{5} + 12 \, b^{6}\right)} \sqrt{-a^{2} + b^{2}} A {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} {\left| -a + b \right|} - 3 \, {\left(2 \, a^{5} b + 2 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - a^{2} b^{4} + 2 \, a b^{5}\right)} \sqrt{-a^{2} + b^{2}} B {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} {\left| -a + b \right|} - {\left(a^{15} - a^{14} b + 8 \, a^{13} b^{2} - 28 \, a^{12} b^{3} - 42 \, a^{11} b^{4} + 111 \, a^{10} b^{5} + 68 \, a^{9} b^{6} - 158 \, a^{8} b^{7} - 47 \, a^{7} b^{8} + 100 \, a^{6} b^{9} + 12 \, a^{5} b^{10} - 24 \, a^{4} b^{11}\right)} \sqrt{-a^{2} + b^{2}} A {\left| -a + b \right|} + 3 \, {\left(2 \, a^{14} b - 6 \, a^{13} b^{2} - 8 \, a^{12} b^{3} + 21 \, a^{11} b^{4} + 12 \, a^{10} b^{5} - 28 \, a^{9} b^{6} - 8 \, a^{8} b^{7} + 17 \, a^{7} b^{8} + 2 \, a^{6} b^{9} - 4 \, a^{5} b^{10}\right)} \sqrt{-a^{2} + b^{2}} B {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5} + \sqrt{{\left(a^{9} + a^{8} b - 2 \, a^{7} b^{2} - 2 \, a^{6} b^{3} + a^{5} b^{4} + a^{4} b^{5}\right)} {\left(a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}\right)} + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)}^{2}}}{a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}}}}\right)\right)}}{{\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} + {\left(a^{10} b - 2 \, a^{9} b^{2} - a^{8} b^{3} + 4 \, a^{7} b^{4} - a^{6} b^{5} - 2 \, a^{5} b^{6} + a^{4} b^{7}\right)} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|}} + \frac{{\left(A a^{15} - A a^{14} b - 6 \, B a^{14} b + 8 \, A a^{13} b^{2} + 18 \, B a^{13} b^{2} - 28 \, A a^{12} b^{3} + 24 \, B a^{12} b^{3} - 42 \, A a^{11} b^{4} - 63 \, B a^{11} b^{4} + 111 \, A a^{10} b^{5} - 36 \, B a^{10} b^{5} + 68 \, A a^{9} b^{6} + 84 \, B a^{9} b^{6} - 158 \, A a^{8} b^{7} + 24 \, B a^{8} b^{7} - 47 \, A a^{7} b^{8} - 51 \, B a^{7} b^{8} + 100 \, A a^{6} b^{9} - 6 \, B a^{6} b^{9} + 12 \, A a^{5} b^{10} + 12 \, B a^{5} b^{10} - 24 \, A a^{4} b^{11} + A a^{6} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - A a^{5} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 6 \, B a^{5} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 10 \, A a^{4} b^{2} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 6 \, B a^{4} b^{2} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 10 \, A a^{3} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 12 \, B a^{3} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 23 \, A a^{2} b^{4} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 3 \, B a^{2} b^{4} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 6 \, A a b^{5} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 6 \, B a b^{5} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + 12 \, A b^{6} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5} - \sqrt{{\left(a^{9} + a^{8} b - 2 \, a^{7} b^{2} - 2 \, a^{6} b^{3} + a^{5} b^{4} + a^{4} b^{5}\right)} {\left(a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}\right)} + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)}^{2}}}{a^{9} - a^{8} b - 2 \, a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} - a^{4} b^{5}}}}\right)\right)}}{a^{8} b {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - 2 \, a^{6} b^{3} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} + a^{4} b^{5} {\left| a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4} \right|} - {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)}^{2}} + \frac{2 \, {\left(A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 35 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(((a^6 - a^5*b + 10*a^4*b^2 + 10*a^3*b^3 - 23*a^2*b^4 - 6*a*b^5 + 12*b^6)*sqrt(-a^2 + b^2)*A*abs(a^9 - 2*a^7*b^2 + a^5*b^4)*abs(-a + b) - 3*(2*a^5*b + 2*a^4*b^2 - 4*a^3*b^3 - a^2*b^4 + 2*a*b^5)*sqrt(-a^2 + b^2)*B*abs(a^9 - 2*a^7*b^2 + a^5*b^4)*abs(-a + b) - (a^15 - a^14*b + 8*a^13*b^2 - 28*a^12*b^3 - 42*a^11*b^4 + 111*a^10*b^5 + 68*a^9*b^6 - 158*a^8*b^7 - 47*a^7*b^8 + 100*a^6*b^9 + 12*a^5*b^10 - 24*a^4*b^11)*sqrt(-a^2 + b^2)*A*abs(-a + b) + 3*(2*a^14*b - 6*a^13*b^2 - 8*a^12*b^3 + 21*a^11*b^4 + 12*a^10*b^5 - 28*a^9*b^6 - 8*a^8*b^7 + 17*a^7*b^8 + 2*a^6*b^9 - 4*a^5*b^10)*sqrt(-a^2 + b^2)*B*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^8*b - 2*a^6*b^3 + a^4*b^5 + sqrt((a^9 + a^8*b - 2*a^7*b^2 - 2*a^6*b^3 + a^5*b^4 + a^4*b^5)*(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5) + (a^8*b - 2*a^6*b^3 + a^4*b^5)^2))/(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5))))/((a^9 - 2*a^7*b^2 + a^5*b^4)^2*(a^2 - 2*a*b + b^2) + (a^10*b - 2*a^9*b^2 - a^8*b^3 + 4*a^7*b^4 - a^6*b^5 - 2*a^5*b^6 + a^4*b^7)*abs(a^9 - 2*a^7*b^2 + a^5*b^4)) + (A*a^15 - A*a^14*b - 6*B*a^14*b + 8*A*a^13*b^2 + 18*B*a^13*b^2 - 28*A*a^12*b^3 + 24*B*a^12*b^3 - 42*A*a^11*b^4 - 63*B*a^11*b^4 + 111*A*a^10*b^5 - 36*B*a^10*b^5 + 68*A*a^9*b^6 + 84*B*a^9*b^6 - 158*A*a^8*b^7 + 24*B*a^8*b^7 - 47*A*a^7*b^8 - 51*B*a^7*b^8 + 100*A*a^6*b^9 - 6*B*a^6*b^9 + 12*A*a^5*b^10 + 12*B*a^5*b^10 - 24*A*a^4*b^11 + A*a^6*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - A*a^5*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 6*B*a^5*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 10*A*a^4*b^2*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 6*B*a^4*b^2*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 10*A*a^3*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 12*B*a^3*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 23*A*a^2*b^4*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 3*B*a^2*b^4*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 6*A*a*b^5*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 6*B*a*b^5*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + 12*A*b^6*abs(a^9 - 2*a^7*b^2 + a^5*b^4))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a^8*b - 2*a^6*b^3 + a^4*b^5 - sqrt((a^9 + a^8*b - 2*a^7*b^2 - 2*a^6*b^3 + a^5*b^4 + a^4*b^5)*(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5) + (a^8*b - 2*a^6*b^3 + a^4*b^5)^2))/(a^9 - a^8*b - 2*a^7*b^2 + 2*a^6*b^3 + a^5*b^4 - a^4*b^5))))/(a^8*b*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - 2*a^6*b^3*abs(a^9 - 2*a^7*b^2 + a^5*b^4) + a^4*b^5*abs(a^9 - 2*a^7*b^2 + a^5*b^4) - (a^9 - 2*a^7*b^2 + a^5*b^4)^2) + 2*(A*a^7*tan(1/2*d*x + 1/2*c)^7 - 2*B*a^7*tan(1/2*d*x + 1/2*c)^7 + 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 