1,1,109,0,0.407028," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A a + 3 \, C a\right)} x + \frac{C a \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{C a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, A a + 5 \, C a\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a + C a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(6 \, A a + 5 \, C a\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(4*A*a + 3*C*a)*x + 1/80*C*a*sin(5*d*x + 5*c)/d + 1/32*C*a*sin(4*d*x + 4*c)/d + 1/48*(4*A*a + 5*C*a)*sin(3*d*x + 3*c)/d + 1/4*(A*a + C*a)*sin(2*d*x + 2*c)/d + 1/8*(6*A*a + 5*C*a)*sin(d*x + c)/d","A",0
2,1,86,0,1.451169," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A a + 3 \, C a\right)} x + \frac{C a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{C a \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(A a + C a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a + 3 \, C a\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/8*(4*A*a + 3*C*a)*x + 1/32*C*a*sin(4*d*x + 4*c)/d + 1/12*C*a*sin(3*d*x + 3*c)/d + 1/4*(A*a + C*a)*sin(2*d*x + 2*c)/d + 1/4*(4*A*a + 3*C*a)*sin(d*x + c)/d","A",0
3,1,64,0,0.361278," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, A a + C a\right)} x + \frac{C a \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{C a \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a + 3 \, C a\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/2*(2*A*a + C*a)*x + 1/12*C*a*sin(3*d*x + 3*c)/d + 1/4*C*a*sin(2*d*x + 2*c)/d + 1/4*(4*A*a + 3*C*a)*sin(d*x + c)/d","A",0
4,1,99,0,0.436050," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{2 \, A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(2 \, A a + C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*A*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*A*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (2*A*a + C*a)*(d*x + c) + 2*(C*a*tan(1/2*d*x + 1/2*c)^3 + 3*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
5,1,117,0,1.203351," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} C a + A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((d*x + c)*C*a + A*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - A*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - C*a*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) + C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
6,1,105,0,0.534215," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} C a + {\left(A a + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*a + (A*a + 2*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a + 2*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 3*A*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
7,1,156,0,0.474161," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(A a + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(A a + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*a + 2*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(A*a + 2*C*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 + 6*C*a*tan(1/2*d*x + 1/2*c)^5 - 4*A*a*tan(1/2*d*x + 1/2*c)^3 - 12*C*a*tan(1/2*d*x + 1/2*c)^3 + 9*A*a*tan(1/2*d*x + 1/2*c) + 6*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
8,1,188,0,0.642638," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a + 4 \, C a\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 \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 49 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 84 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 39 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a + 4*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(9*A*a*tan(1/2*d*x + 1/2*c)^7 + 12*C*a*tan(1/2*d*x + 1/2*c)^7 - 49*A*a*tan(1/2*d*x + 1/2*c)^5 - 60*C*a*tan(1/2*d*x + 1/2*c)^5 + 31*A*a*tan(1/2*d*x + 1/2*c)^3 + 84*C*a*tan(1/2*d*x + 1/2*c)^3 - 39*A*a*tan(1/2*d*x + 1/2*c) - 36*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
9,1,158,0,1.041975," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{2} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{C a^{2} \sin\left(5 \, d x + 5 \, c\right)}{40 \, d} + \frac{1}{16} \, {\left(14 \, A a^{2} + 11 \, C a^{2}\right)} x + \frac{{\left(2 \, A a^{2} + 5 \, C a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(4 \, A a^{2} + 5 \, C a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{24 \, d} + \frac{{\left(32 \, A a^{2} + 31 \, C a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(6 \, A a^{2} + 5 \, C a^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/192*C*a^2*sin(6*d*x + 6*c)/d + 1/40*C*a^2*sin(5*d*x + 5*c)/d + 1/16*(14*A*a^2 + 11*C*a^2)*x + 1/64*(2*A*a^2 + 5*C*a^2)*sin(4*d*x + 4*c)/d + 1/24*(4*A*a^2 + 5*C*a^2)*sin(3*d*x + 3*c)/d + 1/64*(32*A*a^2 + 31*C*a^2)*sin(2*d*x + 2*c)/d + 1/4*(6*A*a^2 + 5*C*a^2)*sin(d*x + c)/d","A",0
10,1,129,0,0.440703," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{2} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{C a^{2} \sin\left(4 \, d x + 4 \, c\right)}{16 \, d} + \frac{1}{4} \, {\left(4 \, A a^{2} + 3 \, C a^{2}\right)} x + \frac{{\left(4 \, A a^{2} + 9 \, C a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a^{2} + C a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(14 \, A a^{2} + 11 \, C a^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*a^2*sin(5*d*x + 5*c)/d + 1/16*C*a^2*sin(4*d*x + 4*c)/d + 1/4*(4*A*a^2 + 3*C*a^2)*x + 1/48*(4*A*a^2 + 9*C*a^2)*sin(3*d*x + 3*c)/d + 1/2*(A*a^2 + C*a^2)*sin(2*d*x + 2*c)/d + 1/8*(14*A*a^2 + 11*C*a^2)*sin(d*x + c)/d","A",0
11,1,103,0,1.387387," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{C a^{2} \sin\left(3 \, d x + 3 \, c\right)}{6 \, d} + \frac{1}{8} \, {\left(12 \, A a^{2} + 7 \, C a^{2}\right)} x + \frac{{\left(A a^{2} + 2 \, C a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a^{2} + 3 \, C a^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/32*C*a^2*sin(4*d*x + 4*c)/d + 1/6*C*a^2*sin(3*d*x + 3*c)/d + 1/8*(12*A*a^2 + 7*C*a^2)*x + 1/4*(A*a^2 + 2*C*a^2)*sin(2*d*x + 2*c)/d + 1/2*(4*A*a^2 + 3*C*a^2)*sin(d*x + c)/d","A",0
12,1,179,0,0.463421," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{3 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(2 \, A a^{2} + C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(2*A*a^2 + C*a^2)*(d*x + c) + 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 8*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^2*tan(1/2*d*x + 1/2*c) + 9*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
13,1,143,0,0.445056," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{4 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 4 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + {\left(2 \, A a^{2} + 3 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 4*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 4*A*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + (2*A*a^2 + 3*C*a^2)*(d*x + c) + 2*(3*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 5*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
14,1,152,0,1.782923," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{4 \, {\left(d x + c\right)} C a^{2} + \frac{4 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + {\left(3 \, A a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(3 \, A a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*C*a^2 + 4*C*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + (3*A*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (3*A*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 5*A*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
15,1,187,0,0.533691," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} C a^{2} + 3 \, {\left(A a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(A a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*C*a^2 + 3*(A*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(A*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 8*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 6*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 9*A*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
16,1,212,0,0.746818," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(7 \, A a^{2} + 12 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(7 \, A a^{2} + 12 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(21 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 77 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 132 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 83 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 156 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(7*A*a^2 + 12*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(7*A*a^2 + 12*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(21*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 36*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 77*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 132*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 83*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 156*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 75*A*a^2*tan(1/2*d*x + 1/2*c) - 60*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
17,1,246,0,0.468849," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, A a^{2} + 4 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, A a^{2} + 4 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(45 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 210 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 280 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 432 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 560 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 270 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 520 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 195 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(15*(3*A*a^2 + 4*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*A*a^2 + 4*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(45*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 60*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 210*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 280*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 432*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 560*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 270*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 520*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 195*A*a^2*tan(1/2*d*x + 1/2*c) + 180*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
18,1,185,0,0.552677," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{3} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{C a^{3} \sin\left(6 \, d x + 6 \, c\right)}{64 \, d} + \frac{1}{16} \, {\left(26 \, A a^{3} + 21 \, C a^{3}\right)} x + \frac{{\left(4 \, A a^{3} + 19 \, C a^{3}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(6 \, A a^{3} + 11 \, C a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(68 \, A a^{3} + 81 \, C a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(64 \, A a^{3} + 61 \, C a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(184 \, A a^{3} + 155 \, C a^{3}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/448*C*a^3*sin(7*d*x + 7*c)/d + 1/64*C*a^3*sin(6*d*x + 6*c)/d + 1/16*(26*A*a^3 + 21*C*a^3)*x + 1/320*(4*A*a^3 + 19*C*a^3)*sin(5*d*x + 5*c)/d + 1/64*(6*A*a^3 + 11*C*a^3)*sin(4*d*x + 4*c)/d + 1/192*(68*A*a^3 + 81*C*a^3)*sin(3*d*x + 3*c)/d + 1/64*(64*A*a^3 + 61*C*a^3)*sin(2*d*x + 2*c)/d + 1/64*(184*A*a^3 + 155*C*a^3)*sin(d*x + c)/d","A",0
19,1,158,0,0.563702," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{3 \, C a^{3} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{16} \, {\left(30 \, A a^{3} + 23 \, C a^{3}\right)} x + \frac{{\left(2 \, A a^{3} + 9 \, C a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(12 \, A a^{3} + 19 \, C a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(64 \, A a^{3} + 63 \, C a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(26 \, A a^{3} + 21 \, C a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*C*a^3*sin(6*d*x + 6*c)/d + 3/80*C*a^3*sin(5*d*x + 5*c)/d + 1/16*(30*A*a^3 + 23*C*a^3)*x + 1/64*(2*A*a^3 + 9*C*a^3)*sin(4*d*x + 4*c)/d + 1/48*(12*A*a^3 + 19*C*a^3)*sin(3*d*x + 3*c)/d + 1/64*(64*A*a^3 + 63*C*a^3)*sin(2*d*x + 2*c)/d + 1/8*(26*A*a^3 + 21*C*a^3)*sin(d*x + c)/d","A",0
20,1,131,0,0.428641," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{3} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{3 \, C a^{3} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(20 \, A a^{3} + 13 \, C a^{3}\right)} x + \frac{{\left(4 \, A a^{3} + 17 \, C a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(3 \, A a^{3} + 4 \, C a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(30 \, A a^{3} + 23 \, C a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*a^3*sin(5*d*x + 5*c)/d + 3/32*C*a^3*sin(4*d*x + 4*c)/d + 1/8*(20*A*a^3 + 13*C*a^3)*x + 1/48*(4*A*a^3 + 17*C*a^3)*sin(3*d*x + 3*c)/d + 1/4*(3*A*a^3 + 4*C*a^3)*sin(2*d*x + 2*c)/d + 1/8*(30*A*a^3 + 23*C*a^3)*sin(d*x + c)/d","A",0
21,1,213,0,0.673363," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{8 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 8 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(28 \, A a^{3} + 15 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(20 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 68 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 55 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 76 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 73 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 49 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(8*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 8*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (28*A*a^3 + 15*C*a^3)*(d*x + c) + 2*(20*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 68*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 55*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 76*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 73*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 28*A*a^3*tan(1/2*d*x + 1/2*c) + 49*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
22,1,210,0,1.489102," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{18 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 18 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + 3 \, {\left(6 \, A a^{3} + 5 \, C a^{3}\right)} {\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} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 18*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 12*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 3*(6*A*a^3 + 5*C*a^3)*(d*x + c) + 2*(6*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*tan(1/2*d*x + 1/2*c) + 33*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
23,1,230,0,2.844725," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(2 \, A a^{3} + 7 \, C a^{3}\right)} {\left(d x + c\right)} + {\left(7 \, A a^{3} + 2 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(7 \, A a^{3} + 2 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(5 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((2*A*a^3 + 7*C*a^3)*(d*x + c) + (7*A*a^3 + 2*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (7*A*a^3 + 2*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(5*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 5*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 9*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*A*a^3*tan(1/2*d*x + 1/2*c) - 7*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","A",0
24,1,219,0,0.506805," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{18 \, {\left(d x + c\right)} C a^{3} + \frac{12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 3 \, {\left(5 \, A a^{3} + 6 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(5 \, A a^{3} + 6 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*(d*x + c)*C*a^3 + 12*C*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 3*(5*A*a^3 + 6*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(5*A*a^3 + 6*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 33*A*a^3*tan(1/2*d*x + 1/2*c) + 6*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
25,1,222,0,2.319917," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{8 \, {\left(d x + c\right)} C a^{3} + {\left(15 \, A a^{3} + 28 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(15 \, A a^{3} + 28 \, C a^{3}\right)} \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)^{7} + 20 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 55 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 68 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 73 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 76 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 49 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 28 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(8*(d*x + c)*C*a^3 + (15*A*a^3 + 28*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (15*A*a^3 + 28*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 20*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 55*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 68*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 73*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 76*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 49*A*a^3*tan(1/2*d*x + 1/2*c) - 28*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
26,1,246,0,1.240900," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(13 \, A a^{3} + 20 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(13 \, A a^{3} + 20 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(195 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 300 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 910 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1400 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1664 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2560 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1330 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 765 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 660 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(13*A*a^3 + 20*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(13*A*a^3 + 20*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(195*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 300*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 910*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 1400*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 1664*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 2560*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 1330*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 2120*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 765*A*a^3*tan(1/2*d*x + 1/2*c) + 660*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
27,1,280,0,0.673239," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{15 \, {\left(23 \, A a^{3} + 30 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(23 \, A a^{3} + 30 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(345 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1955 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2550 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4554 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5940 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5814 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 7500 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5130 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1470 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(23*A*a^3 + 30*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(23*A*a^3 + 30*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(345*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 450*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 1955*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 2550*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 4554*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 5940*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 5814*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 7500*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 3165*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 5130*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 1575*A*a^3*tan(1/2*d*x + 1/2*c) - 1470*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
28,1,211,0,0.510652," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{4} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{C a^{4} \sin\left(7 \, d x + 7 \, c\right)}{112 \, d} + \frac{1}{128} \, {\left(392 \, A a^{4} + 323 \, C a^{4}\right)} x + \frac{{\left(A a^{4} + 8 \, C a^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(4 \, A a^{4} + 11 \, C a^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(30 \, A a^{4} + 47 \, C a^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{{\left(36 \, A a^{4} + 41 \, C a^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(127 \, A a^{4} + 120 \, C a^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(88 \, A a^{4} + 75 \, C a^{4}\right)} \sin\left(d x + c\right)}{16 \, d}"," ",0,"1/1024*C*a^4*sin(8*d*x + 8*c)/d + 1/112*C*a^4*sin(7*d*x + 7*c)/d + 1/128*(392*A*a^4 + 323*C*a^4)*x + 1/192*(A*a^4 + 8*C*a^4)*sin(6*d*x + 6*c)/d + 1/80*(4*A*a^4 + 11*C*a^4)*sin(5*d*x + 5*c)/d + 1/128*(30*A*a^4 + 47*C*a^4)*sin(4*d*x + 4*c)/d + 1/48*(36*A*a^4 + 41*C*a^4)*sin(3*d*x + 3*c)/d + 1/64*(127*A*a^4 + 120*C*a^4)*sin(2*d*x + 2*c)/d + 1/16*(88*A*a^4 + 75*C*a^4)*sin(d*x + c)/d","A",0
29,1,185,0,1.533243," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{4} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{C a^{4} \sin\left(6 \, d x + 6 \, c\right)}{48 \, d} + \frac{1}{4} \, {\left(14 \, A a^{4} + 11 \, C a^{4}\right)} x + \frac{{\left(4 \, A a^{4} + 31 \, C a^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(2 \, A a^{4} + 5 \, C a^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{16 \, d} + \frac{{\left(116 \, A a^{4} + 157 \, C a^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(32 \, A a^{4} + 31 \, C a^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{16 \, d} + \frac{{\left(392 \, A a^{4} + 323 \, C a^{4}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/448*C*a^4*sin(7*d*x + 7*c)/d + 1/48*C*a^4*sin(6*d*x + 6*c)/d + 1/4*(14*A*a^4 + 11*C*a^4)*x + 1/320*(4*A*a^4 + 31*C*a^4)*sin(5*d*x + 5*c)/d + 1/16*(2*A*a^4 + 5*C*a^4)*sin(4*d*x + 4*c)/d + 1/192*(116*A*a^4 + 157*C*a^4)*sin(3*d*x + 3*c)/d + 1/16*(32*A*a^4 + 31*C*a^4)*sin(2*d*x + 2*c)/d + 1/64*(392*A*a^4 + 323*C*a^4)*sin(d*x + c)/d","A",0
30,1,158,0,1.699669," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{4} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{C a^{4} \sin\left(5 \, d x + 5 \, c\right)}{20 \, d} + \frac{7}{16} \, {\left(10 \, A a^{4} + 7 \, C a^{4}\right)} x + \frac{{\left(2 \, A a^{4} + 15 \, C a^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(4 \, A a^{4} + 9 \, C a^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(112 \, A a^{4} + 127 \, C a^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(14 \, A a^{4} + 11 \, C a^{4}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/192*C*a^4*sin(6*d*x + 6*c)/d + 1/20*C*a^4*sin(5*d*x + 5*c)/d + 7/16*(10*A*a^4 + 7*C*a^4)*x + 1/64*(2*A*a^4 + 15*C*a^4)*sin(4*d*x + 4*c)/d + 1/12*(4*A*a^4 + 9*C*a^4)*sin(3*d*x + 3*c)/d + 1/64*(112*A*a^4 + 127*C*a^4)*sin(2*d*x + 2*c)/d + 1/2*(14*A*a^4 + 11*C*a^4)*sin(d*x + c)/d","A",0
31,1,248,0,0.873934," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{30 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 30 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 15 \, {\left(12 \, A a^{4} + 7 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(150 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 105 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 680 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 490 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1180 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 896 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 920 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 790 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 270 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 375 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(30*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 30*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 15*(12*A*a^4 + 7*C*a^4)*(d*x + c) + 2*(150*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 105*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 680*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 490*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 1180*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 896*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 920*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 790*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 270*A*a^4*tan(1/2*d*x + 1/2*c) + 375*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
32,1,244,0,0.572557," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{96 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 96 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{48 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + 3 \, {\left(52 \, A a^{4} + 35 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(84 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 276 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 300 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 511 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 108 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 279 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(96*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 96*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 48*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 3*(52*A*a^4 + 35*C*a^4)*(d*x + c) + 2*(84*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 105*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 276*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 385*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 300*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 511*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 108*A*a^4*tan(1/2*d*x + 1/2*c) + 279*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
33,1,248,0,0.636081," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{12 \, {\left(2 \, A a^{4} + 3 \, C a^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(13 \, A a^{4} + 2 \, C 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} + 2 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{6 \, {\left(7 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{4 \, {\left(3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 38 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*(2*A*a^4 + 3*C*a^4)*(d*x + c) + 3*(13*A*a^4 + 2*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(13*A*a^4 + 2*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*(7*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*A*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 4*(3*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 38*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*tan(1/2*d*x + 1/2*c) + 27*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
34,1,248,0,0.617553," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, A a^{4} + 13 \, C a^{4}\right)} {\left(d x + c\right)} + 12 \, {\left(3 \, A a^{4} + 2 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 12 \, {\left(3 \, A a^{4} + 2 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{6 \, {\left(7 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{4 \, {\left(15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 38 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*A*a^4 + 13*C*a^4)*(d*x + c) + 12*(3*A*a^4 + 2*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 12*(3*A*a^4 + 2*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 6*(7*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - 4*(15*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 38*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 6*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 27*A*a^4*tan(1/2*d*x + 1/2*c) + 3*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
35,1,253,0,0.664726," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{96 \, {\left(d x + c\right)} C a^{4} + \frac{48 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 3 \, {\left(35 \, A a^{4} + 52 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(35 \, A a^{4} + 52 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 84 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 385 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 276 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 511 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 300 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 279 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 108 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(96*(d*x + c)*C*a^4 + 48*C*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 3*(35*A*a^4 + 52*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(35*A*a^4 + 52*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(105*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 84*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 385*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 276*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 511*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 300*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 279*A*a^4*tan(1/2*d*x + 1/2*c) - 108*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
36,1,257,0,0.845614," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{30 \, {\left(d x + c\right)} C a^{4} + 15 \, {\left(7 \, A a^{4} + 12 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(7 \, A a^{4} + 12 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 150 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 490 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 680 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 896 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1180 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 790 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 920 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 375 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 270 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(30*(d*x + c)*C*a^4 + 15*(7*A*a^4 + 12*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(7*A*a^4 + 12*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(105*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 150*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 490*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 680*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 896*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 1180*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 790*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 920*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 375*A*a^4*tan(1/2*d*x + 1/2*c) + 270*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
37,1,280,0,0.694921," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{105 \, {\left(7 \, A a^{4} + 10 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(7 \, A a^{4} + 10 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(735 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1050 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 4165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5950 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 9702 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 13860 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 11802 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16860 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7355 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10690 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2790 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(105*(7*A*a^4 + 10*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(7*A*a^4 + 10*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(735*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 1050*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 4165*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 5950*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 9702*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 13860*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 11802*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 16860*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 7355*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 10690*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 3105*A*a^4*tan(1/2*d*x + 1/2*c) - 2790*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
38,1,314,0,0.789529," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^8,x, algorithm=""giac"")","\frac{105 \, {\left(11 \, A a^{4} + 14 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(11 \, A a^{4} + 14 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(1155 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1470 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 7700 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 9800 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 21791 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 27734 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 33792 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 43008 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 31521 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 39914 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 14700 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21560 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5565 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5250 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{420 \, d}"," ",0,"1/420*(105*(11*A*a^4 + 14*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(11*A*a^4 + 14*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(1155*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 1470*C*a^4*tan(1/2*d*x + 1/2*c)^13 - 7700*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 9800*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 21791*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 27734*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 33792*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 43008*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 31521*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 39914*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 14700*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 21560*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 5565*A*a^4*tan(1/2*d*x + 1/2*c) + 5250*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","A",0
39,1,180,0,0.509330," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{9 \, {\left(d x + c\right)} {\left(4 \, A + 5 \, C\right)}}{a} - \frac{24 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(36 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 75 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 84 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 115 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 109 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"1/24*(9*(d*x + c)*(4*A + 5*C)/a - 24*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(36*A*tan(1/2*d*x + 1/2*c)^7 + 75*C*tan(1/2*d*x + 1/2*c)^7 + 84*A*tan(1/2*d*x + 1/2*c)^5 + 115*C*tan(1/2*d*x + 1/2*c)^5 + 60*A*tan(1/2*d*x + 1/2*c)^3 + 109*C*tan(1/2*d*x + 1/2*c)^3 + 12*A*tan(1/2*d*x + 1/2*c) + 21*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
40,1,152,0,0.405168," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} {\left(2 \, A + 3 \, C\right)}}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(3*(d*x + c)*(2*A + 3*C)/a - 6*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(6*A*tan(1/2*d*x + 1/2*c)^5 + 15*C*tan(1/2*d*x + 1/2*c)^5 + 12*A*tan(1/2*d*x + 1/2*c)^3 + 16*C*tan(1/2*d*x + 1/2*c)^3 + 6*A*tan(1/2*d*x + 1/2*c) + 9*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
41,1,96,0,4.579420," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} {\left(2 \, A + 3 \, C\right)}}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((d*x + c)*(2*A + 3*C)/a - 2*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(3*C*tan(1/2*d*x + 1/2*c)^3 + C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
42,1,74,0,0.397442," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(d x + c\right)} C}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a}}{d}"," ",0,"-((d*x + c)*C/a - (A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
43,1,80,0,0.457309," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} C}{a} + \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"((d*x + c)*C/a + A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a)/d","A",0
44,1,101,0,0.412534," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{2 \, 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,"-(A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
45,1,130,0,0.516199," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(3 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(3 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((3*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (3*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*(3*A*tan(1/2*d*x + 1/2*c)^3 - A*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a))/d","A",0
46,1,185,0,0.367145," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(3 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{3 \, {\left(3 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(3*(3*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - 3*(3*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 6*(A*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*(15*A*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 - 16*A*tan(1/2*d*x + 1/2*c)^3 - 12*C*tan(1/2*d*x + 1/2*c)^3 + 9*A*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
47,1,220,0,0.495418," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)} {\left(28 \, A + 55 \, C\right)}}{a^{2}} + \frac{4 \, {\left(A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{6}} - \frac{2 \, {\left(60 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 195 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 156 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 395 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 132 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 341 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 93 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{2}}}{24 \, d}"," ",0,"1/24*(3*(d*x + c)*(28*A + 55*C)/a^2 + 4*(A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 21*A*a^4*tan(1/2*d*x + 1/2*c) - 33*C*a^4*tan(1/2*d*x + 1/2*c))/a^6 - 2*(60*A*tan(1/2*d*x + 1/2*c)^7 + 195*C*tan(1/2*d*x + 1/2*c)^7 + 156*A*tan(1/2*d*x + 1/2*c)^5 + 395*C*tan(1/2*d*x + 1/2*c)^5 + 132*A*tan(1/2*d*x + 1/2*c)^3 + 341*C*tan(1/2*d*x + 1/2*c)^3 + 36*A*tan(1/2*d*x + 1/2*c) + 93*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^2))/d","A",0
48,1,191,0,0.395214," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(d x + c\right)} {\left(2 \, A + 5 \, C\right)}}{a^{2}} - \frac{4 \, {\left(3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*(2*A + 5*C)/a^2 - 4*(3*A*tan(1/2*d*x + 1/2*c)^5 + 15*C*tan(1/2*d*x + 1/2*c)^5 + 6*A*tan(1/2*d*x + 1/2*c)^3 + 20*C*tan(1/2*d*x + 1/2*c)^3 + 3*A*tan(1/2*d*x + 1/2*c) + 9*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^4*tan(1/2*d*x + 1/2*c) - 27*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
49,1,137,0,0.542645," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)} {\left(2 \, A + 7 \, C\right)}}{a^{2}} - \frac{6 \, {\left(5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*(2*A + 7*C)/a^2 - 6*(5*C*tan(1/2*d*x + 1/2*c)^3 + 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*A*a^4*tan(1/2*d*x + 1/2*c) - 21*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
50,1,114,0,0.403321," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(d x + c\right)} C}{a^{2}} - \frac{12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(12*(d*x + c)*C/a^2 - 12*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^4*tan(1/2*d*x + 1/2*c) - 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
51,1,84,0,0.423834," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} C}{a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*C/a^2 + (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*tan(1/2*d*x + 1/2*c) - 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
52,1,112,0,0.472862," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*A*a^4*tan(1/2*d*x + 1/2*c) - 3*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
53,1,142,0,0.468746," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{12 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\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} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(12*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 12*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 12*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^4*tan(1/2*d*x + 1/2*c) + 3*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
54,1,171,0,0.481594," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(7 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(7 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(7*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(7*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 6*(5*A*tan(1/2*d*x + 1/2*c)^3 - 3*A*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 21*A*a^4*tan(1/2*d*x + 1/2*c) + 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
55,1,225,0,0.482168," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(5 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, {\left(5 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{4 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(5*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*(5*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 4*(15*A*tan(1/2*d*x + 1/2*c)^5 + 3*C*tan(1/2*d*x + 1/2*c)^5 - 20*A*tan(1/2*d*x + 1/2*c)^3 - 6*C*tan(1/2*d*x + 1/2*c)^3 + 9*A*tan(1/2*d*x + 1/2*c) + 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 27*A*a^4*tan(1/2*d*x + 1/2*c) + 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
56,1,228,0,0.507832," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(d x + c\right)} {\left(6 \, A + 23 \, C\right)}}{a^{3}} - \frac{20 \, {\left(6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 51 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 76 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 50 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 735 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(d*x + c)*(6*A + 23*C)/a^3 - 20*(6*A*tan(1/2*d*x + 1/2*c)^5 + 51*C*tan(1/2*d*x + 1/2*c)^5 + 12*A*tan(1/2*d*x + 1/2*c)^3 + 76*C*tan(1/2*d*x + 1/2*c)^3 + 6*A*tan(1/2*d*x + 1/2*c) + 33*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 30*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 50*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*A*a^12*tan(1/2*d*x + 1/2*c) + 735*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
57,1,174,0,0.437098," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(d x + c\right)} {\left(2 \, A + 13 \, C\right)}}{a^{3}} - \frac{60 \, {\left(7 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 465 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(d*x + c)*(2*A + 13*C)/a^3 - 60*(7*C*tan(1/2*d*x + 1/2*c)^3 + 5*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 40*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) + 465*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
58,1,151,0,0.386768," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{180 \, {\left(d x + c\right)} C}{a^{3}} - \frac{120 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(180*(d*x + c)*C/a^3 - 120*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 10*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^12*tan(1/2*d*x + 1/2*c) + 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
59,1,104,0,0.354282," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} C}{a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*C/a^3 - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^12*tan(1/2*d*x + 1/2*c) + 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
60,1,89,0,0.375848," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"1/60*(3*A*tan(1/2*d*x + 1/2*c)^5 + 3*C*tan(1/2*d*x + 1/2*c)^5 + 10*A*tan(1/2*d*x + 1/2*c)^3 - 10*C*tan(1/2*d*x + 1/2*c)^3 + 15*A*tan(1/2*d*x + 1/2*c) + 15*C*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
61,1,131,0,0.513979," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) - 15*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
62,1,178,0,0.479427," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{180 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{180 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\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 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(180*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 180*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 120*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 30*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 10*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*A*a^12*tan(1/2*d*x + 1/2*c) + 15*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
63,1,207,0,0.537822," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(13 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{30 \, {\left(13 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{60 \, {\left(7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(13*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 30*(13*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 60*(7*A*tan(1/2*d*x + 1/2*c)^3 - 5*A*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*A*a^12*tan(1/2*d*x + 1/2*c) + 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
64,1,261,0,0.667721," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(23 \, A + 6 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{30 \, {\left(23 \, A + 6 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{20 \, {\left(51 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 76 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 50 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 735 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(23*A + 6*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 30*(23*A + 6*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 20*(51*A*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 - 76*A*tan(1/2*d*x + 1/2*c)^3 - 12*C*tan(1/2*d*x + 1/2*c)^3 + 33*A*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 50*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 735*A*a^12*tan(1/2*d*x + 1/2*c) + 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
65,1,207,0,0.478975," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(d x + c\right)} {\left(2 \, A + 21 \, C\right)}}{a^{4}} - \frac{840 \, {\left(9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 189 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1365 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 11655 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(420*(d*x + c)*(2*A + 21*C)/a^4 - 840*(9*C*tan(1/2*d*x + 1/2*c)^3 + 7*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 189*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 1365*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 1575*A*a^24*tan(1/2*d*x + 1/2*c) - 11655*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
66,1,184,0,0.476694," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3360 \, {\left(d x + c\right)} C}{a^{4}} - \frac{1680 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 63 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 147 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 805 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5145 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(3360*(d*x + c)*C/a^4 - 1680*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 63*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 147*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 805*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*A*a^24*tan(1/2*d*x + 1/2*c) - 5145*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
67,1,154,0,0.410816," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(d x + c\right)} C}{a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 385 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*(d*x + c)*C/a^4 + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 21*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 105*C*a^24*tan(1/2*d*x + 1/2*c)^5 - 35*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 385*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^24*tan(1/2*d*x + 1/2*c) - 1575*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
68,1,117,0,0.535223," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"-1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 + 15*C*tan(1/2*d*x + 1/2*c)^7 + 21*A*tan(1/2*d*x + 1/2*c)^5 - 63*C*tan(1/2*d*x + 1/2*c)^5 - 35*A*tan(1/2*d*x + 1/2*c)^3 + 105*C*tan(1/2*d*x + 1/2*c)^3 - 105*A*tan(1/2*d*x + 1/2*c) - 105*C*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
69,1,117,0,0.385945," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 63 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 + 15*C*tan(1/2*d*x + 1/2*c)^7 + 63*A*tan(1/2*d*x + 1/2*c)^5 - 21*C*tan(1/2*d*x + 1/2*c)^5 + 105*A*tan(1/2*d*x + 1/2*c)^3 - 35*C*tan(1/2*d*x + 1/2*c)^3 + 105*A*tan(1/2*d*x + 1/2*c) + 105*C*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
70,1,182,0,0.608058," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{840 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 840*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 21*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 35*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 1575*A*a^24*tan(1/2*d*x + 1/2*c) - 105*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
71,1,212,0,0.515910," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3360 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3360 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\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 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 147 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 805 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5145 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(3360*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3360*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 1680*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 147*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 63*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 805*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 105*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 5145*A*a^24*tan(1/2*d*x + 1/2*c) + 105*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
72,1,241,0,0.595058," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(21 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{420 \, {\left(21 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{840 \, {\left(9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 189 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1365 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 385 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11655 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1575 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(420*(21*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 420*(21*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 840*(9*A*tan(1/2*d*x + 1/2*c)^3 - 7*A*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 189*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 1365*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 385*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 11655*A*a^24*tan(1/2*d*x + 1/2*c) + 1575*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
73,1,295,0,0.576024," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{1680 \, {\left(11 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{1680 \, {\left(11 \, A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{560 \, {\left(39 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 62 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 231 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 147 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2065 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 805 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21945 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5145 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(1680*(11*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 1680*(11*A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 560*(39*A*tan(1/2*d*x + 1/2*c)^5 + 3*C*tan(1/2*d*x + 1/2*c)^5 - 62*A*tan(1/2*d*x + 1/2*c)^3 - 6*C*tan(1/2*d*x + 1/2*c)^3 + 27*A*tan(1/2*d*x + 1/2*c) + 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 231*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 147*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 2065*A*a^24*tan(1/2*d*x + 1/2*c)^3 + 805*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 21945*A*a^24*tan(1/2*d*x + 1/2*c) + 5145*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
74,1,223,0,0.673760," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{55440} \, \sqrt{2} {\left(\frac{315 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{385 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{495 \, {\left(4 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{693 \, {\left(4 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{2310 \, {\left(6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{6930 \, {\left(6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/55440*sqrt(2)*(315*C*sgn(cos(1/2*d*x + 1/2*c))*sin(11/2*d*x + 11/2*c)/d + 385*C*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 495*(4*A*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 693*(4*A*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 2310*(6*A*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 6930*(6*A*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
75,1,202,0,0.614383," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{35 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{630 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{252 \, {\left(A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{420 \, {\left(A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{1260 \, {\left(2 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(35*C*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 45*C*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 630*C*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d + 252*(A*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 420*(A*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 1260*(2*A*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
76,1,141,0,0.559173," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{420} \, \sqrt{2} {\left(\frac{15 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{21 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{35 \, {\left(4 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{105 \, {\left(4 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/420*sqrt(2)*(15*C*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 21*C*sgn(cos(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)/d + 35*(4*A*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 105*(4*A*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
77,1,99,0,0.453602," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{30} \, \sqrt{2} {\left(\frac{3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{5 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{30 \, {\left(2 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/30*sqrt(2)*(3*C*sgn(cos(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)/d + 5*C*sgn(cos(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)/d + 30*(2*A*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
78,1,5325,0,45.061264," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{a} {\left(\frac{3 \, \sqrt{2} {\left(A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} + 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 20 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} - 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} - A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) + 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} - A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) - 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) + A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \log\left(\frac{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} + \frac{3 \, \sqrt{2} {\left(A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 20 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} - 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} + A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} + 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) - 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 60 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} - A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) + 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \log\left(\frac{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{4} \, d x + c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{4} \, d x + c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} + \frac{8 \, {\left(3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{6} - 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{5} - 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{6} + 36 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{6} - 2 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{6} + 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{3} + 675 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{4} - 540 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{4} + 30 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{4} - 270 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{5} + 288 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{5} - 36 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{5} + 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 120 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 30 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{6} - 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{6} + 18 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right) - 675 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{2} + 540 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{2} - 30 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{2} + 900 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{3} - 960 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{3} + 120 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{3} - 675 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 1800 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} - 450 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{4} - 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{4} + 270 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 960 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} + 540 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{5} - 6 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{6} + 36 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 30 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{6} + 12 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{6} + 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{4} - 36 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{5} + 2 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{6} - 270 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right) + 288 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right) - 36 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right) + 675 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 1800 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} + 450 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{2} + 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{2} - 900 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 3200 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} - 1800 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{3} + 20 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{4} - 540 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 450 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 675 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{4} - 180 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{4} - 18 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{5} + 288 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} - 540 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} + 90 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{5} + 2 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 40 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} - 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{2} \, c\right)^{2} + 120 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} - 30 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} - 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{6} + 270 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 960 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) + 540 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right) - 6 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right) - 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{2} + 540 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 450 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 675 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{2} + 180 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} \tan\left(\frac{1}{4} \, c\right)^{2} + 60 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{3} - 960 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 1800 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} - 300 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{3} - 30 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} - 675 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 600 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 36 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 90 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 12 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{5} - 36 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 30 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 12 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{5} - 18 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{4} \tan\left(\frac{1}{4} \, c\right) + 288 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) - 540 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) + 90 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right) + 30 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} + 675 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 600 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 120 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 300 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 180 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 6 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} - 2 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{3} - 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 40 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 36 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 90 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 180 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 20 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) - 12 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) + 6 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{6} \tan\left(\frac{1}{4} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} + \tan\left(\frac{1}{2} \, c\right)^{6} + 9 \, \tan\left(\frac{1}{2} \, c\right)^{4} \tan\left(\frac{1}{4} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{4} + 9 \, \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{4} \, d x + c\right)^{2} + 1\right)}^{3}}\right)}}{6 \, d}"," ",0,"1/6*sqrt(2)*sqrt(a)*(3*sqrt(2)*(A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 + 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 - 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 + 20*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 - 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 - A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^6 + 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^5 - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) + 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 - 60*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 + 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^4 - A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^3 - 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) - 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c) - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) + A*sgn(cos(1/2*d*x + 1/2*c)))*log(abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 - 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 - 2*tan(1/4*d*x + c) + 6*tan(1/2*c) + 2)/abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 + 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 - 2*tan(1/4*d*x + c) + 6*tan(1/2*c) + 2))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) + 3*sqrt(2)*(A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 + 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 - 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 - 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 - 20*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 + 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 - 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 + A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^6 + 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^5 + 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) - 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 + 60*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 - 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^4 - A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^3 + 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2 - 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) + 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c) - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) - A*sgn(cos(1/2*d*x + 1/2*c)))*log(abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 - 6*tan(1/4*d*x + c)*tan(1/2*c)^2 + 2*tan(1/2*c)^3 - 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 + 2*tan(1/4*d*x + c) - 6*tan(1/2*c) + 2)/abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 - 6*tan(1/4*d*x + c)*tan(1/2*c)^2 + 2*tan(1/2*c)^3 + 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 + 2*tan(1/4*d*x + c) - 6*tan(1/2*c) + 2))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) + 8*(3*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^6*tan(1/4*c)^6 - 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^6*tan(1/4*c)^4 + 18*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^6*tan(1/4*c)^5 - 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^4*tan(1/4*c)^6 + 36*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^5*tan(1/4*c)^6 - 2*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6*tan(1/4*c)^6 + 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^6*tan(1/4*c)^2 - 60*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^6*tan(1/4*c)^3 + 675*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^4*tan(1/4*c)^4 - 540*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^5*tan(1/4*c)^4 + 30*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6*tan(1/4*c)^4 - 270*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^4*tan(1/4*c)^5 + 288*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^5*tan(1/4*c)^5 - 36*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^6*tan(1/4*c)^5 + 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^2*tan(1/4*c)^6 - 120*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^3*tan(1/4*c)^6 + 30*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4*tan(1/4*c)^6 + 3*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c)^6 - 3*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^6 + 18*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^6*tan(1/4*c) - 675*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^4*tan(1/4*c)^2 + 540*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^5*tan(1/4*c)^2 - 30*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6*tan(1/4*c)^2 + 900*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^4*tan(1/4*c)^3 - 960*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^5*tan(1/4*c)^3 + 120*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^6*tan(1/4*c)^3 - 675*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^2*tan(1/4*c)^4 + 1800*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^3*tan(1/4*c)^4 - 450*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4*tan(1/4*c)^4 - 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c)^4 + 270*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^2*tan(1/4*c)^5 - 960*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^3*tan(1/4*c)^5 + 540*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^4*tan(1/4*c)^5 - 6*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c)^5 - 3*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/4*c)^6 + 36*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)*tan(1/4*c)^6 - 30*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2*tan(1/4*c)^6 - 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^6 + 12*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^6 + 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^4 - 36*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^5 + 2*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^6 - 270*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^4*tan(1/4*c) + 288*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^5*tan(1/4*c) - 36*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^6*tan(1/4*c) + 675*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^2*tan(1/4*c)^2 - 1800*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^3*tan(1/4*c)^2 + 450*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4*tan(1/4*c)^2 + 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6*tan(1/4*c)^2 - 900*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^2*tan(1/4*c)^3 + 3200*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^3*tan(1/4*c)^3 - 1800*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^4*tan(1/4*c)^3 + 20*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c)^3 + 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/4*c)^4 - 540*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)*tan(1/4*c)^4 + 450*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2*tan(1/4*c)^4 + 675*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^4 - 180*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^4 - 18*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/4*c)^5 + 288*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)*tan(1/4*c)^5 - 540*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^2*tan(1/4*c)^5 + 90*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^5 + 2*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/4*c)^6 + 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^6 - 40*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 - 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/2*c)^2 + 120*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^3 - 30*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^4 - 3*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^6 + 270*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)^2*tan(1/4*c) - 960*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^3*tan(1/4*c) + 540*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^4*tan(1/4*c) - 6*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^6*tan(1/4*c) - 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5*tan(1/4*c)^2 + 540*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c)*tan(1/4*c)^2 - 450*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2*tan(1/4*c)^2 - 675*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4*tan(1/4*c)^2 + 180*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^5*tan(1/4*c)^2 + 60*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/4*c)^3 - 960*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)*tan(1/4*c)^3 + 1800*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^2*tan(1/4*c)^3 - 300*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c)^3 - 30*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/4*c)^4 - 675*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^4 + 600*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 36*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/4*c)^5 - 90*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^6 + 12*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 + 3*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^5 - 36*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/2*c) + 30*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)^2 + 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^4 - 12*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^5 - 18*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^4*tan(1/4*c) + 288*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/2*c)*tan(1/4*c) - 540*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/2*c)^2*tan(1/4*c) + 90*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^4*tan(1/4*c) + 30*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3*tan(1/4*c)^2 + 675*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2*tan(1/4*c)^2 - 600*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 120*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/4*c)^3 + 300*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^4 - 180*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 + 6*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^5 - 2*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^3 - 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/2*c)^2 + 40*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 36*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)^2*tan(1/4*c) - 90*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^2 + 180*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 - 20*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^3 + 3*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c) - 12*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c) + 6*C*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c))/((tan(1/2*c)^6*tan(1/4*c)^6 + 3*tan(1/2*c)^6*tan(1/4*c)^4 + 3*tan(1/2*c)^4*tan(1/4*c)^6 + 3*tan(1/2*c)^6*tan(1/4*c)^2 + 9*tan(1/2*c)^4*tan(1/4*c)^4 + 3*tan(1/2*c)^2*tan(1/4*c)^6 + tan(1/2*c)^6 + 9*tan(1/2*c)^4*tan(1/4*c)^2 + 9*tan(1/2*c)^2*tan(1/4*c)^4 + tan(1/4*c)^6 + 3*tan(1/2*c)^4 + 9*tan(1/2*c)^2*tan(1/4*c)^2 + 3*tan(1/4*c)^4 + 3*tan(1/2*c)^2 + 3*tan(1/4*c)^2 + 1)*(tan(1/4*d*x + c)^2 + 1)^3))/d","B",0
79,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^5*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,1,275,0,0.428355," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{18480} \, \sqrt{2} {\left(\frac{105 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{385 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{165 \, {\left(4 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{231 \, {\left(12 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 13 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{770 \, {\left(10 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 9 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{2310 \, {\left(6 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{9240 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/18480*sqrt(2)*(105*C*a*sgn(cos(1/2*d*x + 1/2*c))*sin(11/2*d*x + 11/2*c)/d + 385*C*a*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 165*(4*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 231*(12*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 13*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 770*(10*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 9*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 2310*(6*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 9240*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
84,1,190,0,0.325181," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{35 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{135 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{126 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{210 \, {\left(6 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{1260 \, {\left(4 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(35*C*a*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 135*C*a*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 126*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 210*(6*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 1260*(4*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
85,1,189,0,0.409674," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{420} \, \sqrt{2} {\left(\frac{15 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{63 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{35 \, {\left(4 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{105 \, {\left(4 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{420 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/420*sqrt(2)*(15*C*a*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 63*C*a*sgn(cos(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)/d + 35*(4*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 105*(4*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 420*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
86,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,1,345,0,1.974791," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{1441440} \, \sqrt{2} {\left(\frac{3465 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} + \frac{20475 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{10010 \, {\left(2 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{64350 \, {\left(2 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{27027 \, {\left(16 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 17 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{15015 \, {\left(80 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 71 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{180180 \, {\left(12 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{2522520 \, {\left(A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/1441440*sqrt(2)*(3465*C*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(13/2*d*x + 13/2*c)/d + 20475*C*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(11/2*d*x + 11/2*c)/d + 10010*(2*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(9/2*d*x + 9/2*c)/d + 64350*(2*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 27027*(16*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 17*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 15015*(80*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 71*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 180180*(12*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 2522520*(A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
93,1,253,0,1.440243," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{11088} \, \sqrt{2} {\left(\frac{63 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{385 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{99 \, {\left(4 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 13 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{693 \, {\left(4 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{462 \, {\left(22 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 19 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{1386 \, {\left(30 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 23 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/11088*sqrt(2)*(63*C*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(11/2*d*x + 11/2*c)/d + 385*C*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 99*(4*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 13*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 693*(4*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 462*(22*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 19*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 1386*(30*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 23*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
94,1,250,0,0.626723," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{35 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{225 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{252 \, {\left(A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{2100 \, {\left(A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{630 \, {\left(12 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{1260 \, {\left(4 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(35*C*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 225*C*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 252*(A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 2100*(A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 630*(12*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 1260*(4*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
95,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,1,227,0,5.883522," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{315 \, {\left(\sqrt{2} A + \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} + \frac{2 \, {\left(315 \, \sqrt{2} A a^{4} + 315 \, \sqrt{2} C a^{4} + {\left(1050 \, \sqrt{2} A a^{4} + 840 \, \sqrt{2} C a^{4} + {\left(1512 \, \sqrt{2} A a^{4} + 1638 \, \sqrt{2} C a^{4} + {\left(1134 \, \sqrt{2} A a^{4} + 936 \, \sqrt{2} C a^{4} + {\left(357 \, \sqrt{2} A a^{4} + 383 \, \sqrt{2} C a^{4}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{9}{2}}}}{315 \, d}"," ",0,"1/315*(315*(sqrt(2)*A + sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) + 2*(315*sqrt(2)*A*a^4 + 315*sqrt(2)*C*a^4 + (1050*sqrt(2)*A*a^4 + 840*sqrt(2)*C*a^4 + (1512*sqrt(2)*A*a^4 + 1638*sqrt(2)*C*a^4 + (1134*sqrt(2)*A*a^4 + 936*sqrt(2)*C*a^4 + (357*sqrt(2)*A*a^4 + 383*sqrt(2)*C*a^4)*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)^(9/2))/d","A",0
103,1,158,0,1.883138," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{105 \, \sqrt{2} {\left(A + C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} + \frac{4 \, {\left({\left(\sqrt{2} {\left(35 \, A a^{3} + 46 \, C a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 14 \, \sqrt{2} {\left(5 \, A a^{3} + 4 \, C a^{3}\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, \sqrt{2} {\left(A a^{3} + 2 \, C a^{3}\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}}{105 \, d}"," ",0,"-1/105*(105*sqrt(2)*(A + C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) + 4*((sqrt(2)*(35*A*a^3 + 46*C*a^3)*tan(1/2*d*x + 1/2*c)^2 + 14*sqrt(2)*(5*A*a^3 + 4*C*a^3))*tan(1/2*d*x + 1/2*c)^2 + 35*sqrt(2)*(A*a^3 + 2*C*a^3))*tan(1/2*d*x + 1/2*c)^3/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","A",0
104,1,165,0,1.151264," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(\sqrt{2} A + \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} + \frac{2 \, {\left(15 \, \sqrt{2} A a^{2} + 15 \, \sqrt{2} C a^{2} + {\left(30 \, \sqrt{2} A a^{2} + 20 \, \sqrt{2} C a^{2} + {\left(15 \, \sqrt{2} A a^{2} + 17 \, \sqrt{2} C a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}}{15 \, d}"," ",0,"1/15*(15*(sqrt(2)*A + sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) + 2*(15*sqrt(2)*A*a^2 + 15*sqrt(2)*C*a^2 + (30*sqrt(2)*A*a^2 + 20*sqrt(2)*C*a^2 + (15*sqrt(2)*A*a^2 + 17*sqrt(2)*C*a^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","A",0
105,1,86,0,0.931094," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{4 \, \sqrt{2} C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}} + \frac{3 \, \sqrt{2} {\left(A + C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}}}{3 \, d}"," ",0,"-1/3*(4*sqrt(2)*C*a*tan(1/2*d*x + 1/2*c)^3/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) + 3*sqrt(2)*(A + C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a))/d","A",0
106,1,191,0,1.612241," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(A + C\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{a}} + \frac{4 \, \sqrt{2} C \tan\left(\frac{1}{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{2 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{a}} - \frac{2 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{a}}}{2 \, d}"," ",0,"1/2*(sqrt(2)*(A + C)*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/sqrt(a) + 4*sqrt(2)*C*tan(1/2*d*x + 1/2*c)/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + 2*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/sqrt(a) - 2*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/sqrt(a))/d","A",0
107,1,290,0,1.925279," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} {\left(A + C\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{a}} + \frac{A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{a}} - \frac{A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{a}} - \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 a^{\frac{3}{2}}\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*(sqrt(2)*(A + C)*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/sqrt(a) + A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/sqrt(a) - A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/sqrt(a) - 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*a^(3/2))/((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
108,1,397,0,8.977972," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{4 \, \sqrt{2} {\left(A + C\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{a}} + \frac{{\left(7 \, A \sqrt{a} + 8 \, C \sqrt{a}\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)}{a} - \frac{{\left(7 \, A \sqrt{a} + 8 \, C \sqrt{a}\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)}{a} - \frac{4 \, \sqrt{2} {\left(17 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{a} - 57 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a^{\frac{3}{2}} + 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 a^{\frac{5}{2}} - 3 \, A a^{\frac{7}{2}}\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*(4*sqrt(2)*(A + C)*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/sqrt(a) + (7*A*sqrt(a) + 8*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a - (7*A*sqrt(a) + 8*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a - 4*sqrt(2)*(17*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(a) - 57*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a^(3/2) + 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*a^(5/2) - 3*A*a^(7/2))/((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
109,1,691,0,2.279901," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{24 \, \sqrt{2} {\left(A + C\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{a}} + \frac{3 \, {\left(9 \, A \sqrt{a} + 8 \, C \sqrt{a}\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)}{a} - \frac{3 \, {\left(9 \, A \sqrt{a} + 8 \, C \sqrt{a}\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)}{a} - \frac{4 \, \sqrt{2} {\left(165 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{a} + 72 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{a} - 1323 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A a^{\frac{3}{2}} - 888 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C a^{\frac{3}{2}} + 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 a^{\frac{5}{2}} + 3024 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C a^{\frac{5}{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 a^{\frac{7}{2}} - 1776 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C a^{\frac{7}{2}} + 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 a^{\frac{9}{2}} + 360 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C a^{\frac{9}{2}} - 31 \, A a^{\frac{11}{2}} - 24 \, C a^{\frac{11}{2}}\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*(24*sqrt(2)*(A + C)*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/sqrt(a) + 3*(9*A*sqrt(a) + 8*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a - 3*(9*A*sqrt(a) + 8*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a - 4*sqrt(2)*(165*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(a) + 72*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(a) - 1323*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*a^(3/2) - 888*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*a^(3/2) + 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*a^(5/2) + 3024*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*a^(5/2) - 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*a^(7/2) - 1776*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*a^(7/2) + 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*a^(9/2) + 360*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*a^(9/2) - 31*A*a^(11/2) - 24*C*a^(11/2))/((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
110,1,855,0,2.922072," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{192 \, \sqrt{2} {\left(A + C\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{\sqrt{a}} + \frac{3 \, {\left(107 \, A \sqrt{a} + 112 \, C \sqrt{a}\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)}{a} - \frac{3 \, {\left(107 \, A \sqrt{a} + 112 \, C \sqrt{a}\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)}{a} - \frac{4 \, \sqrt{2} {\left(1599 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{a} + 816 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{a} - 18219 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A a^{\frac{3}{2}} - 12528 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C a^{\frac{3}{2}} + 91467 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A a^{\frac{5}{2}} + 64752 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C a^{\frac{5}{2}} - 177735 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A a^{\frac{7}{2}} - 124848 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C a^{\frac{7}{2}} + 100413 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A a^{\frac{9}{2}} + 70032 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C a^{\frac{9}{2}} - 26881 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a^{\frac{11}{2}} - 19152 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C a^{\frac{11}{2}} + 3321 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{\frac{13}{2}} + 2640 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C a^{\frac{13}{2}} - 205 \, A a^{\frac{15}{2}} - 144 \, C a^{\frac{15}{2}}\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*(192*sqrt(2)*(A + C)*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/sqrt(a) + 3*(107*A*sqrt(a) + 112*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a - 3*(107*A*sqrt(a) + 112*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a - 4*sqrt(2)*(1599*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(a) + 816*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(a) - 18219*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*a^(3/2) - 12528*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*a^(3/2) + 91467*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*a^(5/2) + 64752*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*a^(5/2) - 177735*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*a^(7/2) - 124848*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*a^(7/2) + 100413*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*a^(9/2) + 70032*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*a^(9/2) - 26881*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a^(11/2) - 19152*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*a^(11/2) + 3321*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^(13/2) + 2640*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*a^(13/2) - 205*A*a^(15/2) - 144*C*a^(15/2))/((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
111,1,254,0,1.356320," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(11 \, \sqrt{2} A + 19 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}} + \frac{{\left({\left({\left({\left(\frac{105 \, {\left(\sqrt{2} A a^{5} + \sqrt{2} C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} + \frac{4 \, {\left(455 \, \sqrt{2} A a^{5} + 877 \, \sqrt{2} C a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{14 \, {\left(305 \, \sqrt{2} A a^{5} + 517 \, \sqrt{2} C a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{140 \, {\left(25 \, \sqrt{2} A a^{5} + 47 \, \sqrt{2} C a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{105 \, {\left(9 \, \sqrt{2} A a^{5} + 17 \, \sqrt{2} C a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}}{420 \, d}"," ",0,"-1/420*(105*(11*sqrt(2)*A + 19*sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2) + ((((105*(sqrt(2)*A*a^5 + sqrt(2)*C*a^5)*tan(1/2*d*x + 1/2*c)^2/a^3 + 4*(455*sqrt(2)*A*a^5 + 877*sqrt(2)*C*a^5)/a^3)*tan(1/2*d*x + 1/2*c)^2 + 14*(305*sqrt(2)*A*a^5 + 517*sqrt(2)*C*a^5)/a^3)*tan(1/2*d*x + 1/2*c)^2 + 140*(25*sqrt(2)*A*a^5 + 47*sqrt(2)*C*a^5)/a^3)*tan(1/2*d*x + 1/2*c)^2 + 105*(9*sqrt(2)*A*a^5 + 17*sqrt(2)*C*a^5)/a^3)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","A",0
112,1,201,0,1.776328," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{5 \, \sqrt{2} {\left(7 \, A + 15 \, C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}} + \frac{{\left({\left({\left(\frac{5 \, \sqrt{2} {\left(A a^{3} + C a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2}} + \frac{\sqrt{2} {\left(55 \, A a^{3} + 127 \, C a^{3}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, \sqrt{2} {\left(19 \, A a^{3} + 35 \, C a^{3}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, \sqrt{2} {\left(9 \, A a^{3} + 17 \, C a^{3}\right)}}{a^{2}}\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)}^{\frac{5}{2}}}}{20 \, d}"," ",0,"1/20*(5*sqrt(2)*(7*A + 15*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2) + (((5*sqrt(2)*(A*a^3 + C*a^3)*tan(1/2*d*x + 1/2*c)^2/a^2 + sqrt(2)*(55*A*a^3 + 127*C*a^3)/a^2)*tan(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*(19*A*a^3 + 35*C*a^3)/a^2)*tan(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*(9*A*a^3 + 17*C*a^3)/a^2)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","A",0
113,1,167,0,3.533324," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(3 \, \sqrt{2} A + 11 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}} + \frac{{\left({\left(\frac{3 \, {\left(\sqrt{2} A a + \sqrt{2} C a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a} + \frac{2 \, {\left(3 \, \sqrt{2} A a + 23 \, \sqrt{2} C a\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{3 \, {\left(\sqrt{2} A a + 9 \, \sqrt{2} C a\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)}^{\frac{3}{2}}}}{12 \, d}"," ",0,"-1/12*(3*(3*sqrt(2)*A + 11*sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2) + ((3*(sqrt(2)*A*a + sqrt(2)*C*a)*tan(1/2*d*x + 1/2*c)^2/a + 2*(3*sqrt(2)*A*a + 23*sqrt(2)*C*a)/a)*tan(1/2*d*x + 1/2*c)^2 + 3*(sqrt(2)*A*a + 9*sqrt(2)*C*a)/a)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2))/d","A",0
114,1,129,0,2.932138," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(\frac{\sqrt{2} {\left(A a^{2} + C a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} + \frac{\sqrt{2} {\left(A a^{2} + 9 \, C a^{2}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{\sqrt{2} {\left(A - 7 \, C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}}}{4 \, d}"," ",0,"1/4*((sqrt(2)*(A*a^2 + C*a^2)*tan(1/2*d*x + 1/2*c)^2/a^3 + sqrt(2)*(A*a^2 + 9*C*a^2)/a^3)*tan(1/2*d*x + 1/2*c)/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(2)*(A - 7*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2))/d","A",0
115,1,213,0,4.922910," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(5 \, A \sqrt{a} - 3 \, C \sqrt{a}\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)}{a^{2}} + \frac{8 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{\frac{3}{2}}} - \frac{8 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{\frac{3}{2}}} - \frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\sqrt{2} A a + \sqrt{2} C a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}}}{8 \, d}"," ",0,"1/8*(sqrt(2)*(5*A*sqrt(a) - 3*C*sqrt(a))*log((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 + 8*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^(3/2) - 8*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^(3/2) - 2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(sqrt(2)*A*a + sqrt(2)*C*a)*tan(1/2*d*x + 1/2*c)/a^3)/d","B",0
116,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)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)/2))]Discontinuities at zeroes of cos((d*t_nostep+c)/2) were not checkedEvaluation time: 0.97Error index.cc index_gcd Error: Bad Argument Value","F(-2)",0
117,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)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)/2))]Discontinuities at zeroes of cos((d*t_nostep+c)/2) were not checkedEvaluation time: 0.95Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[23574053482485268906770432,0]:[1,0,-2]%%},[16]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0]%%%} / %%%{%%%{%%{[604462909807314587353088,0]:[1,0,-2]%%},[16]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
118,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)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)/2))]Discontinuities at zeroes of cos((d*t_nostep+c)/2) were not checkedEvaluation time: 1.08Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[7975367974709495237422842361682067456000,0]:[1,0,-2]%%},[30]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0]%%%} / %%%{%%%{%%{[63802943797675961899382738893456539648,0]:[1,0,-2]%%},[30]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
119,1,256,0,5.783533," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(75 \, \sqrt{2} A + 283 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}} - \frac{{\left({\left({\left(15 \, {\left(\frac{2 \, {\left(\sqrt{2} A a^{2} + \sqrt{2} C a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2}} - \frac{13 \, \sqrt{2} A a^{2} + 29 \, \sqrt{2} C a^{2}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{1725 \, \sqrt{2} A a^{2} + 6733 \, \sqrt{2} C a^{2}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{5 \, {\left(549 \, \sqrt{2} A a^{2} + 1973 \, \sqrt{2} C a^{2}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{15 \, {\left(83 \, \sqrt{2} A a^{2} + 291 \, \sqrt{2} C a^{2}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}}{480 \, d}"," ",0,"1/480*(15*(75*sqrt(2)*A + 283*sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2) - (((15*(2*(sqrt(2)*A*a^2 + sqrt(2)*C*a^2)*tan(1/2*d*x + 1/2*c)^2/a^2 - (13*sqrt(2)*A*a^2 + 29*sqrt(2)*C*a^2)/a^2)*tan(1/2*d*x + 1/2*c)^2 - (1725*sqrt(2)*A*a^2 + 6733*sqrt(2)*C*a^2)/a^2)*tan(1/2*d*x + 1/2*c)^2 - 5*(549*sqrt(2)*A*a^2 + 1973*sqrt(2)*C*a^2)/a^2)*tan(1/2*d*x + 1/2*c)^2 - 15*(83*sqrt(2)*A*a^2 + 291*sqrt(2)*C*a^2)/a^2)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","A",0
120,1,203,0,4.922060," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(3 \, {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{6}} - \frac{\sqrt{2} {\left(7 \, A a^{5} + 23 \, C a^{5}\right)}}{a^{6}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{4 \, \sqrt{2} {\left(15 \, A a^{5} + 167 \, C a^{5}\right)}}{a^{6}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{3 \, \sqrt{2} {\left(11 \, A a^{5} + 155 \, C a^{5}\right)}}{a^{6}}\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)}^{\frac{3}{2}}} - \frac{3 \, \sqrt{2} {\left(19 \, A + 163 \, C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{96 \, d}"," ",0,"1/96*(((3*(2*sqrt(2)*(A*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/a^6 - sqrt(2)*(7*A*a^5 + 23*C*a^5)/a^6)*tan(1/2*d*x + 1/2*c)^2 - 4*sqrt(2)*(15*A*a^5 + 167*C*a^5)/a^6)*tan(1/2*d*x + 1/2*c)^2 - 3*sqrt(2)*(11*A*a^5 + 155*C*a^5)/a^6)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) - 3*sqrt(2)*(19*A + 163*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
121,1,178,0,1.424912," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(\frac{2 \, {\left(\sqrt{2} A a^{6} + \sqrt{2} C a^{6}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} - \frac{\sqrt{2} A a^{6} + 17 \, \sqrt{2} C a^{6}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{3 \, \sqrt{2} A a^{6} + 83 \, \sqrt{2} C a^{6}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{5 \, {\left(\sqrt{2} A - 15 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{32 \, d}"," ",0,"-1/32*(((2*(sqrt(2)*A*a^6 + sqrt(2)*C*a^6)*tan(1/2*d*x + 1/2*c)^2/a^8 - (sqrt(2)*A*a^6 + 17*sqrt(2)*C*a^6)/a^8)*tan(1/2*d*x + 1/2*c)^2 - (3*sqrt(2)*A*a^6 + 83*sqrt(2)*C*a^6)/a^8)*tan(1/2*d*x + 1/2*c)/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + 5*(sqrt(2)*A - 15*sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
122,1,133,0,1.504112," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{\sqrt{2} {\left(5 \, A a^{5} - 11 \, C a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{\sqrt{2} {\left(3 \, A + 19 \, C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{32 \, d}"," ",0,"1/32*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/a^8 + sqrt(2)*(5*A*a^5 - 11*C*a^5)/a^8)*tan(1/2*d*x + 1/2*c) - sqrt(2)*(3*A + 19*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
123,1,249,0,3.858968," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{\sqrt{2} {\left(13 \, A a^{5} - 3 \, C a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{\sqrt{2} {\left(43 \, A \sqrt{a} - 5 \, C \sqrt{a}\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)}{a^{3}} - \frac{64 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{\frac{5}{2}}} + \frac{64 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{\frac{5}{2}}}}{64 \, d}"," ",0,"-1/64*(2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/a^8 + sqrt(2)*(13*A*a^5 - 3*C*a^5)/a^8)*tan(1/2*d*x + 1/2*c) - sqrt(2)*(43*A*sqrt(a) - 5*C*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a^3 - 64*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^(5/2) + 64*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^(5/2))/d","A",0
124,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)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)/2))]Discontinuities at zeroes of cos((d*t_nostep+c)/2) were not checkedEvaluation time: 1.71Error index.cc index_gcd Error: Bad Argument Value","F(-2)",0
125,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)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)/2))]Discontinuities at zeroes of cos((d*t_nostep+c)/2) were not checkedEvaluation time: 1.86Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[663535861056963827345930584064,0]:[1,0,-2]%%},[16]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0]%%%} / %%%{%%%{%%{[9903520314283042199192993792,0]:[1,0,-2]%%},[16]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
126,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
127,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
128,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
129,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
130,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
131,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
132,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
133,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
134,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
135,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
136,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
137,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
138,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
139,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
140,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
141,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(11/2), x)","F",0
142,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
143,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
145,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
146,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
147,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
148,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
149,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
150,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(13/2), x)","F",0
151,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
152,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
153,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
154,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
155,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
156,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
157,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
158,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^2, x)","F",0
159,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^2, x)","F",0
160,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
161,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
162,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
163,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
164,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^3, x)","F",0
165,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^3, x)","F",0
166,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^3, x)","F",0
167,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^3, x)","F",0
168,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
169,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
170,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
171,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
172,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
173,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
180,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
181,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
189,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
190,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/sqrt(a*cos(d*x + c) + a), x)","F",0
199,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/sqrt(a*cos(d*x + c) + a), x)","F",0
200,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
201,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
202,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
203,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
204,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
205,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
206,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
207,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
208,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
209,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
210,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
211,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
212,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
213,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
214,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
215,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
216,1,77,0,0.372093," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{3}{8} \, B x + \frac{C \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{B \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{5 \, C \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{B \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{5 \, C \sin\left(d x + c\right)}{8 \, d}"," ",0,"3/8*B*x + 1/80*C*sin(5*d*x + 5*c)/d + 1/32*B*sin(4*d*x + 4*c)/d + 5/48*C*sin(3*d*x + 3*c)/d + 1/4*B*sin(2*d*x + 2*c)/d + 5/8*C*sin(d*x + c)/d","A",0
217,1,62,0,0.592252," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{3}{8} \, C x + \frac{C \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{B \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{C \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{3 \, B \sin\left(d x + c\right)}{4 \, d}"," ",0,"3/8*C*x + 1/32*C*sin(4*d*x + 4*c)/d + 1/12*B*sin(3*d*x + 3*c)/d + 1/4*C*sin(2*d*x + 2*c)/d + 3/4*B*sin(d*x + c)/d","A",0
218,1,47,0,0.530196," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2} \, B x + \frac{C \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{B \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{3 \, C \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/2*B*x + 1/12*C*sin(3*d*x + 3*c)/d + 1/4*B*sin(2*d*x + 2*c)/d + 3/4*C*sin(d*x + c)/d","A",0
219,1,32,0,0.267970," ","integrate(B*cos(d*x+c)+C*cos(d*x+c)^2,x, algorithm=""giac"")","\frac{1}{4} \, C {\left(2 \, x + \frac{\sin\left(2 \, d x + 2 \, c\right)}{d}\right)} + \frac{B \sin\left(d x + c\right)}{d}"," ",0,"1/4*C*(2*x + sin(2*d*x + 2*c)/d) + B*sin(d*x + c)/d","A",0
220,1,39,0,0.350169," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} B + \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"((d*x + c)*B + 2*C*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
221,1,43,0,0.632412," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} C + B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{d}"," ",0,"((d*x + c)*C + B*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - B*log(abs(tan(1/2*d*x + 1/2*c) - 1)))/d","B",0
222,1,63,0,0.773809," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, 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,"(C*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - C*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*B*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
223,1,105,0,0.508322," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(B*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - B*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(B*tan(1/2*d*x + 1/2*c)^3 - 2*C*tan(1/2*d*x + 1/2*c)^3 + B*tan(1/2*d*x + 1/2*c) + 2*C*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
224,1,122,0,0.505441," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, C \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*C*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*C*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*B*tan(1/2*d*x + 1/2*c)^5 - 3*C*tan(1/2*d*x + 1/2*c)^5 - 4*B*tan(1/2*d*x + 1/2*c)^3 + 6*B*tan(1/2*d*x + 1/2*c) + 3*C*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
225,1,164,0,0.596754," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{9 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 9 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, C \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)^{3} - 40 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(9*B*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 9*B*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*B*tan(1/2*d*x + 1/2*c)^7 - 24*C*tan(1/2*d*x + 1/2*c)^7 + 9*B*tan(1/2*d*x + 1/2*c)^5 + 40*C*tan(1/2*d*x + 1/2*c)^5 + 9*B*tan(1/2*d*x + 1/2*c)^3 - 40*C*tan(1/2*d*x + 1/2*c)^3 + 15*B*tan(1/2*d*x + 1/2*c) + 24*C*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
226,1,112,0,0.370411," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{3}{8} \, {\left(B a + C a\right)} x + \frac{C a \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(B a + C a\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, B a + 5 \, C a\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(B a + C a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(6 \, B a + 5 \, C a\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"3/8*(B*a + C*a)*x + 1/80*C*a*sin(5*d*x + 5*c)/d + 1/32*(B*a + C*a)*sin(4*d*x + 4*c)/d + 1/48*(4*B*a + 5*C*a)*sin(3*d*x + 3*c)/d + 1/4*(B*a + C*a)*sin(2*d*x + 2*c)/d + 1/8*(6*B*a + 5*C*a)*sin(d*x + c)/d","A",0
227,1,89,0,0.382010," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, B a + 3 \, C a\right)} x + \frac{C a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(B a + C a\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(B a + C a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{3 \, {\left(B a + C a\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/8*(4*B*a + 3*C*a)*x + 1/32*C*a*sin(4*d*x + 4*c)/d + 1/12*(B*a + C*a)*sin(3*d*x + 3*c)/d + 1/4*(B*a + C*a)*sin(2*d*x + 2*c)/d + 3/4*(B*a + C*a)*sin(d*x + c)/d","A",0
228,1,68,0,0.443894," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(B a + C a\right)} x + \frac{C a \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(B a + C a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, B a + 3 \, C a\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/2*(B*a + C*a)*x + 1/12*C*a*sin(3*d*x + 3*c)/d + 1/4*(B*a + C*a)*sin(2*d*x + 2*c)/d + 1/4*(4*B*a + 3*C*a)*sin(d*x + c)/d","A",0
229,1,93,0,0.311616," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{{\left(2 \, B a + C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((2*B*a + C*a)*(d*x + c) + 2*(2*B*a*tan(1/2*d*x + 1/2*c)^3 + C*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*a*tan(1/2*d*x + 1/2*c) + 3*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
230,1,79,0,0.389588," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,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(B a + C a\right)} {\left(d x + c\right)} + \frac{2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(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)) + (B*a + C*a)*(d*x + c) + 2*C*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
231,1,84,0,0.677071," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} C a + {\left(B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, 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)*C*a + (B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*B*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
232,1,124,0,0.402986," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{{\left(B a + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((B*a + 2*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a + 2*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(B*a*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*tan(1/2*d*x + 1/2*c)^3 - 3*B*a*tan(1/2*d*x + 1/2*c) - 2*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
233,1,154,0,0.457964," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(B a + C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a + C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*B*a*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*tan(1/2*d*x + 1/2*c)^5 - 4*B*a*tan(1/2*d*x + 1/2*c)^3 - 12*C*a*tan(1/2*d*x + 1/2*c)^3 + 9*B*a*tan(1/2*d*x + 1/2*c) + 9*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
234,1,188,0,0.383951," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, B a + 4 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, B a + 4 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 49 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 28 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 52 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 39 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*B*a + 4*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*B*a + 4*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(9*B*a*tan(1/2*d*x + 1/2*c)^7 + 12*C*a*tan(1/2*d*x + 1/2*c)^7 - 49*B*a*tan(1/2*d*x + 1/2*c)^5 - 28*C*a*tan(1/2*d*x + 1/2*c)^5 + 31*B*a*tan(1/2*d*x + 1/2*c)^3 + 52*C*a*tan(1/2*d*x + 1/2*c)^3 - 39*B*a*tan(1/2*d*x + 1/2*c) - 36*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
235,1,137,0,0.301140," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{2} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(7 \, B a^{2} + 6 \, C a^{2}\right)} x + \frac{{\left(B a^{2} + 2 \, C a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(8 \, B a^{2} + 9 \, C a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(B a^{2} + C a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(12 \, B a^{2} + 11 \, C a^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*a^2*sin(5*d*x + 5*c)/d + 1/8*(7*B*a^2 + 6*C*a^2)*x + 1/32*(B*a^2 + 2*C*a^2)*sin(4*d*x + 4*c)/d + 1/48*(8*B*a^2 + 9*C*a^2)*sin(3*d*x + 3*c)/d + 1/2*(B*a^2 + C*a^2)*sin(2*d*x + 2*c)/d + 1/8*(12*B*a^2 + 11*C*a^2)*sin(d*x + c)/d","A",0
236,1,110,0,0.244910," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(8 \, B a^{2} + 7 \, C a^{2}\right)} x + \frac{{\left(B a^{2} + 2 \, C a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(B a^{2} + C a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(7 \, B a^{2} + 6 \, C a^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/32*C*a^2*sin(4*d*x + 4*c)/d + 1/8*(8*B*a^2 + 7*C*a^2)*x + 1/12*(B*a^2 + 2*C*a^2)*sin(3*d*x + 3*c)/d + 1/2*(B*a^2 + C*a^2)*sin(2*d*x + 2*c)/d + 1/4*(7*B*a^2 + 6*C*a^2)*sin(d*x + c)/d","A",0
237,1,142,0,0.384079," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{3 \, {\left(3 \, B a^{2} + 2 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(3*B*a^2 + 2*C*a^2)*(d*x + c) + 2*(9*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 24*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 16*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^2*tan(1/2*d*x + 1/2*c) + 18*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
238,1,145,0,0.686841," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,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(4 \, B a^{2} + 3 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*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)) + (4*B*a^2 + 3*C*a^2)*(d*x + c) + 2*(2*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^2*tan(1/2*d*x + 1/2*c) + 5*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
239,1,155,0,0.513352," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(B a^{2} + 2 \, C a^{2}\right)} {\left(d x + c\right)} + {\left(2 \, B a^{2} + C a^{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} + C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((B*a^2 + 2*C*a^2)*(d*x + c) + (2*B*a^2 + C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*B*a^2 + C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(B*a^2*tan(1/2*d*x + 1/2*c)^3 - C*a^2*tan(1/2*d*x + 1/2*c)^3 + B*a^2*tan(1/2*d*x + 1/2*c) + C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
240,1,154,0,0.517879," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} C a^{2} + {\left(3 \, B a^{2} + 4 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(3 \, B a^{2} + 4 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*a^2 + (3*B*a^2 + 4*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (3*B*a^2 + 4*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 5*B*a^2*tan(1/2*d*x + 1/2*c) - 2*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
241,1,178,0,0.473111," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, B a^{2} + 3 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, B a^{2} + 3 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*B*a^2 + 3*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*B*a^2 + 3*C*a^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 + 9*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 16*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 18*B*a^2*tan(1/2*d*x + 1/2*c) + 15*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
242,1,212,0,1.042354," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{3 \, {\left(7 \, B a^{2} + 8 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(7 \, B a^{2} + 8 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(21 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 77 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 88 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 83 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 136 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(7*B*a^2 + 8*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(7*B*a^2 + 8*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(21*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 24*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 77*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 88*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 83*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 136*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 75*B*a^2*tan(1/2*d*x + 1/2*c) - 72*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
243,1,246,0,0.799793," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{15 \, {\left(6 \, B a^{2} + 7 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(6 \, B a^{2} + 7 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(90 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 105 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 420 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 490 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 864 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 540 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 790 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 390 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 375 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(6*B*a^2 + 7*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(6*B*a^2 + 7*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(90*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 105*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 420*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 490*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 864*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 540*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 790*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 390*B*a^2*tan(1/2*d*x + 1/2*c) + 375*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
244,1,166,0,0.674785," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{1}{16} \, {\left(26 \, B a^{3} + 23 \, C a^{3}\right)} x + \frac{{\left(B a^{3} + 3 \, C a^{3}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{3 \, {\left(2 \, B a^{3} + 3 \, C a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(17 \, B a^{3} + 19 \, C a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(64 \, B a^{3} + 63 \, C a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(23 \, B a^{3} + 21 \, C a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*C*a^3*sin(6*d*x + 6*c)/d + 1/16*(26*B*a^3 + 23*C*a^3)*x + 1/80*(B*a^3 + 3*C*a^3)*sin(5*d*x + 5*c)/d + 3/64*(2*B*a^3 + 3*C*a^3)*sin(4*d*x + 4*c)/d + 1/48*(17*B*a^3 + 19*C*a^3)*sin(3*d*x + 3*c)/d + 1/64*(64*B*a^3 + 63*C*a^3)*sin(2*d*x + 2*c)/d + 1/8*(23*B*a^3 + 21*C*a^3)*sin(d*x + c)/d","A",0
245,1,136,0,0.681261," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{3} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(15 \, B a^{3} + 13 \, C a^{3}\right)} x + \frac{{\left(B a^{3} + 3 \, C a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(12 \, B a^{3} + 17 \, C a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(B a^{3} + C a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{d} + \frac{{\left(26 \, B a^{3} + 23 \, C a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*a^3*sin(5*d*x + 5*c)/d + 1/8*(15*B*a^3 + 13*C*a^3)*x + 1/32*(B*a^3 + 3*C*a^3)*sin(4*d*x + 4*c)/d + 1/48*(12*B*a^3 + 17*C*a^3)*sin(3*d*x + 3*c)/d + (B*a^3 + C*a^3)*sin(2*d*x + 2*c)/d + 1/8*(26*B*a^3 + 23*C*a^3)*sin(d*x + c)/d","A",0