2*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^7 - 6*B*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^7*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^7*tan(1/2*d*x + 1/2*c)^5 + 2*B*a^7*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 10*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 35*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 18*B*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 36*A*b^7*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^7*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^7*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 10*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 35*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^3 - 18*B*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^7*tan(1/2*d*x + 1/2*c)^3 - A*a^7*tan(1/2*d*x + 1/2*c) - 2*B*a^7*tan(1/2*d*x + 1/2*c) + 4*A*a^6*b*tan(1/2*d*x + 1/2*c) - 4*B*a^6*b*tan(1/2*d*x + 1/2*c) + 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c) + 2*B*a^5*b^2*tan(1/2*d*x + 1/2*c) - 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c) + 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c) - 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c) + 9*B*a^3*b^4*tan(1/2*d*x + 1/2*c) - 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c) - 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c) + 18*A*a*b^6*tan(1/2*d*x + 1/2*c) - 6*B*a*b^6*tan(1/2*d*x + 1/2*c) + 12*A*b^7*tan(1/2*d*x + 1/2*c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2))/d","B",0
336,1,1005,0,0.470498," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, B a^{8} - 2 \, A a^{7} b - 28 \, B a^{6} b^{2} + 7 \, A a^{5} b^{3} + 35 \, B a^{4} b^{4} - 8 \, A a^{3} b^{5} - 20 \, B a^{2} b^{6} + 8 \, A a b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{18 \, B a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, B a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, A a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 236 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, B a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, A a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}} - \frac{3 \, {\left(4 \, B a - A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{5}} + \frac{3 \, {\left(4 \, B a - A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{5}} - \frac{6 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b^{4}}}{3 \, d}"," ",0,"1/3*(3*(8*B*a^8 - 2*A*a^7*b - 28*B*a^6*b^2 + 7*A*a^5*b^3 + 35*B*a^4*b^4 - 8*A*a^3*b^5 - 20*B*a^2*b^6 + 8*A*a*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*sqrt(-a^2 + b^2)) - (18*B*a^9*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 42*B*a^8*b*tan(1/2*d*x + 1/2*c)^5 + 15*A*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 - 24*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 117*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 45*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 105*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 60*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 60*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 36*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^9*tan(1/2*d*x + 1/2*c)^3 + 12*A*a^8*b*tan(1/2*d*x + 1/2*c)^3 + 152*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 - 56*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 - 236*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 + 116*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 + 120*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 + 18*B*a^9*tan(1/2*d*x + 1/2*c) - 6*A*a^8*b*tan(1/2*d*x + 1/2*c) + 42*B*a^8*b*tan(1/2*d*x + 1/2*c) - 15*A*a^7*b^2*tan(1/2*d*x + 1/2*c) - 24*B*a^7*b^2*tan(1/2*d*x + 1/2*c) + 6*A*a^6*b^3*tan(1/2*d*x + 1/2*c) - 117*B*a^6*b^3*tan(1/2*d*x + 1/2*c) + 45*A*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*B*a^5*b^4*tan(1/2*d*x + 1/2*c) + 6*A*a^4*b^5*tan(1/2*d*x + 1/2*c) + 105*B*a^4*b^5*tan(1/2*d*x + 1/2*c) - 60*A*a^3*b^6*tan(1/2*d*x + 1/2*c) + 60*B*a^3*b^6*tan(1/2*d*x + 1/2*c) - 36*A*a^2*b^7*tan(1/2*d*x + 1/2*c))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) - 3*(4*B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^5 + 3*(4*B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^5 - 6*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^4))/d","B",0
337,1,844,0,0.455757," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, B a^{7} - 7 \, B a^{5} b^{2} + 8 \, B a^{3} b^{4} + 3 \, A a^{2} b^{5} - 8 \, B a b^{6} + 2 \, A b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{3 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} + \frac{3 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} - \frac{6 \, B a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, B a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(2*B*a^7 - 7*B*a^5*b^2 + 8*B*a^3*b^4 + 3*A*a^2*b^5 - 8*B*a*b^6 + 2*A*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*sqrt(-a^2 + b^2)) - 3*B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 + 3*B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 - (6*B*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*B*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 45*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 60*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 27*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 18*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^8*tan(1/2*d*x + 1/2*c)^3 + 56*B*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^3 - 116*B*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 32*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^3 + 72*B*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^7*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^8*tan(1/2*d*x + 1/2*c) + 15*B*a^7*b*tan(1/2*d*x + 1/2*c) - 6*B*a^6*b^2*tan(1/2*d*x + 1/2*c) - 6*A*a^5*b^3*tan(1/2*d*x + 1/2*c) - 45*B*a^5*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a^4*b^4*tan(1/2*d*x + 1/2*c) - 6*B*a^4*b^4*tan(1/2*d*x + 1/2*c) - 6*A*a^3*b^5*tan(1/2*d*x + 1/2*c) + 60*B*a^3*b^5*tan(1/2*d*x + 1/2*c) - 27*A*a^2*b^6*tan(1/2*d*x + 1/2*c) + 36*B*a^2*b^6*tan(1/2*d*x + 1/2*c) - 18*A*a*b^7*tan(1/2*d*x + 1/2*c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
338,1,693,0,0.421143," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(A a^{3} - 3 \, B a^{2} b + 4 \, A a b^{2} - 2 \, B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{3 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(A*a^3 - 3*B*a^2*b + 4*A*a*b^2 - 2*B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) + (3*A*a^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^5*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 3*B*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 18*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^5*tan(1/2*d*x + 1/2*c)^5 + 4*B*a^5*tan(1/2*d*x + 1/2*c)^3 - 28*A*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 32*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 16*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^5*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^5*tan(1/2*d*x + 1/2*c) - 6*B*a^5*tan(1/2*d*x + 1/2*c) + 12*A*a^4*b*tan(1/2*d*x + 1/2*c) - 3*B*a^4*b*tan(1/2*d*x + 1/2*c) + 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - 6*B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 12*A*a^2*b^3*tan(1/2*d*x + 1/2*c) - 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 6*A*a*b^4*tan(1/2*d*x + 1/2*c) - 18*B*a*b^4*tan(1/2*d*x + 1/2*c) + 6*A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
339,1,726,0,1.987242," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(B a^{3} - 4 \, A a^{2} b + 4 \, B a b^{2} - A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(B*a^3 - 4*A*a^2*b + 4*B*a*b^2 - A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) - (6*A*a^5*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*b^5*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^5*tan(1/2*d*x + 1/2*c)^3 + 28*B*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 16*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 16*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 28*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 12*B*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^5*tan(1/2*d*x + 1/2*c) + 3*B*a^5*tan(1/2*d*x + 1/2*c) + 6*A*a^4*b*tan(1/2*d*x + 1/2*c) - 12*B*a^4*b*tan(1/2*d*x + 1/2*c) + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - 27*B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c) - 12*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 12*A*a*b^4*tan(1/2*d*x + 1/2*c) - 6*B*a*b^4*tan(1/2*d*x + 1/2*c) - 3*A*b^5*tan(1/2*d*x + 1/2*c) - 6*B*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
340,1,693,0,0.403522," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, A a^{3} - 4 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(2*A*a^3 - 4*B*a^2*b + 3*A*a*b^2 - B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(-a^2 + b^2)) + (6*B*a^5*tan(1/2*d*x + 1/2*c)^5 - 18*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*B*b^5*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^5*tan(1/2*d*x + 1/2*c)^3 + 36*A*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 16*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 32*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 28*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 4*A*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^5*tan(1/2*d*x + 1/2*c) - 18*A*a^4*b*tan(1/2*d*x + 1/2*c) + 6*B*a^4*b*tan(1/2*d*x + 1/2*c) - 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 12*B*a^3*b^2*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a*b^4*tan(1/2*d*x + 1/2*c) + 12*B*a*b^4*tan(1/2*d*x + 1/2*c) - 6*A*b^5*tan(1/2*d*x + 1/2*c) - 3*B*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
341,1,814,0,0.414127," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, B a^{7} - 8 \, A a^{6} b + 3 \, B a^{5} b^{2} + 8 \, A a^{4} b^{3} - 7 \, A a^{2} b^{5} + 2 \, A b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{3 \, {\left(d x + c\right)} A}{a^{4}} + \frac{18 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(2*B*a^7 - 8*A*a^6*b + 3*B*a^5*b^2 + 8*A*a^4*b^3 - 7*A*a^2*b^5 + 2*A*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*sqrt(-a^2 + b^2)) + 3*(d*x + c)*A/a^4 + (18*B*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*B*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 15*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 - 6*A*b^8*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^7*b*tan(1/2*d*x + 1/2*c)^3 + 72*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 32*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^3 - 116*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^3 + 56*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^8*tan(1/2*d*x + 1/2*c)^3 + 18*B*a^7*b*tan(1/2*d*x + 1/2*c) - 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c) + 27*B*a^6*b^2*tan(1/2*d*x + 1/2*c) - 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c) + 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c) + 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c) + 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c) + 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c) + 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c) + 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c) - 15*A*a*b^7*tan(1/2*d*x + 1/2*c) - 6*A*b^8*tan(1/2*d*x + 1/2*c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3))/d","B",0
342,1,966,0,1.964088," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, B a^{7} b - 20 \, A a^{6} b^{2} - 8 \, B a^{5} b^{3} + 35 \, A a^{4} b^{4} + 7 \, B a^{3} b^{5} - 28 \, A a^{2} b^{6} - 2 \, B a b^{7} + 8 \, A b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{36 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 236 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}} - \frac{3 \, {\left(B a - 4 \, A b\right)} {\left(d x + c\right)}}{a^{5}} - \frac{6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{4}}}{3 \, d}"," ",0,"-1/3*(3*(8*B*a^7*b - 20*A*a^6*b^2 - 8*B*a^5*b^3 + 35*A*a^4*b^4 + 7*B*a^3*b^5 - 28*A*a^2*b^6 - 2*B*a*b^7 + 8*A*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*sqrt(-a^2 + b^2)) + (36*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 60*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 + 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 45*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 15*B*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 + 42*A*a*b^8*tan(1/2*d*x + 1/2*c)^5 + 6*B*a*b^8*tan(1/2*d*x + 1/2*c)^5 - 18*A*b^9*tan(1/2*d*x + 1/2*c)^5 - 72*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 + 116*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 - 