246,1,176,0,0.429859," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{15 \, {\left(4 \, B a^{3} + 3 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(60 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 45 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 220 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 165 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 292 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 219 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 132 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 147 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(15*(4*B*a^3 + 3*C*a^3)*(d*x + c) + 2*(60*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 45*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 220*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 165*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 292*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 219*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 132*B*a^3*tan(1/2*d*x + 1/2*c) + 147*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
247,1,180,0,0.585408," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,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(7 \, B a^{3} + 5 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*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*(7*B*a^3 + 5*C*a^3)*(d*x + c) + 2*(15*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 21*B*a^3*tan(1/2*d*x + 1/2*c) + 33*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
248,1,192,0,0.562445," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,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(6 \, B a^{3} + 7 \, C a^{3}\right)} {\left(d x + c\right)} - 2 \, {\left(3 \, B a^{3} + C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(3 \, B a^{3} + C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*B*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (6*B*a^3 + 7*C*a^3)*(d*x + c) - 2*(3*B*a^3 + C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(3*B*a^3 + C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 5*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^3*tan(1/2*d*x + 1/2*c) + 7*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
249,1,192,0,1.066805," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{\frac{4 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(B a^{3} + 3 \, C a^{3}\right)} {\left(d x + c\right)} + {\left(7 \, B a^{3} + 6 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(7 \, B a^{3} + 6 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(5 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*C*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(B*a^3 + 3*C*a^3)*(d*x + c) + (7*B*a^3 + 6*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (7*B*a^3 + 6*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(5*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*B*a^3*tan(1/2*d*x + 1/2*c) - 2*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
250,1,189,0,0.361170," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} C a^{3} + 3 \, {\left(5 \, B a^{3} + 7 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(5 \, B a^{3} + 7 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*C*a^3 + 3*(5*B*a^3 + 7*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(5*B*a^3 + 7*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 36*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 33*B*a^3*tan(1/2*d*x + 1/2*c) + 21*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
251,1,212,0,0.367852," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{3} + 4 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, B a^{3} + 4 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(45 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 165 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 220 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 219 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 292 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 147 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 132 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(15*(3*B*a^3 + 4*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*B*a^3 + 4*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(45*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 165*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 220*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 219*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 292*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 147*B*a^3*tan(1/2*d*x + 1/2*c) - 132*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
252,1,246,0,0.413789," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{15 \, {\left(13 \, B a^{3} + 15 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(13 \, B a^{3} + 15 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(195 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 225 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 910 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1050 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1664 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1920 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1330 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1830 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 765 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 735 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(13*B*a^3 + 15*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(13*B*a^3 + 15*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(195*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 225*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 910*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 1050*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 1664*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 1920*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 1330*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 1830*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 765*B*a^3*tan(1/2*d*x + 1/2*c) + 735*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
253,1,151,0,0.587833," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{9 \, {\left(d x + c\right)} {\left(B - C\right)}}{a} - \frac{6 \, {\left(B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"1/6*(9*(d*x + c)*(B - C)/a - 6*(B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a - 2*(9*B*tan(1/2*d*x + 1/2*c)^5 - 15*C*tan(1/2*d*x + 1/2*c)^5 + 12*B*tan(1/2*d*x + 1/2*c)^3 - 16*C*tan(1/2*d*x + 1/2*c)^3 + 3*B*tan(1/2*d*x + 1/2*c) - 9*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
254,1,124,0,0.323046," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(d x + c\right)} {\left(2 \, B - 3 \, C\right)}}{a} - \frac{2 \, {\left(B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"-1/2*((d*x + c)*(2*B - 3*C)/a - 2*(B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a - 2*(2*B*tan(1/2*d*x + 1/2*c)^3 - 3*C*tan(1/2*d*x + 1/2*c)^3 + 2*B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
255,1,78,0,0.397325," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} {\left(B - C\right)}}{a} - \frac{B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a}}{d}"," ",0,"((d*x + c)*(B - C)/a - (B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a + 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
256,1,43,0,0.365008," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} C}{a} + \frac{B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"((d*x + c)*C/a + (B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a)/d","A",0
257,1,71,0,0.612070," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(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{B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"(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 - (B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a)/d","A",0
258,1,110,0,0.608329," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{2 \, 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,"-((B - C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (B - C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a + 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
259,1,157,0,0.440655," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(3 \, B - 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(3 \, B - 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((3*B - 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (3*B - 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a + 2*(3*B*tan(1/2*d*x + 1/2*c)^3 - 2*C*tan(1/2*d*x + 1/2*c)^3 - B*tan(1/2*d*x + 1/2*c) + 2*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a))/d","A",0
260,1,182,0,0.388272," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{9 \, {\left(B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{9 \, {\left(B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{6 \, {\left(B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(9*(B - C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - 9*(B - C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 6*(B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/a + 2*(15*B*tan(1/2*d*x + 1/2*c)^5 - 9*C*tan(1/2*d*x + 1/2*c)^5 - 16*B*tan(1/2*d*x + 1/2*c)^3 + 12*C*tan(1/2*d*x + 1/2*c)^3 + 9*B*tan(1/2*d*x + 1/2*c) - 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
261,1,192,0,0.448478," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)} {\left(7 \, B - 10 \, C\right)}}{a^{2}} - \frac{2 \, {\left(15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}} + \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*(7*B - 10*C)/a^2 - 2*(15*B*tan(1/2*d*x + 1/2*c)^5 - 30*C*tan(1/2*d*x + 1/2*c)^5 + 24*B*tan(1/2*d*x + 1/2*c)^3 - 40*C*tan(1/2*d*x + 1/2*c)^3 + 9*B*tan(1/2*d*x + 1/2*c) - 18*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2) + (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 - 21*B*a^4*tan(1/2*d*x + 1/2*c) + 27*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
262,1,164,0,0.409094," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} {\left(4 \, B - 7 \, C\right)}}{a^{2}} - \frac{6 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(d*x + c)*(4*B - 7*C)/a^2 - 6*(2*B*tan(1/2*d*x + 1/2*c)^3 - 5*C*tan(1/2*d*x + 1/2*c)^3 + 2*B*tan(1/2*d*x + 1/2*c) - 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 - 15*B*a^4*tan(1/2*d*x + 1/2*c) + 21*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
263,1,119,0,0.486271," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} {\left(B - 2 \, C\right)}}{a^{2}} + \frac{12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} + \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*(B - 2*C)/a^2 + 12*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) + (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*B*a^4*tan(1/2*d*x + 1/2*c) + 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
264,1,86,0,0.441824," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} C}{a^{2}} - \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*C/a^2 - (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 - 3*B*a^4*tan(1/2*d*x + 1/2*c) + 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
265,1,60,0,0.353526," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{6 \, a^{2} d}"," ",0,"1/6*(B*tan(1/2*d*x + 1/2*c)^3 - C*tan(1/2*d*x + 1/2*c)^3 + 3*B*tan(1/2*d*x + 1/2*c) + 3*C*tan(1/2*d*x + 1/2*c))/(a^2*d)","A",0
266,1,113,0,0.348043," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(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{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*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 - (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*B*a^4*tan(1/2*d*x + 1/2*c) - 3*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
267,1,155,0,0.504239," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(2 \, B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, {\left(2 \, B - C\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{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(2*B - C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*(2*B - C)*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) - (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^4*tan(1/2*d*x + 1/2*c) - 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
268,1,198,0,0.393409," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(7 \, B - 4 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(7 \, B - 4 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(5 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}} - \frac{B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(7*B - 4*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(7*B - 4*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 6*(5*B*tan(1/2*d*x + 1/2*c)^3 - 2*C*tan(1/2*d*x + 1/2*c)^3 - 3*B*tan(1/2*d*x + 1/2*c) + 2*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2) - (B*a^4*tan(1/2*d*x + 1/2*c)^3 - C*a^4*tan(1/2*d*x + 1/2*c)^3 + 21*B*a^4*tan(1/2*d*x + 1/2*c) - 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
269,1,200,0,0.656399," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(d x + c\right)} {\left(6 \, B - 13 \, C\right)}}{a^{3}} - \frac{60 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} - \frac{3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 465 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(d*x + c)*(6*B - 13*C)/a^3 - 60*(2*B*tan(1/2*d*x + 1/2*c)^3 - 7*C*tan(1/2*d*x + 1/2*c)^3 + 2*B*tan(1/2*d*x + 1/2*c) - 5*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) - (3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 40*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*B*a^12*tan(1/2*d*x + 1/2*c) - 465*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
270,1,155,0,2.400908," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} {\left(B - 3 \, C\right)}}{a^{3}} + \frac{120 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}} - \frac{3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*(B - 3*C)/a^3 + 120*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) - (3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*B*a^12*tan(1/2*d*x + 1/2*c) - 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
271,1,120,0,0.309372," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} C}{a^{3}} + \frac{3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*C/a^3 + (3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 10*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^12*tan(1/2*d*x + 1/2*c) - 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
272,1,75,0,0.337615," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"-1/60*(3*B*tan(1/2*d*x + 1/2*c)^5 - 3*C*tan(1/2*d*x + 1/2*c)^5 + 10*C*tan(1/2*d*x + 1/2*c)^3 - 15*B*tan(1/2*d*x + 1/2*c) - 15*C*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
273,1,75,0,0.380367," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"1/60*(3*B*tan(1/2*d*x + 1/2*c)^5 - 3*C*tan(1/2*d*x + 1/2*c)^5 + 10*B*tan(1/2*d*x + 1/2*c)^3 + 15*B*tan(1/2*d*x + 1/2*c) + 15*C*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
274,1,148,0,2.093513," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(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 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*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*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 10*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*B*a^12*tan(1/2*d*x + 1/2*c) - 15*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
275,1,190,0,0.480580," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(3 \, B - C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, {\left(3 \, B - C\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 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(60*(3*B - C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*(3*B - C)*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*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*B*a^12*tan(1/2*d*x + 1/2*c) - 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
276,1,233,0,0.485119," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(13 \, B - 6 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{30 \, {\left(13 \, B - 6 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{60 \, {\left(7 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}} - \frac{3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(13*B - 6*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 30*(13*B - 6*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 60*(7*B*tan(1/2*d*x + 1/2*c)^3 - 2*C*tan(1/2*d*x + 1/2*c)^3 - 5*B*tan(1/2*d*x + 1/2*c) + 2*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3) - (3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 40*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*B*a^12*tan(1/2*d*x + 1/2*c) - 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
277,1,124,0,1.100290," ","integrate((a+a*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{30} \, \sqrt{2} {\left(\frac{3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{30 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{30 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{5 \, {\left(2 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/30*sqrt(2)*(3*C*sgn(cos(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)/d + 30*B*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d + 30*C*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d + 5*(2*B*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d)*sqrt(a)","A",0
278,1,205,0,0.513294," ","integrate((a+a*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{420} \, \sqrt{2} {\left(\frac{15 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{21 \, {\left(2 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{35 \, {\left(6 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{105 \, {\left(4 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{420 \, {\left(B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/420*sqrt(2)*(15*C*a*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 21*(2*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 35*(6*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 105*(4*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 420*(B*a*sgn(cos(1/2*d*x + 1/2*c)) + C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
279,1,272,0,1.138160," ","integrate((a+a*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{35 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{45 \, {\left(2 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{126 \, {\left(5 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{210 \, {\left(11 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 10 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{630 \, {\left(8 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{630 \, {\left(7 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(35*C*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 45*(2*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 126*(5*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 6*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 210*(11*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 10*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 630*(8*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 630*(7*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 6*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
280,1,113,0,1.059960," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, \sqrt{2} {\left(B - C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} + \frac{2 \, {\left(\sqrt{2} {\left(3 \, B a - 2 \, C a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, \sqrt{2} B 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)}^{\frac{3}{2}}}}{3 \, d}"," ",0,"1/3*(3*sqrt(2)*(B - C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) + 2*(sqrt(2)*(3*B*a - 2*C*a)*tan(1/2*d*x + 1/2*c)^2 + 3*sqrt(2)*B*a)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2))/d","A",0
281,1,131,0,1.184905," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(\frac{\sqrt{2} {\left(B a^{2} - C a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} + \frac{\sqrt{2} {\left(B a^{2} - 9 \, C a^{2}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{\sqrt{2} {\left(3 \, B - 7 \, C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}}}{4 \, d}"," ",0,"-1/4*((sqrt(2)*(B*a^2 - C*a^2)*tan(1/2*d*x + 1/2*c)^2/a^3 + sqrt(2)*(B*a^2 - 9*C*a^2)/a^3)*tan(1/2*d*x + 1/2*c)/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(2)*(3*B - 7*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2))/d","A",0
282,1,134,0,1.397869," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(B a^{5} - C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} - \frac{\sqrt{2} {\left(3 \, B a^{5} - 11 \, C a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(5 \, B + 19 \, C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{32 \, d}"," ",0,"-1/32*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(B*a^5 - C*a^5)*tan(1/2*d*x + 1/2*c)^2/a^8 - sqrt(2)*(3*B*a^5 - 11*C*a^5)/a^8)*tan(1/2*d*x + 1/2*c) + sqrt(2)*(5*B + 19*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
283,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2), x)","F",0
284,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
285,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
286,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
287,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/cos(d*x + c)^(5/2), x)","F",0
288,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/cos(d*x + c)^(7/2), x)","F",0
289,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/cos(d*x + c)^(9/2), x)","F",0
290,1,110,0,0.419666," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{16} \, {\left(6 \, A + 5 \, C\right)} x + \frac{C \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{B \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(2 \, A + 3 \, C\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{5 \, B \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(16 \, A + 15 \, C\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{5 \, B \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/16*(6*A + 5*C)*x + 1/192*C*sin(6*d*x + 6*c)/d + 1/80*B*sin(5*d*x + 5*c)/d + 1/64*(2*A + 3*C)*sin(4*d*x + 4*c)/d + 5/48*B*sin(3*d*x + 3*c)/d + 1/64*(16*A + 15*C)*sin(2*d*x + 2*c)/d + 5/8*B*sin(d*x + c)/d","A",0
291,1,89,0,0.443006," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{3}{8} \, B x + \frac{C \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{B \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, A + 5 \, C\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{B \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(6 \, A + 5 \, C\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"3/8*B*x + 1/80*C*sin(5*d*x + 5*c)/d + 1/32*B*sin(4*d*x + 4*c)/d + 1/48*(4*A + 5*C)*sin(3*d*x + 3*c)/d + 1/4*B*sin(2*d*x + 2*c)/d + 1/8*(6*A + 5*C)*sin(d*x + c)/d","A",0
292,1,70,0,0.625080," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A + 3 \, C\right)} x + \frac{C \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{B \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(A + C\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{3 \, B \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/8*(4*A + 3*C)*x + 1/32*C*sin(4*d*x + 4*c)/d + 1/12*B*sin(3*d*x + 3*c)/d + 1/4*(A + C)*sin(2*d*x + 2*c)/d + 3/4*B*sin(d*x + c)/d","A",0
293,1,53,0,0.504349," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2} \, B x + \frac{C \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{B \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A + 3 \, C\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/2*B*x + 1/12*C*sin(3*d*x + 3*c)/d + 1/4*B*sin(2*d*x + 2*c)/d + 1/4*(4*A + 3*C)*sin(d*x + c)/d","A",0
294,1,35,0,0.544922," ","integrate(A+B*cos(d*x+c)+C*cos(d*x+c)^2,x, algorithm=""giac"")","\frac{1}{4} \, C {\left(2 \, x + \frac{\sin\left(2 \, d x + 2 \, c\right)}{d}\right)} + A x + \frac{B \sin\left(d x + c\right)}{d}"," ",0,"1/4*C*(2*x + sin(2*d*x + 2*c)/d) + A*x + B*sin(d*x + c)/d","A",0
295,1,70,0,1.631443," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} B + A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"((d*x + c)*B + A*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - A*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*C*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
296,1,70,0,0.535334," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} C + B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, 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)*C + B*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - B*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*A*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
297,1,113,0,0.496995," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(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}}}{2 \, d}"," ",0,"1/2*((A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(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)/d","B",0
298,1,162,0,0.463593," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, 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} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*B*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*B*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*tan(1/2*d*x + 1/2*c)^5 - 3*B*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 - 4*A*tan(1/2*d*x + 1/2*c)^3 - 12*C*tan(1/2*d*x + 1/2*c)^3 + 6*A*tan(1/2*d*x + 1/2*c) + 3*B*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
299,1,230,0,0.460732," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A + 4 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A + 4 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, 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} - 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A + 4*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A + 4*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*tan(1/2*d*x + 1/2*c)^7 - 24*B*tan(1/2*d*x + 1/2*c)^7 + 12*C*tan(1/2*d*x + 1/2*c)^7 + 9*A*tan(1/2*d*x + 1/2*c)^5 + 40*B*tan(1/2*d*x + 1/2*c)^5 - 12*C*tan(1/2*d*x + 1/2*c)^5 + 9*A*tan(1/2*d*x + 1/2*c)^3 - 40*B*tan(1/2*d*x + 1/2*c)^3 - 12*C*tan(1/2*d*x + 1/2*c)^3 + 15*A*tan(1/2*d*x + 1/2*c) + 24*B*tan(1/2*d*x + 1/2*c) + 12*C*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
300,1,246,0,0.492951," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{45 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 45 \, B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(45*B*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 45*B*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*tan(1/2*d*x + 1/2*c)^9 - 75*B*tan(1/2*d*x + 1/2*c)^9 + 120*C*tan(1/2*d*x + 1/2*c)^9 - 160*A*tan(1/2*d*x + 1/2*c)^7 + 30*B*tan(1/2*d*x + 1/2*c)^7 - 320*C*tan(1/2*d*x + 1/2*c)^7 + 464*A*tan(1/2*d*x + 1/2*c)^5 + 400*C*tan(1/2*d*x + 1/2*c)^5 - 160*A*tan(1/2*d*x + 1/2*c)^3 - 30*B*tan(1/2*d*x + 1/2*c)^3 - 320*C*tan(1/2*d*x + 1/2*c)^3 + 120*A*tan(1/2*d*x + 1/2*c) + 75*B*tan(1/2*d*x + 1/2*c) + 120*C*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
301,1,129,0,0.518179," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A a + 3 \, B a + 3 \, C a\right)} x + \frac{C a \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(B a + C a\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, A a + 4 \, B a + 5 \, C a\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a + B a + C a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(6 \, A a + 6 \, B a + 5 \, C a\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(4*A*a + 3*B*a + 3*C*a)*x + 1/80*C*a*sin(5*d*x + 5*c)/d + 1/32*(B*a + C*a)*sin(4*d*x + 4*c)/d + 1/48*(4*A*a + 4*B*a + 5*C*a)*sin(3*d*x + 3*c)/d + 1/4*(A*a + B*a + C*a)*sin(2*d*x + 2*c)/d + 1/8*(6*A*a + 6*B*a + 5*C*a)*sin(d*x + c)/d","A",0
302,1,102,0,0.435621," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A a + 4 \, B a + 3 \, C a\right)} x + \frac{C a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(B a + C a\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(A a + B a + C a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a + 3 \, B a + 3 \, C a\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/8*(4*A*a + 4*B*a + 3*C*a)*x + 1/32*C*a*sin(4*d*x + 4*c)/d + 1/12*(B*a + C*a)*sin(3*d*x + 3*c)/d + 1/4*(A*a + B*a + C*a)*sin(2*d*x + 2*c)/d + 1/4*(4*A*a + 3*B*a + 3*C*a)*sin(d*x + c)/d","A",0
303,1,76,0,1.096540," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, A a + B a + C a\right)} x + \frac{C a \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(B a + C a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a + 4 \, B a + 3 \, C a\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/2*(2*A*a + B*a + C*a)*x + 1/12*C*a*sin(3*d*x + 3*c)/d + 1/4*(B*a + C*a)*sin(2*d*x + 2*c)/d + 1/4*(4*A*a + 4*B*a + 3*C*a)*sin(d*x + c)/d","A",0
304,1,131,0,1.937874," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{2 \, A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(2 \, A a + 2 \, B a + C a\right)} {\left(d x + c\right)} + \frac{2 \, {\left(2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*A*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*A*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (2*A*a + 2*B*a + C*a)*(d*x + c) + 2*(2*B*a*tan(1/2*d*x + 1/2*c)^3 + C*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*a*tan(1/2*d*x + 1/2*c) + 3*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
305,1,132,0,0.514372," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(B a + C a\right)} {\left(d x + c\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) - {\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(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((B*a + C*a)*(d*x + c) + (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*(A*a*tan(1/2*d*x + 1/2*c)^3 - C*a*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) + C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
306,1,141,0,0.567420," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} C a + {\left(A a + 2 \, B a + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a + 2 \, B a + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*a + (A*a + 2*B*a + 2*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a + 2*B*a + 2*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 + 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
307,1,205,0,0.406347," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(A a + B a + 2 \, C 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 + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*a + B*a + 2*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(A*a + B*a + 2*C*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 + 6*C*a*tan(1/2*d*x + 1/2*c)^5 - 4*A*a*tan(1/2*d*x + 1/2*c)^3 - 12*B*a*tan(1/2*d*x + 1/2*c)^3 - 12*C*a*tan(1/2*d*x + 1/2*c)^3 + 9*A*a*tan(1/2*d*x + 1/2*c) + 9*B*a*tan(1/2*d*x + 1/2*c) + 6*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
308,1,254,0,0.529053," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, B a + 4 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a + 4 \, B a + 4 \, C a\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 \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 49 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 28 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 52 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 84 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 39 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*B*a + 4*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a + 4*B*a + 4*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(9*A*a*tan(1/2*d*x + 1/2*c)^7 + 12*B*a*tan(1/2*d*x + 1/2*c)^7 + 12*C*a*tan(1/2*d*x + 1/2*c)^7 - 49*A*a*tan(1/2*d*x + 1/2*c)^5 - 28*B*a*tan(1/2*d*x + 1/2*c)^5 - 60*C*a*tan(1/2*d*x + 1/2*c)^5 + 31*A*a*tan(1/2*d*x + 1/2*c)^3 + 52*B*a*tan(1/2*d*x + 1/2*c)^3 + 84*C*a*tan(1/2*d*x + 1/2*c)^3 - 39*A*a*tan(1/2*d*x + 1/2*c) - 36*B*a*tan(1/2*d*x + 1/2*c) - 36*C*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
309,1,196,0,0.517560," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{2} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{1}{16} \, {\left(14 \, A a^{2} + 12 \, B a^{2} + 11 \, C a^{2}\right)} x + \frac{{\left(B a^{2} + 2 \, C a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(2 \, A a^{2} + 4 \, B a^{2} + 5 \, C a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(8 \, A a^{2} + 9 \, B a^{2} + 10 \, C a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(32 \, A a^{2} + 32 \, B a^{2} + 31 \, C a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(12 \, A a^{2} + 11 \, B a^{2} + 10 \, C a^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*C*a^2*sin(6*d*x + 6*c)/d + 1/16*(14*A*a^2 + 12*B*a^2 + 11*C*a^2)*x + 1/80*(B*a^2 + 2*C*a^2)*sin(5*d*x + 5*c)/d + 1/64*(2*A*a^2 + 4*B*a^2 + 5*C*a^2)*sin(4*d*x + 4*c)/d + 1/48*(8*A*a^2 + 9*B*a^2 + 10*C*a^2)*sin(3*d*x + 3*c)/d + 1/64*(32*A*a^2 + 32*B*a^2 + 31*C*a^2)*sin(2*d*x + 2*c)/d + 1/8*(12*A*a^2 + 11*B*a^2 + 10*C*a^2)*sin(d*x + c)/d","A",0
310,1,160,0,0.527138," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{2} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(8 \, A a^{2} + 7 \, B a^{2} + 6 \, C a^{2}\right)} x + \frac{{\left(B a^{2} + 2 \, C a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, A a^{2} + 8 \, B a^{2} + 9 \, C a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a^{2} + B a^{2} + C a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(14 \, A a^{2} + 12 \, B a^{2} + 11 \, C a^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*a^2*sin(5*d*x + 5*c)/d + 1/8*(8*A*a^2 + 7*B*a^2 + 6*C*a^2)*x + 1/32*(B*a^2 + 2*C*a^2)*sin(4*d*x + 4*c)/d + 1/48*(4*A*a^2 + 8*B*a^2 + 9*C*a^2)*sin(3*d*x + 3*c)/d + 1/2*(A*a^2 + B*a^2 + C*a^2)*sin(2*d*x + 2*c)/d + 1/8*(14*A*a^2 + 12*B*a^2 + 11*C*a^2)*sin(d*x + c)/d","A",0
311,1,129,0,0.602094," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(12 \, A a^{2} + 8 \, B a^{2} + 7 \, C a^{2}\right)} x + \frac{{\left(B a^{2} + 2 \, C a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(A a^{2} + 2 \, B a^{2} + 2 \, C a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(8 \, A a^{2} + 7 \, B a^{2} + 6 \, C a^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/32*C*a^2*sin(4*d*x + 4*c)/d + 1/8*(12*A*a^2 + 8*B*a^2 + 7*C*a^2)*x + 1/12*(B*a^2 + 2*C*a^2)*sin(3*d*x + 3*c)/d + 1/4*(A*a^2 + 2*B*a^2 + 2*C*a^2)*sin(2*d*x + 2*c)/d + 1/4*(8*A*a^2 + 7*B*a^2 + 6*C*a^2)*sin(d*x + c)/d","A",0
312,1,235,0,0.488940," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{6 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(4 \, A a^{2} + 3 \, B a^{2} + 2 \, C a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(4*A*a^2 + 3*B*a^2 + 2*C*a^2)*(d*x + c) + 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 16*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 15*B*a^2*tan(1/2*d*x + 1/2*c) + 18*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
313,1,198,0,0.958045," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - {\left(2 \, A a^{2} + 4 \, B a^{2} + 3 \, C a^{2}\right)} {\left(d x + c\right)} - 2 \, {\left(2 \, A a^{2} + B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(2 \, A a^{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(2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*A*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (2*A*a^2 + 4*B*a^2 + 3*C*a^2)*(d*x + c) - 2*(2*A*a^2 + B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(2*A*a^2 + B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^2*tan(1/2*d*x + 1/2*c) + 5*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
314,1,204,0,0.851332," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{\frac{4 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(B a^{2} + 2 \, C a^{2}\right)} {\left(d x + c\right)} + {\left(3 \, A a^{2} + 4 \, B a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(3 \, A a^{2} + 4 \, B a^{2} + 2 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*C*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(B*a^2 + 2*C*a^2)*(d*x + c) + (3*A*a^2 + 4*B*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (3*A*a^2 + 4*B*a^2 + 2*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 5*A*a^2*tan(1/2*d*x + 1/2*c) - 2*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
315,1,250,0,0.541221," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} C a^{2} + 3 \, {\left(2 \, A a^{2} + 3 \, B a^{2} + 4 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a^{2} + 3 \, B a^{2} + 4 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*C*a^2 + 3*(2*A*a^2 + 3*B*a^2 + 4*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a^2 + 3*B*a^2 + 4*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 16*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 18*A*a^2*tan(1/2*d*x + 1/2*c) + 15*B*a^2*tan(1/2*d*x + 1/2*c) + 6*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
316,1,290,0,0.693090," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(7 \, A a^{2} + 8 \, B a^{2} + 12 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(7 \, A a^{2} + 8 \, B a^{2} + 12 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(21 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 77 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 88 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 132 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 83 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 136 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 156 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(7*A*a^2 + 8*B*a^2 + 12*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(7*A*a^2 + 8*B*a^2 + 12*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(21*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 24*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 36*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 77*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 88*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 132*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 83*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 136*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 156*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 75*A*a^2*tan(1/2*d*x + 1/2*c) - 72*B*a^2*tan(1/2*d*x + 1/2*c) - 60*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
317,1,341,0,1.383020," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(6 \, A a^{2} + 7 \, B a^{2} + 8 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(6 \, A a^{2} + 7 \, B a^{2} + 8 \, C a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(90 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 105 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 420 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 490 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 560 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 864 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 540 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 790 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1040 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 390 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 375 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(6*A*a^2 + 7*B*a^2 + 8*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(6*A*a^2 + 7*B*a^2 + 8*C*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(90*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 105*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 420*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 490*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 560*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 864*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 1120*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 540*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 790*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 1040*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 390*A*a^2*tan(1/2*d*x + 1/2*c) + 375*B*a^2*tan(1/2*d*x + 1/2*c) + 360*C*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
318,1,229,0,1.458913," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{3} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{1}{16} \, {\left(26 \, A a^{3} + 23 \, B a^{3} + 21 \, C a^{3}\right)} x + \frac{{\left(B a^{3} + 3 \, C a^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(4 \, A a^{3} + 12 \, B a^{3} + 19 \, C a^{3}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(6 \, A a^{3} + 9 \, B a^{3} + 11 \, C a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(68 \, A a^{3} + 76 \, B a^{3} + 81 \, C a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(64 \, A a^{3} + 63 \, B a^{3} + 61 \, C a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(184 \, A a^{3} + 168 \, B a^{3} + 155 \, C a^{3}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/448*C*a^3*sin(7*d*x + 7*c)/d + 1/16*(26*A*a^3 + 23*B*a^3 + 21*C*a^3)*x + 1/192*(B*a^3 + 3*C*a^3)*sin(6*d*x + 6*c)/d + 1/320*(4*A*a^3 + 12*B*a^3 + 19*C*a^3)*sin(5*d*x + 5*c)/d + 1/64*(6*A*a^3 + 9*B*a^3 + 11*C*a^3)*sin(4*d*x + 4*c)/d + 1/192*(68*A*a^3 + 76*B*a^3 + 81*C*a^3)*sin(3*d*x + 3*c)/d + 1/64*(64*A*a^3 + 63*B*a^3 + 61*C*a^3)*sin(2*d*x + 2*c)/d + 1/64*(184*A*a^3 + 168*B*a^3 + 155*C*a^3)*sin(d*x + c)/d","A",0
319,1,196,0,0.591509," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{1}{16} \, {\left(30 \, A a^{3} + 26 \, B a^{3} + 23 \, C a^{3}\right)} x + \frac{{\left(B a^{3} + 3 \, C a^{3}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(2 \, A a^{3} + 6 \, B a^{3} + 9 \, C a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(12 \, A a^{3} + 17 \, B a^{3} + 19 \, C a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(64 \, A a^{3} + 64 \, B a^{3} + 63 \, C a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(26 \, A a^{3} + 23 \, B a^{3} + 21 \, C a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*C*a^3*sin(6*d*x + 6*c)/d + 1/16*(30*A*a^3 + 26*B*a^3 + 23*C*a^3)*x + 1/80*(B*a^3 + 3*C*a^3)*sin(5*d*x + 5*c)/d + 1/64*(2*A*a^3 + 6*B*a^3 + 9*C*a^3)*sin(4*d*x + 4*c)/d + 1/48*(12*A*a^3 + 17*B*a^3 + 19*C*a^3)*sin(3*d*x + 3*c)/d + 1/64*(64*A*a^3 + 64*B*a^3 + 63*C*a^3)*sin(2*d*x + 2*c)/d + 1/8*(26*A*a^3 + 23*B*a^3 + 21*C*a^3)*sin(d*x + c)/d","A",0
320,1,163,0,0.430459," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{3} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(20 \, A a^{3} + 15 \, B a^{3} + 13 \, C a^{3}\right)} x + \frac{{\left(B a^{3} + 3 \, C a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, A a^{3} + 12 \, B a^{3} + 17 \, C a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(3 \, A a^{3} + 4 \, B a^{3} + 4 \, C a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(30 \, A a^{3} + 26 \, B a^{3} + 23 \, C a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*a^3*sin(5*d*x + 5*c)/d + 1/8*(20*A*a^3 + 15*B*a^3 + 13*C*a^3)*x + 1/32*(B*a^3 + 3*C*a^3)*sin(4*d*x + 4*c)/d + 1/48*(4*A*a^3 + 12*B*a^3 + 17*C*a^3)*sin(3*d*x + 3*c)/d + 1/4*(3*A*a^3 + 4*B*a^3 + 4*C*a^3)*sin(2*d*x + 2*c)/d + 1/8*(30*A*a^3 + 26*B*a^3 + 23*C*a^3)*sin(d*x + c)/d","A",0
321,1,286,0,0.597801," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{24 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(28 \, A a^{3} + 20 \, B a^{3} + 15 \, C a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(60 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 45 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 204 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 220 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 165 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 228 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 292 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 219 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 84 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 132 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 147 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(28*A*a^3 + 20*B*a^3 + 15*C*a^3)*(d*x + c) + 2*(60*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 45*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 204*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 220*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 165*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 228*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 292*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 219*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 84*A*a^3*tan(1/2*d*x + 1/2*c) + 132*B*a^3*tan(1/2*d*x + 1/2*c) + 147*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
322,1,281,0,0.829538," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(6 \, A a^{3} + 7 \, B a^{3} + 5 \, C a^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(3 \, A a^{3} + B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 6 \, {\left(3 \, A a^{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(6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(12*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(6*A*a^3 + 7*B*a^3 + 5*C*a^3)*(d*x + c) - 6*(3*A*a^3 + B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 6*(3*A*a^3 + B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*tan(1/2*d*x + 1/2*c) + 21*B*a^3*tan(1/2*d*x + 1/2*c) + 33*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
323,1,280,0,0.673660," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(2 \, A a^{3} + 6 \, B a^{3} + 7 \, C a^{3}\right)} {\left(d x + c\right)} + {\left(7 \, A a^{3} + 6 \, B a^{3} + 2 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(7 \, A a^{3} + 6 \, B a^{3} + 2 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(5 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((2*A*a^3 + 6*B*a^3 + 7*C*a^3)*(d*x + c) + (7*A*a^3 + 6*B*a^3 + 2*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (7*A*a^3 + 6*B*a^3 + 2*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(5*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 5*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 4*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 9*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*A*a^3*tan(1/2*d*x + 1/2*c) - 4*B*a^3*tan(1/2*d*x + 1/2*c) - 7*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","A",0
324,1,288,0,0.550291," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{\frac{12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 6 \, {\left(B a^{3} + 3 \, C a^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(5 \, A a^{3} + 7 \, B a^{3} + 6 \, C a^{3}\right)} \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} + 6 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*C*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 6*(B*a^3 + 3*C*a^3)*(d*x + c) + 3*(5*A*a^3 + 7*B*a^3 + 6*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(5*A*a^3 + 7*B*a^3 + 6*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 33*A*a^3*tan(1/2*d*x + 1/2*c) + 21*B*a^3*tan(1/2*d*x + 1/2*c) + 6*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
325,1,301,0,0.589226," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} C a^{3} + 3 \, {\left(15 \, A a^{3} + 20 \, B a^{3} + 28 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(15 \, A a^{3} + 20 \, B a^{3} + 28 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(45 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 220 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 204 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 219 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 292 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 228 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 147 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 132 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 84 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)*C*a^3 + 3*(15*A*a^3 + 20*B*a^3 + 28*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(15*A*a^3 + 20*B*a^3 + 28*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(45*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 165*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 220*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 204*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 219*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 292*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 228*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 147*A*a^3*tan(1/2*d*x + 1/2*c) - 132*B*a^3*tan(1/2*d*x + 1/2*c) - 84*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
326,1,341,0,0.674838," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(13 \, A a^{3} + 15 \, B a^{3} + 20 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(13 \, A a^{3} + 15 \, B a^{3} + 20 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(195 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 225 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 300 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 910 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1050 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1400 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1664 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1920 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2560 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1330 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1830 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 765 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 735 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 660 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(13*A*a^3 + 15*B*a^3 + 20*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(13*A*a^3 + 15*B*a^3 + 20*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(195*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 225*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 300*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 910*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 1050*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 1400*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 1664*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1920*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 2560*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 1330*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 1830*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 2120*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 765*A*a^3*tan(1/2*d*x + 1/2*c) + 735*B*a^3*tan(1/2*d*x + 1/2*c) + 660*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
327,1,392,0,0.679105," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{15 \, {\left(23 \, A a^{3} + 26 \, B a^{3} + 30 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(23 \, A a^{3} + 26 \, B a^{3} + 30 \, C a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(345 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 390 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1955 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2210 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2550 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4554 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5148 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5940 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5814 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5988 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 7500 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4190 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5130 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1530 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1470 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(23*A*a^3 + 26*B*a^3 + 30*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(23*A*a^3 + 26*B*a^3 + 30*C*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(345*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 390*B*a^3*tan(1/2*d*x + 1/2*c)^11 + 450*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 1955*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 2210*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 2550*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 4554*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 5148*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 5940*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 5814*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 5988*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 7500*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 3165*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 4190*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 5130*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 1575*A*a^3*tan(1/2*d*x + 1/2*c) - 1530*B*a^3*tan(1/2*d*x + 1/2*c) - 1470*C*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
328,1,261,0,0.597327," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{4} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{1}{128} \, {\left(392 \, A a^{4} + 352 \, B a^{4} + 323 \, C a^{4}\right)} x + \frac{{\left(B a^{4} + 4 \, C a^{4}\right)} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{{\left(A a^{4} + 4 \, B a^{4} + 8 \, C a^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(16 \, A a^{4} + 31 \, B a^{4} + 44 \, C a^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(30 \, A a^{4} + 40 \, B a^{4} + 47 \, C a^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{{\left(144 \, A a^{4} + 157 \, B a^{4} + 164 \, C a^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(127 \, A a^{4} + 124 \, B a^{4} + 120 \, C a^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(352 \, A a^{4} + 323 \, B a^{4} + 300 \, C a^{4}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/1024*C*a^4*sin(8*d*x + 8*c)/d + 1/128*(392*A*a^4 + 352*B*a^4 + 323*C*a^4)*x + 1/448*(B*a^4 + 4*C*a^4)*sin(7*d*x + 7*c)/d + 1/192*(A*a^4 + 4*B*a^4 + 8*C*a^4)*sin(6*d*x + 6*c)/d + 1/320*(16*A*a^4 + 31*B*a^4 + 44*C*a^4)*sin(5*d*x + 5*c)/d + 1/128*(30*A*a^4 + 40*B*a^4 + 47*C*a^4)*sin(4*d*x + 4*c)/d + 1/192*(144*A*a^4 + 157*B*a^4 + 164*C*a^4)*sin(3*d*x + 3*c)/d + 1/64*(127*A*a^4 + 124*B*a^4 + 120*C*a^4)*sin(2*d*x + 2*c)/d + 1/64*(352*A*a^4 + 323*B*a^4 + 300*C*a^4)*sin(d*x + c)/d","A",0
329,1,229,0,0.542827," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{4} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{1}{16} \, {\left(56 \, A a^{4} + 49 \, B a^{4} + 44 \, C a^{4}\right)} x + \frac{{\left(B a^{4} + 4 \, C a^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(4 \, A a^{4} + 16 \, B a^{4} + 31 \, C a^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(8 \, A a^{4} + 15 \, B a^{4} + 20 \, C a^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(116 \, A a^{4} + 144 \, B a^{4} + 157 \, C a^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(128 \, A a^{4} + 127 \, B a^{4} + 124 \, C a^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(392 \, A a^{4} + 352 \, B a^{4} + 323 \, C a^{4}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/448*C*a^4*sin(7*d*x + 7*c)/d + 1/16*(56*A*a^4 + 49*B*a^4 + 44*C*a^4)*x + 1/192*(B*a^4 + 4*C*a^4)*sin(6*d*x + 6*c)/d + 1/320*(4*A*a^4 + 16*B*a^4 + 31*C*a^4)*sin(5*d*x + 5*c)/d + 1/64*(8*A*a^4 + 15*B*a^4 + 20*C*a^4)*sin(4*d*x + 4*c)/d + 1/192*(116*A*a^4 + 144*B*a^4 + 157*C*a^4)*sin(3*d*x + 3*c)/d + 1/64*(128*A*a^4 + 127*B*a^4 + 124*C*a^4)*sin(2*d*x + 2*c)/d + 1/64*(392*A*a^4 + 352*B*a^4 + 323*C*a^4)*sin(d*x + c)/d","A",0
330,1,196,0,0.550658," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C a^{4} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{7}{16} \, {\left(10 \, A a^{4} + 8 \, B a^{4} + 7 \, C a^{4}\right)} x + \frac{{\left(B a^{4} + 4 \, C a^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(2 \, A a^{4} + 8 \, B a^{4} + 15 \, C a^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(16 \, A a^{4} + 29 \, B a^{4} + 36 \, C a^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(112 \, A a^{4} + 128 \, B a^{4} + 127 \, C a^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(56 \, A a^{4} + 49 \, B a^{4} + 44 \, C a^{4}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*C*a^4*sin(6*d*x + 6*c)/d + 7/16*(10*A*a^4 + 8*B*a^4 + 7*C*a^4)*x + 1/80*(B*a^4 + 4*C*a^4)*sin(5*d*x + 5*c)/d + 1/64*(2*A*a^4 + 8*B*a^4 + 15*C*a^4)*sin(4*d*x + 4*c)/d + 1/48*(16*A*a^4 + 29*B*a^4 + 36*C*a^4)*sin(3*d*x + 3*c)/d + 1/64*(112*A*a^4 + 128*B*a^4 + 127*C*a^4)*sin(2*d*x + 2*c)/d + 1/8*(56*A*a^4 + 49*B*a^4 + 44*C*a^4)*sin(d*x + c)/d","A",0
331,1,337,0,0.539310," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{120 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 120 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 15 \, {\left(48 \, A a^{4} + 35 \, B a^{4} + 28 \, C a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(600 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 525 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 420 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2720 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2450 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1960 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4720 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4480 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3584 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3680 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3950 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3160 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1080 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1395 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1500 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(120*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 120*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 15*(48*A*a^4 + 35*B*a^4 + 28*C*a^4)*(d*x + c) + 2*(600*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 525*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 420*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 2720*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 2450*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 1960*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 4720*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 4480*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 3584*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 3680*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 3950*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 3160*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 1080*A*a^4*tan(1/2*d*x + 1/2*c) + 1395*B*a^4*tan(1/2*d*x + 1/2*c) + 1500*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
332,1,332,0,2.547922," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{48 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(52 \, A a^{4} + 48 \, B a^{4} + 35 \, C a^{4}\right)} {\left(d x + c\right)} - 24 \, {\left(4 \, A a^{4} + B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 24 \, {\left(4 \, A a^{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(84 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 276 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 424 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 300 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 520 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 511 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 108 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 216 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 279 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"-1/24*(48*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(52*A*a^4 + 48*B*a^4 + 35*C*a^4)*(d*x + c) - 24*(4*A*a^4 + B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 24*(4*A*a^4 + B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(84*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 120*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 105*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 276*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 424*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 385*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 300*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 520*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 511*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 108*A*a^4*tan(1/2*d*x + 1/2*c) + 216*B*a^4*tan(1/2*d*x + 1/2*c) + 279*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
333,1,347,0,0.605252," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{3 \, {\left(8 \, A a^{4} + 13 \, B a^{4} + 12 \, C a^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(13 \, A a^{4} + 8 \, B a^{4} + 2 \, C 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} + 8 \, B a^{4} + 2 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{6 \, {\left(7 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{2 \, {\left(6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 76 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 54 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(8*A*a^4 + 13*B*a^4 + 12*C*a^4)*(d*x + c) + 3*(13*A*a^4 + 8*B*a^4 + 2*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(13*A*a^4 + 8*B*a^4 + 2*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*(7*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*A*a^4*tan(1/2*d*x + 1/2*c) - 2*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 2*(6*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 21*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 30*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 48*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 76*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^4*tan(1/2*d*x + 1/2*c) + 27*B*a^4*tan(1/2*d*x + 1/2*c) + 54*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