236*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 - 56*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 152*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*b^8*tan(1/2*d*x + 1/2*c)^3 - 36*A*b^9*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^7*b^2*tan(1/2*d*x + 1/2*c) - 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c) + 60*B*a^6*b^3*tan(1/2*d*x + 1/2*c) - 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c) - 6*B*a^5*b^4*tan(1/2*d*x + 1/2*c) + 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c) - 45*B*a^4*b^5*tan(1/2*d*x + 1/2*c) + 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c) - 6*B*a^3*b^6*tan(1/2*d*x + 1/2*c) + 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c) + 15*B*a^2*b^7*tan(1/2*d*x + 1/2*c) - 42*A*a*b^8*tan(1/2*d*x + 1/2*c) + 6*B*a*b^8*tan(1/2*d*x + 1/2*c) - 18*A*b^9*tan(1/2*d*x + 1/2*c))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) - 3*(B*a - 4*A*b)*(d*x + c)/a^5 - 6*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4))/d","B",0
343,1,1052,0,0.412616," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(20 \, B a^{7} b^{2} - 40 \, A a^{6} b^{3} - 35 \, B a^{5} b^{4} + 84 \, A a^{4} b^{5} + 28 \, B a^{3} b^{6} - 69 \, A a^{2} b^{7} - 8 \, B a b^{8} + 20 \, A b^{9}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{{\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{2 \, {\left(60 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, B a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, B a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, B a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 120 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 236 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 392 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 152 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 284 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, B a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, B a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{3}} + \frac{3 \, {\left(A a^{2} - 8 \, B a b + 20 \, A b^{2}\right)} {\left(d x + c\right)}}{a^{6}} - \frac{6 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{5}}}{6 \, d}"," ",0,"1/6*(6*(20*B*a^7*b^2 - 40*A*a^6*b^3 - 35*B*a^5*b^4 + 84*A*a^4*b^5 + 28*B*a^3*b^6 - 69*A*a^2*b^7 - 8*B*a*b^8 + 20*A*b^9)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(-a^2 + b^2)))/((a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*sqrt(-a^2 + b^2)) + 2*(60*B*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 - 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 105*B*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 + 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 - 24*B*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 + 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 + 117*B*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 24*B*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 + 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 - 42*B*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 + 81*A*a*b^9*tan(1/2*d*x + 1/2*c)^5 + 18*B*a*b^9*tan(1/2*d*x + 1/2*c)^5 - 36*A*b^10*tan(1/2*d*x + 1/2*c)^5 - 120*B*a^7*b^3*tan(1/2*d*x + 1/2*c)^3 + 180*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 + 236*B*a^5*b^5*tan(1/2*d*x + 1/2*c)^3 - 392*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 - 152*B*a^3*b^7*tan(1/2*d*x + 1/2*c)^3 + 284*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^9*tan(1/2*d*x + 1/2*c)^3 - 72*A*b^10*tan(1/2*d*x + 1/2*c)^3 + 60*B*a^7*b^3*tan(1/2*d*x + 1/2*c) - 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c) + 105*B*a^6*b^4*tan(1/2*d*x + 1/2*c) - 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c) - 24*B*a^5*b^5*tan(1/2*d*x + 1/2*c) + 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c) - 117*B*a^4*b^6*tan(1/2*d*x + 1/2*c) + 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c) - 24*B*a^3*b^7*tan(1/2*d*x + 1/2*c) + 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c) + 42*B*a^2*b^8*tan(1/2*d*x + 1/2*c) - 81*A*a*b^9*tan(1/2*d*x + 1/2*c) + 18*B*a*b^9*tan(1/2*d*x + 1/2*c) - 36*A*b^10*tan(1/2*d*x + 1/2*c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 - a - b)^3) + 3*(A*a^2 - 8*B*a*b + 20*A*b^2)*(d*x + c)/a^6 - 6*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 8*A*b*tan(1/2*d*x + 1/2*c)^3 - A*a*tan(1/2*d*x + 1/2*c) - 2*B*a*tan(1/2*d*x + 1/2*c) + 8*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^5))/d","B",0
344,1,187,0,0.708011," ","integrate((b*B/a+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\sqrt{-a^{2} + b^{2}} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a b + \sqrt{a^{2} b^{2} + {\left(a^{2} + a b\right)} {\left(a^{2} - a b\right)}}}{a^{2} - a b}}}\right)\right)} B {\left| -a + b \right|}}{a^{3} - a^{2} b} + \frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{-\frac{a b - \sqrt{a^{2} b^{2} + {\left(a^{2} + a b\right)} {\left(a^{2} - a b\right)}}}{a^{2} - a b}}}\right)\right)} B b}{a^{2}}\right)}}{d}"," ",0,"2*(sqrt(-a^2 + b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a*b + sqrt(a^2*b^2 + (a^2 + a*b)*(a^2 - a*b)))/(a^2 - a*b))))*B*abs(-a + b)/(a^3 - a^2*b) + (pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt(-(a*b - sqrt(a^2*b^2 + (a^2 + a*b)*(a^2 - a*b)))/(a^2 - a*b))))*B*b/a^2)/d","B",0
345,1,13,0,0.241374," ","integrate((a*B/b+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} B}{b d}"," ",0,"(d*x + c)*B/(b*d)","B",0
346,1,139,0,0.773444," ","integrate((a+b*sec(d*x+c))/(b+a*sec(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} a}{b^{2}} - \frac{2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} b} - \frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} \sqrt{a^{2} - b^{2}}}{b^{2}}}{d}"," ",0,"((d*x + c)*a/b^2 - 2*a*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)*b) - 2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*sqrt(a^2 - b^2)/b^2)/d","A",0
347,1,58,0,0.318387," ","integrate((3+sec(d*x+c))/(2-sec(d*x+c)),x, algorithm=""giac"")","\frac{9 \, d x - 5 \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}{{\left| 2 \, \sqrt{3} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}\right) + 9 \, c}{6 \, d}"," ",0,"1/6*(9*d*x - 5*sqrt(3)*log(abs(-2*sqrt(3) + 6*tan(1/2*d*x + 1/2*c))/abs(2*sqrt(3) + 6*tan(1/2*d*x + 1/2*c))) + 9*c)/d","A",0
348,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