334,1,347,0,0.647153," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, A a^{4} + 8 \, B a^{4} + 13 \, C a^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(12 \, A a^{4} + 13 \, B a^{4} + 8 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(12 \, A a^{4} + 13 \, B a^{4} + 8 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{6 \, {\left(2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{2 \, {\left(30 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 76 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 54 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*A*a^4 + 8*B*a^4 + 13*C*a^4)*(d*x + c) + 3*(12*A*a^4 + 13*B*a^4 + 8*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(12*A*a^4 + 13*B*a^4 + 8*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 6*(2*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 7*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^4*tan(1/2*d*x + 1/2*c) + 9*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - 2*(30*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 21*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 76*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 48*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 54*A*a^4*tan(1/2*d*x + 1/2*c) + 27*B*a^4*tan(1/2*d*x + 1/2*c) + 6*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
335,1,339,0,0.701877," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{\frac{48 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 24 \, {\left(B a^{4} + 4 \, C a^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(35 \, A a^{4} + 48 \, B a^{4} + 52 \, C a^{4}\right)} \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} + 52 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 84 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 385 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 424 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 276 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 511 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 520 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 300 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 279 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 216 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 108 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(48*C*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 24*(B*a^4 + 4*C*a^4)*(d*x + c) + 3*(35*A*a^4 + 48*B*a^4 + 52*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(35*A*a^4 + 48*B*a^4 + 52*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(105*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 120*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 84*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 385*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 424*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 276*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 511*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 520*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 300*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 279*A*a^4*tan(1/2*d*x + 1/2*c) - 216*B*a^4*tan(1/2*d*x + 1/2*c) - 108*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
336,1,352,0,0.685229," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{120 \, {\left(d x + c\right)} C a^{4} + 15 \, {\left(28 \, A a^{4} + 35 \, B a^{4} + 48 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(28 \, A a^{4} + 35 \, B a^{4} + 48 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(420 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 525 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 600 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1960 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2450 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2720 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3584 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4480 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4720 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3950 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3680 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1500 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1395 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1080 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(120*(d*x + c)*C*a^4 + 15*(28*A*a^4 + 35*B*a^4 + 48*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(28*A*a^4 + 35*B*a^4 + 48*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(420*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 525*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 600*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 1960*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 2450*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 2720*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 3584*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 4480*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 4720*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 3160*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 3950*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 3680*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 1500*A*a^4*tan(1/2*d*x + 1/2*c) + 1395*B*a^4*tan(1/2*d*x + 1/2*c) + 1080*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
337,1,392,0,0.779124," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{105 \, {\left(7 \, A a^{4} + 8 \, B a^{4} + 10 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(7 \, A a^{4} + 8 \, B a^{4} + 10 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(735 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 840 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1050 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 4165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4760 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5950 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 9702 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11088 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 13860 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 11802 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 13488 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16860 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7355 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9320 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10690 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3000 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2790 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(105*(7*A*a^4 + 8*B*a^4 + 10*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(7*A*a^4 + 8*B*a^4 + 10*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(735*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 840*B*a^4*tan(1/2*d*x + 1/2*c)^11 + 1050*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 4165*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 4760*B*a^4*tan(1/2*d*x + 1/2*c)^9 - 5950*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 9702*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 11088*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 13860*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 11802*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 13488*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 16860*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 7355*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 9320*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 10690*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 3105*A*a^4*tan(1/2*d*x + 1/2*c) - 3000*B*a^4*tan(1/2*d*x + 1/2*c) - 2790*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
338,1,443,0,0.748075," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^8,x, algorithm=""giac"")","\frac{105 \, {\left(44 \, A a^{4} + 49 \, B a^{4} + 56 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(44 \, A a^{4} + 49 \, B a^{4} + 56 \, C a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(4620 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5145 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5880 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 30800 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 34300 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 39200 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 87164 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 97069 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 110936 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 135168 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 150528 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 172032 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 126084 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 134099 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 159656 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 58800 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 73220 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 86240 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 22260 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21735 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21000 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(44*A*a^4 + 49*B*a^4 + 56*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(44*A*a^4 + 49*B*a^4 + 56*C*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(4620*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 5145*B*a^4*tan(1/2*d*x + 1/2*c)^13 + 5880*C*a^4*tan(1/2*d*x + 1/2*c)^13 - 30800*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 34300*B*a^4*tan(1/2*d*x + 1/2*c)^11 - 39200*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 87164*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 97069*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 110936*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 135168*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 150528*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 172032*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 126084*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 134099*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 159656*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 58800*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 73220*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 86240*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 22260*A*a^4*tan(1/2*d*x + 1/2*c) + 21735*B*a^4*tan(1/2*d*x + 1/2*c) + 21000*C*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","A",0
339,1,249,0,0.372128," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{9 \, {\left(d x + c\right)} {\left(4 \, A - 4 \, B + 5 \, C\right)}}{a} - \frac{24 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(36 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 75 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 84 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 124 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 115 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 100 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 109 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"1/24*(9*(d*x + c)*(4*A - 4*B + 5*C)/a - 24*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(36*A*tan(1/2*d*x + 1/2*c)^7 - 60*B*tan(1/2*d*x + 1/2*c)^7 + 75*C*tan(1/2*d*x + 1/2*c)^7 + 84*A*tan(1/2*d*x + 1/2*c)^5 - 124*B*tan(1/2*d*x + 1/2*c)^5 + 115*C*tan(1/2*d*x + 1/2*c)^5 + 60*A*tan(1/2*d*x + 1/2*c)^3 - 100*B*tan(1/2*d*x + 1/2*c)^3 + 109*C*tan(1/2*d*x + 1/2*c)^3 + 12*A*tan(1/2*d*x + 1/2*c) - 36*B*tan(1/2*d*x + 1/2*c) + 21*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
340,1,207,0,0.967348," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} {\left(2 \, A - 3 \, B + 3 \, C\right)}}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(3*(d*x + c)*(2*A - 3*B + 3*C)/a - 6*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a - 2*(6*A*tan(1/2*d*x + 1/2*c)^5 - 9*B*tan(1/2*d*x + 1/2*c)^5 + 15*C*tan(1/2*d*x + 1/2*c)^5 + 12*A*tan(1/2*d*x + 1/2*c)^3 - 12*B*tan(1/2*d*x + 1/2*c)^3 + 16*C*tan(1/2*d*x + 1/2*c)^3 + 6*A*tan(1/2*d*x + 1/2*c) - 3*B*tan(1/2*d*x + 1/2*c) + 9*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
341,1,138,0,0.530415," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} {\left(2 \, A - 2 \, B + 3 \, C\right)}}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((d*x + c)*(2*A - 2*B + 3*C)/a - 2*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*(2*B*tan(1/2*d*x + 1/2*c)^3 - 3*C*tan(1/2*d*x + 1/2*c)^3 + 2*B*tan(1/2*d*x + 1/2*c) - C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
342,1,88,0,0.541190," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} {\left(B - C\right)}}{a} + \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a}}{d}"," ",0,"((d*x + c)*(B - C)/a + (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
343,1,92,0,0.442763," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} C}{a} + \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"((d*x + c)*C/a + A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a)/d","A",0
344,1,121,0,0.424257," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(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) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a}}{d}"," ",0,"-((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) + C*tan(1/2*d*x + 1/2*c))/a + 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
345,1,174,0,1.230174," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(3 \, A - 2 \, B + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(3 \, A - 2 \, B + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(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*((3*A - 2*B + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (3*A - 2*B + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*(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
346,1,243,0,0.509717," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(3 \, A - 3 \, B + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{3 \, {\left(3 \, A - 3 \, B + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(3*(3*A - 3*B + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - 3*(3*A - 3*B + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 6*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c) + C*tan(1/2*d*x + 1/2*c))/a + 2*(15*A*tan(1/2*d*x + 1/2*c)^5 - 9*B*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 - 16*A*tan(1/2*d*x + 1/2*c)^3 + 12*B*tan(1/2*d*x + 1/2*c)^3 - 12*C*tan(1/2*d*x + 1/2*c)^3 + 9*A*tan(1/2*d*x + 1/2*c) - 3*B*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
347,1,266,0,1.073499," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} {\left(4 \, A - 7 \, B + 10 \, C\right)}}{a^{2}} - \frac{2 \, {\left(6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(d*x + c)*(4*A - 7*B + 10*C)/a^2 - 2*(6*A*tan(1/2*d*x + 1/2*c)^5 - 15*B*tan(1/2*d*x + 1/2*c)^5 + 30*C*tan(1/2*d*x + 1/2*c)^5 + 12*A*tan(1/2*d*x + 1/2*c)^3 - 24*B*tan(1/2*d*x + 1/2*c)^3 + 40*C*tan(1/2*d*x + 1/2*c)^3 + 6*A*tan(1/2*d*x + 1/2*c) - 9*B*tan(1/2*d*x + 1/2*c) + 18*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^4*tan(1/2*d*x + 1/2*c) + 21*B*a^4*tan(1/2*d*x + 1/2*c) - 27*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
348,1,198,0,0.685928," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)} {\left(2 \, A - 4 \, B + 7 \, C\right)}}{a^{2}} + \frac{6 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*(2*A - 4*B + 7*C)/a^2 + 6*(2*B*tan(1/2*d*x + 1/2*c)^3 - 5*C*tan(1/2*d*x + 1/2*c)^3 + 2*B*tan(1/2*d*x + 1/2*c) - 3*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*A*a^4*tan(1/2*d*x + 1/2*c) + 15*B*a^4*tan(1/2*d*x + 1/2*c) - 21*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
349,1,151,0,0.731850," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} {\left(B - 2 \, C\right)}}{a^{2}} + \frac{12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*(B - 2*C)/a^2 + 12*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^4*tan(1/2*d*x + 1/2*c) + 9*B*a^4*tan(1/2*d*x + 1/2*c) - 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
350,1,116,0,0.415308," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} C}{a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*C/a^2 + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*tan(1/2*d*x + 1/2*c) + 3*B*a^4*tan(1/2*d*x + 1/2*c) - 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
351,1,144,0,0.430494," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*A*a^4*tan(1/2*d*x + 1/2*c) - 3*B*a^4*tan(1/2*d*x + 1/2*c) - 3*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
352,1,186,0,1.140023," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(2 \, A - 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 - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(2*A - B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*(2*A - B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 12*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^4*tan(1/2*d*x + 1/2*c) - 9*B*a^4*tan(1/2*d*x + 1/2*c) + 3*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
353,1,235,0,0.585738," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(7 \, A - 4 \, B + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(7 \, A - 4 \, B + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(7*A - 4*B + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(7*A - 4*B + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 6*(5*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 - 3*A*tan(1/2*d*x + 1/2*c) + 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 21*A*a^4*tan(1/2*d*x + 1/2*c) - 15*B*a^4*tan(1/2*d*x + 1/2*c) + 9*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
354,1,303,0,0.855782," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(10 \, A - 7 \, B + 4 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(10 \, A - 7 \, B + 4 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(30 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(10*A - 7*B + 4*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(10*A - 7*B + 4*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 2*(30*A*tan(1/2*d*x + 1/2*c)^5 - 15*B*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 - 40*A*tan(1/2*d*x + 1/2*c)^3 + 24*B*tan(1/2*d*x + 1/2*c)^3 - 12*C*tan(1/2*d*x + 1/2*c)^3 + 18*A*tan(1/2*d*x + 1/2*c) - 9*B*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + C*a^4*tan(1/2*d*x + 1/2*c)^3 + 27*A*a^4*tan(1/2*d*x + 1/2*c) - 21*B*a^4*tan(1/2*d*x + 1/2*c) + 15*C*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
355,1,320,0,0.457463," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(d x + c\right)} {\left(6 \, A - 13 \, B + 23 \, C\right)}}{a^{3}} - \frac{20 \, {\left(6 \, 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} + 51 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 76 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 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} - 50 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 465 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 735 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(d*x + c)*(6*A - 13*B + 23*C)/a^3 - 20*(6*A*tan(1/2*d*x + 1/2*c)^5 - 21*B*tan(1/2*d*x + 1/2*c)^5 + 51*C*tan(1/2*d*x + 1/2*c)^5 + 12*A*tan(1/2*d*x + 1/2*c)^3 - 36*B*tan(1/2*d*x + 1/2*c)^3 + 76*C*tan(1/2*d*x + 1/2*c)^3 + 6*A*tan(1/2*d*x + 1/2*c) - 15*B*tan(1/2*d*x + 1/2*c) + 33*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 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 - 50*C*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) + 735*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
356,1,252,0,0.588286," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(d x + c\right)} {\left(2 \, A - 6 \, B + 13 \, C\right)}}{a^{3}} + \frac{60 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 465 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(d*x + c)*(2*A - 6*B + 13*C)/a^3 + 60*(2*B*tan(1/2*d*x + 1/2*c)^3 - 7*C*tan(1/2*d*x + 1/2*c)^3 + 2*B*tan(1/2*d*x + 1/2*c) - 5*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 40*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) - 255*B*a^12*tan(1/2*d*x + 1/2*c) + 465*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
357,1,203,0,0.468886," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} {\left(B - 3 \, C\right)}}{a^{3}} + \frac{120 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}} + \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*(B - 3*C)/a^3 + 120*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) + (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 - 10*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^12*tan(1/2*d*x + 1/2*c) - 105*B*a^12*tan(1/2*d*x + 1/2*c) + 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
358,1,153,0,0.659379," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} C}{a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*C/a^3 - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 10*B*a^12*tan(1/2*d*x + 1/2*c)^3 - 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^12*tan(1/2*d*x + 1/2*c) - 15*B*a^12*tan(1/2*d*x + 1/2*c) + 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
359,1,115,0,0.709270," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"1/60*(3*A*tan(1/2*d*x + 1/2*c)^5 - 3*B*tan(1/2*d*x + 1/2*c)^5 + 3*C*tan(1/2*d*x + 1/2*c)^5 + 10*A*tan(1/2*d*x + 1/2*c)^3 - 10*C*tan(1/2*d*x + 1/2*c)^3 + 15*A*tan(1/2*d*x + 1/2*c) + 15*B*tan(1/2*d*x + 1/2*c) + 15*C*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
360,1,180,0,0.893000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 10*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) - 15*B*a^12*tan(1/2*d*x + 1/2*c) - 15*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
361,1,239,0,0.757932," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(3 \, A - 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(3 \, A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{120 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(60*(3*A - B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*(3*A - B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 120*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 30*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 10*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*A*a^12*tan(1/2*d*x + 1/2*c) - 105*B*a^12*tan(1/2*d*x + 1/2*c) + 15*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
362,1,288,0,0.691521," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(13 \, A - 6 \, B + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{30 \, {\left(13 \, A - 6 \, B + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{60 \, {\left(7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(13*A - 6*B + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 30*(13*A - 6*B + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 60*(7*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 - 5*A*tan(1/2*d*x + 1/2*c) + 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 20*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*A*a^12*tan(1/2*d*x + 1/2*c) - 255*B*a^12*tan(1/2*d*x + 1/2*c) + 105*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
363,1,356,0,0.614871," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(23 \, A - 13 \, B + 6 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{30 \, {\left(23 \, A - 13 \, B + 6 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{20 \, {\left(51 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 76 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 50 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 735 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 465 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 255 \, C a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(23*A - 13*B + 6*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 30*(23*A - 13*B + 6*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 20*(51*A*tan(1/2*d*x + 1/2*c)^5 - 21*B*tan(1/2*d*x + 1/2*c)^5 + 6*C*tan(1/2*d*x + 1/2*c)^5 - 76*A*tan(1/2*d*x + 1/2*c)^3 + 36*B*tan(1/2*d*x + 1/2*c)^3 - 12*C*tan(1/2*d*x + 1/2*c)^3 + 33*A*tan(1/2*d*x + 1/2*c) - 15*B*tan(1/2*d*x + 1/2*c) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^12*tan(1/2*d*x + 1/2*c)^5 + 50*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 30*C*a^12*tan(1/2*d*x + 1/2*c)^3 + 735*A*a^12*tan(1/2*d*x + 1/2*c) - 465*B*a^12*tan(1/2*d*x + 1/2*c) + 255*C*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
364,1,302,0,0.672362," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(d x + c\right)} {\left(2 \, A - 8 \, B + 21 \, C\right)}}{a^{4}} + \frac{840 \, {\left(2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 147 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 189 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 805 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1365 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5145 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 11655 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(420*(d*x + c)*(2*A - 8*B + 21*C)/a^4 + 840*(2*B*tan(1/2*d*x + 1/2*c)^3 - 9*C*tan(1/2*d*x + 1/2*c)^3 + 2*B*tan(1/2*d*x + 1/2*c) - 7*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 147*B*a^24*tan(1/2*d*x + 1/2*c)^5 - 189*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 805*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 1365*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 1575*A*a^24*tan(1/2*d*x + 1/2*c) + 5145*B*a^24*tan(1/2*d*x + 1/2*c) - 11655*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
365,1,255,0,0.516754," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(d x + c\right)} {\left(B - 4 \, C\right)}}{a^{4}} + \frac{1680 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 63 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 147 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 385 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 805 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1575 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5145 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*(d*x + c)*(B - 4*C)/a^4 + 1680*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 63*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*B*a^24*tan(1/2*d*x + 1/2*c)^5 - 147*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 385*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 805*C*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*A*a^24*tan(1/2*d*x + 1/2*c) + 1575*B*a^24*tan(1/2*d*x + 1/2*c) - 5145*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
366,1,220,0,0.571259," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(d x + c\right)} C}{a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 385 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*(d*x + c)*C/a^4 + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 - 21*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 63*B*a^24*tan(1/2*d*x + 1/2*c)^5 - 105*C*a^24*tan(1/2*d*x + 1/2*c)^5 - 35*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 385*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^24*tan(1/2*d*x + 1/2*c) + 105*B*a^24*tan(1/2*d*x + 1/2*c) - 1575*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
367,1,171,0,0.580947," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"-1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 - 15*B*tan(1/2*d*x + 1/2*c)^7 + 15*C*tan(1/2*d*x + 1/2*c)^7 + 21*A*tan(1/2*d*x + 1/2*c)^5 + 21*B*tan(1/2*d*x + 1/2*c)^5 - 63*C*tan(1/2*d*x + 1/2*c)^5 - 35*A*tan(1/2*d*x + 1/2*c)^3 + 35*B*tan(1/2*d*x + 1/2*c)^3 + 105*C*tan(1/2*d*x + 1/2*c)^3 - 105*A*tan(1/2*d*x + 1/2*c) - 105*B*tan(1/2*d*x + 1/2*c) - 105*C*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
368,1,171,0,0.715813," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 63 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 - 15*B*tan(1/2*d*x + 1/2*c)^7 + 15*C*tan(1/2*d*x + 1/2*c)^7 + 63*A*tan(1/2*d*x + 1/2*c)^5 - 21*B*tan(1/2*d*x + 1/2*c)^5 - 21*C*tan(1/2*d*x + 1/2*c)^5 + 105*A*tan(1/2*d*x + 1/2*c)^3 + 35*B*tan(1/2*d*x + 1/2*c)^3 - 35*C*tan(1/2*d*x + 1/2*c)^3 + 105*A*tan(1/2*d*x + 1/2*c) + 105*B*tan(1/2*d*x + 1/2*c) + 105*C*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
369,1,248,0,1.388970," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{840 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 840*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 63*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 21*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*B*a^24*tan(1/2*d*x + 1/2*c)^3 - 35*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 1575*A*a^24*tan(1/2*d*x + 1/2*c) - 105*B*a^24*tan(1/2*d*x + 1/2*c) - 105*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
370,1,290,0,1.150400," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{840 \, {\left(4 \, A - 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(4 \, A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{1680 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 147 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 805 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 385 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5145 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(840*(4*A - B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 840*(4*A - B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 1680*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 147*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 105*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 63*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 805*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 385*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 105*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 5145*A*a^24*tan(1/2*d*x + 1/2*c) - 1575*B*a^24*tan(1/2*d*x + 1/2*c) + 105*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
371,1,339,0,0.748295," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{420 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{840 \, {\left(9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 189 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 147 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1365 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 805 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 385 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11655 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5145 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1575 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(420*(21*A - 8*B + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 420*(21*A - 8*B + 2*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 840*(9*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 - 7*A*tan(1/2*d*x + 1/2*c) + 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 189*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 147*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 1365*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 805*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 385*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 11655*A*a^24*tan(1/2*d*x + 1/2*c) - 5145*B*a^24*tan(1/2*d*x + 1/2*c) + 1575*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
372,1,407,0,0.624323," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{420 \, {\left(44 \, A - 21 \, B + 8 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{420 \, {\left(44 \, A - 21 \, B + 8 \, C\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\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} + 6 \, C \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} - 12 \, C \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) + 6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 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} + 147 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2065 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1365 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 805 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 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) + 5145 \, C a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(420*(44*A - 21*B + 8*C)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 420*(44*A - 21*B + 8*C)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/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 + 6*C*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 - 12*C*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) + 6*C*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 15*C*a^24*tan(1/2*d*x + 1/2*c)^7 + 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 + 147*C*a^24*tan(1/2*d*x + 1/2*c)^5 + 2065*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 1365*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 805*C*a^24*tan(1/2*d*x + 1/2*c)^3 + 21945*A*a^24*tan(1/2*d*x + 1/2*c) - 11655*B*a^24*tan(1/2*d*x + 1/2*c) + 5145*C*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
373,1,290,0,2.488731," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{55440} \, \sqrt{2} {\left(\frac{315 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{385 \, {\left(2 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{495 \, {\left(4 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{693 \, {\left(4 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 8 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{2310 \, {\left(6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 4 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{6930 \, {\left(6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/55440*sqrt(2)*(315*C*sgn(cos(1/2*d*x + 1/2*c))*sin(11/2*d*x + 11/2*c)/d + 385*(2*B*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(9/2*d*x + 9/2*c)/d + 495*(4*A*sgn(cos(1/2*d*x + 1/2*c)) + 2*B*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 693*(4*A*sgn(cos(1/2*d*x + 1/2*c)) + 8*B*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 2310*(6*A*sgn(cos(1/2*d*x + 1/2*c)) + 4*B*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 6930*(6*A*sgn(cos(1/2*d*x + 1/2*c)) + 6*B*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
374,1,261,0,0.757737," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{35 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{45 \, {\left(2 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{126 \, {\left(2 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{210 \, {\left(2 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{1260 \, {\left(2 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{630 \, {\left(3 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(35*C*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 45*(2*B*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 126*(2*A*sgn(cos(1/2*d*x + 1/2*c)) + B*sgn(cos(1/2*d*x + 1/2*c)) + 2*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 210*(2*A*sgn(cos(1/2*d*x + 1/2*c)) + 3*B*sgn(cos(1/2*d*x + 1/2*c)) + 2*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 1260*(2*A*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 630*(3*B*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
375,1,182,0,0.542615," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{420} \, \sqrt{2} {\left(\frac{15 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{21 \, {\left(2 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{35 \, {\left(4 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{105 \, {\left(4 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 4 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/420*sqrt(2)*(15*C*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 21*(2*B*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 35*(4*A*sgn(cos(1/2*d*x + 1/2*c)) + 2*B*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 105*(4*A*sgn(cos(1/2*d*x + 1/2*c)) + 4*B*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
376,1,139,0,1.045735," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{30} \, \sqrt{2} {\left(\frac{3 \, C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{30 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{5 \, {\left(2 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{30 \, {\left(2 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/30*sqrt(2)*(3*C*sgn(cos(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)/d + 30*B*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d + 5*(2*B*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 30*(2*A*sgn(cos(1/2*d*x + 1/2*c)) + C*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
377,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,1,361,0,4.346536," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{55440} \, \sqrt{2} {\left(\frac{315 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{385 \, {\left(2 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{495 \, {\left(4 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{693 \, {\left(12 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 12 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 13 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{2310 \, {\left(10 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 10 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 9 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{6930 \, {\left(6 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 8 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{27720 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/55440*sqrt(2)*(315*C*a*sgn(cos(1/2*d*x + 1/2*c))*sin(11/2*d*x + 11/2*c)/d + 385*(2*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(9/2*d*x + 9/2*c)/d + 495*(4*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 6*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 693*(12*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 12*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 13*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 2310*(10*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 10*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 9*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 6930*(6*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 8*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 27720*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + B*a*sgn(cos(1/2*d*x + 1/2*c)) + C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
383,1,249,0,1.189880," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{35 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{45 \, {\left(2 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{126 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{210 \, {\left(6 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{630 \, {\left(8 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(35*C*a*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 45*(2*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 126*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 210*(6*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 5*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 630*(8*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 7*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 6*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
384,1,247,0,0.903689," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{420} \, \sqrt{2} {\left(\frac{15 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{21 \, {\left(2 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{35 \, {\left(4 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{105 \, {\left(4 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 4 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{420 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + C a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/420*sqrt(2)*(15*C*a*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 21*(2*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 35*(4*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 6*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 105*(4*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 4*B*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 420*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + B*a*sgn(cos(1/2*d*x + 1/2*c)) + C*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
385,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,1,462,0,5.965956," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{1441440} \, \sqrt{2} {\left(\frac{3465 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} + \frac{4095 \, {\left(2 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{10010 \, {\left(2 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{12870 \, {\left(10 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 13 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 15 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{9009 \, {\left(48 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 50 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 51 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{15015 \, {\left(80 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 76 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 71 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{180180 \, {\left(14 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 15 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 14 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{180180 \, {\left(12 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 8 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/1441440*sqrt(2)*(3465*C*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(13/2*d*x + 13/2*c)/d + 4095*(2*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(11/2*d*x + 11/2*c)/d + 10010*(2*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 5*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(9/2*d*x + 9/2*c)/d + 12870*(10*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 13*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 15*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 9009*(48*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 50*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 51*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 15015*(80*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 76*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 71*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 180180*(14*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 15*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 14*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 180180*(12*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 8*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
392,1,336,0,1.309623," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{55440} \, \sqrt{2} {\left(\frac{315 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{385 \, {\left(2 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{495 \, {\left(4 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 10 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 13 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{693 \, {\left(20 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 24 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 25 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{2310 \, {\left(22 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 20 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 19 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{6930 \, {\left(30 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 26 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 23 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/55440*sqrt(2)*(315*C*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(11/2*d*x + 11/2*c)/d + 385*(2*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(9/2*d*x + 9/2*c)/d + 495*(4*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 10*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 13*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 693*(20*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 24*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 25*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 2310*(22*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 20*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 19*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 6930*(30*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 26*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 23*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
393,1,336,0,0.777532," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{35 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{45 \, {\left(2 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{126 \, {\left(2 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{210 \, {\left(10 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 11 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 10 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{630 \, {\left(12 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 8 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{630 \, {\left(8 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6 \, C a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(35*C*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 45*(2*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 5*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 126*(2*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 5*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 6*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 210*(10*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 11*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 10*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 630*(12*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 8*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 7*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 630*(8*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 7*B*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 6*C*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
394,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,1,269,0,1.821068," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{315 \, {\left(\sqrt{2} A - \sqrt{2} B + \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} + \frac{2 \, {\left(315 \, \sqrt{2} A a^{4} + 315 \, \sqrt{2} C a^{4} + {\left(1050 \, \sqrt{2} A a^{4} - 420 \, \sqrt{2} B a^{4} + 840 \, \sqrt{2} C a^{4} + {\left(1512 \, \sqrt{2} A a^{4} - 756 \, \sqrt{2} B a^{4} + 1638 \, \sqrt{2} C a^{4} + {\left(1134 \, \sqrt{2} A a^{4} - 612 \, \sqrt{2} B a^{4} + 936 \, \sqrt{2} C a^{4} + {\left(357 \, \sqrt{2} A a^{4} - 276 \, \sqrt{2} B a^{4} + 383 \, \sqrt{2} C a^{4}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{9}{2}}}}{315 \, d}"," ",0,"1/315*(315*(sqrt(2)*A - sqrt(2)*B + sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) + 2*(315*sqrt(2)*A*a^4 + 315*sqrt(2)*C*a^4 + (1050*sqrt(2)*A*a^4 - 420*sqrt(2)*B*a^4 + 840*sqrt(2)*C*a^4 + (1512*sqrt(2)*A*a^4 - 756*sqrt(2)*B*a^4 + 1638*sqrt(2)*C*a^4 + (1134*sqrt(2)*A*a^4 - 612*sqrt(2)*B*a^4 + 936*sqrt(2)*C*a^4 + (357*sqrt(2)*A*a^4 - 276*sqrt(2)*B*a^4 + 383*sqrt(2)*C*a^4)*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)^(9/2))/d","A",0
402,1,201,0,1.124240," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{105 \, \sqrt{2} {\left(A - B + C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} - \frac{2 \, {\left(105 \, \sqrt{2} B a^{3} - {\left({\left(\sqrt{2} {\left(70 \, A a^{3} - 119 \, B a^{3} + 92 \, C a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, \sqrt{2} {\left(20 \, A a^{3} - 37 \, B a^{3} + 16 \, C a^{3}\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, \sqrt{2} {\left(2 \, A a^{3} - 7 \, B a^{3} + 4 \, C a^{3}\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)}^{\frac{7}{2}}}}{105 \, d}"," ",0,"-1/105*(105*sqrt(2)*(A - B + C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) - 2*(105*sqrt(2)*B*a^3 - ((sqrt(2)*(70*A*a^3 - 119*B*a^3 + 92*C*a^3)*tan(1/2*d*x + 1/2*c)^2 + 7*sqrt(2)*(20*A*a^3 - 37*B*a^3 + 16*C*a^3))*tan(1/2*d*x + 1/2*c)^2 + 35*sqrt(2)*(2*A*a^3 - 7*B*a^3 + 4*C*a^3))*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)^(7/2))/d","A",0
403,1,189,0,1.221667," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(\sqrt{2} A - \sqrt{2} B + \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} + \frac{2 \, {\left(15 \, \sqrt{2} A a^{2} + 15 \, \sqrt{2} C a^{2} + {\left(30 \, \sqrt{2} A a^{2} - 10 \, \sqrt{2} B a^{2} + 20 \, \sqrt{2} C a^{2} + {\left(15 \, \sqrt{2} A a^{2} - 10 \, \sqrt{2} B a^{2} + 17 \, \sqrt{2} C a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}}{15 \, d}"," ",0,"1/15*(15*(sqrt(2)*A - sqrt(2)*B + sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) + 2*(15*sqrt(2)*A*a^2 + 15*sqrt(2)*C*a^2 + (30*sqrt(2)*A*a^2 - 10*sqrt(2)*B*a^2 + 20*sqrt(2)*C*a^2 + (15*sqrt(2)*A*a^2 - 10*sqrt(2)*B*a^2 + 17*sqrt(2)*C*a^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","A",0
404,1,114,0,1.187810," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} {\left(A - B + C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} - \frac{2 \, {\left(\sqrt{2} {\left(3 \, B a - 2 \, C a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, \sqrt{2} B 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)}^{\frac{3}{2}}}}{3 \, d}"," ",0,"-1/3*(3*sqrt(2)*(A - B + C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) - 2*(sqrt(2)*(3*B*a - 2*C*a)*tan(1/2*d*x + 1/2*c)^2 + 3*sqrt(2)*B*a)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2))/d","A",0
405,1,205,0,2.150728," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{4 \, \sqrt{2} C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{\sqrt{2} {\left(A \sqrt{a} - B \sqrt{a} + C \sqrt{a}\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)}{a} + \frac{2 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{a}} - \frac{2 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{a}}}{2 \, d}"," ",0,"1/2*(4*sqrt(2)*C*tan(1/2*d*x + 1/2*c)/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(2)*(A*sqrt(a) - B*sqrt(a) + C*sqrt(a))*log((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*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/sqrt(a) - 2*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/sqrt(a))/d","B",0
406,1,326,0,4.826209," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} {\left(A \sqrt{a} - B \sqrt{a} + C \sqrt{a}\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)}{a} + \frac{{\left(A \sqrt{a} - 2 \, B \sqrt{a}\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)}{a} - \frac{{\left(A \sqrt{a} - 2 \, B \sqrt{a}\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)}{a} - \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 a^{\frac{3}{2}}\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*(sqrt(2)*(A*sqrt(a) - B*sqrt(a) + C*sqrt(a))*log((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*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a - (A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a - 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*a^(3/2))/((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
407,1,552,0,6.757932," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{4 \, \sqrt{2} {\left(A \sqrt{a} - B \sqrt{a} + C \sqrt{a}\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)}{a} + \frac{{\left(7 \, A \sqrt{a} - 4 \, B \sqrt{a} + 8 \, C \sqrt{a}\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)}{a} - \frac{{\left(7 \, A \sqrt{a} - 4 \, B \sqrt{a} + 8 \, C \sqrt{a}\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)}{a} - \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 a^{\frac{3}{2}} + 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^{\frac{3}{2}} + 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 a^{\frac{5}{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^{\frac{5}{2}} - 3 \, A a^{\frac{7}{2}} + 4 \, B a^{\frac{7}{2}}\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*(4*sqrt(2)*(A*sqrt(a) - B*sqrt(a) + C*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a + (7*A*sqrt(a) - 4*B*sqrt(a) + 8*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a - (7*A*sqrt(a) - 4*B*sqrt(a) + 8*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a - 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*a^(3/2) + 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^(3/2) + 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*a^(5/2) - 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^(5/2) - 3*A*a^(7/2) + 4*B*a^(7/2))/((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
408,1,928,0,3.379716," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{24 \, \sqrt{2} {\left(A \sqrt{a} - B \sqrt{a} + C \sqrt{a}\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)}{a} + \frac{3 \, {\left(9 \, A \sqrt{a} - 14 \, B \sqrt{a} + 8 \, C \sqrt{a}\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)}{a} - \frac{3 \, {\left(9 \, A \sqrt{a} - 14 \, B \sqrt{a} + 8 \, C \sqrt{a}\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)}{a} - \frac{4 \, \sqrt{2} {\left(165 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A \sqrt{a} - 102 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B \sqrt{a} + 72 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C \sqrt{a} - 1323 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A a^{\frac{3}{2}} + 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 a^{\frac{3}{2}} - 888 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C a^{\frac{3}{2}} + 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 a^{\frac{5}{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 a^{\frac{5}{2}} + 3024 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C a^{\frac{5}{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 a^{\frac{7}{2}} + 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 a^{\frac{7}{2}} - 1776 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C a^{\frac{7}{2}} + 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 a^{\frac{9}{2}} - 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 a^{\frac{9}{2}} + 360 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C a^{\frac{9}{2}} - 31 \, A a^{\frac{11}{2}} + 18 \, B a^{\frac{11}{2}} - 24 \, C a^{\frac{11}{2}}\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*(24*sqrt(2)*(A*sqrt(a) - B*sqrt(a) + C*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a + 3*(9*A*sqrt(a) - 14*B*sqrt(a) + 8*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a - 3*(9*A*sqrt(a) - 14*B*sqrt(a) + 8*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a - 4*sqrt(2)*(165*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*sqrt(a) - 102*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*sqrt(a) + 72*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*sqrt(a) - 1323*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*a^(3/2) + 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*a^(3/2) - 888*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*a^(3/2) + 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*a^(5/2) - 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*a^(5/2) + 3024*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*a^(5/2) - 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*a^(7/2) + 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*a^(7/2) - 1776*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*a^(7/2) + 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*a^(9/2) - 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*a^(9/2) + 360*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*a^(9/2) - 31*A*a^(11/2) + 18*B*a^(11/2) - 24*C*a^(11/2))/((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
409,1,1174,0,2.916655," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{192 \, \sqrt{2} {\left(A \sqrt{a} - B \sqrt{a} + C \sqrt{a}\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)}{a} + \frac{3 \, {\left(107 \, A \sqrt{a} - 72 \, B \sqrt{a} + 112 \, C \sqrt{a}\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)}{a} - \frac{3 \, {\left(107 \, A \sqrt{a} - 72 \, B \sqrt{a} + 112 \, C \sqrt{a}\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)}{a} - \frac{4 \, \sqrt{2} {\left(1599 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} A \sqrt{a} - 1320 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} B \sqrt{a} + 816 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{14} C \sqrt{a} - 18219 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} A a^{\frac{3}{2}} + 18504 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} B a^{\frac{3}{2}} - 12528 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{12} C a^{\frac{3}{2}} + 91467 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} A a^{\frac{5}{2}} - 96072 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} B a^{\frac{5}{2}} + 64752 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{10} C a^{\frac{5}{2}} - 177735 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} A a^{\frac{7}{2}} + 215016 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} B a^{\frac{7}{2}} - 124848 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} C a^{\frac{7}{2}} + 100413 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A a^{\frac{9}{2}} - 136056 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B a^{\frac{9}{2}} + 70032 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} C a^{\frac{9}{2}} - 26881 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a^{\frac{11}{2}} + 36056 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B a^{\frac{11}{2}} - 19152 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} C a^{\frac{11}{2}} + 3321 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{\frac{13}{2}} - 4632 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B a^{\frac{13}{2}} + 2640 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} C a^{\frac{13}{2}} - 205 \, A a^{\frac{15}{2}} + 248 \, B a^{\frac{15}{2}} - 144 \, C a^{\frac{15}{2}}\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*(192*sqrt(2)*(A*sqrt(a) - B*sqrt(a) + C*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a + 3*(107*A*sqrt(a) - 72*B*sqrt(a) + 112*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a - 3*(107*A*sqrt(a) - 72*B*sqrt(a) + 112*C*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a - 4*sqrt(2)*(1599*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^14*A*sqrt(a) - 1320*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^14*B*sqrt(a) + 816*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^14*C*sqrt(a) - 18219*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^12*A*a^(3/2) + 18504*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^12*B*a^(3/2) - 12528*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^12*C*a^(3/2) + 91467*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*A*a^(5/2) - 96072*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*B*a^(5/2) + 64752*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^10*C*a^(5/2) - 177735*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*A*a^(7/2) + 215016*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*B*a^(7/2) - 124848*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*C*a^(7/2) + 100413*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*a^(9/2) - 136056*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*a^(9/2) + 70032*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*C*a^(9/2) - 26881*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a^(11/2) + 36056*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*a^(11/2) - 19152*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*C*a^(11/2) + 3321*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^(13/2) - 4632*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*a^(13/2) + 2640*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*C*a^(13/2) - 205*A*a^(15/2) + 248*B*a^(15/2) - 144*C*a^(15/2))/((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
410,1,305,0,3.501526," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(11 \, \sqrt{2} A - 15 \, \sqrt{2} B + 19 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}} + \frac{{\left({\left({\left({\left(\frac{105 \, {\left(\sqrt{2} A a^{5} - \sqrt{2} B a^{5} + \sqrt{2} C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} + \frac{4 \, {\left(455 \, \sqrt{2} A a^{5} - 693 \, \sqrt{2} B a^{5} + 877 \, \sqrt{2} C a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{14 \, {\left(305 \, \sqrt{2} A a^{5} - 453 \, \sqrt{2} B a^{5} + 517 \, \sqrt{2} C a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{140 \, {\left(25 \, \sqrt{2} A a^{5} - 39 \, \sqrt{2} B a^{5} + 47 \, \sqrt{2} C a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{105 \, {\left(9 \, \sqrt{2} A a^{5} - 17 \, \sqrt{2} B a^{5} + 17 \, \sqrt{2} C a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}}{420 \, d}"," ",0,"-1/420*(105*(11*sqrt(2)*A - 15*sqrt(2)*B + 19*sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2) + ((((105*(sqrt(2)*A*a^5 - sqrt(2)*B*a^5 + sqrt(2)*C*a^5)*tan(1/2*d*x + 1/2*c)^2/a^3 + 4*(455*sqrt(2)*A*a^5 - 693*sqrt(2)*B*a^5 + 877*sqrt(2)*C*a^5)/a^3)*tan(1/2*d*x + 1/2*c)^2 + 14*(305*sqrt(2)*A*a^5 - 453*sqrt(2)*B*a^5 + 517*sqrt(2)*C*a^5)/a^3)*tan(1/2*d*x + 1/2*c)^2 + 140*(25*sqrt(2)*A*a^5 - 39*sqrt(2)*B*a^5 + 47*sqrt(2)*C*a^5)/a^3)*tan(1/2*d*x + 1/2*c)^2 + 105*(9*sqrt(2)*A*a^5 - 17*sqrt(2)*B*a^5 + 17*sqrt(2)*C*a^5)/a^3)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","A",0
411,1,228,0,1.751173," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{15 \, \sqrt{2} {\left(7 \, A - 11 \, B + 15 \, C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}} + \frac{{\left({\left({\left(\frac{15 \, \sqrt{2} {\left(A a^{3} - B a^{3} + C a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2}} + \frac{\sqrt{2} {\left(165 \, A a^{3} - 245 \, B a^{3} + 381 \, C a^{3}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, \sqrt{2} {\left(57 \, A a^{3} - 73 \, B a^{3} + 105 \, C a^{3}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{15 \, \sqrt{2} {\left(9 \, A a^{3} - 9 \, B a^{3} + 17 \, C a^{3}\right)}}{a^{2}}\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)}^{\frac{5}{2}}}}{60 \, d}"," ",0,"1/60*(15*sqrt(2)*(7*A - 11*B + 15*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2) + (((15*sqrt(2)*(A*a^3 - B*a^3 + C*a^3)*tan(1/2*d*x + 1/2*c)^2/a^2 + sqrt(2)*(165*A*a^3 - 245*B*a^3 + 381*C*a^3)/a^2)*tan(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*(57*A*a^3 - 73*B*a^3 + 105*C*a^3)/a^2)*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)*(9*A*a^3 - 9*B*a^3 + 17*C*a^3)/a^2)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","A",0
412,1,194,0,1.445440," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(3 \, \sqrt{2} A - 7 \, \sqrt{2} B + 11 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}} + \frac{{\left({\left(\frac{3 \, {\left(\sqrt{2} A a - \sqrt{2} B a + \sqrt{2} C a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a} + \frac{2 \, {\left(3 \, \sqrt{2} A a - 15 \, \sqrt{2} B a + 23 \, \sqrt{2} C a\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{3 \, {\left(\sqrt{2} A a - 9 \, \sqrt{2} B a + 9 \, \sqrt{2} C a\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)}^{\frac{3}{2}}}}{12 \, d}"," ",0,"-1/12*(3*(3*sqrt(2)*A - 7*sqrt(2)*B + 11*sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2) + ((3*(sqrt(2)*A*a - sqrt(2)*B*a + sqrt(2)*C*a)*tan(1/2*d*x + 1/2*c)^2/a + 2*(3*sqrt(2)*A*a - 15*sqrt(2)*B*a + 23*sqrt(2)*C*a)/a)*tan(1/2*d*x + 1/2*c)^2 + 3*(sqrt(2)*A*a - 9*sqrt(2)*B*a + 9*sqrt(2)*C*a)/a)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2))/d","A",0
413,1,144,0,1.373463," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(\frac{\sqrt{2} {\left(A a^{2} - B a^{2} + C a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} + \frac{\sqrt{2} {\left(A a^{2} - B a^{2} + 9 \, C a^{2}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{\sqrt{2} {\left(A + 3 \, B - 7 \, C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}}}{4 \, d}"," ",0,"1/4*((sqrt(2)*(A*a^2 - B*a^2 + C*a^2)*tan(1/2*d*x + 1/2*c)^2/a^3 + sqrt(2)*(A*a^2 - B*a^2 + 9*C*a^2)/a^3)*tan(1/2*d*x + 1/2*c)/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(2)*(A + 3*B - 7*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2))/d","A",0
414,1,226,0,2.952449," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(5 \, A \sqrt{a} - B \sqrt{a} - 3 \, C \sqrt{a}\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)}{a^{2}} + \frac{8 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{\frac{3}{2}}} - \frac{8 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{\frac{3}{2}}} - \frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\sqrt{2} A a - \sqrt{2} B a + \sqrt{2} C a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}}}{8 \, d}"," ",0,"1/8*(sqrt(2)*(5*A*sqrt(a) - B*sqrt(a) - 3*C*sqrt(a))*log((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 + 8*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^(3/2) - 8*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^(3/2) - 2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(sqrt(2)*A*a - sqrt(2)*B*a + sqrt(2)*C*a)*tan(1/2*d*x + 1/2*c)/a^3)/d","B",0
415,1,384,0,3.140307," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} {\left(9 \, A \sqrt{a} - 5 \, B \sqrt{a} + C \sqrt{a}\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)}{a^{2}} + \frac{4 \, {\left(3 \, A \sqrt{a} - 2 \, B \sqrt{a}\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)}{a^{2}} - \frac{4 \, {\left(3 \, A \sqrt{a} - 2 \, B \sqrt{a}\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)}{a^{2}} - \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 \sqrt{a} - A a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} a} - \frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\sqrt{2} A a - \sqrt{2} B a + \sqrt{2} C a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}}}{8 \, d}"," ",0,"-1/8*(sqrt(2)*(9*A*sqrt(a) - 5*B*sqrt(a) + C*sqrt(a))*log((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 + 4*(3*A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^2 - 4*(3*A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^2 - 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*sqrt(a) - A*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*a) - 2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(sqrt(2)*A*a - sqrt(2)*B*a + sqrt(2)*C*a)*tan(1/2*d*x + 1/2*c)/a^3)/d","B",0
416,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)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)/2))]Discontinuities at zeroes of cos((d*t_nostep+c)/2) were not checkedEvaluation time: 1.21Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[23574053482485268906770432,0]:[1,0,-2]%%},[16]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0]%%%} / %%%{%%%{%%{[604462909807314587353088,0]:[1,0,-2]%%},[16]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
417,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)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)/2))]Discontinuities at zeroes of cos((d*t_nostep+c)/2) were not checkedEvaluation time: 1.45Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[7975367974709495237422842361682067456000,0]:[1,0,-2]%%},[30]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0]%%%} / %%%{%%%{%%{[63802943797675961899382738893456539648,0]:[1,0,-2]%%},[30]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
418,1,307,0,2.676794," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(75 \, \sqrt{2} A - 163 \, \sqrt{2} B + 283 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}} - \frac{{\left({\left({\left(15 \, {\left(\frac{2 \, {\left(\sqrt{2} A a^{2} - \sqrt{2} B a^{2} + \sqrt{2} C a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2}} - \frac{13 \, \sqrt{2} A a^{2} - 21 \, \sqrt{2} B a^{2} + 29 \, \sqrt{2} C a^{2}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{1725 \, \sqrt{2} A a^{2} - 3685 \, \sqrt{2} B a^{2} + 6733 \, \sqrt{2} C a^{2}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{5 \, {\left(549 \, \sqrt{2} A a^{2} - 1133 \, \sqrt{2} B a^{2} + 1973 \, \sqrt{2} C a^{2}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{15 \, {\left(83 \, \sqrt{2} A a^{2} - 155 \, \sqrt{2} B a^{2} + 291 \, \sqrt{2} C a^{2}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}}{480 \, d}"," ",0,"1/480*(15*(75*sqrt(2)*A - 163*sqrt(2)*B + 283*sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2) - (((15*(2*(sqrt(2)*A*a^2 - sqrt(2)*B*a^2 + sqrt(2)*C*a^2)*tan(1/2*d*x + 1/2*c)^2/a^2 - (13*sqrt(2)*A*a^2 - 21*sqrt(2)*B*a^2 + 29*sqrt(2)*C*a^2)/a^2)*tan(1/2*d*x + 1/2*c)^2 - (1725*sqrt(2)*A*a^2 - 3685*sqrt(2)*B*a^2 + 6733*sqrt(2)*C*a^2)/a^2)*tan(1/2*d*x + 1/2*c)^2 - 5*(549*sqrt(2)*A*a^2 - 1133*sqrt(2)*B*a^2 + 1973*sqrt(2)*C*a^2)/a^2)*tan(1/2*d*x + 1/2*c)^2 - 15*(83*sqrt(2)*A*a^2 - 155*sqrt(2)*B*a^2 + 291*sqrt(2)*C*a^2)/a^2)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","A",0
419,1,230,0,2.370318," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(3 \, {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{6}} - \frac{\sqrt{2} {\left(7 \, A a^{5} - 15 \, B a^{5} + 23 \, C a^{5}\right)}}{a^{6}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{4 \, \sqrt{2} {\left(15 \, A a^{5} - 75 \, B a^{5} + 167 \, C a^{5}\right)}}{a^{6}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{3 \, \sqrt{2} {\left(11 \, A a^{5} - 83 \, B a^{5} + 155 \, C a^{5}\right)}}{a^{6}}\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)}^{\frac{3}{2}}} - \frac{3 \, \sqrt{2} {\left(19 \, A - 75 \, B + 163 \, C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{96 \, d}"," ",0,"1/96*(((3*(2*sqrt(2)*(A*a^5 - B*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/a^6 - sqrt(2)*(7*A*a^5 - 15*B*a^5 + 23*C*a^5)/a^6)*tan(1/2*d*x + 1/2*c)^2 - 4*sqrt(2)*(15*A*a^5 - 75*B*a^5 + 167*C*a^5)/a^6)*tan(1/2*d*x + 1/2*c)^2 - 3*sqrt(2)*(11*A*a^5 - 83*B*a^5 + 155*C*a^5)/a^6)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) - 3*sqrt(2)*(19*A - 75*B + 163*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
420,1,211,0,1.989009," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(\frac{2 \, {\left(\sqrt{2} A a^{6} - \sqrt{2} B a^{6} + \sqrt{2} C a^{6}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} - \frac{\sqrt{2} A a^{6} - 9 \, \sqrt{2} B a^{6} + 17 \, \sqrt{2} C a^{6}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{3 \, \sqrt{2} A a^{6} - 11 \, \sqrt{2} B a^{6} + 83 \, \sqrt{2} C a^{6}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{{\left(5 \, \sqrt{2} A + 19 \, \sqrt{2} B - 75 \, \sqrt{2} C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{32 \, d}"," ",0,"-1/32*(((2*(sqrt(2)*A*a^6 - sqrt(2)*B*a^6 + sqrt(2)*C*a^6)*tan(1/2*d*x + 1/2*c)^2/a^8 - (sqrt(2)*A*a^6 - 9*sqrt(2)*B*a^6 + 17*sqrt(2)*C*a^6)/a^8)*tan(1/2*d*x + 1/2*c)^2 - (3*sqrt(2)*A*a^6 - 11*sqrt(2)*B*a^6 + 83*sqrt(2)*C*a^6)/a^8)*tan(1/2*d*x + 1/2*c)/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + (5*sqrt(2)*A + 19*sqrt(2)*B - 75*sqrt(2)*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
421,1,148,0,2.465955," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{\sqrt{2} {\left(5 \, A a^{5} + 3 \, B a^{5} - 11 \, C a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{\sqrt{2} {\left(3 \, A + 5 \, B + 19 \, C\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{32 \, d}"," ",0,"1/32*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/a^8 + sqrt(2)*(5*A*a^5 + 3*B*a^5 - 11*C*a^5)/a^8)*tan(1/2*d*x + 1/2*c) - sqrt(2)*(3*A + 5*B + 19*C)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
422,1,267,0,4.070038," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{\sqrt{2} {\left(13 \, A a^{5} - 5 \, B a^{5} - 3 \, C a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{\sqrt{2} {\left(43 \, A \sqrt{a} - 3 \, B \sqrt{a} - 5 \, C \sqrt{a}\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)}{a^{3}} - \frac{64 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{\frac{5}{2}}} + \frac{64 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{\frac{5}{2}}}}{64 \, d}"," ",0,"-1/64*(2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/a^8 + sqrt(2)*(13*A*a^5 - 5*B*a^5 - 3*C*a^5)/a^8)*tan(1/2*d*x + 1/2*c) - sqrt(2)*(43*A*sqrt(a) - 3*B*sqrt(a) - 5*C*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a^3 - 64*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^(5/2) + 64*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^(5/2))/d","A",0
423,1,426,0,6.837086," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5} + C a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{\sqrt{2} {\left(21 \, A a^{5} - 13 \, B a^{5} + 5 \, C a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{\sqrt{2} {\left(115 \, A \sqrt{a} - 43 \, B \sqrt{a} + 3 \, C \sqrt{a}\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)}{a^{3}} - \frac{32 \, {\left(5 \, A \sqrt{a} - 2 \, B \sqrt{a}\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)}{a^{3}} + \frac{32 \, {\left(5 \, A \sqrt{a} - 2 \, B \sqrt{a}\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)}{a^{3}} + \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 \sqrt{a} - A a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} a^{2}}}{64 \, d}"," ",0,"1/64*(2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5 + C*a^5)*tan(1/2*d*x + 1/2*c)^2/a^8 + sqrt(2)*(21*A*a^5 - 13*B*a^5 + 5*C*a^5)/a^8)*tan(1/2*d*x + 1/2*c) - sqrt(2)*(115*A*sqrt(a) - 43*B*sqrt(a) + 3*C*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a^3 - 32*(5*A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^3 + 32*(5*A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^3 + 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*sqrt(a) - A*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*a^2))/d","B",0
424,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)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)/2))]Discontinuities at zeroes of cos((d*t_nostep+c)/2) were not checkedEvaluation time: 2.39Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[663535861056963827345930584064,0]:[1,0,-2]%%},[16]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0]%%%} / %%%{%%%{%%{[9903520314283042199192993792,0]:[1,0,-2]%%},[16]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
425,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2), x)","F",0
426,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c)), x)","F",0
427,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sqrt(cos(d*x + c)), x)","F",0
428,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/cos(d*x + c)^(3/2), x)","F",0
429,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/cos(d*x + c)^(5/2), x)","F",0
430,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/cos(d*x + c)^(7/2), x)","F",0
431,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
432,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
433,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
434,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
435,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
436,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
437,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
438,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
439,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
440,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
441,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
442,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
443,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
444,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
445,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
446,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(11/2), x)","F",0
447,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
448,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
449,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
450,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
451,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
452,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
453,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
454,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
455,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(13/2), x)","F",0
456,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
457,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
458,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
459,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
460,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
461,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
462,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
463,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^2, x)","F",0
464,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^2, x)","F",0
465,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
466,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
467,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
468,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
469,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^3, x)","F",0
470,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^3, x)","F",0
471,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^3, x)","F",0
472,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^3, x)","F",0
473,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
474,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
475,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
476,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
477,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
478,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
485,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
486,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
491,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
494,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
495,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(a*cos(d*x + c) + a), x)","F",0
504,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(a*cos(d*x + c) + a), x)","F",0
505,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
506,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
507,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
508,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
509,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
510,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(cos(d*x + c))/sqrt(a*cos(d*x + c) + a), x)","F",0
511,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
512,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
513,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
514,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
515,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
516,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
517,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
518,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
519,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
520,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
521,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
522,1,109,0,0.334106," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A a + 3 \, C a\right)} x + \frac{C b \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{C a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, A b + 5 \, C b\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a + C a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(6 \, A b + 5 \, C b\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(4*A*a + 3*C*a)*x + 1/80*C*b*sin(5*d*x + 5*c)/d + 1/32*C*a*sin(4*d*x + 4*c)/d + 1/48*(4*A*b + 5*C*b)*sin(3*d*x + 3*c)/d + 1/4*(A*a + C*a)*sin(2*d*x + 2*c)/d + 1/8*(6*A*b + 5*C*b)*sin(d*x + c)/d","A",0
523,1,86,0,0.373846," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A b + 3 \, C b\right)} x + \frac{C b \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{C a \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(A b + C b\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a + 3 \, C a\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/8*(4*A*b + 3*C*b)*x + 1/32*C*b*sin(4*d*x + 4*c)/d + 1/12*C*a*sin(3*d*x + 3*c)/d + 1/4*(A*b + C*b)*sin(2*d*x + 2*c)/d + 1/4*(4*A*a + 3*C*a)*sin(d*x + c)/d","A",0
524,1,64,0,0.344892," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, A a + C a\right)} x + \frac{C b \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{C a \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A b + 3 \, C b\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/2*(2*A*a + C*a)*x + 1/12*C*b*sin(3*d*x + 3*c)/d + 1/4*C*a*sin(2*d*x + 2*c)/d + 1/4*(4*A*b + 3*C*b)*sin(d*x + c)/d","A",0
525,1,127,0,0.356076," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{2 \, A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(2 \, A b + C b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*A*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*A*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (2*A*b + C*b)*(d*x + c) + 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 - C*b*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
526,1,117,0,0.389642," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} C a + A b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - A b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((d*x + c)*C*a + A*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)) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - C*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
527,1,132,0,0.397005," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} C b + {\left(A a + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a + 2 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*b + (A*a + 2*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a + 2*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*A*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) + 2*A*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
528,1,184,0,0.420315," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(A b + 2 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(A b + 2 \, C 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} + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*b + 2*C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(A*b + 2*C*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 + 6*C*a*tan(1/2*d*x + 1/2*c)^5 - 3*A*b*tan(1/2*d*x + 1/2*c)^5 - 4*A*a*tan(1/2*d*x + 1/2*c)^3 - 12*C*a*tan(1/2*d*x + 1/2*c)^3 + 6*A*a*tan(1/2*d*x + 1/2*c) + 6*C*a*tan(1/2*d*x + 1/2*c) + 3*A*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
529,1,304,0,0.448214," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, C a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a + 4 \, C a\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 \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*C*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a + 4*C*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a*tan(1/2*d*x + 1/2*c)^7 + 12*C*a*tan(1/2*d*x + 1/2*c)^7 - 24*A*b*tan(1/2*d*x + 1/2*c)^7 - 24*C*b*tan(1/2*d*x + 1/2*c)^7 + 9*A*a*tan(1/2*d*x + 1/2*c)^5 - 12*C*a*tan(1/2*d*x + 1/2*c)^5 + 40*A*b*tan(1/2*d*x + 1/2*c)^5 + 72*C*b*tan(1/2*d*x + 1/2*c)^5 + 9*A*a*tan(1/2*d*x + 1/2*c)^3 - 12*C*a*tan(1/2*d*x + 1/2*c)^3 - 40*A*b*tan(1/2*d*x + 1/2*c)^3 - 72*C*b*tan(1/2*d*x + 1/2*c)^3 + 15*A*a*tan(1/2*d*x + 1/2*c) + 12*C*a*tan(1/2*d*x + 1/2*c) + 24*A*b*tan(1/2*d*x + 1/2*c) + 24*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
530,1,334,0,0.392740," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, A b + 4 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, A b + 4 \, C b\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 \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*A*b + 4*C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*A*b + 4*C*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*a*tan(1/2*d*x + 1/2*c)^9 + 120*C*a*tan(1/2*d*x + 1/2*c)^9 - 75*A*b*tan(1/2*d*x + 1/2*c)^9 - 60*C*b*tan(1/2*d*x + 1/2*c)^9 - 160*A*a*tan(1/2*d*x + 1/2*c)^7 - 320*C*a*tan(1/2*d*x + 1/2*c)^7 + 30*A*b*tan(1/2*d*x + 1/2*c)^7 + 120*C*b*tan(1/2*d*x + 1/2*c)^7 + 464*A*a*tan(1/2*d*x + 1/2*c)^5 + 400*C*a*tan(1/2*d*x + 1/2*c)^5 - 160*A*a*tan(1/2*d*x + 1/2*c)^3 - 320*C*a*tan(1/2*d*x + 1/2*c)^3 - 30*A*b*tan(1/2*d*x + 1/2*c)^3 - 120*C*b*tan(1/2*d*x + 1/2*c)^3 + 120*A*a*tan(1/2*d*x + 1/2*c) + 120*C*a*tan(1/2*d*x + 1/2*c) + 75*A*b*tan(1/2*d*x + 1/2*c) + 60*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
531,1,183,0,0.389243," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{2} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{C a b \sin\left(5 \, d x + 5 \, c\right)}{40 \, d} + \frac{1}{16} \, {\left(8 \, A a^{2} + 6 \, C a^{2} + 6 \, A b^{2} + 5 \, C b^{2}\right)} x + \frac{{\left(2 \, C a^{2} + 2 \, A b^{2} + 3 \, C b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(4 \, A a b + 5 \, C a b\right)} \sin\left(3 \, d x + 3 \, c\right)}{24 \, d} + \frac{{\left(16 \, A a^{2} + 16 \, C a^{2} + 16 \, A b^{2} + 15 \, C b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(6 \, A a b + 5 \, C a b\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/192*C*b^2*sin(6*d*x + 6*c)/d + 1/40*C*a*b*sin(5*d*x + 5*c)/d + 1/16*(8*A*a^2 + 6*C*a^2 + 6*A*b^2 + 5*C*b^2)*x + 1/64*(2*C*a^2 + 2*A*b^2 + 3*C*b^2)*sin(4*d*x + 4*c)/d + 1/24*(4*A*a*b + 5*C*a*b)*sin(3*d*x + 3*c)/d + 1/64*(16*A*a^2 + 16*C*a^2 + 16*A*b^2 + 15*C*b^2)*sin(2*d*x + 2*c)/d + 1/4*(6*A*a*b + 5*C*a*b)*sin(d*x + c)/d","A",0
532,1,142,0,0.392994," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{2} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{C a b \sin\left(4 \, d x + 4 \, c\right)}{16 \, d} + \frac{1}{4} \, {\left(4 \, A a b + 3 \, C a b\right)} x + \frac{{\left(4 \, C a^{2} + 4 \, A b^{2} + 5 \, C b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a b + C a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(8 \, A a^{2} + 6 \, C a^{2} + 6 \, A b^{2} + 5 \, C b^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*b^2*sin(5*d*x + 5*c)/d + 1/16*C*a*b*sin(4*d*x + 4*c)/d + 1/4*(4*A*a*b + 3*C*a*b)*x + 1/48*(4*C*a^2 + 4*A*b^2 + 5*C*b^2)*sin(3*d*x + 3*c)/d + 1/2*(A*a*b + C*a*b)*sin(2*d*x + 2*c)/d + 1/8*(8*A*a^2 + 6*C*a^2 + 6*A*b^2 + 5*C*b^2)*sin(d*x + c)/d","A",0
533,1,116,0,0.376762," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{C a b \sin\left(3 \, d x + 3 \, c\right)}{6 \, d} + \frac{1}{8} \, {\left(8 \, A a^{2} + 4 \, C a^{2} + 4 \, A b^{2} + 3 \, C b^{2}\right)} x + \frac{{\left(C a^{2} + A b^{2} + C b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a b + 3 \, C a b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/32*C*b^2*sin(4*d*x + 4*c)/d + 1/6*C*a*b*sin(3*d*x + 3*c)/d + 1/8*(8*A*a^2 + 4*C*a^2 + 4*A*b^2 + 3*C*b^2)*x + 1/4*(C*a^2 + A*b^2 + C*b^2)*sin(2*d*x + 2*c)/d + 1/2*(4*A*a*b + 3*C*a*b)*sin(d*x + c)/d","A",0
534,1,256,0,0.930658," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{3 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(2 \, A a b + C a b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(2*A*a*b + C*a*b)*(d*x + c) + 2*(3*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a*b*tan(1/2*d*x + 1/2*c) + 3*A*b^2*tan(1/2*d*x + 1/2*c) + 3*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
535,1,175,0,1.967125," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{4 \, A a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 4 \, A a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + {\left(2 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*A*a*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 4*A*a*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 4*A*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + (2*C*a^2 + 2*A*b^2 + C*b^2)*(d*x + c) + 2*(4*C*a*b*tan(1/2*d*x + 1/2*c)^3 - C*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*a*b*tan(1/2*d*x + 1/2*c) + C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
536,1,189,0,0.485199," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{4 \, {\left(d x + c\right)} C a b + \frac{4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + {\left(A a^{2} + 2 \, C a^{2} + 2 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a^{2} + 2 \, C a^{2} + 2 \, 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} - 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*C*a*b + 4*C*b^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + (A*a^2 + 2*C*a^2 + 2*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a^2 + 2*C*a^2 + 2*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 - 4*A*a*b*tan(1/2*d*x + 1/2*c)^3 + A*a^2*tan(1/2*d*x + 1/2*c) + 4*A*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
537,1,262,0,0.483819," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} C b^{2} + 3 \, {\left(A a b + 2 \, C a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(A a b + 2 \, C a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*C*b^2 + 3*(A*a*b + 2*C*a*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(A*a*b + 2*C*a*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 2*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 6*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 6*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a^2*tan(1/2*d*x + 1/2*c) + 3*A*a*b*tan(1/2*d*x + 1/2*c) + 3*A*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
538,1,426,0,0.500781," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a^{2} + 4 \, C a^{2} + 4 \, A b^{2} + 8 \, C b^{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} + 4 \, C a^{2} + 4 \, A b^{2} + 8 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 144 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 144 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^2 + 4*C*a^2 + 4*A*b^2 + 8*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a^2 + 4*C*a^2 + 4*A*b^2 + 8*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*A*a*b*tan(1/2*d*x + 1/2*c)^7 - 48*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 80*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 144*C*a*b*tan(1/2*d*x + 1/2*c)^5 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 144*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^2*tan(1/2*d*x + 1/2*c) + 12*C*a^2*tan(1/2*d*x + 1/2*c) + 48*A*a*b*tan(1/2*d*x + 1/2*c) + 48*C*a*b*tan(1/2*d*x + 1/2*c) + 12*A*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
539,1,532,0,0.555736," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, A a b + 4 \, C a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, A a b + 4 \, C a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 80 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 160 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 240 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 232 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 200 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 200 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 360 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(15*(3*A*a*b + 4*C*a*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*A*a*b + 4*C*a*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(60*A*a^2*tan(1/2*d*x + 1/2*c)^9 + 60*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 75*A*a*b*tan(1/2*d*x + 1/2*c)^9 - 60*C*a*b*tan(1/2*d*x + 1/2*c)^9 + 60*A*b^2*tan(1/2*d*x + 1/2*c)^9 + 60*C*b^2*tan(1/2*d*x + 1/2*c)^9 - 80*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 160*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 30*A*a*b*tan(1/2*d*x + 1/2*c)^7 + 120*C*a*b*tan(1/2*d*x + 1/2*c)^7 - 160*A*b^2*tan(1/2*d*x + 1/2*c)^7 - 240*C*b^2*tan(1/2*d*x + 1/2*c)^7 + 232*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 200*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 200*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 360*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 80*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 160*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 30*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 120*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 160*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 240*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 60*A*a^2*tan(1/2*d*x + 1/2*c) + 60*C*a^2*tan(1/2*d*x + 1/2*c) + 75*A*a*b*tan(1/2*d*x + 1/2*c) + 60*C*a*b*tan(1/2*d*x + 1/2*c) + 60*A*b^2*tan(1/2*d*x + 1/2*c) + 60*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
540,1,216,0,2.593733," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{3 \, C a b^{2} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{16} \, {\left(24 \, A a^{2} b + 18 \, C a^{2} b + 6 \, A b^{3} + 5 \, C b^{3}\right)} x + \frac{{\left(6 \, C a^{2} b + 2 \, A b^{3} + 3 \, C b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(4 \, C a^{3} + 12 \, A a b^{2} + 15 \, C a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(48 \, A a^{2} b + 48 \, C a^{2} b + 16 \, A b^{3} + 15 \, C b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(8 \, A a^{3} + 6 \, C a^{3} + 18 \, A a b^{2} + 15 \, C a b^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*C*b^3*sin(6*d*x + 6*c)/d + 3/80*C*a*b^2*sin(5*d*x + 5*c)/d + 1/16*(24*A*a^2*b + 18*C*a^2*b + 6*A*b^3 + 5*C*b^3)*x + 1/64*(6*C*a^2*b + 2*A*b^3 + 3*C*b^3)*sin(4*d*x + 4*c)/d + 1/48*(4*C*a^3 + 12*A*a*b^2 + 15*C*a*b^2)*sin(3*d*x + 3*c)/d + 1/64*(48*A*a^2*b + 48*C*a^2*b + 16*A*b^3 + 15*C*b^3)*sin(2*d*x + 2*c)/d + 1/8*(8*A*a^3 + 6*C*a^3 + 18*A*a*b^2 + 15*C*a*b^2)*sin(d*x + c)/d","A",0
541,1,174,0,0.983120," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{3} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{3 \, C a b^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(8 \, A a^{3} + 4 \, C a^{3} + 12 \, A a b^{2} + 9 \, C a b^{2}\right)} x + \frac{{\left(12 \, C a^{2} b + 4 \, A b^{3} + 5 \, C b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(C a^{3} + 3 \, A a b^{2} + 3 \, C a b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(24 \, A a^{2} b + 18 \, C a^{2} b + 6 \, A b^{3} + 5 \, C b^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*b^3*sin(5*d*x + 5*c)/d + 3/32*C*a*b^2*sin(4*d*x + 4*c)/d + 1/8*(8*A*a^3 + 4*C*a^3 + 12*A*a*b^2 + 9*C*a*b^2)*x + 1/48*(12*C*a^2*b + 4*A*b^3 + 5*C*b^3)*sin(3*d*x + 3*c)/d + 1/4*(C*a^3 + 3*A*a*b^2 + 3*C*a*b^2)*sin(2*d*x + 2*c)/d + 1/8*(24*A*a^2*b + 18*C*a^2*b + 6*A*b^3 + 5*C*b^3)*sin(d*x + c)/d","A",0
542,1,503,0,1.889421," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{8 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 8 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(24 \, A a^{2} b + 12 \, C a^{2} b + 4 \, A b^{3} + 3 \, C b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(8 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(8*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 8*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (24*A*a^2*b + 12*C*a^2*b + 4*A*b^3 + 3*C*b^3)*(d*x + c) + 2*(8*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 24*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 4*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 5*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 24*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 72*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 40*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 24*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 72*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 40*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*C*a^3*tan(1/2*d*x + 1/2*c) + 12*C*a^2*b*tan(1/2*d*x + 1/2*c) + 24*A*a*b^2*tan(1/2*d*x + 1/2*c) + 24*C*a*b^2*tan(1/2*d*x + 1/2*c) + 4*A*b^3*tan(1/2*d*x + 1/2*c) + 5*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
543,1,306,0,1.136869," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{18 \, A a^{2} b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 18 \, A a^{2} b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + 3 \, {\left(2 \, C a^{3} + 6 \, A a b^{2} + 3 \, C a b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*A*a^2*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 18*A*a^2*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 12*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 3*(2*C*a^3 + 6*A*a*b^2 + 3*C*a*b^2)*(d*x + c) + 2*(18*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 9*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^2*b*tan(1/2*d*x + 1/2*c) + 9*C*a*b^2*tan(1/2*d*x + 1/2*c) + 6*A*b^3*tan(1/2*d*x + 1/2*c) + 6*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
544,1,385,0,0.422484," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(6 \, C a^{2} b + 2 \, A b^{3} + C b^{3}\right)} {\left(d x + c\right)} + {\left(A a^{3} + 2 \, C a^{3} + 6 \, A a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a^{3} + 2 \, C a^{3} + 6 \, A 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^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((6*C*a^2*b + 2*A*b^3 + C*b^3)*(d*x + c) + (A*a^3 + 2*C*a^3 + 6*A*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a^3 + 2*C*a^3 + 6*A*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a^3*tan(1/2*d*x + 1/2*c)^7 - 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - C*b^3*tan(1/2*d*x + 1/2*c)^7 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*C*b^3*tan(1/2*d*x + 1/2*c)^3 + A*a^3*tan(1/2*d*x + 1/2*c) + 6*A*a^2*b*tan(1/2*d*x + 1/2*c) + 6*C*a*b^2*tan(1/2*d*x + 1/2*c) + C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","B",0
545,1,322,0,1.378289," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{18 \, {\left(d x + c\right)} C a b^{2} + \frac{12 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 3 \, {\left(3 \, A a^{2} b + 6 \, C a^{2} b + 2 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a^{2} b + 6 \, C a^{2} 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(6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*(d*x + c)*C*a*b^2 + 12*C*b^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 3*(3*A*a^2*b + 6*C*a^2*b + 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a^2*b + 6*C*a^2*b + 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*tan(1/2*d*x + 1/2*c) + 6*C*a^3*tan(1/2*d*x + 1/2*c) + 9*A*a^2*b*tan(1/2*d*x + 1/2*c) + 18*A*a*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
546,1,526,0,1.045772," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{8 \, {\left(d x + c\right)} C b^{3} + {\left(3 \, A a^{3} + 4 \, C a^{3} + 12 \, A a b^{2} + 24 \, C a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(3 \, A a^{3} + 4 \, C a^{3} + 12 \, A a b^{2} + 24 \, C a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(5 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(8*(d*x + c)*C*b^3 + (3*A*a^3 + 4*C*a^3 + 12*A*a*b^2 + 24*C*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (3*A*a^3 + 4*C*a^3 + 12*A*a*b^2 + 24*C*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(5*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 4*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 24*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 8*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 4*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 24*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 24*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^3*tan(1/2*d*x + 1/2*c) + 4*C*a^3*tan(1/2*d*x + 1/2*c) + 24*A*a^2*b*tan(1/2*d*x + 1/2*c) + 24*C*a^2*b*tan(1/2*d*x + 1/2*c) + 12*A*a*b^2*tan(1/2*d*x + 1/2*c) + 8*A*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
547,1,656,0,0.523253," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(9 \, A a^{2} b + 12 \, C a^{2} b + 4 \, A b^{3} + 8 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(9 \, A a^{2} b + 12 \, C a^{2} b + 4 \, A b^{3} + 8 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1440 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2160 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1440 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(9*A*a^2*b + 12*C*a^2*b + 4*A*b^3 + 8*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(9*A*a^2*b + 12*C*a^2*b + 4*A*b^3 + 8*C*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 + 120*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 225*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 180*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*b^3*tan(1/2*d*x + 1/2*c)^9 - 160*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 320*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 1440*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 120*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 400*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 2160*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 160*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 320*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 1440*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^3*tan(1/2*d*x + 1/2*c) + 120*C*a^3*tan(1/2*d*x + 1/2*c) + 225*A*a^2*b*tan(1/2*d*x + 1/2*c) + 180*C*a^2*b*tan(1/2*d*x + 1/2*c) + 360*A*a*b^2*tan(1/2*d*x + 1/2*c) + 360*C*a*b^2*tan(1/2*d*x + 1/2*c) + 60*A*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
548,1,932,0,0.475641," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{15 \, {\left(5 \, A a^{3} + 6 \, C a^{3} + 18 \, A a b^{2} + 24 \, C a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(5 \, A a^{3} + 6 \, C a^{3} + 18 \, A a b^{2} + 24 \, C a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 150 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 25 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 210 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1680 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2640 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 630 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1080 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 880 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1200 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3744 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4320 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1440 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3744 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4320 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1440 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1680 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2640 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 630 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1080 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 880 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1200 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 450 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*A*a^3 + 6*C*a^3 + 18*A*a*b^2 + 24*C*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(5*A*a^3 + 6*C*a^3 + 18*A*a*b^2 + 24*C*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(165*A*a^3*tan(1/2*d*x + 1/2*c)^11 + 150*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 720*A*a^2*b*tan(1/2*d*x + 1/2*c)^11 - 720*C*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 450*A*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 240*A*b^3*tan(1/2*d*x + 1/2*c)^11 - 240*C*b^3*tan(1/2*d*x + 1/2*c)^11 + 25*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 210*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 1680*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 2640*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 630*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 1080*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 880*A*b^3*tan(1/2*d*x + 1/2*c)^9 + 1200*C*b^3*tan(1/2*d*x + 1/2*c)^9 + 450*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 3744*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 4320*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 180*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 1440*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 2400*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 450*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 60*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 3744*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 4320*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 180*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 1440*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 2400*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 25*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 210*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 1680*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 2640*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 630*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 1080*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 880*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 1200*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 165*A*a^3*tan(1/2*d*x + 1/2*c) + 150*C*a^3*tan(1/2*d*x + 1/2*c) + 720*A*a^2*b*tan(1/2*d*x + 1/2*c) + 720*C*a^2*b*tan(1/2*d*x + 1/2*c) + 450*A*a*b^2*tan(1/2*d*x + 1/2*c) + 360*C*a*b^2*tan(1/2*d*x + 1/2*c) + 240*A*b^3*tan(1/2*d*x + 1/2*c) + 240*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
549,1,290,0,0.456770," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{4} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{C a b^{3} \sin\left(6 \, d x + 6 \, c\right)}{48 \, d} + \frac{1}{4} \, {\left(8 \, A a^{3} b + 6 \, C a^{3} b + 6 \, A a b^{3} + 5 \, C a b^{3}\right)} x + \frac{{\left(24 \, C a^{2} b^{2} + 4 \, A b^{4} + 7 \, C b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(2 \, C a^{3} b + 2 \, A a b^{3} + 3 \, C a b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{16 \, d} + \frac{{\left(16 \, C a^{4} + 96 \, A a^{2} b^{2} + 120 \, C a^{2} b^{2} + 20 \, A b^{4} + 21 \, C b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(16 \, A a^{3} b + 16 \, C a^{3} b + 16 \, A a b^{3} + 15 \, C a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{16 \, d} + \frac{{\left(64 \, A a^{4} + 48 \, C a^{4} + 288 \, A a^{2} b^{2} + 240 \, C a^{2} b^{2} + 40 \, A b^{4} + 35 \, C b^{4}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/448*C*b^4*sin(7*d*x + 7*c)/d + 1/48*C*a*b^3*sin(6*d*x + 6*c)/d + 1/4*(8*A*a^3*b + 6*C*a^3*b + 6*A*a*b^3 + 5*C*a*b^3)*x + 1/320*(24*C*a^2*b^2 + 4*A*b^4 + 7*C*b^4)*sin(5*d*x + 5*c)/d + 1/16*(2*C*a^3*b + 2*A*a*b^3 + 3*C*a*b^3)*sin(4*d*x + 4*c)/d + 1/192*(16*C*a^4 + 96*A*a^2*b^2 + 120*C*a^2*b^2 + 20*A*b^4 + 21*C*b^4)*sin(3*d*x + 3*c)/d + 1/16*(16*A*a^3*b + 16*C*a^3*b + 16*A*a*b^3 + 15*C*a*b^3)*sin(2*d*x + 2*c)/d + 1/64*(64*A*a^4 + 48*C*a^4 + 288*A*a^2*b^2 + 240*C*a^2*b^2 + 40*A*b^4 + 35*C*b^4)*sin(d*x + c)/d","A",0
550,1,247,0,0.469143," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{4} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{C a b^{3} \sin\left(5 \, d x + 5 \, c\right)}{20 \, d} + \frac{1}{16} \, {\left(16 \, A a^{4} + 8 \, C a^{4} + 48 \, A a^{2} b^{2} + 36 \, C a^{2} b^{2} + 6 \, A b^{4} + 5 \, C b^{4}\right)} x + \frac{{\left(12 \, C a^{2} b^{2} + 2 \, A b^{4} + 3 \, C b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(4 \, C a^{3} b + 4 \, A a b^{3} + 5 \, C a b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(16 \, C a^{4} + 96 \, A a^{2} b^{2} + 96 \, C a^{2} b^{2} + 16 \, A b^{4} + 15 \, C b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(8 \, A a^{3} b + 6 \, C a^{3} b + 6 \, A a b^{3} + 5 \, C a b^{3}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/192*C*b^4*sin(6*d*x + 6*c)/d + 1/20*C*a*b^3*sin(5*d*x + 5*c)/d + 1/16*(16*A*a^4 + 8*C*a^4 + 48*A*a^2*b^2 + 36*C*a^2*b^2 + 6*A*b^4 + 5*C*b^4)*x + 1/64*(12*C*a^2*b^2 + 2*A*b^4 + 3*C*b^4)*sin(4*d*x + 4*c)/d + 1/12*(4*C*a^3*b + 4*A*a*b^3 + 5*C*a*b^3)*sin(3*d*x + 3*c)/d + 1/64*(16*C*a^4 + 96*A*a^2*b^2 + 96*C*a^2*b^2 + 16*A*b^4 + 15*C*b^4)*sin(2*d*x + 2*c)/d + 1/2*(8*A*a^3*b + 6*C*a^3*b + 6*A*a*b^3 + 5*C*a*b^3)*sin(d*x + c)/d","A",0
551,1,753,0,0.473834," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{30 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 30 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 15 \, {\left(8 \, A a^{3} b + 4 \, C a^{3} b + 4 \, A a b^{3} + 3 \, C a b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(30 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 80 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 40 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1080 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 600 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 100 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 116 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(30*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 30*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 15*(8*A*a^3*b + 4*C*a^3*b + 4*A*a*b^3 + 3*C*a*b^3)*(d*x + c) + 2*(30*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 60*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 180*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 180*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 75*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 30*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 30*C*b^4*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 120*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 480*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 120*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 30*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 80*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 40*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 180*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 1080*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 600*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 100*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 116*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 120*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 120*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 480*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 30*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 80*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 40*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 30*C*a^4*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b*tan(1/2*d*x + 1/2*c) + 180*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 180*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a*b^3*tan(1/2*d*x + 1/2*c) + 75*C*a*b^3*tan(1/2*d*x + 1/2*c) + 30*A*b^4*tan(1/2*d*x + 1/2*c) + 30*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
552,1,558,0,0.534043," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{96 \, A a^{3} b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 96 \, A a^{3} b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{48 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + 3 \, {\left(8 \, C a^{4} + 48 \, A a^{2} b^{2} + 24 \, C a^{2} b^{2} + 4 \, A b^{4} + 3 \, C b^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(96*A*a^3*b*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 96*A*a^3*b*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 48*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 3*(8*C*a^4 + 48*A*a^2*b^2 + 24*C*a^2*b^2 + 4*A*b^4 + 3*C*b^4)*(d*x + c) + 2*(96*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 96*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 96*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 12*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 15*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 160*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 9*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 160*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 9*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 96*C*a^3*b*tan(1/2*d*x + 1/2*c) + 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 96*A*a*b^3*tan(1/2*d*x + 1/2*c) + 96*C*a*b^3*tan(1/2*d*x + 1/2*c) + 12*A*b^4*tan(1/2*d*x + 1/2*c) + 15*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
553,1,396,0,0.593331," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{12 \, {\left(2 \, C a^{3} b + 2 \, A a b^{3} + C a b^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(A a^{4} + 2 \, C a^{4} + 12 \, A a^{2} b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(A a^{4} + 2 \, C a^{4} + 12 \, A a^{2} b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{6 \, {\left(A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{4 \, {\left(18 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*(2*C*a^3*b + 2*A*a*b^3 + C*a*b^3)*(d*x + c) + 3*(A*a^4 + 2*C*a^4 + 12*A*a^2*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(A*a^4 + 2*C*a^4 + 12*A*a^2*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 6*(A*a^4*tan(1/2*d*x + 1/2*c)^3 - 8*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 + A*a^4*tan(1/2*d*x + 1/2*c) + 8*A*a^3*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 4*(18*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 6*C*a*b^3*tan(1/2*d*x + 1/2*c) + 3*A*b^4*tan(1/2*d*x + 1/2*c) + 3*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
554,1,397,0,0.335375," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(12 \, C a^{2} b^{2} + 2 \, A b^{4} + C b^{4}\right)} {\left(d x + c\right)} + 12 \, {\left(A a^{3} b + 2 \, C a^{3} b + 2 \, A a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 12 \, {\left(A a^{3} b + 2 \, C a^{3} b + 2 \, A a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{6 \, {\left(8 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{4 \, {\left(3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(12*C*a^2*b^2 + 2*A*b^4 + C*b^4)*(d*x + c) + 12*(A*a^3*b + 2*C*a^3*b + 2*A*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 12*(A*a^3*b + 2*C*a^3*b + 2*A*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 6*(8*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - C*b^4*tan(1/2*d*x + 1/2*c)^3 + 8*C*a*b^3*tan(1/2*d*x + 1/2*c) + C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - 4*(3*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 2*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 6*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 36*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*tan(1/2*d*x + 1/2*c) + 3*C*a^4*tan(1/2*d*x + 1/2*c) + 6*A*a^3*b*tan(1/2*d*x + 1/2*c) + 18*A*a^2*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
555,1,590,0,0.598017," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{96 \, {\left(d x + c\right)} C a b^{3} + \frac{48 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 3 \, {\left(3 \, A a^{4} + 4 \, C a^{4} + 24 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 8 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a^{4} + 4 \, C a^{4} + 24 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 8 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(96*(d*x + c)*C*a*b^3 + 48*C*b^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 3*(3*A*a^4 + 4*C*a^4 + 24*A*a^2*b^2 + 48*C*a^2*b^2 + 8*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a^4 + 4*C*a^4 + 24*A*a^2*b^2 + 48*C*a^2*b^2 + 8*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 96*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 96*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 96*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^4*tan(1/2*d*x + 1/2*c) + 12*C*a^4*tan(1/2*d*x + 1/2*c) + 96*A*a^3*b*tan(1/2*d*x + 1/2*c) + 96*C*a^3*b*tan(1/2*d*x + 1/2*c) + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 96*A*a*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
556,1,778,0,0.584105," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{30 \, {\left(d x + c\right)} C b^{4} + 15 \, {\left(3 \, A a^{3} b + 4 \, C a^{3} b + 4 \, A a b^{3} + 8 \, C a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, A a^{3} b + 4 \, C a^{3} b + 4 \, A a b^{3} + 8 \, C a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(30 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 180 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 30 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 40 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 116 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 100 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 600 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1080 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 180 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(30*(d*x + c)*C*b^4 + 15*(3*A*a^3*b + 4*C*a^3*b + 4*A*a*b^3 + 8*C*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*A*a^3*b + 4*C*a^3*b + 4*A*a*b^3 + 8*C*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(30*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 30*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 75*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 60*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 180*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 180*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 30*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 40*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 80*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 30*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 120*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 480*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 120*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 120*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 116*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 100*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 600*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 1080*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 180*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 40*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 80*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 30*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 120*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 480*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 120*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 30*A*a^4*tan(1/2*d*x + 1/2*c) + 30*C*a^4*tan(1/2*d*x + 1/2*c) + 75*A*a^3*b*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b*tan(1/2*d*x + 1/2*c) + 180*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 180*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a*b^3*tan(1/2*d*x + 1/2*c) + 30*A*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
557,1,1100,0,0.752949," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{15 \, {\left(5 \, A a^{4} + 6 \, C a^{4} + 36 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 8 \, A b^{4} + 16 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(5 \, A a^{4} + 6 \, C a^{4} + 36 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 8 \, A b^{4} + 16 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 150 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 210 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2160 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9600 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9600 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2160 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*A*a^4 + 6*C*a^4 + 36*A*a^2*b^2 + 48*C*a^2*b^2 + 8*A*b^4 + 16*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(5*A*a^4 + 6*C*a^4 + 36*A*a^2*b^2 + 48*C*a^2*b^2 + 8*A*b^4 + 16*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(165*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 150*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 960*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 960*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 960*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 960*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^11 + 25*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 210*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 2160*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 4800*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 360*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 450*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 1440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 9600*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 450*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 60*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 1440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 9600*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 240*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 25*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 210*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 2160*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 4800*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 360*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 165*A*a^4*tan(1/2*d*x + 1/2*c) + 150*C*a^4*tan(1/2*d*x + 1/2*c) + 960*A*a^3*b*tan(1/2*d*x + 1/2*c) + 960*C*a^3*b*tan(1/2*d*x + 1/2*c) + 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 960*A*a*b^3*tan(1/2*d*x + 1/2*c) + 960*C*a*b^3*tan(1/2*d*x + 1/2*c) + 120*A*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