349,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
350,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
351,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
352,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a), x)","F",0
353,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
354,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
355,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
356,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
357,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
358,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
359,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2), x)","F",0
360,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
361,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
362,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
363,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
364,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
365,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
366,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2), x)","F",0
367,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
368,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
369,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
370,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
371,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
372,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
373,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
374,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/sqrt(b*sec(d*x + c) + a), x)","F",0
375,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
376,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
377,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
378,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^3/(b*sec(d*x + c) + a)^(3/2), x)","F",0
379,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
380,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
381,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
382,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
383,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
384,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^3/(b*sec(d*x + c) + a)^(3/2), x)","F",0
385,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{4}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^4/(b*sec(d*x + c) + a)^(5/2), x)","F",0
386,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^3/(b*sec(d*x + c) + a)^(5/2), x)","F",0
387,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
388,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
389,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
390,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
391,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
392,0,0,0,0.000000," ","integrate(sec(f*x+e)*(A+A*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(A \sec\left(f x + e\right) + A\right)} \sec\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((A*sec(f*x + e) + A)*sec(f*x + e)/sqrt(b*sec(f*x + e) + a), x)","F",0
393,0,0,0,0.000000," ","integrate(sec(f*x+e)*(A-A*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(A \sec\left(f x + e\right) - A\right)} \sec\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(-(A*sec(f*x + e) - A)*sec(f*x + e)/sqrt(b*sec(f*x + e) + a), x)","F",0
394,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
395,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
396,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
397,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
398,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
399,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
400,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
401,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
402,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
403,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
404,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
405,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
406,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(9/2), x)","F",0
407,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
408,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
409,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
410,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
411,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(5/2), x)","F",0
412,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(7/2), x)","F",0
413,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(9/2), x)","F",0
414,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(11/2), x)","F",0
415,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a), x)","F",0
416,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
417,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
418,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
419,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
420,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
421,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
422,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a)^2, x)","F",0
423,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^2, x)","F",0
424,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
425,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
426,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
427,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
428,0,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(9/2)/(b*sec(d*x + c) + a)^3, x)","F",0
429,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a)^3, x)","F",0
430,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^3, x)","F",0
431,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^3, x)","F",0
432,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^3, x)","F",0
433,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
434,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
435,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
436,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
437,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
438,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
439,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
440,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