558,1,1280,0,0.811037," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^8,x, algorithm=""giac"")","\frac{105 \, {\left(5 \, A a^{3} b + 6 \, C a^{3} b + 6 \, A a b^{3} + 8 \, C a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(5 \, A a^{3} b + 6 \, C a^{3} b + 6 \, A a b^{3} + 8 \, C a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(420 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 420 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1155 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1050 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2520 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2520 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1050 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 840 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 420 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 420 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 840 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1400 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 980 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 2520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 8400 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 11760 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 2520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3360 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1960 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 2520 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3612 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3164 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2975 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1890 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 18984 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 24360 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1890 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4200 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4060 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 6300 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2544 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4368 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 26208 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30240 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5040 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8400 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3612 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3164 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2975 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1890 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18984 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24360 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1890 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4200 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4060 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6300 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 840 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1400 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 980 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8400 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 11760 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3360 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1960 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2520 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 420 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1155 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1050 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2520 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2520 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1050 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 840 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 420 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{420 \, d}"," ",0,"1/420*(105*(5*A*a^3*b + 6*C*a^3*b + 6*A*a*b^3 + 8*C*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(5*A*a^3*b + 6*C*a^3*b + 6*A*a*b^3 + 8*C*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(420*A*a^4*tan(1/2*d*x + 1/2*c)^13 + 420*C*a^4*tan(1/2*d*x + 1/2*c)^13 - 1155*A*a^3*b*tan(1/2*d*x + 1/2*c)^13 - 1050*C*a^3*b*tan(1/2*d*x + 1/2*c)^13 + 2520*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 + 2520*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 - 1050*A*a*b^3*tan(1/2*d*x + 1/2*c)^13 - 840*C*a*b^3*tan(1/2*d*x + 1/2*c)^13 + 420*A*b^4*tan(1/2*d*x + 1/2*c)^13 + 420*C*b^4*tan(1/2*d*x + 1/2*c)^13 - 840*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 1400*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 980*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 2520*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 8400*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 11760*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 2520*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 3360*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 1960*A*b^4*tan(1/2*d*x + 1/2*c)^11 - 2520*C*b^4*tan(1/2*d*x + 1/2*c)^11 + 3612*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 3164*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 2975*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 1890*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 18984*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 24360*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 1890*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 4200*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 4060*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 6300*C*b^4*tan(1/2*d*x + 1/2*c)^9 - 2544*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 4368*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 26208*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 30240*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 5040*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 8400*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 3612*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 3164*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 2975*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 1890*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 18984*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 24360*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 1890*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 4200*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 4060*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 6300*C*b^4*tan(1/2*d*x + 1/2*c)^5 - 840*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 1400*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 980*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 2520*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 8400*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 11760*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 2520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 3360*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 1960*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 2520*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 420*A*a^4*tan(1/2*d*x + 1/2*c) + 420*C*a^4*tan(1/2*d*x + 1/2*c) + 1155*A*a^3*b*tan(1/2*d*x + 1/2*c) + 1050*C*a^3*b*tan(1/2*d*x + 1/2*c) + 2520*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 2520*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 1050*A*a*b^3*tan(1/2*d*x + 1/2*c) + 840*C*a*b^3*tan(1/2*d*x + 1/2*c) + 420*A*b^4*tan(1/2*d*x + 1/2*c) + 420*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","B",0
559,1,147,0,2.905005," ","integrate((a+b*cos(d*x+c))^3*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""giac"")","-\frac{b^{5} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{3 \, a b^{4} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(8 \, a^{5} + 8 \, a^{3} b^{2} - 9 \, a b^{4}\right)} x - \frac{{\left(8 \, a^{2} b^{3} + 5 \, b^{5}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(24 \, a^{4} b - 12 \, a^{2} b^{3} - 5 \, b^{5}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/80*b^5*sin(5*d*x + 5*c)/d - 3/32*a*b^4*sin(4*d*x + 4*c)/d + 1/8*(8*a^5 + 8*a^3*b^2 - 9*a*b^4)*x - 1/48*(8*a^2*b^3 + 5*b^5)*sin(3*d*x + 3*c)/d + 1/4*(2*a^3*b^2 - 3*a*b^4)*sin(2*d*x + 2*c)/d + 1/8*(24*a^4*b - 12*a^2*b^3 - 5*b^5)*sin(d*x + c)/d","A",0
560,1,91,0,2.913857," ","integrate((a+b*cos(d*x+c))^2*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""giac"")","-\frac{b^{4} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{a b^{3} \sin\left(3 \, d x + 3 \, c\right)}{6 \, d} - \frac{b^{4} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{1}{8} \, {\left(8 \, a^{4} - 3 \, b^{4}\right)} x + \frac{{\left(4 \, a^{3} b - 3 \, a b^{3}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/32*b^4*sin(4*d*x + 4*c)/d - 1/6*a*b^3*sin(3*d*x + 3*c)/d - 1/4*b^4*sin(2*d*x + 2*c)/d + 1/8*(8*a^4 - 3*b^4)*x + 1/2*(4*a^3*b - 3*a*b^3)*sin(d*x + c)/d","A",0
561,1,74,0,2.937668," ","integrate((a+b*cos(d*x+c))*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""giac"")","-\frac{b^{3} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{a b^{2} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{1}{2} \, {\left(2 \, a^{3} - a b^{2}\right)} x + \frac{{\left(4 \, a^{2} b - 3 \, b^{3}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"-1/12*b^3*sin(3*d*x + 3*c)/d - 1/4*a*b^2*sin(2*d*x + 2*c)/d + 1/2*(2*a^3 - a*b^2)*x + 1/4*(4*a^2*b - 3*b^3)*sin(d*x + c)/d","A",0
562,1,574,0,3.919870," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, C a^{4} + 8 \, A a^{2} b^{2} + 4 \, C a^{2} b^{2} + 4 \, A b^{4} + 3 \, C b^{4}\right)} {\left(d x + c\right)}}{b^{5}} + \frac{48 \, {\left(C a^{5} + A a^{3} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{5}} - \frac{2 \, {\left(24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} b^{4}}}{24 \, d}"," ",0,"1/24*(3*(8*C*a^4 + 8*A*a^2*b^2 + 4*C*a^2*b^2 + 4*A*b^4 + 3*C*b^4)*(d*x + c)/b^5 + 48*(C*a^5 + A*a^3*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^5) - 2*(24*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 24*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 15*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 72*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 72*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 40*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 9*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 72*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 40*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 9*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 24*C*a^3*tan(1/2*d*x + 1/2*c) - 12*C*a^2*b*tan(1/2*d*x + 1/2*c) + 24*A*a*b^2*tan(1/2*d*x + 1/2*c) + 24*C*a*b^2*tan(1/2*d*x + 1/2*c) - 12*A*b^3*tan(1/2*d*x + 1/2*c) - 15*C*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^4))/d","B",0
563,1,326,0,2.735194," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{3} + 2 \, A a b^{2} + C a b^{2}\right)} {\left(d x + c\right)}}{b^{4}} + \frac{12 \, {\left(C a^{4} + A a^{2} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} - \frac{2 \, {\left(6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*C*a^3 + 2*A*a*b^2 + C*a*b^2)*(d*x + c)/b^4 + 12*(C*a^4 + A*a^2*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) - 2*(6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 3*C*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^3))/d","B",0
564,1,199,0,0.495901," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} {\left(d x + c\right)}}{b^{3}} + \frac{4 \, {\left(C a^{3} + A a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{3}} - \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*((2*C*a^2 + 2*A*b^2 + C*b^2)*(d*x + c)/b^3 + 4*(C*a^3 + A*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^3) - 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^2))/d","A",0
565,1,136,0,0.357032," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(d x + c\right)} C a}{b^{2}} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b} + \frac{2 \, {\left(C a^{2} + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{2}}}{d}"," ",0,"-((d*x + c)*C*a/b^2 - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b) + 2*(C*a^2 + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^2))/d","A",0
566,1,143,0,0.412037," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} C}{b} + \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(C a^{2} + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a b}}{d}"," ",0,"((d*x + c)*C/b + A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(C*a^2 + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a*b))/d","A",0
567,1,164,0,0.667855," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{A b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{A b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a} + \frac{2 \, {\left(C a^{2} + 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,"-(A*b*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - A*b*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a) + 2*(C*a^2 + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^2))/d","A",0
568,1,242,0,0.658091," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(A a^{2} + 2 \, C a^{2} + 2 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{{\left(A a^{2} + 2 \, C a^{2} + 2 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{4 \, {\left(C a^{2} b + A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3}} + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*((A*a^2 + 2*C*a^2 + 2*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (A*a^2 + 2*C*a^2 + 2*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 4*(C*a^2*b + A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 + 2*A*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) - 2*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2))/d","A",0
569,1,372,0,0.445033," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(A a^{2} b + 2 \, C a^{2} b + 2 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3 \, {\left(A a^{2} b + 2 \, C a^{2} b + 2 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{12 \, {\left(C a^{2} b^{2} + A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4}} + \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"-1/6*(3*(A*a^2*b + 2*C*a^2*b + 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3*(A*a^2*b + 2*C*a^2*b + 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 12*(C*a^2*b^2 + A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4) + 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 3*A*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^3))/d","B",0
570,1,439,0,0.818047," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(4 \, C a^{6} + 2 \, A a^{4} b^{2} - 5 \, C a^{4} b^{2} - 3 \, A a^{2} b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{5} - b^{7}\right)} \sqrt{a^{2} - b^{2}}} - \frac{6 \, {\left(C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} + \frac{3 \, {\left(4 \, C a^{3} + 2 \, A a b^{2} + C a b^{2}\right)} {\left(d x + c\right)}}{b^{5}} - \frac{2 \, {\left(9 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{4}}}{3 \, d}"," ",0,"-1/3*(6*(4*C*a^6 + 2*A*a^4*b^2 - 5*C*a^4*b^2 - 3*A*a^2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^5 - b^7)*sqrt(a^2 - b^2)) - 6*(C*a^5*tan(1/2*d*x + 1/2*c) + A*a^3*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) + 3*(4*C*a^3 + 2*A*a*b^2 + C*a*b^2)*(d*x + c)/b^5 - 2*(9*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 18*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 9*C*a^2*tan(1/2*d*x + 1/2*c) - 3*C*a*b*tan(1/2*d*x + 1/2*c) + 3*A*b^2*tan(1/2*d*x + 1/2*c) + 3*C*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^4))/d","A",0
571,1,311,0,0.642815," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(3 \, C a^{5} + A a^{3} b^{2} - 4 \, C a^{3} b^{2} - 2 \, A a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{4 \, {\left(C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} + \frac{{\left(6 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} {\left(d x + c\right)}}{b^{4}} - \frac{2 \, {\left(4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{3}}}{2 \, d}"," ",0,"1/2*(4*(3*C*a^5 + A*a^3*b^2 - 4*C*a^3*b^2 - 2*A*a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - 4*(C*a^4*tan(1/2*d*x + 1/2*c) + A*a^2*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b^3 - b^5)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) + (6*C*a^2 + 2*A*b^2 + C*b^2)*(d*x + c)/b^4 - 2*(4*C*a*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 + 4*C*a*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^3))/d","A",0
572,1,998,0,1.034626," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(4 \, C a^{6} b^{2} - 2 \, C a^{5} b^{3} - 9 \, C a^{4} b^{4} + 4 \, C a^{3} b^{5} - A a^{2} b^{6} + 5 \, C a^{2} b^{6} - 2 \, C a b^{7} + A b^{8} + 2 \, C a^{3} {\left| -a^{2} b^{3} + b^{5} \right|} - C a^{2} b {\left| -a^{2} b^{3} + b^{5} \right|} - 2 \, C a b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} - A b^{3} {\left| -a^{2} b^{3} + b^{5} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a^{3} b^{2} - 2 \, a b^{4} + \sqrt{-4 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)}^{2}}}{a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}}}}\right)\right)}}{a^{3} b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} - a b^{4} {\left| -a^{2} b^{3} + b^{5} \right|} + {\left(a^{2} b^{3} - b^{5}\right)}^{2}} + \frac{{\left(\sqrt{a^{2} - b^{2}} A b^{3} {\left| -a^{2} b^{3} + b^{5} \right|} {\left| -a + b \right|} - {\left(2 \, a^{3} - a^{2} b - 2 \, a b^{2}\right)} \sqrt{a^{2} - b^{2}} C {\left| -a^{2} b^{3} + b^{5} \right|} {\left| -a + b \right|} - {\left(a^{2} b^{6} - b^{8}\right)} \sqrt{a^{2} - b^{2}} A {\left| -a + b \right|} + {\left(4 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 9 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + 5 \, a^{2} b^{6} - 2 \, a b^{7}\right)} \sqrt{a^{2} - b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a^{3} b^{2} - 2 \, a b^{4} - \sqrt{-4 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)}^{2}}}{a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} {\left| -a^{2} b^{3} + b^{5} \right|}} + \frac{2 \, {\left(2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\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)}}}{d}"," ",0,"((4*C*a^6*b^2 - 2*C*a^5*b^3 - 9*C*a^4*b^4 + 4*C*a^3*b^5 - A*a^2*b^6 + 5*C*a^2*b^6 - 2*C*a*b^7 + A*b^8 + 2*C*a^3*abs(-a^2*b^3 + b^5) - C*a^2*b*abs(-a^2*b^3 + b^5) - 2*C*a*b^2*abs(-a^2*b^3 + b^5) - A*b^3*abs(-a^2*b^3 + b^5))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a^3*b^2 - 2*a*b^4 + sqrt(-4*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5) + 4*(a^3*b^2 - a*b^4)^2))/(a^3*b^2 - a^2*b^3 - a*b^4 + b^5))))/(a^3*b^2*abs(-a^2*b^3 + b^5) - a*b^4*abs(-a^2*b^3 + b^5) + (a^2*b^3 - b^5)^2) + (sqrt(a^2 - b^2)*A*b^3*abs(-a^2*b^3 + b^5)*abs(-a + b) - (2*a^3 - a^2*b - 2*a*b^2)*sqrt(a^2 - b^2)*C*abs(-a^2*b^3 + b^5)*abs(-a + b) - (a^2*b^6 - b^8)*sqrt(a^2 - b^2)*A*abs(-a + b) + (4*a^6*b^2 - 2*a^5*b^3 - 9*a^4*b^4 + 4*a^3*b^5 + 5*a^2*b^6 - 2*a*b^7)*sqrt(a^2 - b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a^3*b^2 - 2*a*b^4 - sqrt(-4*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5) + 4*(a^3*b^2 - a*b^4)^2))/(a^3*b^2 - a^2*b^3 - a*b^4 + b^5))))/((a^2*b^3 - b^5)^2*(a^2 - 2*a*b + b^2) - (a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*abs(-a^2*b^3 + b^5)) + 2*(2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + C*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^3*tan(1/2*d*x + 1/2*c) + C*a^2*b*tan(1/2*d*x + 1/2*c) + A*a*b^2*tan(1/2*d*x + 1/2*c) - C*a*b^2*tan(1/2*d*x + 1/2*c) - C*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)*(a^2*b^2 - b^4)))/d","B",0
573,1,201,0,0.464919," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{3} - A a b^{2} - 2 \, C a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{{\left(d x + c\right)} C}{b^{2}} - \frac{2 \, {\left(C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b - b^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}}}{d}"," ",0,"(2*(C*a^3 - A*a*b^2 - 2*C*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^2 - b^4)*sqrt(a^2 - b^2)) + (d*x + c)*C/b^2 - 2*(C*a^2*tan(1/2*d*x + 1/2*c) + A*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b - b^3)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)))/d","A",0
574,1,226,0,1.217328," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(2 \, A a^{2} b + C a^{2} b - A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{a^{2} - b^{2}}} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} + \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}}}{d}"," ",0,"-(2*(2*A*a^2*b + C*a^2*b - A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - a^2*b^2)*sqrt(a^2 - b^2)) - A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 + A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 2*(C*a^2*tan(1/2*d*x + 1/2*c) + A*b^2*tan(1/2*d*x + 1/2*c))/((a^3 - a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)))/d","A",0
575,1,382,0,0.866897," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(C a^{4} + 3 \, A a^{2} b^{2} - 2 \, A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{A b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{A b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\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)}}\right)}}{d}"," ",0,"-2*((C*a^4 + 3*A*a^2*b^2 - 2*A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^5 - a^3*b^2)*sqrt(a^2 - b^2)) + A*b*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - A*b*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + (A*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^3*tan(1/2*d*x + 1/2*c)^3 + A*a^3*tan(1/2*d*x + 1/2*c) + A*a^2*b*tan(1/2*d*x + 1/2*c) - C*a^2*b*tan(1/2*d*x + 1/2*c) - A*a*b^2*tan(1/2*d*x + 1/2*c) - 2*A*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^4 - a^2*b^2)))/d","B",0
576,1,353,0,0.544948," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(2 \, C a^{4} b + 4 \, A a^{2} b^{3} - C a^{2} b^{3} - 3 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{4 \, {\left(C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} + \frac{{\left(A a^{2} + 2 \, C a^{2} + 6 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{{\left(A a^{2} + 2 \, C a^{2} + 6 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}}}{2 \, d}"," ",0,"1/2*(4*(2*C*a^4*b + 4*A*a^2*b^3 - C*a^2*b^3 - 3*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - a^4*b^2)*sqrt(a^2 - b^2)) + 4*(C*a^2*b^2*tan(1/2*d*x + 1/2*c) + A*b^4*tan(1/2*d*x + 1/2*c))/((a^5 - a^3*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) + (A*a^2 + 2*C*a^2 + 6*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - (A*a^2 + 2*C*a^2 + 6*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 + 4*A*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) - 4*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3))/d","A",0
577,1,483,0,0.678494," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(3 \, C a^{4} b^{2} + 5 \, A a^{2} b^{4} - 2 \, C a^{2} b^{4} - 4 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{7} - a^{5} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{6 \, {\left(C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} + \frac{3 \, {\left(A a^{2} b + 2 \, C a^{2} b + 4 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} - \frac{3 \, {\left(A a^{2} b + 2 \, C a^{2} b + 4 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}} + \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{4}}}{3 \, d}"," ",0,"-1/3*(6*(3*C*a^4*b^2 + 5*A*a^2*b^4 - 2*C*a^2*b^4 - 4*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^7 - a^5*b^2)*sqrt(a^2 - b^2)) + 6*(C*a^2*b^3*tan(1/2*d*x + 1/2*c) + A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - a^4*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) + 3*(A*a^2*b + 2*C*a^2*b + 4*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 - 3*(A*a^2*b + 2*C*a^2*b + 4*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5 + 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 9*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 2*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 6*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 18*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a^2*tan(1/2*d*x + 1/2*c) - 3*A*a*b*tan(1/2*d*x + 1/2*c) + 9*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^4))/d","A",0
578,1,2494,0,2.438302," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(2 \, a^{4} b^{2} - a^{3} b^{3} - 4 \, a^{2} b^{4} + 4 \, a b^{5} + 2 \, b^{6}\right)} \sqrt{a^{2} - b^{2}} A {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} {\left| -a + b \right|} + {\left(12 \, a^{6} - 6 \, a^{5} b - 23 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} - a b^{5} + b^{6}\right)} \sqrt{a^{2} - b^{2}} C {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} {\left| -a + b \right|} + {\left(4 \, a^{9} b^{6} - 2 \, a^{8} b^{7} - 17 \, a^{7} b^{8} + 8 \, a^{6} b^{9} + 30 \, a^{5} b^{10} - 12 \, a^{4} b^{11} - 25 \, a^{3} b^{12} + 8 \, a^{2} b^{13} + 8 \, a b^{14} - 2 \, b^{15}\right)} \sqrt{a^{2} - b^{2}} A {\left| -a + b \right|} + {\left(24 \, a^{11} b^{4} - 12 \, a^{10} b^{5} - 100 \, a^{9} b^{6} + 47 \, a^{8} b^{7} + 158 \, a^{7} b^{8} - 68 \, a^{6} b^{9} - 111 \, a^{5} b^{10} + 42 \, a^{4} b^{11} + 28 \, a^{3} b^{12} - 8 \, a^{2} b^{13} + a b^{14} - b^{15}\right)} \sqrt{a^{2} - b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{4 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 4 \, a b^{8} + \sqrt{-16 \, {\left(a^{5} b^{4} + a^{4} b^{5} - 2 \, a^{3} b^{6} - 2 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} {\left(a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} + 16 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)}^{2}}}{a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}}}}\right)\right)}}{{\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} + {\left(a^{7} b^{4} - 2 \, a^{6} b^{5} - a^{5} b^{6} + 4 \, a^{4} b^{7} - a^{3} b^{8} - 2 \, a^{2} b^{9} + a b^{10}\right)} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|}} - \frac{{\left(24 \, C a^{11} b^{4} - 12 \, C a^{10} b^{5} + 4 \, A a^{9} b^{6} - 100 \, C a^{9} b^{6} - 2 \, A a^{8} b^{7} + 47 \, C a^{8} b^{7} - 17 \, A a^{7} b^{8} + 158 \, C a^{7} b^{8} + 8 \, A a^{6} b^{9} - 68 \, C a^{6} b^{9} + 30 \, A a^{5} b^{10} - 111 \, C a^{5} b^{10} - 12 \, A a^{4} b^{11} + 42 \, C a^{4} b^{11} - 25 \, A a^{3} b^{12} + 28 \, C a^{3} b^{12} + 8 \, A a^{2} b^{13} - 8 \, C a^{2} b^{13} + 8 \, A a b^{14} + C a b^{14} - 2 \, A b^{15} - C b^{15} - 12 \, C a^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, C a^{5} b {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 2 \, A a^{4} b^{2} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 23 \, C a^{4} b^{2} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + A a^{3} b^{3} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 10 \, C a^{3} b^{3} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 4 \, A a^{2} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 10 \, C a^{2} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 4 \, A a b^{5} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + C a b^{5} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 2 \, A b^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - C b^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{4 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 4 \, a b^{8} - \sqrt{-16 \, {\left(a^{5} b^{4} + a^{4} b^{5} - 2 \, a^{3} b^{6} - 2 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} {\left(a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} + 16 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)}^{2}}}{a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}}}}\right)\right)}}{a^{5} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 2 \, a^{3} b^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + a b^{8} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)}^{2}} + \frac{2 \, {\left(12 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 67 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 29 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 26 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 17 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(((2*a^4*b^2 - a^3*b^3 - 4*a^2*b^4 + 4*a*b^5 + 2*b^6)*sqrt(a^2 - b^2)*A*abs(a^4*b^5 - 2*a^2*b^7 + b^9)*abs(-a + b) + (12*a^6 - 6*a^5*b - 23*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 - a*b^5 + b^6)*sqrt(a^2 - b^2)*C*abs(a^4*b^5 - 2*a^2*b^7 + b^9)*abs(-a + b) + (4*a^9*b^6 - 2*a^8*b^7 - 17*a^7*b^8 + 8*a^6*b^9 + 30*a^5*b^10 - 12*a^4*b^11 - 25*a^3*b^12 + 8*a^2*b^13 + 8*a*b^14 - 2*b^15)*sqrt(a^2 - b^2)*A*abs(-a + b) + (24*a^11*b^4 - 12*a^10*b^5 - 100*a^9*b^6 + 47*a^8*b^7 + 158*a^7*b^8 - 68*a^6*b^9 - 111*a^5*b^10 + 42*a^4*b^11 + 28*a^3*b^12 - 8*a^2*b^13 + a*b^14 - b^15)*sqrt(a^2 - b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*tan(1/2*d*x + 1/2*c)/sqrt((4*a^5*b^4 - 8*a^3*b^6 + 4*a*b^8 + sqrt(-16*(a^5*b^4 + a^4*b^5 - 2*a^3*b^6 - 2*a^2*b^7 + a*b^8 + b^9)*(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9) + 16*(a^5*b^4 - 2*a^3*b^6 + a*b^8)^2))/(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9))))/((a^4*b^5 - 2*a^2*b^7 + b^9)^2*(a^2 - 2*a*b + b^2) + (a^7*b^4 - 2*a^6*b^5 - a^5*b^6 + 4*a^4*b^7 - a^3*b^8 - 2*a^2*b^9 + a*b^10)*abs(a^4*b^5 - 2*a^2*b^7 + b^9)) - (24*C*a^11*b^4 - 12*C*a^10*b^5 + 4*A*a^9*b^6 - 100*C*a^9*b^6 - 2*A*a^8*b^7 + 47*C*a^8*b^7 - 17*A*a^7*b^8 + 158*C*a^7*b^8 + 8*A*a^6*b^9 - 68*C*a^6*b^9 + 30*A*a^5*b^10 - 111*C*a^5*b^10 - 12*A*a^4*b^11 + 42*C*a^4*b^11 - 25*A*a^3*b^12 + 28*C*a^3*b^12 + 8*A*a^2*b^13 - 8*C*a^2*b^13 + 8*A*a*b^14 + C*a*b^14 - 2*A*b^15 - C*b^15 - 12*C*a^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*C*a^5*b*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 2*A*a^4*b^2*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 23*C*a^4*b^2*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + A*a^3*b^3*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 10*C*a^3*b^3*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 4*A*a^2*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 10*C*a^2*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 4*A*a*b^5*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + C*a*b^5*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 2*A*b^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - C*b^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*tan(1/2*d*x + 1/2*c)/sqrt((4*a^5*b^4 - 8*a^3*b^6 + 4*a*b^8 - sqrt(-16*(a^5*b^4 + a^4*b^5 - 2*a^3*b^6 - 2*a^2*b^7 + a*b^8 + b^9)*(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9) + 16*(a^5*b^4 - 2*a^3*b^6 + a*b^8)^2))/(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9))))/(a^5*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 2*a^3*b^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + a*b^8*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - (a^4*b^5 - 2*a^2*b^7 + b^9)^2) + 2*(12*C*a^7*tan(1/2*d*x + 1/2*c)^7 - 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 2*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 17*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 5*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 2*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 13*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^7 + C*b^7*tan(1/2*d*x + 1/2*c)^7 + 36*C*a^7*tan(1/2*d*x + 1/2*c)^5 - 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 67*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 29*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 15*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 26*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 5*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 3*C*b^7*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^7*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 67*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 26*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 5*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 3*C*b^7*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^7*tan(1/2*d*x + 1/2*c) + 18*C*a^6*b*tan(1/2*d*x + 1/2*c) + 2*A*a^5*b^2*tan(1/2*d*x + 1/2*c) - 17*C*a^5*b^2*tan(1/2*d*x + 1/2*c) + 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c) - 33*C*a^4*b^3*tan(1/2*d*x + 1/2*c) - 5*A*a^3*b^4*tan(1/2*d*x + 1/2*c) - 2*C*a^3*b^4*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c) + 13*C*a^2*b^5*tan(1/2*d*x + 1/2*c) + 4*C*a*b^6*tan(1/2*d*x + 1/2*c) - C*b^7*tan(1/2*d*x + 1/2*c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
579,1,489,0,0.942171," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, C a^{6} - 15 \, C a^{4} b^{2} + A a^{2} b^{4} + 12 \, C a^{2} b^{4} + 2 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, {\left(d x + c\right)} C a}{b^{4}} - \frac{4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b^{3}}}{d}"," ",0,"-((6*C*a^6 - 15*C*a^4*b^2 + A*a^2*b^4 + 12*C*a^2*b^4 + 2*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(a^2 - b^2)) + 3*(d*x + c)*C*a/b^4 - (4*C*a^6*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*A*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*C*a^6*tan(1/2*d*x + 1/2*c) + 5*C*a^5*b*tan(1/2*d*x + 1/2*c) - 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c) + A*a^3*b^3*tan(1/2*d*x + 1/2*c) - 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a^2*b^4*tan(1/2*d*x + 1/2*c) - 4*A*a*b^5*tan(1/2*d*x + 1/2*c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b^3))/d","A",0
580,1,479,0,7.822461," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, C a^{5} - 5 \, C a^{3} b^{2} + 3 \, A a b^{4} + 6 \, C a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{a^{2} - b^{2}}} - \frac{{\left(d x + c\right)} C}{b^{3}} + \frac{2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"-((2*C*a^5 - 5*C*a^3*b^2 + 3*A*a*b^4 + 6*C*a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(a^2 - b^2)) - (d*x + c)*C/b^3 + (2*C*a^5*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 2*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - A*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^5*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^5*tan(1/2*d*x + 1/2*c) + 3*C*a^4*b*tan(1/2*d*x + 1/2*c) - 2*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c) - A*a^2*b^3*tan(1/2*d*x + 1/2*c) - 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c) - A*a*b^4*tan(1/2*d*x + 1/2*c) - 2*A*b^5*tan(1/2*d*x + 1/2*c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
581,1,369,0,3.033255," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, A a^{2} + C a^{2} + A b^{2} + 2 \, C b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"((2*A*a^2 + C*a^2 + A*b^2 + 2*C*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) - (C*a^3*tan(1/2*d*x + 1/2*c)^3 + 4*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - A*b^3*tan(1/2*d*x + 1/2*c)^3 - C*a^3*tan(1/2*d*x + 1/2*c) + 4*A*a^2*b*tan(1/2*d*x + 1/2*c) + 3*C*a^2*b*tan(1/2*d*x + 1/2*c) + 3*A*a*b^2*tan(1/2*d*x + 1/2*c) + 4*C*a*b^2*tan(1/2*d*x + 1/2*c) - A*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
582,1,504,0,0.939743," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, A a^{4} b + 3 \, C a^{4} b - 5 \, A a^{2} b^{3} + 2 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} + \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"-((6*A*a^4*b + 3*C*a^4*b - 5*A*a^2*b^3 + 2*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(a^2 - b^2)) - A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 + A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - (2*C*a^5*tan(1/2*d*x + 1/2*c)^3 - C*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^5*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^5*tan(1/2*d*x + 1/2*c) + C*a^4*b*tan(1/2*d*x + 1/2*c) + 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 2*C*a^2*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a*b^4*tan(1/2*d*x + 1/2*c) - 2*A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
583,1,517,0,1.033776," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, C a^{6} + 12 \, A a^{4} b^{2} + C a^{4} b^{2} - 15 \, A a^{2} b^{4} + 6 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, A b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3 \, A b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{4 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} + \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}}}{d}"," ",0,"-((2*C*a^6 + 12*A*a^4*b^2 + C*a^4*b^2 - 15*A*a^2*b^4 + 6*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(a^2 - b^2)) + 3*A*b*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3*A*b*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + (4*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 5*A*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*A*b^6*tan(1/2*d*x + 1/2*c)^3 + 4*C*a^5*b*tan(1/2*d*x + 1/2*c) + 3*C*a^4*b^2*tan(1/2*d*x + 1/2*c) + 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c) - C*a^3*b^3*tan(1/2*d*x + 1/2*c) + 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c) - 5*A*a*b^5*tan(1/2*d*x + 1/2*c) - 4*A*b^6*tan(1/2*d*x + 1/2*c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) + 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3))/d","B",0
584,1,1191,0,1.000314," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(6 \, C a^{6} b + 20 \, A a^{4} b^{3} - 5 \, C a^{4} b^{3} - 29 \, A a^{2} b^{5} + 2 \, C a^{2} b^{5} + 12 \, 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^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} + \frac{{\left(A a^{2} + 2 \, C a^{2} + 12 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} - \frac{{\left(A a^{2} + 2 \, C a^{2} + 12 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}}}{2 \, d}"," ",0,"1/2*(2*(6*C*a^6*b + 20*A*a^4*b^3 - 5*C*a^4*b^3 - 29*A*a^2*b^5 + 2*C*a^2*b^5 + 12*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^9 - 2*a^7*b^2 + a^5*b^4)*sqrt(a^2 - b^2)) + 2*(A*a^7*tan(1/2*d*x + 1/2*c)^7 + 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 5*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 2*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^7*tan(1/2*d*x + 1/2*c)^7 + 3*A*a^7*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 36*A*b^7*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^7*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^7*tan(1/2*d*x + 1/2*c)^3 + A*a^7*tan(1/2*d*x + 1/2*c) - 4*A*a^6*b*tan(1/2*d*x + 1/2*c) - 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c) + 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c) + 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c) + 5*C*a^4*b^3*tan(1/2*d*x + 1/2*c) + 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c) - 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c) + 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c) - 2*C*a^2*b^5*tan(1/2*d*x + 1/2*c) - 18*A*a*b^6*tan(1/2*d*x + 1/2*c) - 12*A*b^7*tan(1/2*d*x + 1/2*c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) + (A*a^2 + 2*C*a^2 + 12*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 - (A*a^2 + 2*C*a^2 + 12*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5)/d","B",0
585,1,1029,0,9.651194," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(20 \, C a^{9} + 2 \, A a^{7} b^{2} - 69 \, C a^{7} b^{2} - 7 \, A a^{5} b^{4} + 84 \, C a^{5} b^{4} + 8 \, A a^{3} b^{6} - 40 \, C a^{3} b^{6} - 8 \, A a b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - b^{12}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(36 \, C a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 81 \, C a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, A a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 213 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 162 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 90 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 284 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 392 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 180 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 81 \, C a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, A a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 213 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 162 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 90 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\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(20 \, C a^{2} + 2 \, A b^{2} + C b^{2}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{6 \, {\left(8 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{5}}}{6 \, d}"," ",0,"1/6*(6*(20*C*a^9 + 2*A*a^7*b^2 - 69*C*a^7*b^2 - 7*A*a^5*b^4 + 84*C*a^5*b^4 + 8*A*a^3*b^6 - 40*C*a^3*b^6 - 8*A*a*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12)*sqrt(a^2 - b^2)) - 2*(36*C*a^10*tan(1/2*d*x + 1/2*c)^5 - 81*C*a^9*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^8*b^2*tan(1/2*d*x + 1/2*c)^5 - 48*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^5 - 15*A*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 + 213*C*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 48*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 + 45*A*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 - 162*C*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 + 90*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 60*A*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^10*tan(1/2*d*x + 1/2*c)^3 + 12*A*a^8*b^2*tan(1/2*d*x + 1/2*c)^3 - 284*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^3 - 56*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 + 392*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 + 116*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 - 180*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^10*tan(1/2*d*x + 1/2*c) + 81*C*a^9*b*tan(1/2*d*x + 1/2*c) + 6*A*a^8*b^2*tan(1/2*d*x + 1/2*c) - 48*C*a^8*b^2*tan(1/2*d*x + 1/2*c) + 15*A*a^7*b^3*tan(1/2*d*x + 1/2*c) - 213*C*a^7*b^3*tan(1/2*d*x + 1/2*c) - 6*A*a^6*b^4*tan(1/2*d*x + 1/2*c) - 48*C*a^6*b^4*tan(1/2*d*x + 1/2*c) - 45*A*a^5*b^5*tan(1/2*d*x + 1/2*c) + 162*C*a^5*b^5*tan(1/2*d*x + 1/2*c) - 6*A*a^4*b^6*tan(1/2*d*x + 1/2*c) + 90*C*a^4*b^6*tan(1/2*d*x + 1/2*c) + 60*A*a^3*b^7*tan(1/2*d*x + 1/2*c) + 36*A*a^2*b^8*tan(1/2*d*x + 1/2*c))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) + 3*(20*C*a^2 + 2*A*b^2 + C*b^2)*(d*x + c)/b^6 - 6*(8*C*a*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 + 8*C*a*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^5))/d","B",0
586,1,846,0,15.797534," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, C a^{8} - 28 \, C a^{6} b^{2} + 35 \, C a^{4} b^{4} - 3 \, A a^{2} b^{6} - 20 \, C a^{2} b^{6} - 2 \, A b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} \sqrt{a^{2} - b^{2}}} + \frac{12 \, {\left(d x + c\right)} C a}{b^{5}} - \frac{18 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 152 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 236 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}} - \frac{6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b^{4}}}{3 \, d}"," ",0,"-1/3*(3*(8*C*a^8 - 28*C*a^6*b^2 + 35*C*a^4*b^4 - 3*A*a^2*b^6 - 20*C*a^2*b^6 - 2*A*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*sqrt(a^2 - b^2)) + 12*(d*x + c)*C*a/b^5 - (18*C*a^9*tan(1/2*d*x + 1/2*c)^5 - 42*C*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 24*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 117*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 105*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 60*C*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^8*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^9*tan(1/2*d*x + 1/2*c)^3 - 152*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 + 236*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 + 32*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 - 120*C*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^8*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^9*tan(1/2*d*x + 1/2*c) + 42*C*a^8*b*tan(1/2*d*x + 1/2*c) - 24*C*a^7*b^2*tan(1/2*d*x + 1/2*c) - 117*C*a^6*b^3*tan(1/2*d*x + 1/2*c) + 6*A*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*C*a^5*b^4*tan(1/2*d*x + 1/2*c) + 3*A*a^4*b^5*tan(1/2*d*x + 1/2*c) + 105*C*a^4*b^5*tan(1/2*d*x + 1/2*c) + 6*A*a^3*b^6*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b^6*tan(1/2*d*x + 1/2*c) + 27*A*a^2*b^7*tan(1/2*d*x + 1/2*c) + 18*A*a*b^8*tan(1/2*d*x + 1/2*c))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) - 6*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b^4))/d","B",0
587,1,845,0,1.570176," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, C a^{7} - 7 \, C a^{5} b^{2} - A a^{3} b^{4} + 8 \, C a^{3} b^{4} - 4 \, A a b^{6} - 8 \, C a b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, {\left(d x + c\right)} C}{b^{4}} - \frac{6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(2*C*a^7 - 7*C*a^5*b^2 - A*a^3*b^4 + 8*C*a^3*b^4 - 4*A*a*b^6 - 8*C*a*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*sqrt(a^2 - b^2)) + 3*(d*x + c)*C/b^4 - (6*C*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 45*C*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^8*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^8*tan(1/2*d*x + 1/2*c)^3 - 56*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 28*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 116*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 16*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 72*C*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^8*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^8*tan(1/2*d*x + 1/2*c) + 15*C*a^7*b*tan(1/2*d*x + 1/2*c) - 6*C*a^6*b^2*tan(1/2*d*x + 1/2*c) - 3*A*a^5*b^3*tan(1/2*d*x + 1/2*c) - 45*C*a^5*b^3*tan(1/2*d*x + 1/2*c) + 12*A*a^4*b^4*tan(1/2*d*x + 1/2*c) - 6*C*a^4*b^4*tan(1/2*d*x + 1/2*c) + 27*A*a^3*b^5*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b^5*tan(1/2*d*x + 1/2*c) + 12*A*a^2*b^6*tan(1/2*d*x + 1/2*c) + 36*C*a^2*b^6*tan(1/2*d*x + 1/2*c) + 6*A*a*b^7*tan(1/2*d*x + 1/2*c) + 6*A*b^8*tan(1/2*d*x + 1/2*c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
588,1,689,0,0.991542," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(4 \, A a^{2} b + 3 \, C a^{2} b + A b^{3} + 2 \, C b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(4*A*a^2*b + 3*C*a^2*b + A*b^3 + 2*C*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + (6*A*a^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 18*C*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^5*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^5*tan(1/2*d*x + 1/2*c)^3 + 4*C*a^5*tan(1/2*d*x + 1/2*c)^3 + 16*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 32*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 28*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 36*C*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^5*tan(1/2*d*x + 1/2*c) + 6*C*a^5*tan(1/2*d*x + 1/2*c) + 6*A*a^4*b*tan(1/2*d*x + 1/2*c) + 3*C*a^4*b*tan(1/2*d*x + 1/2*c) + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 6*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 27*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 12*A*a*b^4*tan(1/2*d*x + 1/2*c) + 18*C*a*b^4*tan(1/2*d*x + 1/2*c) - 3*A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
589,1,689,0,1.811350," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, A a^{3} + C a^{3} + 3 \, A a b^{2} + 4 \, C a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(2*A*a^3 + C*a^3 + 3*A*a*b^2 + 4*C*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + (3*C*a^5*tan(1/2*d*x + 1/2*c)^5 + 18*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^5*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 28*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 32*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 16*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*A*b^5*tan(1/2*d*x + 1/2*c)^3 - 12*C*b^5*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^5*tan(1/2*d*x + 1/2*c) + 18*A*a^4*b*tan(1/2*d*x + 1/2*c) + 12*C*a^4*b*tan(1/2*d*x + 1/2*c) + 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 27*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 12*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 3*A*a*b^4*tan(1/2*d*x + 1/2*c) + 6*C*a*b^4*tan(1/2*d*x + 1/2*c) + 6*A*b^5*tan(1/2*d*x + 1/2*c) + 6*C*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
590,1,868,0,16.652889," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, A a^{6} b + 4 \, C a^{6} b - 8 \, A a^{4} b^{3} + C a^{4} b^{3} + 7 \, A a^{2} b^{5} - 2 \, A b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{3 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} + \frac{3 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(8*A*a^6*b + 4*C*a^6*b - 8*A*a^4*b^3 + C*a^4*b^3 + 7*A*a^2*b^5 - 2*A*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*sqrt(a^2 - b^2)) - 3*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 + 3*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - (6*C*a^8*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^7*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 15*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^8*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^8*tan(1/2*d*x + 1/2*c)^3 + 72*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 16*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 - 116*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 28*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 56*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^8*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^8*tan(1/2*d*x + 1/2*c) + 6*C*a^7*b*tan(1/2*d*x + 1/2*c) + 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c) + 12*C*a^6*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c) + 27*C*a^5*b^3*tan(1/2*d*x + 1/2*c) - 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c) + 12*C*a^4*b^4*tan(1/2*d*x + 1/2*c) - 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c) - 3*C*a^3*b^5*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c) + 15*A*a*b^7*tan(1/2*d*x + 1/2*c) + 6*A*b^8*tan(1/2*d*x + 1/2*c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
591,1,871,0,6.246712," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{8} + 20 \, A a^{6} b^{2} + 3 \, C a^{6} b^{2} - 35 \, A a^{4} b^{4} + 28 \, A a^{2} b^{6} - 8 \, A b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{12 \, A b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} - \frac{12 \, A b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}} + \frac{18 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 236 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}} + \frac{6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{4}}}{3 \, d}"," ",0,"-1/3*(3*(2*C*a^8 + 20*A*a^6*b^2 + 3*C*a^6*b^2 - 35*A*a^4*b^4 + 28*A*a^2*b^6 - 8*A*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*sqrt(a^2 - b^2)) + 12*A*b*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 - 12*A*b*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5 + (18*C*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 42*A*a*b^8*tan(1/2*d*x + 1/2*c)^5 + 18*A*b^9*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^8*b*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 - 32*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 - 236*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 + 152*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 - 36*A*b^9*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^8*b*tan(1/2*d*x + 1/2*c) + 27*C*a^7*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c) + 6*C*a^6*b^3*tan(1/2*d*x + 1/2*c) + 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c) + 3*C*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c) + 6*C*a^4*b^5*tan(1/2*d*x + 1/2*c) - 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c) - 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c) + 42*A*a*b^8*tan(1/2*d*x + 1/2*c) + 18*A*b^9*tan(1/2*d*x + 1/2*c))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) + 6*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^4))/d","B",0
592,1,1070,0,1.201954," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(8 \, C a^{8} b + 40 \, A a^{6} b^{3} - 8 \, C a^{6} b^{3} - 84 \, A a^{4} b^{5} + 7 \, C a^{4} b^{5} + 69 \, A a^{2} b^{7} - 2 \, C a^{2} b^{7} - 20 \, A b^{9}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(36 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 392 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 284 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}} + \frac{3 \, {\left(A a^{2} + 2 \, C a^{2} + 20 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{6}} - \frac{3 \, {\left(A a^{2} + 2 \, C a^{2} + 20 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{6}} + \frac{6 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{5}}}{6 \, d}"," ",0,"1/6*(6*(8*C*a^8*b + 40*A*a^6*b^3 - 8*C*a^6*b^3 - 84*A*a^4*b^5 + 7*C*a^4*b^5 + 69*A*a^2*b^7 - 2*C*a^2*b^7 - 20*A*b^9)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*sqrt(a^2 - b^2)) + 2*(36*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 + 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 + 45*C*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 - 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 + 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 - 81*A*a*b^9*tan(1/2*d*x + 1/2*c)^5 + 36*A*b^10*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^3 + 180*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 - 116*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 - 392*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 + 56*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 + 284*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 - 72*A*b^10*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^8*b^2*tan(1/2*d*x + 1/2*c) + 60*C*a^7*b^3*tan(1/2*d*x + 1/2*c) + 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c) - 6*C*a^6*b^4*tan(1/2*d*x + 1/2*c) + 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c) - 45*C*a^5*b^5*tan(1/2*d*x + 1/2*c) - 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c) - 6*C*a^4*b^6*tan(1/2*d*x + 1/2*c) - 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c) + 15*C*a^3*b^7*tan(1/2*d*x + 1/2*c) - 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c) + 6*C*a^2*b^8*tan(1/2*d*x + 1/2*c) + 81*A*a*b^9*tan(1/2*d*x + 1/2*c) + 36*A*b^10*tan(1/2*d*x + 1/2*c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) + 3*(A*a^2 + 2*C*a^2 + 20*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^6 - 3*(A*a^2 + 2*C*a^2 + 20*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^6 + 6*(A*a*tan(1/2*d*x + 1/2*c)^3 + 8*A*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) - 8*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^5))/d","B",0
593,1,370,0,0.438787," ","integrate(cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, a^{4} - 4 \, a^{2} b^{2} - b^{4}\right)} {\left(d x + c\right)}}{b^{5}} + \frac{48 \, {\left(a^{5} - a^{3} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{5}} - \frac{2 \, {\left(24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 32 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, 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} b^{4}}}{24 \, d}"," ",0,"-1/24*(3*(8*a^4 - 4*a^2*b^2 - b^4)*(d*x + c)/b^5 + 48*(a^5 - a^3*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^5) - 2*(24*a^3*tan(1/2*d*x + 1/2*c)^7 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 3*b^3*tan(1/2*d*x + 1/2*c)^7 + 72*a^3*tan(1/2*d*x + 1/2*c)^5 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 32*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 21*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 32*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 21*b^3*tan(1/2*d*x + 1/2*c)^3 + 24*a^3*tan(1/2*d*x + 1/2*c) - 12*a^2*b*tan(1/2*d*x + 1/2*c) - 3*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^4))/d","B",0
594,1,229,0,1.382838," ","integrate(cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{3} - a b^{2}\right)} {\left(d x + c\right)}}{b^{4}} + \frac{12 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} - \frac{2 \, {\left(6 \, a^{2} \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} + 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*a^3 - a*b^2)*(d*x + c)/b^4 + 12*(a^4 - a^2*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) - 2*(6*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*a^2*tan(1/2*d*x + 1/2*c)^3 - 8*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*tan(1/2*d*x + 1/2*c) - 3*a*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^3))/d","A",0
595,1,186,0,0.328352," ","integrate(cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, a^{2} - b^{2}\right)} {\left(d x + c\right)}}{b^{3}} + \frac{4 \, {\left(a^{3} - a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{3}} - \frac{2 \, {\left(2 \, 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} + 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} b^{2}}}{2 \, d}"," ",0,"-1/2*((2*a^2 - b^2)*(d*x + c)/b^3 + 4*(a^3 - a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^3) - 2*(2*a*tan(1/2*d*x + 1/2*c)^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*b^2))/d","A",0
596,1,122,0,0.394737," ","integrate((1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} a}{b^{2}} + \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}} - \frac{2 \, \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}}{d}"," ",0,"((d*x + c)*a/b^2 + 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 - 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b))/d","A",0
597,1,130,0,0.431722," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{d x + c}{b} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \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}}}{a b}}{d}"," ",0,"-((d*x + c)/b - log(abs(tan(1/2*d*x + 1/2*c) + 1))/a + log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*sqrt(a^2 - b^2)/(a*b))/d","A",0
598,1,150,0,0.416713," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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^{2}} - \frac{b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \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}}}{a^{2}} + \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a}}{d}"," ",0,"-(b*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - b*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 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 + 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","B",0
599,1,219,0,1.863335," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(a^{2} - 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{{\left(a^{2} - 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{4 \, {\left(a^{2} b - b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3}} - \frac{2 \, {\left(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}}}{2 \, d}"," ",0,"-1/2*((a^2 - 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (a^2 - 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 4*(a^2*b - b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3) - 2*(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^2))/d","B",0
600,1,266,0,1.896639," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a^{2} b - 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3 \, {\left(a^{2} b - 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{12 \, {\left(a^{2} b^{2} - b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4}} - \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"1/6*(3*(a^2*b - 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3*(a^2*b - 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 12*(a^2*b^2 - b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4) - 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*b^2*tan(1/2*d*x + 1/2*c)^5 + 8*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*a*b*tan(1/2*d*x + 1/2*c) + 6*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^3))/d","A",0
601,1,421,0,0.953843," ","integrate(cos(d*x+c)^4*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{48 \, a^{4} \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^{5}} - \frac{3 \, {\left(40 \, a^{4} - 12 \, a^{2} b^{2} - b^{4}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{48 \, {\left(5 \, a^{5} - 4 \, a^{3} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{6}} + \frac{2 \, {\left(96 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 288 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 64 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 64 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 96 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, 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} b^{5}}}{24 \, d}"," ",0,"1/24*(48*a^4*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^5) - 3*(40*a^4 - 12*a^2*b^2 - b^4)*(d*x + c)/b^6 - 48*(5*a^5 - 4*a^3*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^6) + 2*(96*a^3*tan(1/2*d*x + 1/2*c)^7 + 36*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 3*b^3*tan(1/2*d*x + 1/2*c)^7 + 288*a^3*tan(1/2*d*x + 1/2*c)^5 + 36*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 64*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 21*b^3*tan(1/2*d*x + 1/2*c)^5 + 288*a^3*tan(1/2*d*x + 1/2*c)^3 - 36*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 64*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 21*b^3*tan(1/2*d*x + 1/2*c)^3 + 96*a^3*tan(1/2*d*x + 1/2*c) - 36*a^2*b*tan(1/2*d*x + 1/2*c) - 3*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^5))/d","A",0
602,1,280,0,0.866348," ","integrate(cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} b^{4}} - \frac{3 \, {\left(4 \, a^{3} - a b^{2}\right)} {\left(d x + c\right)}}{b^{5}} - \frac{6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{5}} + \frac{2 \, {\left(9 \, a^{2} \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} + 18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{4}}}{3 \, d}"," ",0,"-1/3*(6*a^3*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^4) - 3*(4*a^3 - a*b^2)*(d*x + c)/b^5 - 6*(4*a^4 - 3*a^2*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^5) + 2*(9*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*a*b*tan(1/2*d*x + 1/2*c)^5 + 18*a^2*tan(1/2*d*x + 1/2*c)^3 - 4*b^2*tan(1/2*d*x + 1/2*c)^3 + 9*a^2*tan(1/2*d*x + 1/2*c) - 3*a*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^4))/d","A",0
603,1,238,0,2.856621," ","integrate(cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} b^{3}} - \frac{{\left(6 \, a^{2} - b^{2}\right)} {\left(d x + c\right)}}{b^{4}} - \frac{4 \, {\left(3 \, a^{3} - 2 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} + \frac{2 \, {\left(4 \, 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} + 4 \, 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} b^{3}}}{2 \, d}"," ",0,"1/2*(4*a^2*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)*b^3) - (6*a^2 - b^2)*(d*x + c)/b^4 - 4*(3*a^3 - 2*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) + 2*(4*a*tan(1/2*d*x + 1/2*c)^3 + b*tan(1/2*d*x + 1/2*c)^3 + 4*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*b^3))/d","A",0
604,1,422,0,3.928397," ","integrate(cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{{\left(\sqrt{a^{2} - b^{2}} {\left(2 \, a - b\right)} {\left| -a + b \right|} {\left| b \right|} + {\left(4 \, a^{2} - 2 \, a b - b^{2}\right)} \sqrt{a^{2} - b^{2}} {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{a b^{2} + \sqrt{a^{2} b^{4} - {\left(a b^{2} + b^{3}\right)} {\left(a b^{2} - b^{3}\right)}}}{a b^{2} - b^{3}}}}\right)\right)}}{{\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} b^{2} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} {\left| b \right|}} + \frac{{\left(4 \, a^{2} - 2 \, a b - b^{2} - 2 \, a {\left| b \right|} + b {\left| 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 b^{2} - \sqrt{a^{2} b^{4} - {\left(a b^{2} + b^{3}\right)} {\left(a b^{2} - b^{3}\right)}}}{a b^{2} - b^{3}}}}\right)\right)}}{b^{4} - a b^{2} {\left| b \right|}} + \frac{2 \, {\left(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)^{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(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)} b^{2}}}{d}"," ",0,"-((sqrt(a^2 - b^2)*(2*a - b)*abs(-a + b)*abs(b) + (4*a^2 - 2*a*b - b^2)*sqrt(a^2 - b^2)*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt((a*b^2 + sqrt(a^2*b^4 - (a*b^2 + b^3)*(a*b^2 - b^3)))/(a*b^2 - b^3))))/((a^2*b^2 - 2*a*b^3 + b^4)*b^2 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*abs(b)) + (4*a^2 - 2*a*b - b^2 - 2*a*abs(b) + b*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(tan(1/2*d*x + 1/2*c)/sqrt((a*b^2 - sqrt(a^2*b^4 - (a*b^2 + b^3)*(a*b^2 - b^3)))/(a*b^2 - b^3))))/(b^4 - a*b^2*abs(b)) + 2*(2*a*tan(1/2*d*x + 1/2*c)^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))/((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)*b^2))/d","B",0
605,1,140,0,0.387370," ","integrate((1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\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)} a}{\sqrt{a^{2} - b^{2}} b^{2}} + \frac{d x + c}{b^{2}} - \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} b}}{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/(sqrt(a^2 - b^2)*b^2) + (d*x + c)/b^2 - 2*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)*b))/d","A",0
606,1,165,0,0.425790," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\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)} b}{\sqrt{a^{2} - b^{2}} a^{2}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} a}}{d}"," ",0,"-(2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*b/(sqrt(a^2 - b^2)*a^2) - log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 + log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 2*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)*a))/d","A",0