441,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
442,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
443,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
444,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
445,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
446,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
447,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(9/2), x)","F",0
448,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
449,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
450,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
451,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
452,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(5/2), x)","F",0
453,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(7/2), x)","F",0
454,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(9/2), x)","F",0
455,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(11/2), x)","F",0
456,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
457,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
458,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
459,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
460,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
461,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
462,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
463,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
464,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(3/2), x)","F",0
465,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
466,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
467,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2)), x)","F",0
468,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
469,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
470,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
471,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
472,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
473,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
474,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(2/3), x)","F",0
475,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(1/3), x)","F",0
476,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(1/3), x)","F",0
477,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(2/3), x)","F",0
478,0,0,0,0.000000," ","integrate((c*sec(f*x+e))^n*(a+b*sec(f*x+e))^m*(A+B*sec(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sec\left(f x + e\right) + A\right)} {\left(b \sec\left(f x + e\right) + a\right)}^{m} \left(c \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sec(f*x + e) + A)*(b*sec(f*x + e) + a)^m*(c*sec(f*x + e))^n, x)","F",0
479,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^4*sec(d*x + c)^m, x)","F",0
480,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*sec(d*x + c)^m, x)","F",0
481,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sec(d*x + c)^m, x)","F",0
482,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sec(d*x + c)^m, x)","F",0
483,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
484,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
485,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
486,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
487,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
488,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
489,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(9/2), x)","F",0
490,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
491,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
492,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
493,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
494,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
495,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
496,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
497,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
498,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
499,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
500,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
501,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
502,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
503,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
504,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
505,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
506,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
507,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
508,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2)), x)","F",0
509,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
510,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
511,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
512,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
513,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
514,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2)), x)","F",0
515,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
516,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
517,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
518,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
519,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
520,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
521,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
522,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{a \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(a*sec(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
523,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(11/2), x)","F",0
524,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(9/2), x)","F",0
525,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2), x)","F",0
526,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2), x)","F",0
527,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
528,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
529,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
530,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
531,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(5/2), x)","F",0
532,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(11/2), x)","F",0
533,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(9/2), x)","F",0
534,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2), x)","F",0
535,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2), x)","F",0
536,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
537,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
538,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
539,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
540,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(5/2), x)","F",0
541,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(7/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
542,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
543,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(a*sec(d*x + c) + a), x)","F",0
544,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
545,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
546,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
547,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{a \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
548,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
549,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
550,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^(3/2), x)","F",0
551,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
552,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
553,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
554,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
555,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
556,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
557,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^(5/2), x)","F",0
558,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
559,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
560,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
561,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2)), x)","F",0
562,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
563,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
564,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
565,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
566,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
567,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
568,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
569,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
570,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
571,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
572,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
573,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
574,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
575,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
576,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
577,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
578,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
579,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
580,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
581,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
582,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
583,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
584,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
585,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
586,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2)), x)","F",0
587,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^3, x)","F",0
588,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^3, x)","F",0
589,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
590,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
591,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
592,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2)), x)","F",0
593,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^3*cos(d*x + c)^(9/2)), x)","F",0
594,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
595,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
596,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
597,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\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)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
598,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
599,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
600,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(9/2), x)","F",0
601,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2), x)","F",0
602,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2), x)","F",0
603,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
604,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
605,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
606,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
607,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(11/2), x)","F",0
608,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(9/2), x)","F",0
609,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2), x)","F",0
610,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2), x)","F",0
611,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
612,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
613,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
614,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
615,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
616,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
617,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
618,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
619,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
620,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
621,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
622,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
623,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^(3/2), x)","F",0
624,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
625,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
626,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
627,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
628,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
629,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
630,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
631,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
632,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
633,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
634,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2)), x)","F",0