607,1,235,0,0.513629," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \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^{2} - 2 \, b^{2}\right)}}{\sqrt{a^{2} - b^{2}} a^{3}} + \frac{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)}{{\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)} a^{2}}\right)}}{d}"," ",0,"-2*(b*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - b*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^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 - 2*b^2)/(sqrt(a^2 - b^2)*a^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))/((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^2))/d","B",0
608,1,269,0,0.580982," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} a^{3}} + \frac{{\left(a^{2} - 6 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{{\left(a^{2} - 6 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{4 \, {\left(2 \, a^{2} b - 3 \, 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^{4}} - \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, 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) - 4 \, 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*b^2*tan(1/2*d*x + 1/2*c)/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)*a^3) + (a^2 - 6*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - (a^2 - 6*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 4*(2*a^2*b - 3*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^4) - 2*(a*tan(1/2*d*x + 1/2*c)^3 + 4*b*tan(1/2*d*x + 1/2*c)^3 + a*tan(1/2*d*x + 1/2*c) - 4*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
609,1,316,0,0.612164," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} a^{4}} + \frac{3 \, {\left(a^{2} b - 4 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} - \frac{3 \, {\left(a^{2} b - 4 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}} + \frac{6 \, {\left(3 \, a^{2} b^{2} - 4 \, 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^{5}} - \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{4}}}{3 \, d}"," ",0,"1/3*(6*b^3*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^4) + 3*(a^2*b - 4*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 - 3*(a^2*b - 4*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5 + 6*(3*a^2*b^2 - 4*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^5) - 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 + 9*b^2*tan(1/2*d*x + 1/2*c)^5 + 4*a^2*tan(1/2*d*x + 1/2*c)^3 - 18*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*a*b*tan(1/2*d*x + 1/2*c) + 9*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
610,1,435,0,1.088754," ","integrate(cos(d*x+c)^4*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(20 \, a^{6} - 33 \, a^{4} b^{2} + 12 \, a^{2} b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{6} - b^{8}\right)} \sqrt{a^{2} - b^{2}}} - \frac{6 \, {\left(8 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(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{3 \, {\left(20 \, a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{2 \, {\left(36 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{5}}}{6 \, d}"," ",0,"1/6*(6*(20*a^6 - 33*a^4*b^2 + 12*a^2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^6 - b^8)*sqrt(a^2 - b^2)) - 6*(8*a^6*tan(1/2*d*x + 1/2*c)^3 - 9*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 7*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 8*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*a^6*tan(1/2*d*x + 1/2*c) + 9*a^5*b*tan(1/2*d*x + 1/2*c) - 7*a^4*b^2*tan(1/2*d*x + 1/2*c) - 8*a^3*b^3*tan(1/2*d*x + 1/2*c))/((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*(20*a^3 - 3*a*b^2)*(d*x + c)/b^6 - 2*(36*a^2*tan(1/2*d*x + 1/2*c)^5 + 9*a*b*tan(1/2*d*x + 1/2*c)^5 + 72*a^2*tan(1/2*d*x + 1/2*c)^3 - 8*b^2*tan(1/2*d*x + 1/2*c)^3 + 36*a^2*tan(1/2*d*x + 1/2*c) - 9*a*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^5))/d","A",0
611,1,1194,0,3.057262," ","integrate(cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(24 \, a^{7} b^{4} - 12 \, a^{6} b^{5} - 56 \, a^{5} b^{6} + 25 \, a^{4} b^{7} + 39 \, a^{3} b^{8} - 14 \, a^{2} b^{9} - 7 \, a b^{10} + b^{11} + 12 \, a^{4} {\left| -a^{2} b^{5} + b^{7} \right|} - 6 \, a^{3} b {\left| -a^{2} b^{5} + b^{7} \right|} - 13 \, a^{2} b^{2} {\left| -a^{2} b^{5} + b^{7} \right|} + 5 \, a b^{3} {\left| -a^{2} b^{5} + b^{7} \right|} + b^{4} {\left| -a^{2} b^{5} + b^{7} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{4 \, a^{3} b^{4} - 4 \, a b^{6} + \sqrt{-16 \, {\left(a^{3} b^{4} + a^{2} b^{5} - a b^{6} - b^{7}\right)} {\left(a^{3} b^{4} - a^{2} b^{5} - a b^{6} + b^{7}\right)} + 16 \, {\left(a^{3} b^{4} - a b^{6}\right)}^{2}}}{a^{3} b^{4} - a^{2} b^{5} - a b^{6} + b^{7}}}}\right)\right)}}{a^{3} b^{4} {\left| -a^{2} b^{5} + b^{7} \right|} - a b^{6} {\left| -a^{2} b^{5} + b^{7} \right|} + {\left(a^{2} b^{5} - b^{7}\right)}^{2}} - \frac{{\left({\left(12 \, a^{4} - 6 \, a^{3} b - 13 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \sqrt{a^{2} - b^{2}} {\left| -a^{2} b^{5} + b^{7} \right|} {\left| -a + b \right|} - {\left(24 \, a^{7} b^{4} - 12 \, a^{6} b^{5} - 56 \, a^{5} b^{6} + 25 \, a^{4} b^{7} + 39 \, a^{3} b^{8} - 14 \, a^{2} b^{9} - 7 \, a b^{10} + b^{11}\right)} \sqrt{a^{2} - b^{2}} {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{4 \, a^{3} b^{4} - 4 \, a b^{6} - \sqrt{-16 \, {\left(a^{3} b^{4} + a^{2} b^{5} - a b^{6} - b^{7}\right)} {\left(a^{3} b^{4} - a^{2} b^{5} - a b^{6} + b^{7}\right)} + 16 \, {\left(a^{3} b^{4} - a b^{6}\right)}^{2}}}{a^{3} b^{4} - a^{2} b^{5} - a b^{6} + b^{7}}}}\right)\right)}}{{\left(a^{2} b^{5} - b^{7}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{5} b^{4} - 2 \, a^{4} b^{5} + 2 \, a^{2} b^{7} - a b^{8}\right)} {\left| -a^{2} b^{5} + b^{7} \right|}} + \frac{2 \, {\left(12 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 18 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 37 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 14 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 37 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 14 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\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}}}{2 \, d}"," ",0,"1/2*((24*a^7*b^4 - 12*a^6*b^5 - 56*a^5*b^6 + 25*a^4*b^7 + 39*a^3*b^8 - 14*a^2*b^9 - 7*a*b^10 + b^11 + 12*a^4*abs(-a^2*b^5 + b^7) - 6*a^3*b*abs(-a^2*b^5 + b^7) - 13*a^2*b^2*abs(-a^2*b^5 + b^7) + 5*a*b^3*abs(-a^2*b^5 + b^7) + b^4*abs(-a^2*b^5 + b^7))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*tan(1/2*d*x + 1/2*c)/sqrt((4*a^3*b^4 - 4*a*b^6 + sqrt(-16*(a^3*b^4 + a^2*b^5 - a*b^6 - b^7)*(a^3*b^4 - a^2*b^5 - a*b^6 + b^7) + 16*(a^3*b^4 - a*b^6)^2))/(a^3*b^4 - a^2*b^5 - a*b^6 + b^7))))/(a^3*b^4*abs(-a^2*b^5 + b^7) - a*b^6*abs(-a^2*b^5 + b^7) + (a^2*b^5 - b^7)^2) - ((12*a^4 - 6*a^3*b - 13*a^2*b^2 + 5*a*b^3 + b^4)*sqrt(a^2 - b^2)*abs(-a^2*b^5 + b^7)*abs(-a + b) - (24*a^7*b^4 - 12*a^6*b^5 - 56*a^5*b^6 + 25*a^4*b^7 + 39*a^3*b^8 - 14*a^2*b^9 - 7*a*b^10 + b^11)*sqrt(a^2 - b^2)*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*tan(1/2*d*x + 1/2*c)/sqrt((4*a^3*b^4 - 4*a*b^6 - sqrt(-16*(a^3*b^4 + a^2*b^5 - a*b^6 - b^7)*(a^3*b^4 - a^2*b^5 - a*b^6 + b^7) + 16*(a^3*b^4 - a*b^6)^2))/(a^3*b^4 - a^2*b^5 - a*b^6 + b^7))))/((a^2*b^5 - b^7)^2*(a^2 - 2*a*b + b^2) - (a^5*b^4 - 2*a^4*b^5 + 2*a^2*b^7 - a*b^8)*abs(-a^2*b^5 + b^7)) + 2*(12*a^5*tan(1/2*d*x + 1/2*c)^7 - 18*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 7*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 + 18*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 - 4*a*b^4*tan(1/2*d*x + 1/2*c)^7 - b^5*tan(1/2*d*x + 1/2*c)^7 + 36*a^5*tan(1/2*d*x + 1/2*c)^5 - 18*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 37*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 14*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 4*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*b^5*tan(1/2*d*x + 1/2*c)^5 + 36*a^5*tan(1/2*d*x + 1/2*c)^3 + 18*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 37*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 14*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 3*b^5*tan(1/2*d*x + 1/2*c)^3 + 12*a^5*tan(1/2*d*x + 1/2*c) + 18*a^4*b*tan(1/2*d*x + 1/2*c) - 7*a^3*b^2*tan(1/2*d*x + 1/2*c) - 18*a^2*b^3*tan(1/2*d*x + 1/2*c) - 4*a*b^4*tan(1/2*d*x + 1/2*c) + b^5*tan(1/2*d*x + 1/2*c))/((a^2*b^4 - b^6)*(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))/d","B",0
612,1,333,0,0.763520," ","integrate(cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(6 \, a^{4} - 9 \, a^{2} b^{2} + 2 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\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)}^{2}} + \frac{3 \, {\left(d x + c\right)} a}{b^{4}} - \frac{2 \, \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*a^4 - 9*a^2*b^2 + 2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - (4*a^4*tan(1/2*d*x + 1/2*c)^3 - 5*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*tan(1/2*d*x + 1/2*c) + 5*a^3*b*tan(1/2*d*x + 1/2*c) - 3*a^2*b^2*tan(1/2*d*x + 1/2*c) - 4*a*b^3*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)^2) + 3*(d*x + c)*a/b^4 - 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b^3))/d","A",0
613,1,290,0,0.661360," ","integrate(cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, a^{3} - 3 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2} 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) - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(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}} + \frac{d x + c}{b^{3}}}{d}"," ",0,"-((2*a^3 - 3*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^3 - b^5)*sqrt(a^2 - b^2)) - (2*a^3*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*b*tan(1/2*d*x + 1/2*c)^3 - a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*a^3*tan(1/2*d*x + 1/2*c) + 3*a^2*b*tan(1/2*d*x + 1/2*c) - a*b^2*tan(1/2*d*x + 1/2*c) - 2*b^3*tan(1/2*d*x + 1/2*c))/((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*x + c)/b^3)/d","B",0
614,1,177,0,0.473294," ","integrate((1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{\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)}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} - \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} - 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)}{{\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} {\left(a^{2} - b^{2}\right)}}}{d}"," ",0,"-((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)^(3/2) - (a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^3 - a*tan(1/2*d*x + 1/2*c) - 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)^2*(a^2 - b^2)))/d","A",0
615,1,311,0,3.705553," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(3 \, a^{2} b - 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^{5} - a^{3} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} 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) - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - a^{2} 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)}^{2}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}}}{d}"," ",0,"-((3*a^2*b - 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^5 - a^3*b^2)*sqrt(a^2 - b^2)) + (2*a^3*tan(1/2*d*x + 1/2*c)^3 - a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*a^3*tan(1/2*d*x + 1/2*c) + a^2*b*tan(1/2*d*x + 1/2*c) - 3*a*b^2*tan(1/2*d*x + 1/2*c) - 2*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - a^2*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) - log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 + log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3)/d","B",0
616,1,357,0,0.758018," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a^{4} - 9 \, a^{2} b^{2} + 6 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{4 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\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)}^{2}} - \frac{3 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} + \frac{3 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}}}{d}"," ",0,"((2*a^4 - 9*a^2*b^2 + 6*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - a^4*b^2)*sqrt(a^2 - b^2)) + (4*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*a^3*b*tan(1/2*d*x + 1/2*c) + 3*a^2*b^2*tan(1/2*d*x + 1/2*c) - 5*a*b^3*tan(1/2*d*x + 1/2*c) - 4*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)^2) - 3*b*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 + 3*b*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - 2*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3))/d","A",0
617,1,637,0,2.958836," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(6 \, a^{4} b - 19 \, a^{2} b^{3} + 12 \, 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} - a^{5} b^{2}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 18 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 14 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 37 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 37 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, 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)^{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}} + \frac{{\left(a^{2} - 12 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} - \frac{{\left(a^{2} - 12 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}}}{2 \, d}"," ",0,"-1/2*(2*(6*a^4*b - 19*a^2*b^3 + 12*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 - a^5*b^2)*sqrt(a^2 - b^2)) - 2*(a^5*tan(1/2*d*x + 1/2*c)^7 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 18*a^3*b^2*tan(1/2*d*x + 1/2*c)^7 + 7*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 18*a*b^4*tan(1/2*d*x + 1/2*c)^7 - 12*b^5*tan(1/2*d*x + 1/2*c)^7 + 3*a^5*tan(1/2*d*x + 1/2*c)^5 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 14*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 37*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 18*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 36*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*a^5*tan(1/2*d*x + 1/2*c)^3 - 4*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 14*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 37*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 18*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 36*b^5*tan(1/2*d*x + 1/2*c)^3 + a^5*tan(1/2*d*x + 1/2*c) - 4*a^4*b*tan(1/2*d*x + 1/2*c) - 18*a^3*b^2*tan(1/2*d*x + 1/2*c) - 7*a^2*b^3*tan(1/2*d*x + 1/2*c) + 18*a*b^4*tan(1/2*d*x + 1/2*c) + 12*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)^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) + (a^2 - 12*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 - (a^2 - 12*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5)/d","B",0
618,1,471,0,1.436044," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(12 \, a^{4} b^{2} - 33 \, a^{2} b^{4} + 20 \, 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} - a^{6} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{6 \, {\left(8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{7} - a^{5} 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)}^{2}} + \frac{3 \, {\left(3 \, a^{2} b - 20 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{6}} - \frac{3 \, {\left(3 \, a^{2} b - 20 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{6}} - \frac{2 \, {\left(9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, 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^{5}}}{6 \, d}"," ",0,"1/6*(6*(12*a^4*b^2 - 33*a^2*b^4 + 20*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 - a^6*b^2)*sqrt(a^2 - b^2)) + 6*(8*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 9*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 8*b^6*tan(1/2*d*x + 1/2*c)^3 + 8*a^3*b^3*tan(1/2*d*x + 1/2*c) + 7*a^2*b^4*tan(1/2*d*x + 1/2*c) - 9*a*b^5*tan(1/2*d*x + 1/2*c) - 8*b^6*tan(1/2*d*x + 1/2*c))/((a^7 - a^5*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) + 3*(3*a^2*b - 20*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^6 - 3*(3*a^2*b - 20*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^6 - 2*(9*a*b*tan(1/2*d*x + 1/2*c)^5 + 36*b^2*tan(1/2*d*x + 1/2*c)^5 + 8*a^2*tan(1/2*d*x + 1/2*c)^3 - 72*b^2*tan(1/2*d*x + 1/2*c)^3 - 9*a*b*tan(1/2*d*x + 1/2*c) + 36*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^5))/d","A",0
619,1,39,0,0.392453," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} a - \frac{2 \, 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 - 2*b*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
620,1,254,0,1.309143," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(\sqrt{a^{2} - b^{2}} {\left(a + b\right)} {\left| a - b \right|} {\left| b \right|} + \sqrt{a^{2} - b^{2}} {\left(3 \, a b - b^{2}\right)} {\left| a - b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} + \frac{{\left(3 \, a b - b^{2} - a {\left| b \right|} - b {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{b^{2} - a {\left| b \right|}}}{d}"," ",0,"((sqrt(a^2 - b^2)*(a + b)*abs(a - b)*abs(b) + sqrt(a^2 - b^2)*(3*a*b - b^2)*abs(a - b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) + (3*a*b - b^2 - a*abs(b) - b*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/(b^2 - a*abs(b)))/d","B",0
621,1,143,0,0.623869," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{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} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} {\left(a^{2} - b^{2}\right)}} - \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^{2} + b^{2}\right)}}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}}\right)}}{d}"," ",0,"-2*(2*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)) - (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)/(a^2 - b^2)^(3/2))/d","A",0
622,1,255,0,0.637310," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(a^{3} + 2 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{4} \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}}\right)}}{d}"," ",0,"-2*((a^3 + 2*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (3*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 2*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - b^4*tan(1/2*d*x + 1/2*c)^3 + 3*a^3*b*tan(1/2*d*x + 1/2*c) + 2*a^2*b^2*tan(1/2*d*x + 1/2*c) + b^4*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","A",0
623,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
624,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a), x)","F",0
626,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
627,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
628,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
629,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
630,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
632,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
634,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
635,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
636,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
637,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^5, x)","F",0
638,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
639,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
640,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2), x)","F",0
641,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
642,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
643,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
644,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
645,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^5, x)","F",0
646,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""giac"")","\int -{\left(b^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(-(b^2*cos(d*x + c)^2 - a^2)*(b*cos(d*x + c) + a)^(3/2), x)","F",0
647,0,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int -{\left(b^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(-(b^2*cos(d*x + c)^2 - a^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
648,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
649,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
650,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
651,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/sqrt(b*cos(d*x + c) + a), x)","F",0
652,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
653,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
654,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
655,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{4}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^4/sqrt(b*cos(d*x + c) + a), x)","F",0
656,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^3/(b*cos(d*x + c) + a)^(3/2), x)","F",0
657,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
658,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
659,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
660,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
661,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
662,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^3/(b*cos(d*x + c) + a)^(3/2), x)","F",0
663,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^3/(b*cos(d*x + c) + a)^(5/2), x)","F",0
664,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
665,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
666,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
667,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
668,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
669,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(b*cos(d*x + c) + a)^(7/2), x)","F",0
670,0,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int -\frac{b^{2} \cos\left(d x + c\right)^{2} - a^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(-(b^2*cos(d*x + c)^2 - a^2)/sqrt(b*cos(d*x + c) + a), x)","F",0
671,0,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int -\frac{b^{2} \cos\left(d x + c\right)^{2} - a^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(b^2*cos(d*x + c)^2 - a^2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
672,0,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int -\frac{b^{2} \cos\left(d x + c\right)^{2} - a^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(b^2*cos(d*x + c)^2 - a^2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
673,0,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int -\frac{b^{2} \cos\left(d x + c\right)^{2} - a^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(b^2*cos(d*x + c)^2 - a^2)/(b*cos(d*x + c) + a)^(7/2), x)","F",0
674,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
675,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
676,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
677,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
678,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
679,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
680,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
681,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
682,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
683,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
684,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
685,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
686,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
687,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
688,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
689,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
690,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
691,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
692,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
693,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
694,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
695,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
696,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sqrt(cos(d*x + c)), x)","F",0
697,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/sqrt(cos(d*x + c)), x)","F",0
698,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(3/2), x)","F",0
699,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(5/2), x)","F",0
700,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(7/2), x)","F",0
701,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(9/2), x)","F",0
702,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(11/2), x)","F",0
703,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(13/2), x)","F",0
704,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(7/2)/(b*cos(d*x + c) + a), x)","F",0
705,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
706,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
707,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
708,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
709,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
710,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
711,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
712,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
713,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(11/2)), x)","F",0
714,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
715,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
716,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
717,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
718,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
719,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
720,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(7/2)), x)","F",0
721,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^3, x)","F",0
722,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^3, x)","F",0
723,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^3, x)","F",0
724,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
725,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
726,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
727,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
728,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
729,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
731,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
733,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
734,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
735,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
736,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
737,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
738,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
739,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
740,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
741,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
742,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
747,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
748,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
749,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
750,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
751,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
752,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
753,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
754,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
755,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
756,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
757,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
758,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
759,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
760,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
761,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
762,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
763,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
764,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
765,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
766,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*cos(d*x + c)^m, x)","F",0
767,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^m, x)","F",0
768,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{m}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^m/(b*cos(d*x + c) + a), x)","F",0
769,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{m}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^m/(b*cos(d*x + c) + a)^2, x)","F",0
770,1,89,0,0.192750," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, B a + 3 \, C b\right)} x + \frac{C b \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(C a + B b\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(B a + C b\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{3 \, {\left(C a + B b\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/8*(4*B*a + 3*C*b)*x + 1/32*C*b*sin(4*d*x + 4*c)/d + 1/12*(C*a + B*b)*sin(3*d*x + 3*c)/d + 1/4*(B*a + C*b)*sin(2*d*x + 2*c)/d + 3/4*(C*a + B*b)*sin(d*x + c)/d","A",0
771,1,68,0,0.190836," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(C a + B b\right)} x + \frac{C b \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(C a + B b\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, B a + 3 \, C b\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/2*(C*a + B*b)*x + 1/12*C*b*sin(3*d*x + 3*c)/d + 1/4*(C*a + B*b)*sin(2*d*x + 2*c)/d + 1/4*(4*B*a + 3*C*b)*sin(d*x + c)/d","A",0
772,1,121,0,0.221264," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{{\left(2 \, B a + C b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((2*B*a + C*b)*(d*x + c) + 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*b*tan(1/2*d*x + 1/2*c)^3 - C*b*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*tan(1/2*d*x + 1/2*c) + 2*B*b*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
773,1,79,0,0.227698," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,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(C a + B b\right)} {\left(d x + c\right)} + \frac{2 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(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)) + (C*a + B*b)*(d*x + c) + 2*C*b*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
774,1,84,0,0.257848," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} C b + {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, 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)*C*b + (C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*B*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
775,1,151,0,0.356098," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{{\left(B a + 2 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a + 2 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((B*a + 2*C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a + 2*C*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(B*a*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 + B*a*tan(1/2*d*x + 1/2*c) + 2*C*a*tan(1/2*d*x + 1/2*c) + 2*B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
776,1,210,0,0.261805," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(C a + B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(C*a + B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*B*a*tan(1/2*d*x + 1/2*c)^5 - 3*C*a*tan(1/2*d*x + 1/2*c)^5 - 3*B*b*tan(1/2*d*x + 1/2*c)^5 + 6*C*b*tan(1/2*d*x + 1/2*c)^5 - 4*B*a*tan(1/2*d*x + 1/2*c)^3 - 12*C*b*tan(1/2*d*x + 1/2*c)^3 + 6*B*a*tan(1/2*d*x + 1/2*c) + 3*C*a*tan(1/2*d*x + 1/2*c) + 3*B*b*tan(1/2*d*x + 1/2*c) + 6*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
777,1,304,0,0.243973," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, B a + 4 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, B a + 4 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*B*a + 4*C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*B*a + 4*C*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*B*a*tan(1/2*d*x + 1/2*c)^7 - 24*C*a*tan(1/2*d*x + 1/2*c)^7 - 24*B*b*tan(1/2*d*x + 1/2*c)^7 + 12*C*b*tan(1/2*d*x + 1/2*c)^7 + 9*B*a*tan(1/2*d*x + 1/2*c)^5 + 40*C*a*tan(1/2*d*x + 1/2*c)^5 + 40*B*b*tan(1/2*d*x + 1/2*c)^5 - 12*C*b*tan(1/2*d*x + 1/2*c)^5 + 9*B*a*tan(1/2*d*x + 1/2*c)^3 - 40*C*a*tan(1/2*d*x + 1/2*c)^3 - 40*B*b*tan(1/2*d*x + 1/2*c)^3 - 12*C*b*tan(1/2*d*x + 1/2*c)^3 + 15*B*a*tan(1/2*d*x + 1/2*c) + 24*C*a*tan(1/2*d*x + 1/2*c) + 24*B*b*tan(1/2*d*x + 1/2*c) + 12*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
778,1,156,0,0.294648," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{2} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(4 \, B a^{2} + 6 \, C a b + 3 \, B b^{2}\right)} x + \frac{{\left(2 \, C a b + B b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, C a^{2} + 8 \, B a b + 5 \, C b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(B a^{2} + 2 \, C a b + B b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(6 \, C a^{2} + 12 \, B a b + 5 \, C b^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*b^2*sin(5*d*x + 5*c)/d + 1/8*(4*B*a^2 + 6*C*a*b + 3*B*b^2)*x + 1/32*(2*C*a*b + B*b^2)*sin(4*d*x + 4*c)/d + 1/48*(4*C*a^2 + 8*B*a*b + 5*C*b^2)*sin(3*d*x + 3*c)/d + 1/4*(B*a^2 + 2*C*a*b + B*b^2)*sin(2*d*x + 2*c)/d + 1/8*(6*C*a^2 + 12*B*a*b + 5*C*b^2)*sin(d*x + c)/d","A",0
779,1,124,0,0.203647," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(4 \, C a^{2} + 8 \, B a b + 3 \, C b^{2}\right)} x + \frac{{\left(2 \, C a b + B b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(C a^{2} + 2 \, B a b + C b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, B a^{2} + 6 \, C a b + 3 \, B b^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/32*C*b^2*sin(4*d*x + 4*c)/d + 1/8*(4*C*a^2 + 8*B*a*b + 3*C*b^2)*x + 1/12*(2*C*a*b + B*b^2)*sin(3*d*x + 3*c)/d + 1/4*(C*a^2 + 2*B*a*b + C*b^2)*sin(2*d*x + 2*c)/d + 1/4*(4*B*a^2 + 6*C*a*b + 3*B*b^2)*sin(d*x + c)/d","A",0
780,1,254,0,0.482012," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{3 \, {\left(2 \, B a^{2} + 2 \, C a b + B b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*B*a^2 + 2*C*a*b + B*b^2)*(d*x + c) + 2*(6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c) + 12*B*a*b*tan(1/2*d*x + 1/2*c) + 6*C*a*b*tan(1/2*d*x + 1/2*c) + 3*B*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
781,1,178,0,0.280044," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,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(2 \, C a^{2} + 4 \, B a b + C b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*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)) + (2*C*a^2 + 4*B*a*b + C*b^2)*(d*x + c) + 2*(4*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^2*tan(1/2*d*x + 1/2*c)^3 - C*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*a*b*tan(1/2*d*x + 1/2*c) + 2*B*b^2*tan(1/2*d*x + 1/2*c) + C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
782,1,152,0,0.383519," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(2 \, C a b + B b^{2}\right)} {\left(d x + c\right)} + {\left(C a^{2} + 2 \, B a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(C a^{2} + 2 \, B a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((2*C*a*b + B*b^2)*(d*x + c) + (C*a^2 + 2*B*a*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (C*a^2 + 2*B*a*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(B*a^2*tan(1/2*d*x + 1/2*c)^3 - C*b^2*tan(1/2*d*x + 1/2*c)^3 + B*a^2*tan(1/2*d*x + 1/2*c) + C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
783,1,190,0,0.439130," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} C b^{2} + {\left(B a^{2} + 4 \, C a b + 2 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a^{2} + 4 \, C a b + 2 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*b^2 + (B*a^2 + 4*C*a*b + 2*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a^2 + 4*C*a*b + 2*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(B*a^2*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b*tan(1/2*d*x + 1/2*c)^3 + B*a^2*tan(1/2*d*x + 1/2*c) + 2*C*a^2*tan(1/2*d*x + 1/2*c) + 4*B*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
784,1,294,0,0.261126," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(C a^{2} + 2 \, B a b + 2 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(C a^{2} + 2 \, B a b + 2 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(C*a^2 + 2*B*a*b + 2*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(C*a^2 + 2*B*a*b + 2*C*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 - 3*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*B*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^2*tan(1/2*d*x + 1/2*c) + 3*C*a^2*tan(1/2*d*x + 1/2*c) + 6*B*a*b*tan(1/2*d*x + 1/2*c) + 12*C*a*b*tan(1/2*d*x + 1/2*c) + 6*B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
785,1,478,0,0.248495," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, B a^{2} + 8 \, C a b + 4 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, B a^{2} + 8 \, C a b + 4 \, 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(15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 80 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*B*a^2 + 8*C*a*b + 4*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*B*a^2 + 8*C*a*b + 4*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 24*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 24*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 12*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*C*b^2*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 40*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 80*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 24*C*a*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 40*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 24*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*B*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^2*tan(1/2*d*x + 1/2*c) + 24*C*a^2*tan(1/2*d*x + 1/2*c) + 48*B*a*b*tan(1/2*d*x + 1/2*c) + 24*C*a*b*tan(1/2*d*x + 1/2*c) + 12*B*b^2*tan(1/2*d*x + 1/2*c) + 24*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
786,1,188,0,0.404420," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{3} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(4 \, C a^{3} + 12 \, B a^{2} b + 9 \, C a b^{2} + 3 \, B b^{3}\right)} x + \frac{{\left(3 \, C a b^{2} + B b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(12 \, C a^{2} b + 12 \, B a b^{2} + 5 \, C b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(C a^{3} + 3 \, B a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(8 \, B a^{3} + 18 \, C a^{2} b + 18 \, B a b^{2} + 5 \, C b^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*b^3*sin(5*d*x + 5*c)/d + 1/8*(4*C*a^3 + 12*B*a^2*b + 9*C*a*b^2 + 3*B*b^3)*x + 1/32*(3*C*a*b^2 + B*b^3)*sin(4*d*x + 4*c)/d + 1/48*(12*C*a^2*b + 12*B*a*b^2 + 5*C*b^3)*sin(3*d*x + 3*c)/d + 1/4*(C*a^3 + 3*B*a^2*b + 3*C*a*b^2 + B*b^3)*sin(2*d*x + 2*c)/d + 1/8*(8*B*a^3 + 18*C*a^2*b + 18*B*a*b^2 + 5*C*b^3)*sin(d*x + c)/d","A",0
787,1,536,0,0.275865," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{3 \, {\left(8 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 3 \, C b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 216 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 216 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(8*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 3*C*b^3)*(d*x + c) + 2*(24*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 72*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 72*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 15*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 72*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 216*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 120*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 40*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 216*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 40*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 9*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 24*C*a^3*tan(1/2*d*x + 1/2*c) + 72*B*a^2*b*tan(1/2*d*x + 1/2*c) + 36*C*a^2*b*tan(1/2*d*x + 1/2*c) + 36*B*a*b^2*tan(1/2*d*x + 1/2*c) + 72*C*a*b^2*tan(1/2*d*x + 1/2*c) + 24*B*b^3*tan(1/2*d*x + 1/2*c) + 15*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
788,1,314,0,0.226105," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,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(2 \, C a^{3} + 6 \, B a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*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*(2*C*a^3 + 6*B*a^2*b + 3*C*a*b^2 + B*b^3)*(d*x + c) + 2*(18*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 9*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^2*b*tan(1/2*d*x + 1/2*c) + 18*B*a*b^2*tan(1/2*d*x + 1/2*c) + 9*C*a*b^2*tan(1/2*d*x + 1/2*c) + 3*B*b^3*tan(1/2*d*x + 1/2*c) + 6*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
789,1,234,0,0.362387," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,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(6 \, C a^{2} b + 6 \, B a b^{2} + C b^{3}\right)} {\left(d x + c\right)} - 2 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*B*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (6*C*a^2*b + 6*B*a*b^2 + C*b^3)*(d*x + c) - 2*(C*a^3 + 3*B*a^2*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(C*a^3 + 3*B*a^2*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 - C*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*C*a*b^2*tan(1/2*d*x + 1/2*c) + 2*B*b^3*tan(1/2*d*x + 1/2*c) + C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
790,1,239,0,0.251529," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{\frac{4 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} {\left(d x + c\right)} + {\left(B a^{3} + 6 \, C a^{2} b + 6 \, B a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a^{3} + 6 \, C a^{2} b + 6 \, 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(B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*C*b^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(3*C*a*b^2 + B*b^3)*(d*x + c) + (B*a^3 + 6*C*a^2*b + 6*B*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a^3 + 6*C*a^2*b + 6*B*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(B*a^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + B*a^3*tan(1/2*d*x + 1/2*c) + 2*C*a^3*tan(1/2*d*x + 1/2*c) + 6*B*a^2*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
791,1,336,0,0.363704," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} C b^{3} + 3 \, {\left(C a^{3} + 3 \, B a^{2} b + 6 \, C a b^{2} + 2 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(C a^{3} + 3 \, B a^{2} b + 6 \, C a b^{2} + 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^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*C*b^3 + 3*(C*a^3 + 3*B*a^2*b + 6*C*a*b^2 + 2*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(C*a^3 + 3*B*a^2*b + 6*C*a*b^2 + 2*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^3*tan(1/2*d*x + 1/2*c) + 3*C*a^3*tan(1/2*d*x + 1/2*c) + 9*B*a^2*b*tan(1/2*d*x + 1/2*c) + 18*C*a^2*b*tan(1/2*d*x + 1/2*c) + 18*B*a*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
792,1,586,0,0.427381," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 8 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 8 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 216 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 216 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 8*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 8*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 72*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*b^3*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 120*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 216*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 120*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 216*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^3*tan(1/2*d*x + 1/2*c) + 24*C*a^3*tan(1/2*d*x + 1/2*c) + 72*B*a^2*b*tan(1/2*d*x + 1/2*c) + 36*C*a^2*b*tan(1/2*d*x + 1/2*c) + 36*B*a*b^2*tan(1/2*d*x + 1/2*c) + 72*C*a*b^2*tan(1/2*d*x + 1/2*c) + 24*B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
793,1,722,0,0.336833," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b + 12 \, C a b^{2} + 4 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b + 12 \, C a b^{2} + 4 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 90 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 90 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*C*a^3 + 9*B*a^2*b + 12*C*a*b^2 + 4*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*C*a^3 + 9*B*a^2*b + 12*C*a*b^2 + 4*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 75*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 225*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 180*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*B*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*C*b^3*tan(1/2*d*x + 1/2*c)^9 - 160*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 30*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 90*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 120*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 480*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 464*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1200*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 720*C*b^3*tan(1/2*d*x + 1/2*c)^5 - 160*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 30*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 90*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 480*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*B*a^3*tan(1/2*d*x + 1/2*c) + 75*C*a^3*tan(1/2*d*x + 1/2*c) + 225*B*a^2*b*tan(1/2*d*x + 1/2*c) + 360*C*a^2*b*tan(1/2*d*x + 1/2*c) + 360*B*a*b^2*tan(1/2*d*x + 1/2*c) + 180*C*a*b^2*tan(1/2*d*x + 1/2*c) + 60*B*b^3*tan(1/2*d*x + 1/2*c) + 120*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
794,1,360,0,0.274863," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{3} - 2 \, B a^{2} b + C a b^{2} - B b^{3}\right)} {\left(d x + c\right)}}{b^{4}} + \frac{12 \, {\left(C a^{4} - B a^{3} b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} - \frac{2 \, {\left(6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*C*a^3 - 2*B*a^2*b + C*a*b^2 - B*b^3)*(d*x + c)/b^4 + 12*(C*a^4 - B*a^3*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) - 2*(6*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 6*B*a*b*tan(1/2*d*x + 1/2*c) - 3*C*a*b*tan(1/2*d*x + 1/2*c) + 3*B*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^3))/d","B",0
795,1,227,0,0.210165," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, C a^{2} - 2 \, B a b + C b^{2}\right)} {\left(d x + c\right)}}{b^{3}} + \frac{4 \, {\left(C a^{3} - B a^{2} b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{3}} - \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*((2*C*a^2 - 2*B*a*b + C*b^2)*(d*x + c)/b^3 + 4*(C*a^3 - B*a^2*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^3) - 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*tan(1/2*d*x + 1/2*c) - 2*B*b*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^2))/d","A",0
796,1,142,0,0.210265," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(C a - B b\right)} {\left(d x + c\right)}}{b^{2}} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b} + \frac{2 \, {\left(C a^{2} - B a b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{2}}}{d}"," ",0,"-((C*a - B*b)*(d*x + c)/b^2 - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b) + 2*(C*a^2 - B*a*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^2))/d","A",0
797,1,296,0,0.536727," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(\sqrt{a^{2} - b^{2}} C {\left(2 \, a - b\right)} {\left| a - b \right|} - \sqrt{a^{2} - b^{2}} B b {\left| a - b \right|} - \sqrt{a^{2} - b^{2}} B {\left| a - b \right|} {\left| b \right|} + \sqrt{a^{2} - b^{2}} C {\left| a - b \right|} {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} + \frac{{\left(2 \, C a - B b - C b + B {\left| b \right|} - C {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{b^{2} - a {\left| b \right|}}}{d}"," ",0,"-((sqrt(a^2 - b^2)*C*(2*a - b)*abs(a - b) - sqrt(a^2 - b^2)*B*b*abs(a - b) - sqrt(a^2 - b^2)*B*abs(a - b)*abs(b) + sqrt(a^2 - b^2)*C*abs(a - b)*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) + (2*C*a - B*b - C*b + B*abs(b) - C*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/(b^2 - a*abs(b)))/d","B",0
798,1,128,0,0.234105," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(C a - B b\right)}}{\sqrt{a^{2} - b^{2}} 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 - 2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*(C*a - B*b)/(sqrt(a^2 - b^2)*a))/d","A",0
799,1,175,0,0.285001," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{{\left(C a - B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a} + \frac{2 \, {\left(C a b - B b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{2}}}{d}"," ",0,"((C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - (C*a - B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a) + 2*(C*a*b - B*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^2))/d","A",0
800,1,269,0,0.277133," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(B a^{2} - 2 \, C a b + 2 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{{\left(B a^{2} - 2 \, C a b + 2 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{4 \, {\left(C a b^{2} - B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3}} + \frac{2 \, {\left(B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*((B*a^2 - 2*C*a*b + 2*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (B*a^2 - 2*C*a*b + 2*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - 4*(C*a*b^2 - B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3) + 2*(B*a*tan(1/2*d*x + 1/2*c)^3 - 2*C*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*b*tan(1/2*d*x + 1/2*c)^3 + B*a*tan(1/2*d*x + 1/2*c) + 2*C*a*tan(1/2*d*x + 1/2*c) - 2*B*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2))/d","B",0
801,1,338,0,0.214976," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(3 \, C a^{5} - 2 \, B a^{4} b - 4 \, C a^{3} b^{2} + 3 \, B a^{2} b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{4 \, {\left(C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} + \frac{{\left(6 \, C a^{2} - 4 \, B a b + C b^{2}\right)} {\left(d x + c\right)}}{b^{4}} - \frac{2 \, {\left(4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{3}}}{2 \, d}"," ",0,"1/2*(4*(3*C*a^5 - 2*B*a^4*b - 4*C*a^3*b^2 + 3*B*a^2*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - 4*(C*a^4*tan(1/2*d*x + 1/2*c) - B*a^3*b*tan(1/2*d*x + 1/2*c))/((a^2*b^3 - b^5)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) + (6*C*a^2 - 4*B*a*b + C*b^2)*(d*x + c)/b^4 - 2*(4*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 + 4*C*a*tan(1/2*d*x + 1/2*c) - 2*B*b*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^3))/d","A",0
802,1,1116,0,0.962052," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(4 \, C a^{6} b^{2} - 2 \, B a^{5} b^{3} - 2 \, C a^{5} b^{3} + B a^{4} b^{4} - 9 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 4 \, C a^{3} b^{5} - 2 \, B a^{2} b^{6} + 5 \, C a^{2} b^{6} - 3 \, B a b^{7} - 2 \, C a b^{7} + B b^{8} + 2 \, C a^{3} {\left| -a^{2} b^{3} + b^{5} \right|} - B a^{2} b {\left| -a^{2} b^{3} + b^{5} \right|} - C a^{2} b {\left| -a^{2} b^{3} + b^{5} \right|} + B a b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} - 2 \, C a b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} + B b^{3} {\left| -a^{2} b^{3} + b^{5} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a^{3} b^{2} - 2 \, a b^{4} + \sqrt{-4 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)}^{2}}}{a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}}}}\right)\right)}}{a^{3} b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} - a b^{4} {\left| -a^{2} b^{3} + b^{5} \right|} + {\left(a^{2} b^{3} - b^{5}\right)}^{2}} + \frac{{\left({\left(a^{2} b - a b^{2} - b^{3}\right)} \sqrt{a^{2} - b^{2}} B {\left| -a^{2} b^{3} + b^{5} \right|} {\left| -a + b \right|} - {\left(2 \, a^{3} - a^{2} b - 2 \, a b^{2}\right)} \sqrt{a^{2} - b^{2}} C {\left| -a^{2} b^{3} + b^{5} \right|} {\left| -a + b \right|} - {\left(2 \, a^{5} b^{3} - a^{4} b^{4} - 5 \, a^{3} b^{5} + 2 \, a^{2} b^{6} + 3 \, a b^{7} - b^{8}\right)} \sqrt{a^{2} - b^{2}} B {\left| -a + b \right|} + {\left(4 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 9 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + 5 \, a^{2} b^{6} - 2 \, a b^{7}\right)} \sqrt{a^{2} - b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a^{3} b^{2} - 2 \, a b^{4} - \sqrt{-4 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)}^{2}}}{a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} {\left| -a^{2} b^{3} + b^{5} \right|}} + \frac{2 \, {\left(2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} {\left(a^{2} b^{2} - b^{4}\right)}}}{d}"," ",0,"((4*C*a^6*b^2 - 2*B*a^5*b^3 - 2*C*a^5*b^3 + B*a^4*b^4 - 9*C*a^4*b^4 + 5*B*a^3*b^5 + 4*C*a^3*b^5 - 2*B*a^2*b^6 + 5*C*a^2*b^6 - 3*B*a*b^7 - 2*C*a*b^7 + B*b^8 + 2*C*a^3*abs(-a^2*b^3 + b^5) - B*a^2*b*abs(-a^2*b^3 + b^5) - C*a^2*b*abs(-a^2*b^3 + b^5) + B*a*b^2*abs(-a^2*b^3 + b^5) - 2*C*a*b^2*abs(-a^2*b^3 + b^5) + B*b^3*abs(-a^2*b^3 + b^5))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a^3*b^2 - 2*a*b^4 + sqrt(-4*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5) + 4*(a^3*b^2 - a*b^4)^2))/(a^3*b^2 - a^2*b^3 - a*b^4 + b^5))))/(a^3*b^2*abs(-a^2*b^3 + b^5) - a*b^4*abs(-a^2*b^3 + b^5) + (a^2*b^3 - b^5)^2) + ((a^2*b - a*b^2 - b^3)*sqrt(a^2 - b^2)*B*abs(-a^2*b^3 + b^5)*abs(-a + b) - (2*a^3 - a^2*b - 2*a*b^2)*sqrt(a^2 - b^2)*C*abs(-a^2*b^3 + b^5)*abs(-a + b) - (2*a^5*b^3 - a^4*b^4 - 5*a^3*b^5 + 2*a^2*b^6 + 3*a*b^7 - b^8)*sqrt(a^2 - b^2)*B*abs(-a + b) + (4*a^6*b^2 - 2*a^5*b^3 - 9*a^4*b^4 + 4*a^3*b^5 + 5*a^2*b^6 - 2*a*b^7)*sqrt(a^2 - b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a^3*b^2 - 2*a*b^4 - sqrt(-4*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5) + 4*(a^3*b^2 - a*b^4)^2))/(a^3*b^2 - a^2*b^3 - a*b^4 + b^5))))/((a^2*b^3 - b^5)^2*(a^2 - 2*a*b + b^2) - (a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*abs(-a^2*b^3 + b^5)) + 2*(2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + C*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^3*tan(1/2*d*x + 1/2*c) - B*a^2*b*tan(1/2*d*x + 1/2*c) + C*a^2*b*tan(1/2*d*x + 1/2*c) - C*a*b^2*tan(1/2*d*x + 1/2*c) - C*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)*(a^2*b^2 - b^4)))/d","B",0
803,1,199,0,0.217335," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{3} - 2 \, C a b^{2} + B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{{\left(d x + c\right)} C}{b^{2}} - \frac{2 \, {\left(C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b - b^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}}}{d}"," ",0,"(2*(C*a^3 - 2*C*a*b^2 + B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^2 - b^4)*sqrt(a^2 - b^2)) + (d*x + c)*C/b^2 - 2*(C*a^2*tan(1/2*d*x + 1/2*c) - B*a*b*tan(1/2*d*x + 1/2*c))/((a^2*b - b^3)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)))/d","A",0
804,1,157,0,0.287446," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(B a - C b\right)}}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} + \frac{C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} {\left(a^{2} - b^{2}\right)}}\right)}}{d}"," ",0,"2*((pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*(B*a - C*b)/(a^2 - b^2)^(3/2) + (C*a*tan(1/2*d*x + 1/2*c) - B*b*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)*(a^2 - b^2)))/d","A",0
805,1,225,0,0.473232," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(C a^{3} - 2 \, B a^{2} b + B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{a^{2} - b^{2}}} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} + \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}}}{d}"," ",0,"-(2*(C*a^3 - 2*B*a^2*b + B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - a^2*b^2)*sqrt(a^2 - b^2)) - B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 + B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 2*(C*a*b*tan(1/2*d*x + 1/2*c) - B*b^2*tan(1/2*d*x + 1/2*c))/((a^3 - a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)))/d","A",0
806,1,404,0,0.582148," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(2 \, C a^{3} b - 3 \, B a^{2} b^{2} - C a b^{3} + 2 \, B b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{4} - a^{2} b^{2}\right)}} + \frac{{\left(C a - 2 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{{\left(C a - 2 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}}}{d}"," ",0,"(2*(2*C*a^3*b - 3*B*a^2*b^2 - C*a*b^3 + 2*B*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^5 - a^3*b^2)*sqrt(a^2 - b^2)) - 2*(B*a^3*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 + B*a^3*tan(1/2*d*x + 1/2*c) + B*a^2*b*tan(1/2*d*x + 1/2*c) - B*a*b^2*tan(1/2*d*x + 1/2*c) + C*a*b^2*tan(1/2*d*x + 1/2*c) - 2*B*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^4 - a^2*b^2)) + (C*a - 2*B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (C*a - 2*B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3)/d","B",0
807,1,2712,0,0.972836," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(3 \, {\left(2 \, a^{5} b - a^{4} b^{2} - 4 \, a^{3} b^{3} + 2 \, a^{2} b^{4} + 2 \, a b^{5}\right)} \sqrt{a^{2} - b^{2}} B {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} {\left| -a + b \right|} - {\left(12 \, a^{6} - 6 \, a^{5} b - 23 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} - a b^{5} + b^{6}\right)} \sqrt{a^{2} - b^{2}} C {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} {\left| -a + b \right|} + 3 \, {\left(4 \, a^{10} b^{5} - 2 \, a^{9} b^{6} - 17 \, a^{8} b^{7} + 8 \, a^{7} b^{8} + 28 \, a^{6} b^{9} - 12 \, a^{5} b^{10} - 21 \, a^{4} b^{11} + 8 \, a^{3} b^{12} + 6 \, a^{2} b^{13} - 2 \, a b^{14}\right)} \sqrt{a^{2} - b^{2}} B {\left| -a + b \right|} - {\left(24 \, a^{11} b^{4} - 12 \, a^{10} b^{5} - 100 \, a^{9} b^{6} + 47 \, a^{8} b^{7} + 158 \, a^{7} b^{8} - 68 \, a^{6} b^{9} - 111 \, a^{5} b^{10} + 42 \, a^{4} b^{11} + 28 \, a^{3} b^{12} - 8 \, a^{2} b^{13} + a b^{14} - b^{15}\right)} \sqrt{a^{2} - b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{4 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 4 \, a b^{8} + \sqrt{-16 \, {\left(a^{5} b^{4} + a^{4} b^{5} - 2 \, a^{3} b^{6} - 2 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} {\left(a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} + 16 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)}^{2}}}{a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}}}}\right)\right)}}{{\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} + {\left(a^{7} b^{4} - 2 \, a^{6} b^{5} - a^{5} b^{6} + 4 \, a^{4} b^{7} - a^{3} b^{8} - 2 \, a^{2} b^{9} + a b^{10}\right)} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|}} + \frac{{\left(24 \, C a^{11} b^{4} - 12 \, B a^{10} b^{5} - 12 \, C a^{10} b^{5} + 6 \, B a^{9} b^{6} - 100 \, C a^{9} b^{6} + 51 \, B a^{8} b^{7} + 47 \, C a^{8} b^{7} - 24 \, B a^{7} b^{8} + 158 \, C a^{7} b^{8} - 84 \, B a^{6} b^{9} - 68 \, C a^{6} b^{9} + 36 \, B a^{5} b^{10} - 111 \, C a^{5} b^{10} + 63 \, B a^{4} b^{11} + 42 \, C a^{4} b^{11} - 24 \, B a^{3} b^{12} + 28 \, C a^{3} b^{12} - 18 \, B a^{2} b^{13} - 8 \, C a^{2} b^{13} + 6 \, B a b^{14} + C a b^{14} - C b^{15} - 12 \, C a^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, B a^{5} b {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, C a^{5} b {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 3 \, B a^{4} b^{2} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 23 \, C a^{4} b^{2} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 12 \, B a^{3} b^{3} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 10 \, C a^{3} b^{3} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, B a^{2} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 10 \, C a^{2} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, B a b^{5} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + C a b^{5} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - C b^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{4 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 4 \, a b^{8} - \sqrt{-16 \, {\left(a^{5} b^{4} + a^{4} b^{5} - 2 \, a^{3} b^{6} - 2 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} {\left(a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} + 16 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)}^{2}}}{a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}}}}\right)\right)}}{a^{5} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 2 \, a^{3} b^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + a b^{8} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)}^{2}} - \frac{2 \, {\left(12 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 67 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 35 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 29 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 26 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 17 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{2 \, d}"," ",0,"1/2*((3*(2*a^5*b - a^4*b^2 - 4*a^3*b^3 + 2*a^2*b^4 + 2*a*b^5)*sqrt(a^2 - b^2)*B*abs(a^4*b^5 - 2*a^2*b^7 + b^9)*abs(-a + b) - (12*a^6 - 6*a^5*b - 23*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 - a*b^5 + b^6)*sqrt(a^2 - b^2)*C*abs(a^4*b^5 - 2*a^2*b^7 + b^9)*abs(-a + b) + 3*(4*a^10*b^5 - 2*a^9*b^6 - 17*a^8*b^7 + 8*a^7*b^8 + 28*a^6*b^9 - 12*a^5*b^10 - 21*a^4*b^11 + 8*a^3*b^12 + 6*a^2*b^13 - 2*a*b^14)*sqrt(a^2 - b^2)*B*abs(-a + b) - (24*a^11*b^4 - 12*a^10*b^5 - 100*a^9*b^6 + 47*a^8*b^7 + 158*a^7*b^8 - 68*a^6*b^9 - 111*a^5*b^10 + 42*a^4*b^11 + 28*a^3*b^12 - 8*a^2*b^13 + a*b^14 - b^15)*sqrt(a^2 - b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*tan(1/2*d*x + 1/2*c)/sqrt((4*a^5*b^4 - 8*a^3*b^6 + 4*a*b^8 + sqrt(-16*(a^5*b^4 + a^4*b^5 - 2*a^3*b^6 - 2*a^2*b^7 + a*b^8 + b^9)*(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9) + 16*(a^5*b^4 - 2*a^3*b^6 + a*b^8)^2))/(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9))))/((a^4*b^5 - 2*a^2*b^7 + b^9)^2*(a^2 - 2*a*b + b^2) + (a^7*b^4 - 2*a^6*b^5 - a^5*b^6 + 4*a^4*b^7 - a^3*b^8 - 2*a^2*b^9 + a*b^10)*abs(a^4*b^5 - 2*a^2*b^7 + b^9)) + (24*C*a^11*b^4 - 12*B*a^10*b^5 - 12*C*a^10*b^5 + 6*B*a^9*b^6 - 100*C*a^9*b^6 + 51*B*a^8*b^7 + 47*C*a^8*b^7 - 24*B*a^7*b^8 + 158*C*a^7*b^8 - 84*B*a^6*b^9 - 68*C*a^6*b^9 + 36*B*a^5*b^10 - 111*C*a^5*b^10 + 63*B*a^4*b^11 + 42*C*a^4*b^11 - 24*B*a^3*b^12 + 28*C*a^3*b^12 - 18*B*a^2*b^13 - 8*C*a^2*b^13 + 6*B*a*b^14 + C*a*b^14 - C*b^15 - 12*C*a^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*B*a^5*b*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*C*a^5*b*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 3*B*a^4*b^2*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 23*C*a^4*b^2*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 12*B*a^3*b^3*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 10*C*a^3*b^3*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*B*a^2*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 10*C*a^2*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*B*a*b^5*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + C*a*b^5*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - C*b^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*tan(1/2*d*x + 1/2*c)/sqrt((4*a^5*b^4 - 8*a^3*b^6 + 4*a*b^8 - sqrt(-16*(a^5*b^4 + a^4*b^5 - 2*a^3*b^6 - 2*a^2*b^7 + a*b^8 + b^9)*(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9) + 16*(a^5*b^4 - 2*a^3*b^6 + a*b^8)^2))/(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9))))/(a^5*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 2*a^3*b^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + a*b^8*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - (a^4*b^5 - 2*a^2*b^7 + b^9)^2) - 2*(12*C*a^7*tan(1/2*d*x + 1/2*c)^7 - 6*B*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 17*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 2*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 2*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 13*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^7 - 2*B*b^7*tan(1/2*d*x + 1/2*c)^7 + C*b^7*tan(1/2*d*x + 1/2*c)^7 + 36*C*a^7*tan(1/2*d*x + 1/2*c)^5 - 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 67*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 35*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 29*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 26*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 10*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 5*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 2*B*b^7*tan(1/2*d*x + 1/2*c)^5 - 3*C*b^7*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^7*tan(1/2*d*x + 1/2*c)^3 - 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 67*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 35*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 26*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 10*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 5*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^7*tan(1/2*d*x + 1/2*c)^3 + 3*C*b^7*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^7*tan(1/2*d*x + 1/2*c) - 6*B*a^6*b*tan(1/2*d*x + 1/2*c) + 18*C*a^6*b*tan(1/2*d*x + 1/2*c) - 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c) - 17*C*a^5*b^2*tan(1/2*d*x + 1/2*c) + 9*B*a^4*b^3*tan(1/2*d*x + 1/2*c) - 33*C*a^4*b^3*tan(1/2*d*x + 1/2*c) + 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c) - 2*C*a^3*b^4*tan(1/2*d*x + 1/2*c) + 2*B*a^2*b^5*tan(1/2*d*x + 1/2*c) + 13*C*a^2*b^5*tan(1/2*d*x + 1/2*c) - 4*B*a*b^6*tan(1/2*d*x + 1/2*c) + 4*C*a*b^6*tan(1/2*d*x + 1/2*c) - 2*B*b^7*tan(1/2*d*x + 1/2*c) - C*b^7*tan(1/2*d*x + 1/2*c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
808,1,543,0,0.562209," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, C a^{6} - 2 \, B a^{5} b - 15 \, C a^{4} b^{2} + 5 \, B a^{3} b^{3} + 12 \, C a^{2} b^{4} - 6 \, B a b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} - b^{2}}} - \frac{4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} + \frac{{\left(3 \, C a - B b\right)} {\left(d x + c\right)}}{b^{4}} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b^{3}}}{d}"," ",0,"-((6*C*a^6 - 2*B*a^5*b - 15*C*a^4*b^2 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 6*B*a*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(a^2 - b^2)) - (4*C*a^6*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*C*a^6*tan(1/2*d*x + 1/2*c) - 2*B*a^5*b*tan(1/2*d*x + 1/2*c) + 5*C*a^5*b*tan(1/2*d*x + 1/2*c) - 3*B*a^4*b^2*tan(1/2*d*x + 1/2*c) - 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c) + 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c) - 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c) + 6*B*a^2*b^4*tan(1/2*d*x + 1/2*c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) + (3*C*a - B*b)*(d*x + c)/b^4 - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b^3))/d","B",0
809,1,455,0,0.291802," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, C a^{5} - 5 \, C a^{3} b^{2} - B a^{2} b^{3} + 6 \, C a b^{4} - 2 \, B b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{a^{2} - b^{2}}} - \frac{{\left(d x + c\right)} C}{b^{3}} + \frac{2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"-((2*C*a^5 - 5*C*a^3*b^2 - B*a^2*b^3 + 6*C*a*b^4 - 2*B*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(a^2 - b^2)) - (d*x + c)*C/b^3 + (2*C*a^5*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 + B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^5*tan(1/2*d*x + 1/2*c) + 3*C*a^4*b*tan(1/2*d*x + 1/2*c) - B*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*b^3*tan(1/2*d*x + 1/2*c) - 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 4*B*a*b^4*tan(1/2*d*x + 1/2*c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
810,1,391,0,0.314917," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(C a^{2} - 3 \, B a b + 2 \, C b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"((C*a^2 - 3*B*a*b + 2*C*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - C*a^3*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^3*tan(1/2*d*x + 1/2*c) + C*a^3*tan(1/2*d*x + 1/2*c) + B*a^2*b*tan(1/2*d*x + 1/2*c) - 3*C*a^2*b*tan(1/2*d*x + 1/2*c) + B*a*b^2*tan(1/2*d*x + 1/2*c) - 4*C*a*b^2*tan(1/2*d*x + 1/2*c) + 2*B*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
811,1,390,0,0.716741," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, B a^{2} - 3 \, C a b + B b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"((2*B*a^2 - 3*C*a*b + B*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + B*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^3*tan(1/2*d*x + 1/2*c) - 4*B*a^2*b*tan(1/2*d*x + 1/2*c) + C*a^2*b*tan(1/2*d*x + 1/2*c) - 3*B*a*b^2*tan(1/2*d*x + 1/2*c) + C*a*b^2*tan(1/2*d*x + 1/2*c) + B*b^3*tan(1/2*d*x + 1/2*c) + 2*C*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
812,1,481,0,0.505075," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, C a^{5} - 6 \, B a^{4} b + C a^{3} b^{2} + 5 \, B a^{2} b^{3} - 2 \, B b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{4 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"((2*C*a^5 - 6*B*a^4*b + C*a^3*b^2 + 5*B*a^2*b^3 - 2*B*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(a^2 - b^2)) + B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - (4*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 3*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*C*a^4*b*tan(1/2*d*x + 1/2*c) - 6*B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 3*C*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*B*a^2*b^3*tan(1/2*d*x + 1/2*c) - C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 3*B*a*b^4*tan(1/2*d*x + 1/2*c) + 2*B*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
813,1,574,0,0.361721," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(6 \, C a^{5} b - 12 \, B a^{4} b^{2} - 5 \, C a^{3} b^{3} + 15 \, B a^{2} b^{4} + 2 \, C a b^{5} - 6 \, B b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{6 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} + \frac{{\left(C a - 3 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{{\left(C a - 3 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}}}{d}"," ",0,"((6*C*a^5*b - 12*B*a^4*b^2 - 5*C*a^3*b^3 + 15*B*a^2*b^4 + 2*C*a*b^5 - 6*B*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(a^2 - b^2)) + (6*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 8*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 7*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 5*B*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*B*b^6*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^4*b^2*tan(1/2*d*x + 1/2*c) - 8*B*a^3*b^3*tan(1/2*d*x + 1/2*c) + 5*C*a^3*b^3*tan(1/2*d*x + 1/2*c) - 7*B*a^2*b^4*tan(1/2*d*x + 1/2*c) - 3*C*a^2*b^4*tan(1/2*d*x + 1/2*c) + 5*B*a*b^5*tan(1/2*d*x + 1/2*c) - 2*C*a*b^5*tan(1/2*d*x + 1/2*c) + 4*B*b^6*tan(1/2*d*x + 1/2*c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) + (C*a - 3*B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - (C*a - 3*B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3))/d","B",0
814,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*cos(d*x + c), x)","F",0
815,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
816,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
817,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
818,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
819,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
820,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
821,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
823,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
824,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
825,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
826,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^5, x)","F",0
827,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
828,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2), x)","F",0
829,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
830,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
831,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
832,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
833,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^5, x)","F",0
834,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^6, x)","F",0
835,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
836,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
837,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
838,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
839,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
840,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{4}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^4/sqrt(b*cos(d*x + c) + a), x)","F",0
841,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
842,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
843,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
844,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
845,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
846,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^3/(b*cos(d*x + c) + a)^(3/2), x)","F",0
847,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
848,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
849,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
850,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
851,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
852,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^3/(b*cos(d*x + c) + a)^(5/2), x)","F",0
853,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
854,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
856,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
857,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
858,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
859,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
860,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
861,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
862,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
863,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
864,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
865,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
866,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
867,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(11/2), x)","F",0
868,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
869,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
870,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
871,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
872,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
873,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
874,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
875,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(13/2), x)","F",0
876,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
877,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
878,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
879,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
880,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
881,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
882,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
883,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
884,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
885,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
886,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
887,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
888,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
889,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
890,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(7/2)), x)","F",0
891,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^3, x)","F",0
892,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^3, x)","F",0
893,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^3, x)","F",0
894,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
895,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
896,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
897,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
899,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
900,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
901,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
902,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
903,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
904,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
905,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
906,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
908,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(7/2), x)","F",0
909,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(9/2), x)","F",0
910,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(11/2), x)","F",0
911,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
912,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
913,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
914,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(5/2), x)","F",0
915,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(7/2), x)","F",0
916,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(9/2), x)","F",0
917,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(11/2), x)","F",0
918,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(13/2), x)","F",0
919,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{15}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(15/2), x)","F",0
920,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
921,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
922,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
923,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
924,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
925,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
926,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
927,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
928,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
929,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
930,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
931,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
932,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
933,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
934,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
935,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
936,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
937,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
938,1,129,0,0.279265," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A a + 3 \, C a + 3 \, B b\right)} x + \frac{C b \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(C a + B b\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, B a + 4 \, A b + 5 \, C b\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a + C a + B b\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(6 \, B a + 6 \, A b + 5 \, C b\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(4*A*a + 3*C*a + 3*B*b)*x + 1/80*C*b*sin(5*d*x + 5*c)/d + 1/32*(C*a + B*b)*sin(4*d*x + 4*c)/d + 1/48*(4*B*a + 4*A*b + 5*C*b)*sin(3*d*x + 3*c)/d + 1/4*(A*a + C*a + B*b)*sin(2*d*x + 2*c)/d + 1/8*(6*B*a + 6*A*b + 5*C*b)*sin(d*x + c)/d","A",0
939,1,102,0,1.509264," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, B a + 4 \, A b + 3 \, C b\right)} x + \frac{C b \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(C a + B b\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(B a + A b + C b\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a + 3 \, C a + 3 \, B b\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/8*(4*B*a + 4*A*b + 3*C*b)*x + 1/32*C*b*sin(4*d*x + 4*c)/d + 1/12*(C*a + B*b)*sin(3*d*x + 3*c)/d + 1/4*(B*a + A*b + C*b)*sin(2*d*x + 2*c)/d + 1/4*(4*A*a + 3*C*a + 3*B*b)*sin(d*x + c)/d","A",0
940,1,76,0,0.188107," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, A a + C a + B b\right)} x + \frac{C b \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(C a + B b\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, B a + 4 \, A b + 3 \, C b\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/2*(2*A*a + C*a + B*b)*x + 1/12*C*b*sin(3*d*x + 3*c)/d + 1/4*(C*a + B*b)*sin(2*d*x + 2*c)/d + 1/4*(4*B*a + 4*A*b + 3*C*b)*sin(d*x + c)/d","A",0
941,1,159,0,0.239293," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{2 \, A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(2 \, B a + 2 \, A b + C b\right)} {\left(d x + c\right)} + \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*A*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*A*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (2*B*a + 2*A*b + C*b)*(d*x + c) + 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*b*tan(1/2*d*x + 1/2*c)^3 - C*b*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*tan(1/2*d*x + 1/2*c) + 2*B*b*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
942,1,132,0,1.761527," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(C a + B b\right)} {\left(d x + c\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) - {\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(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((C*a + B*b)*(d*x + c) + (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*(A*a*tan(1/2*d*x + 1/2*c)^3 - C*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) + C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
943,1,168,0,1.557644," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} C b + {\left(A a + 2 \, C a + 2 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a + 2 \, C a + 2 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*b + (A*a + 2*C*a + 2*B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a + 2*C*a + 2*B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 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
944,1,261,0,0.243077," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(B a + A b + 2 \, C 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 + 2 \, C 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} + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a + A*b + 2*C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a + A*b + 2*C*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 + 6*C*a*tan(1/2*d*x + 1/2*c)^5 - 3*A*b*tan(1/2*d*x + 1/2*c)^5 + 6*B*b*tan(1/2*d*x + 1/2*c)^5 - 4*A*a*tan(1/2*d*x + 1/2*c)^3 - 12*C*a*tan(1/2*d*x + 1/2*c)^3 - 12*B*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a*tan(1/2*d*x + 1/2*c) + 3*B*a*tan(1/2*d*x + 1/2*c) + 6*C*a*tan(1/2*d*x + 1/2*c) + 3*A*b*tan(1/2*d*x + 1/2*c) + 6*B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
945,1,428,0,0.259656," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, C a + 4 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a + 4 \, C a + 4 \, B b\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 \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*C*a + 4*B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a + 4*C*a + 4*B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a*tan(1/2*d*x + 1/2*c)^7 - 24*B*a*tan(1/2*d*x + 1/2*c)^7 + 12*C*a*tan(1/2*d*x + 1/2*c)^7 - 24*A*b*tan(1/2*d*x + 1/2*c)^7 + 12*B*b*tan(1/2*d*x + 1/2*c)^7 - 24*C*b*tan(1/2*d*x + 1/2*c)^7 + 9*A*a*tan(1/2*d*x + 1/2*c)^5 + 40*B*a*tan(1/2*d*x + 1/2*c)^5 - 12*C*a*tan(1/2*d*x + 1/2*c)^5 + 40*A*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*b*tan(1/2*d*x + 1/2*c)^5 + 72*C*b*tan(1/2*d*x + 1/2*c)^5 + 9*A*a*tan(1/2*d*x + 1/2*c)^3 - 40*B*a*tan(1/2*d*x + 1/2*c)^3 - 12*C*a*tan(1/2*d*x + 1/2*c)^3 - 40*A*b*tan(1/2*d*x + 1/2*c)^3 - 12*B*b*tan(1/2*d*x + 1/2*c)^3 - 72*C*b*tan(1/2*d*x + 1/2*c)^3 + 15*A*a*tan(1/2*d*x + 1/2*c) + 24*B*a*tan(1/2*d*x + 1/2*c) + 12*C*a*tan(1/2*d*x + 1/2*c) + 24*A*b*tan(1/2*d*x + 1/2*c) + 12*B*b*tan(1/2*d*x + 1/2*c) + 24*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
946,1,473,0,0.366436," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a + 3 \, A b + 4 \, C b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, B a + 3 \, A b + 4 \, C b\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 \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a + 3*A*b + 4*C*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*B*a + 3*A*b + 4*C*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*a*tan(1/2*d*x + 1/2*c)^9 - 75*B*a*tan(1/2*d*x + 1/2*c)^9 + 120*C*a*tan(1/2*d*x + 1/2*c)^9 - 75*A*b*tan(1/2*d*x + 1/2*c)^9 + 120*B*b*tan(1/2*d*x + 1/2*c)^9 - 60*C*b*tan(1/2*d*x + 1/2*c)^9 - 160*A*a*tan(1/2*d*x + 1/2*c)^7 + 30*B*a*tan(1/2*d*x + 1/2*c)^7 - 320*C*a*tan(1/2*d*x + 1/2*c)^7 + 30*A*b*tan(1/2*d*x + 1/2*c)^7 - 320*B*b*tan(1/2*d*x + 1/2*c)^7 + 120*C*b*tan(1/2*d*x + 1/2*c)^7 + 464*A*a*tan(1/2*d*x + 1/2*c)^5 + 400*C*a*tan(1/2*d*x + 1/2*c)^5 + 400*B*b*tan(1/2*d*x + 1/2*c)^5 - 160*A*a*tan(1/2*d*x + 1/2*c)^3 - 30*B*a*tan(1/2*d*x + 1/2*c)^3 - 320*C*a*tan(1/2*d*x + 1/2*c)^3 - 30*A*b*tan(1/2*d*x + 1/2*c)^3 - 320*B*b*tan(1/2*d*x + 1/2*c)^3 - 120*C*b*tan(1/2*d*x + 1/2*c)^3 + 120*A*a*tan(1/2*d*x + 1/2*c) + 75*B*a*tan(1/2*d*x + 1/2*c) + 120*C*a*tan(1/2*d*x + 1/2*c) + 75*A*b*tan(1/2*d*x + 1/2*c) + 120*B*b*tan(1/2*d*x + 1/2*c) + 60*C*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
947,1,184,0,0.215622," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{2} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(4 \, B a^{2} + 8 \, A a b + 6 \, C a b + 3 \, B b^{2}\right)} x + \frac{{\left(2 \, C a b + B b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, C a^{2} + 8 \, B a b + 4 \, A b^{2} + 5 \, C b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(B a^{2} + 2 \, A a b + 2 \, C a b + B b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(8 \, A a^{2} + 6 \, C a^{2} + 12 \, B a b + 6 \, A b^{2} + 5 \, C b^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*b^2*sin(5*d*x + 5*c)/d + 1/8*(4*B*a^2 + 8*A*a*b + 6*C*a*b + 3*B*b^2)*x + 1/32*(2*C*a*b + B*b^2)*sin(4*d*x + 4*c)/d + 1/48*(4*C*a^2 + 8*B*a*b + 4*A*b^2 + 5*C*b^2)*sin(3*d*x + 3*c)/d + 1/4*(B*a^2 + 2*A*a*b + 2*C*a*b + B*b^2)*sin(2*d*x + 2*c)/d + 1/8*(8*A*a^2 + 6*C*a^2 + 12*B*a*b + 6*A*b^2 + 5*C*b^2)*sin(d*x + c)/d","A",0
948,1,146,0,0.624295," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(8 \, A a^{2} + 4 \, C a^{2} + 8 \, B a b + 4 \, A b^{2} + 3 \, C b^{2}\right)} x + \frac{{\left(2 \, C a b + B b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(C a^{2} + 2 \, B a b + A b^{2} + C b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, B a^{2} + 8 \, A a b + 6 \, C a b + 3 \, B b^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/32*C*b^2*sin(4*d*x + 4*c)/d + 1/8*(8*A*a^2 + 4*C*a^2 + 8*B*a*b + 4*A*b^2 + 3*C*b^2)*x + 1/12*(2*C*a*b + B*b^2)*sin(3*d*x + 3*c)/d + 1/4*(C*a^2 + 2*B*a*b + A*b^2 + C*b^2)*sin(2*d*x + 2*c)/d + 1/4*(4*B*a^2 + 8*A*a*b + 6*C*a*b + 3*B*b^2)*sin(d*x + c)/d","A",0
949,1,346,0,0.233177," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{6 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(2 \, B a^{2} + 4 \, A a b + 2 \, C a b + B b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(2*B*a^2 + 4*A*a*b + 2*C*a*b + B*b^2)*(d*x + c) + 2*(6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c) + 12*B*a*b*tan(1/2*d*x + 1/2*c) + 6*C*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c) + 3*B*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
950,1,229,0,0.252955," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - {\left(2 \, C a^{2} + 4 \, B a b + 2 \, A b^{2} + C b^{2}\right)} {\left(d x + c\right)} - 2 \, {\left(B a^{2} + 2 \, A a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(B a^{2} + 2 \, 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(4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*A*a^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (2*C*a^2 + 4*B*a*b + 2*A*b^2 + C*b^2)*(d*x + c) - 2*(B*a^2 + 2*A*a*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(B*a^2 + 2*A*a*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(4*C*a*b*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^2*tan(1/2*d*x + 1/2*c)^3 - C*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*a*b*tan(1/2*d*x + 1/2*c) + 2*B*b^2*tan(1/2*d*x + 1/2*c) + C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
951,1,239,0,0.282704," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{\frac{4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(2 \, C a b + B b^{2}\right)} {\left(d x + c\right)} + {\left(A a^{2} + 2 \, C a^{2} + 4 \, B a b + 2 \, A b^{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 \, C a^{2} + 4 \, B a b + 2 \, 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} - 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*C*b^2*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(2*C*a*b + B*b^2)*(d*x + c) + (A*a^2 + 2*C*a^2 + 4*B*a*b + 2*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a^2 + 2*C*a^2 + 4*B*a*b + 2*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 - 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
952,1,364,0,0.518558," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} C b^{2} + 3 \, {\left(B a^{2} + 2 \, A a b + 4 \, C a b + 2 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(B a^{2} + 2 \, A a b + 4 \, C a b + 2 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*C*b^2 + 3*(B*a^2 + 2*A*a*b + 4*C*a*b + 2*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a^2 + 2*A*a*b + 4*C*a*b + 2*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) + 6*C*a^2*tan(1/2*d*x + 1/2*c) + 6*A*a*b*tan(1/2*d*x + 1/2*c) + 12*B*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
953,1,630,0,0.368359," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a^{2} + 4 \, C a^{2} + 8 \, B a b + 4 \, A b^{2} + 8 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a^{2} + 4 \, C a^{2} + 8 \, B a b + 4 \, A b^{2} + 8 \, C b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 144 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 144 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^2 + 4*C*a^2 + 8*B*a*b + 4*A*b^2 + 8*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a^2 + 4*C*a^2 + 8*B*a*b + 4*A*b^2 + 8*C*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*A*a*b*tan(1/2*d*x + 1/2*c)^7 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^7 - 48*C*a*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*b^2*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 40*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 80*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 144*C*a*b*tan(1/2*d*x + 1/2*c)^5 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 144*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^2*tan(1/2*d*x + 1/2*c) + 24*B*a^2*tan(1/2*d*x + 1/2*c) + 12*C*a^2*tan(1/2*d*x + 1/2*c) + 48*A*a*b*tan(1/2*d*x + 1/2*c) + 24*B*a*b*tan(1/2*d*x + 1/2*c) + 48*C*a*b*tan(1/2*d*x + 1/2*c) + 12*A*b^2*tan(1/2*d*x + 1/2*c) + 24*B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
954,1,766,0,0.496219," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{2} + 6 \, A a b + 8 \, C a b + 4 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, B a^{2} + 6 \, A a b + 8 \, C a b + 4 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 150 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 640 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 800 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 640 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a^2 + 6*A*a*b + 8*C*a*b + 4*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*B*a^2 + 6*A*a*b + 8*C*a*b + 4*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*a^2*tan(1/2*d*x + 1/2*c)^9 - 75*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^2*tan(1/2*d*x + 1/2*c)^9 - 150*A*a*b*tan(1/2*d*x + 1/2*c)^9 + 240*B*a*b*tan(1/2*d*x + 1/2*c)^9 - 120*C*a*b*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*B*b^2*tan(1/2*d*x + 1/2*c)^9 + 120*C*b^2*tan(1/2*d*x + 1/2*c)^9 - 160*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 30*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 320*C*a^2*tan(1/2*d*x + 1/2*c)^7 + 60*A*a*b*tan(1/2*d*x + 1/2*c)^7 - 640*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 240*C*a*b*tan(1/2*d*x + 1/2*c)^7 - 320*A*b^2*tan(1/2*d*x + 1/2*c)^7 + 120*B*b^2*tan(1/2*d*x + 1/2*c)^7 - 480*C*b^2*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 400*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 800*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 400*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 720*C*b^2*tan(1/2*d*x + 1/2*c)^5 - 160*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 30*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 320*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 60*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 640*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 240*C*a*b*tan(1/2*d*x + 1/2*c)^3 - 320*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*B*b^2*tan(1/2*d*x + 1/2*c)^3 - 480*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^2*tan(1/2*d*x + 1/2*c) + 75*B*a^2*tan(1/2*d*x + 1/2*c) + 120*C*a^2*tan(1/2*d*x + 1/2*c) + 150*A*a*b*tan(1/2*d*x + 1/2*c) + 240*B*a*b*tan(1/2*d*x + 1/2*c) + 120*C*a*b*tan(1/2*d*x + 1/2*c) + 120*A*b^2*tan(1/2*d*x + 1/2*c) + 60*B*b^2*tan(1/2*d*x + 1/2*c) + 120*C*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
955,1,283,0,0.712496," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{1}{16} \, {\left(8 \, B a^{3} + 24 \, A a^{2} b + 18 \, C a^{2} b + 18 \, B a b^{2} + 6 \, A b^{3} + 5 \, C b^{3}\right)} x + \frac{{\left(3 \, C a b^{2} + B b^{3}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(6 \, C a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3} + 3 \, C b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(4 \, C a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 15 \, C a b^{2} + 5 \, B b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(16 \, B a^{3} + 48 \, A a^{2} b + 48 \, C a^{2} b + 48 \, B a b^{2} + 16 \, A b^{3} + 15 \, C b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(8 \, A a^{3} + 6 \, C a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2} + 15 \, C a b^{2} + 5 \, B b^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*C*b^3*sin(6*d*x + 6*c)/d + 1/16*(8*B*a^3 + 24*A*a^2*b + 18*C*a^2*b + 18*B*a*b^2 + 6*A*b^3 + 5*C*b^3)*x + 1/80*(3*C*a*b^2 + B*b^3)*sin(5*d*x + 5*c)/d + 1/64*(6*C*a^2*b + 6*B*a*b^2 + 2*A*b^3 + 3*C*b^3)*sin(4*d*x + 4*c)/d + 1/48*(4*C*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 15*C*a*b^2 + 5*B*b^3)*sin(3*d*x + 3*c)/d + 1/64*(16*B*a^3 + 48*A*a^2*b + 48*C*a^2*b + 48*B*a*b^2 + 16*A*b^3 + 15*C*b^3)*sin(2*d*x + 2*c)/d + 1/8*(8*A*a^3 + 6*C*a^3 + 18*B*a^2*b + 18*A*a*b^2 + 15*C*a*b^2 + 5*B*b^3)*sin(d*x + c)/d","A",0
956,1,227,0,0.203833," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{3} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(8 \, A a^{3} + 4 \, C a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 9 \, C a b^{2} + 3 \, B b^{3}\right)} x + \frac{{\left(3 \, C a b^{2} + B b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(12 \, C a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3} + 5 \, C b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2} + 3 \, C a b^{2} + B b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(8 \, B a^{3} + 24 \, A a^{2} b + 18 \, C a^{2} b + 18 \, B a b^{2} + 6 \, A b^{3} + 5 \, C b^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*b^3*sin(5*d*x + 5*c)/d + 1/8*(8*A*a^3 + 4*C*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 9*C*a*b^2 + 3*B*b^3)*x + 1/32*(3*C*a*b^2 + B*b^3)*sin(4*d*x + 4*c)/d + 1/48*(12*C*a^2*b + 12*B*a*b^2 + 4*A*b^3 + 5*C*b^3)*sin(3*d*x + 3*c)/d + 1/4*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2 + 3*C*a*b^2 + B*b^3)*sin(2*d*x + 2*c)/d + 1/8*(8*B*a^3 + 24*A*a^2*b + 18*C*a^2*b + 18*B*a*b^2 + 6*A*b^3 + 5*C*b^3)*sin(d*x + c)/d","A",0
957,1,723,0,0.702085," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{24 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(8 \, B a^{3} + 24 \, A a^{2} b + 12 \, C a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3} + 3 \, C b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 216 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 216 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 216 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 216 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(8*B*a^3 + 24*A*a^2*b + 12*C*a^2*b + 12*B*a*b^2 + 4*A*b^3 + 3*C*b^3)*(d*x + c) + 2*(24*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 72*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 72*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 72*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 12*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 24*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 15*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 72*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 216*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 216*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 120*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 40*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 216*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 216*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 40*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 9*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 24*C*a^3*tan(1/2*d*x + 1/2*c) + 72*B*a^2*b*tan(1/2*d*x + 1/2*c) + 36*C*a^2*b*tan(1/2*d*x + 1/2*c) + 72*A*a*b^2*tan(1/2*d*x + 1/2*c) + 36*B*a*b^2*tan(1/2*d*x + 1/2*c) + 72*C*a*b^2*tan(1/2*d*x + 1/2*c) + 12*A*b^3*tan(1/2*d*x + 1/2*c) + 24*B*b^3*tan(1/2*d*x + 1/2*c) + 15*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
958,1,418,0,1.833667," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{12 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2} + 3 \, C a b^{2} + B b^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(12*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(2*C*a^3 + 6*B*a^2*b + 6*A*a*b^2 + 3*C*a*b^2 + B*b^3)*(d*x + c) - 6*(B*a^3 + 3*A*a^2*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 6*(B*a^3 + 3*A*a^2*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(18*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 9*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^2*b*tan(1/2*d*x + 1/2*c) + 18*B*a*b^2*tan(1/2*d*x + 1/2*c) + 9*C*a*b^2*tan(1/2*d*x + 1/2*c) + 6*A*b^3*tan(1/2*d*x + 1/2*c) + 3*B*b^3*tan(1/2*d*x + 1/2*c) + 6*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
959,1,538,0,0.305101," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(6 \, C a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3} + C b^{3}\right)} {\left(d x + c\right)} + {\left(A a^{3} + 2 \, C a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a^{3} + 2 \, C a^{3} + 6 \, B a^{2} b + 6 \, A 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^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((6*C*a^2*b + 6*B*a*b^2 + 2*A*b^3 + C*b^3)*(d*x + c) + (A*a^3 + 2*C*a^3 + 6*B*a^2*b + 6*A*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a^3 + 2*C*a^3 + 6*B*a^2*b + 6*A*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a^3*tan(1/2*d*x + 1/2*c)^7 - 2*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 2*B*b^3*tan(1/2*d*x + 1/2*c)^7 - C*b^3*tan(1/2*d*x + 1/2*c)^7 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 2*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 2*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 6*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*C*b^3*tan(1/2*d*x + 1/2*c)^3 + A*a^3*tan(1/2*d*x + 1/2*c) + 2*B*a^3*tan(1/2*d*x + 1/2*c) + 6*A*a^2*b*tan(1/2*d*x + 1/2*c) + 6*C*a*b^2*tan(1/2*d*x + 1/2*c) + 2*B*b^3*tan(1/2*d*x + 1/2*c) + C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","B",0
960,1,438,0,0.317862," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{\frac{12 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 6 \, {\left(3 \, C a b^{2} + B b^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b + 6 \, C a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3}\right)} \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 \, C a^{2} b + 6 \, B a b^{2} + 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(6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*C*b^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 6*(3*C*a*b^2 + B*b^3)*(d*x + c) + 3*(B*a^3 + 3*A*a^2*b + 6*C*a^2*b + 6*B*a*b^2 + 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a^3 + 3*A*a^2*b + 6*C*a^2*b + 6*B*a*b^2 + 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*tan(1/2*d*x + 1/2*c) + 3*B*a^3*tan(1/2*d*x + 1/2*c) + 6*C*a^3*tan(1/2*d*x + 1/2*c) + 9*A*a^2*b*tan(1/2*d*x + 1/2*c) + 18*B*a^2*b*tan(1/2*d*x + 1/2*c) + 18*A*a*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
961,1,759,0,0.330173," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} C b^{3} + 3 \, {\left(3 \, A a^{3} + 4 \, C a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 24 \, C a b^{2} + 8 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a^{3} + 4 \, C a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 24 \, C a b^{2} + 8 \, B b^{3}\right)} \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)^{7} - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 216 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 216 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 216 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 216 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)*C*b^3 + 3*(3*A*a^3 + 4*C*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 24*C*a*b^2 + 8*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a^3 + 4*C*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 24*C*a*b^2 + 8*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 72*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 120*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 216*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 216*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 120*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 216*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 216*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^3*tan(1/2*d*x + 1/2*c) + 24*B*a^3*tan(1/2*d*x + 1/2*c) + 12*C*a^3*tan(1/2*d*x + 1/2*c) + 72*A*a^2*b*tan(1/2*d*x + 1/2*c) + 36*B*a^2*b*tan(1/2*d*x + 1/2*c) + 72*C*a^2*b*tan(1/2*d*x + 1/2*c) + 36*A*a*b^2*tan(1/2*d*x + 1/2*c) + 72*B*a*b^2*tan(1/2*d*x + 1/2*c) + 24*A*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
962,1,989,0,0.704165," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, C a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3} + 8 \, C b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, C a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3} + 8 \, C b^{3}\right)} \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} - 75 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1440 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2160 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1440 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a^3 + 9*A*a^2*b + 12*C*a^2*b + 12*B*a*b^2 + 4*A*b^3 + 8*C*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*B*a^3 + 9*A*a^2*b + 12*C*a^2*b + 12*B*a*b^2 + 4*A*b^3 + 8*C*b^3)*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 - 75*B*a^3*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^3*tan(1/2*d*x + 1/2*c)^9 - 225*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 180*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 180*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*B*b^3*tan(1/2*d*x + 1/2*c)^9 - 160*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 30*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 320*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 1440*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 120*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 480*B*b^3*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 400*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1200*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 2160*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 720*B*b^3*tan(1/2*d*x + 1/2*c)^5 - 160*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 30*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 320*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 360*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 1440*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 480*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^3*tan(1/2*d*x + 1/2*c) + 75*B*a^3*tan(1/2*d*x + 1/2*c) + 120*C*a^3*tan(1/2*d*x + 1/2*c) + 225*A*a^2*b*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b*tan(1/2*d*x + 1/2*c) + 180*C*a^2*b*tan(1/2*d*x + 1/2*c) + 360*A*a*b^2*tan(1/2*d*x + 1/2*c) + 180*B*a*b^2*tan(1/2*d*x + 1/2*c) + 360*C*a*b^2*tan(1/2*d*x + 1/2*c) + 60*A*b^3*tan(1/2*d*x + 1/2*c) + 120*B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
963,1,1370,0,0.440219," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{15 \, {\left(5 \, A a^{3} + 6 \, C a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2} + 24 \, C a b^{2} + 8 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(5 \, A a^{3} + 6 \, C a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2} + 24 \, C a b^{2} + 8 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 150 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 450 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 25 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 560 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 210 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1680 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 630 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2640 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 630 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2640 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1080 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 880 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1200 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1248 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3744 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4320 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4320 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1440 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1248 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3744 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 180 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4320 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 180 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4320 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1440 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 560 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1680 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 630 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2640 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 630 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2640 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1080 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 880 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1200 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 450 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 450 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*A*a^3 + 6*C*a^3 + 18*B*a^2*b + 18*A*a*b^2 + 24*C*a*b^2 + 8*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(5*A*a^3 + 6*C*a^3 + 18*B*a^2*b + 18*A*a*b^2 + 24*C*a*b^2 + 8*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(165*A*a^3*tan(1/2*d*x + 1/2*c)^11 - 240*B*a^3*tan(1/2*d*x + 1/2*c)^11 + 150*C*a^3*tan(1/2*d*x + 1/2*c)^11 - 720*A*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 450*B*a^2*b*tan(1/2*d*x + 1/2*c)^11 - 720*C*a^2*b*tan(1/2*d*x + 1/2*c)^11 + 450*A*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 720*B*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 360*C*a*b^2*tan(1/2*d*x + 1/2*c)^11 - 240*A*b^3*tan(1/2*d*x + 1/2*c)^11 + 120*B*b^3*tan(1/2*d*x + 1/2*c)^11 - 240*C*b^3*tan(1/2*d*x + 1/2*c)^11 + 25*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 560*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 210*C*a^3*tan(1/2*d*x + 1/2*c)^9 + 1680*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 630*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 2640*C*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 630*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 2640*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 1080*C*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 880*A*b^3*tan(1/2*d*x + 1/2*c)^9 - 360*B*b^3*tan(1/2*d*x + 1/2*c)^9 + 1200*C*b^3*tan(1/2*d*x + 1/2*c)^9 + 450*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 1248*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 3744*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 180*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 4320*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 180*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 4320*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 1440*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*B*b^3*tan(1/2*d*x + 1/2*c)^7 - 2400*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 450*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1248*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 60*C*a^3*tan(1/2*d*x + 1/2*c)^5 + 3744*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 180*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 4320*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 180*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 4320*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 720*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 1440*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 240*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 2400*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 25*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 560*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 210*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 1680*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 630*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 2640*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 630*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 2640*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 1080*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 880*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 360*B*b^3*tan(1/2*d*x + 1/2*c)^3 - 1200*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 165*A*a^3*tan(1/2*d*x + 1/2*c) + 240*B*a^3*tan(1/2*d*x + 1/2*c) + 150*C*a^3*tan(1/2*d*x + 1/2*c) + 720*A*a^2*b*tan(1/2*d*x + 1/2*c) + 450*B*a^2*b*tan(1/2*d*x + 1/2*c) + 720*C*a^2*b*tan(1/2*d*x + 1/2*c) + 450*A*a*b^2*tan(1/2*d*x + 1/2*c) + 720*B*a*b^2*tan(1/2*d*x + 1/2*c) + 360*C*a*b^2*tan(1/2*d*x + 1/2*c) + 240*A*b^3*tan(1/2*d*x + 1/2*c) + 120*B*b^3*tan(1/2*d*x + 1/2*c) + 240*C*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
964,1,390,0,0.285374," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{4} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{1}{16} \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 24 \, C a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 20 \, C a b^{3} + 5 \, B b^{4}\right)} x + \frac{{\left(4 \, C a b^{3} + B b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(24 \, C a^{2} b^{2} + 16 \, B a b^{3} + 4 \, A b^{4} + 7 \, C b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(8 \, C a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3} + 12 \, C a b^{3} + 3 \, B b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(16 \, C a^{4} + 64 \, B a^{3} b + 96 \, A a^{2} b^{2} + 120 \, C a^{2} b^{2} + 80 \, B a b^{3} + 20 \, A b^{4} + 21 \, C b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(16 \, B a^{4} + 64 \, A a^{3} b + 64 \, C a^{3} b + 96 \, B a^{2} b^{2} + 64 \, A a b^{3} + 60 \, C a b^{3} + 15 \, B b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(64 \, A a^{4} + 48 \, C a^{4} + 192 \, B a^{3} b + 288 \, A a^{2} b^{2} + 240 \, C a^{2} b^{2} + 160 \, B a b^{3} + 40 \, A b^{4} + 35 \, C b^{4}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/448*C*b^4*sin(7*d*x + 7*c)/d + 1/16*(8*B*a^4 + 32*A*a^3*b + 24*C*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 20*C*a*b^3 + 5*B*b^4)*x + 1/192*(4*C*a*b^3 + B*b^4)*sin(6*d*x + 6*c)/d + 1/320*(24*C*a^2*b^2 + 16*B*a*b^3 + 4*A*b^4 + 7*C*b^4)*sin(5*d*x + 5*c)/d + 1/64*(8*C*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3 + 12*C*a*b^3 + 3*B*b^4)*sin(4*d*x + 4*c)/d + 1/192*(16*C*a^4 + 64*B*a^3*b + 96*A*a^2*b^2 + 120*C*a^2*b^2 + 80*B*a*b^3 + 20*A*b^4 + 21*C*b^4)*sin(3*d*x + 3*c)/d + 1/64*(16*B*a^4 + 64*A*a^3*b + 64*C*a^3*b + 96*B*a^2*b^2 + 64*A*a*b^3 + 60*C*a*b^3 + 15*B*b^4)*sin(2*d*x + 2*c)/d + 1/64*(64*A*a^4 + 48*C*a^4 + 192*B*a^3*b + 288*A*a^2*b^2 + 240*C*a^2*b^2 + 160*B*a*b^3 + 40*A*b^4 + 35*C*b^4)*sin(d*x + c)/d","A",0
965,1,326,0,0.359432," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{4} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{1}{16} \, {\left(16 \, A a^{4} + 8 \, C a^{4} + 32 \, B a^{3} b + 48 \, A a^{2} b^{2} + 36 \, C a^{2} b^{2} + 24 \, B a b^{3} + 6 \, A b^{4} + 5 \, C b^{4}\right)} x + \frac{{\left(4 \, C a b^{3} + B b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(12 \, C a^{2} b^{2} + 8 \, B a b^{3} + 2 \, A b^{4} + 3 \, C b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 20 \, C a b^{3} + 5 \, B b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(16 \, C a^{4} + 64 \, B a^{3} b + 96 \, A a^{2} b^{2} + 96 \, C a^{2} b^{2} + 64 \, B a b^{3} + 16 \, A b^{4} + 15 \, C b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(8 \, B a^{4} + 32 \, A a^{3} b + 24 \, C a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 20 \, C a b^{3} + 5 \, B b^{4}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*C*b^4*sin(6*d*x + 6*c)/d + 1/16*(16*A*a^4 + 8*C*a^4 + 32*B*a^3*b + 48*A*a^2*b^2 + 36*C*a^2*b^2 + 24*B*a*b^3 + 6*A*b^4 + 5*C*b^4)*x + 1/80*(4*C*a*b^3 + B*b^4)*sin(5*d*x + 5*c)/d + 1/64*(12*C*a^2*b^2 + 8*B*a*b^3 + 2*A*b^4 + 3*C*b^4)*sin(4*d*x + 4*c)/d + 1/48*(16*C*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 20*C*a*b^3 + 5*B*b^4)*sin(3*d*x + 3*c)/d + 1/64*(16*C*a^4 + 64*B*a^3*b + 96*A*a^2*b^2 + 96*C*a^2*b^2 + 64*B*a*b^3 + 16*A*b^4 + 15*C*b^4)*sin(2*d*x + 2*c)/d + 1/8*(8*B*a^4 + 32*A*a^3*b + 24*C*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 20*C*a*b^3 + 5*B*b^4)*sin(d*x + c)/d","A",0
966,1,1094,0,0.326763," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\frac{120 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 120 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 15 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 12 \, C a b^{3} + 3 \, B b^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 300 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1920 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2880 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1920 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1280 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 160 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2880 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4320 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1600 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 464 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 480 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1920 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2880 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1920 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1280 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 300 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(120*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 120*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 15*(8*B*a^4 + 32*A*a^3*b + 16*C*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 12*C*a*b^3 + 3*B*b^4)*(d*x + c) + 2*(120*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 480*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 240*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 240*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 480*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 300*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 75*B*b^4*tan(1/2*d*x + 1/2*c)^9 + 120*C*b^4*tan(1/2*d*x + 1/2*c)^9 + 480*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 1920*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 480*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 2880*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 1920*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 1280*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 120*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 320*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 30*B*b^4*tan(1/2*d*x + 1/2*c)^7 + 160*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 720*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 2880*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 4320*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 2400*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 1600*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 400*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 464*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 480*C*a^4*tan(1/2*d*x + 1/2*c)^3 + 1920*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 480*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 2880*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 1920*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 1280*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 320*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 30*B*b^4*tan(1/2*d*x + 1/2*c)^3 + 160*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 120*C*a^4*tan(1/2*d*x + 1/2*c) + 480*B*a^3*b*tan(1/2*d*x + 1/2*c) + 240*C*a^3*b*tan(1/2*d*x + 1/2*c) + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 240*A*a*b^3*tan(1/2*d*x + 1/2*c) + 480*B*a*b^3*tan(1/2*d*x + 1/2*c) + 300*C*a*b^3*tan(1/2*d*x + 1/2*c) + 120*A*b^4*tan(1/2*d*x + 1/2*c) + 75*B*b^4*tan(1/2*d*x + 1/2*c) + 120*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
967,1,802,0,0.365865," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{48 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(8 \, C a^{4} + 32 \, B a^{3} b + 48 \, A a^{2} b^{2} + 24 \, C a^{2} b^{2} + 16 \, B a b^{3} + 4 \, A b^{4} + 3 \, C b^{4}\right)} {\left(d x + c\right)} - 24 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 24 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"-1/24*(48*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(8*C*a^4 + 32*B*a^3*b + 48*A*a^2*b^2 + 24*C*a^2*b^2 + 16*B*a*b^3 + 4*A*b^4 + 3*C*b^4)*(d*x + c) - 24*(B*a^4 + 4*A*a^3*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 24*(B*a^4 + 4*A*a^3*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(96*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 96*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 48*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 96*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 12*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 24*B*b^4*tan(1/2*d*x + 1/2*c)^7 - 15*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 48*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 160*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 40*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 9*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 48*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 160*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 40*B*b^4*tan(1/2*d*x + 1/2*c)^3 - 9*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 96*C*a^3*b*tan(1/2*d*x + 1/2*c) + 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 96*A*a*b^3*tan(1/2*d*x + 1/2*c) + 48*B*a*b^3*tan(1/2*d*x + 1/2*c) + 96*C*a*b^3*tan(1/2*d*x + 1/2*c) + 12*A*b^4*tan(1/2*d*x + 1/2*c) + 24*B*b^4*tan(1/2*d*x + 1/2*c) + 15*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
968,1,541,0,0.616451," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{3 \, {\left(8 \, C a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3} + 4 \, C a b^{3} + B b^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(A a^{4} + 2 \, C a^{4} + 8 \, B a^{3} b + 12 \, A a^{2} b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(A a^{4} + 2 \, C a^{4} + 8 \, B a^{3} b + 12 \, A a^{2} b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{6 \, {\left(A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} + \frac{2 \, {\left(36 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(8*C*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3 + 4*C*a*b^3 + B*b^4)*(d*x + c) + 3*(A*a^4 + 2*C*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(A*a^4 + 2*C*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 6*(A*a^4*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 8*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 + A*a^4*tan(1/2*d*x + 1/2*c) + 2*B*a^4*tan(1/2*d*x + 1/2*c) + 8*A*a^3*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2 + 2*(36*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 24*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^4*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 48*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 24*B*a*b^3*tan(1/2*d*x + 1/2*c) + 12*C*a*b^3*tan(1/2*d*x + 1/2*c) + 6*A*b^4*tan(1/2*d*x + 1/2*c) + 3*B*b^4*tan(1/2*d*x + 1/2*c) + 6*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
969,1,550,0,0.346078," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(12 \, C a^{2} b^{2} + 8 \, B a b^{3} + 2 \, A b^{4} + C b^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b + 8 \, C a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(B a^{4} + 4 \, A a^{3} b + 8 \, C a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{6 \, {\left(8 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{2 \, {\left(6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(12*C*a^2*b^2 + 8*B*a*b^3 + 2*A*b^4 + C*b^4)*(d*x + c) + 3*(B*a^4 + 4*A*a^3*b + 8*C*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a^4 + 4*A*a^3*b + 8*C*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 6*(8*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^4*tan(1/2*d*x + 1/2*c)^3 - C*b^4*tan(1/2*d*x + 1/2*c)^3 + 8*C*a*b^3*tan(1/2*d*x + 1/2*c) + 2*B*b^4*tan(1/2*d*x + 1/2*c) + C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - 2*(6*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^4*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 24*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^4*tan(1/2*d*x + 1/2*c) + 3*B*a^4*tan(1/2*d*x + 1/2*c) + 6*C*a^4*tan(1/2*d*x + 1/2*c) + 12*A*a^3*b*tan(1/2*d*x + 1/2*c) + 24*B*a^3*b*tan(1/2*d*x + 1/2*c) + 36*A*a^2*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
970,1,840,0,0.381710," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{\frac{48 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 24 \, {\left(4 \, C a b^{3} + B b^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(3 \, A a^{4} + 4 \, C a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a^{4} + 4 \, C a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(48*C*b^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 24*(4*C*a*b^3 + B*b^4)*(d*x + c) + 3*(3*A*a^4 + 4*C*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 48*C*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a^4 + 4*C*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 48*C*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 96*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 96*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 96*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 40*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 288*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^4*tan(1/2*d*x + 1/2*c) + 24*B*a^4*tan(1/2*d*x + 1/2*c) + 12*C*a^4*tan(1/2*d*x + 1/2*c) + 96*A*a^3*b*tan(1/2*d*x + 1/2*c) + 48*B*a^3*b*tan(1/2*d*x + 1/2*c) + 96*C*a^3*b*tan(1/2*d*x + 1/2*c) + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 96*A*a*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
971,1,1140,0,0.367267," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{120 \, {\left(d x + c\right)} C b^{4} + 15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 32 \, C a b^{3} + 8 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 32 \, C a b^{3} + 8 \, B b^{4}\right)} \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)^{9} - 75 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 300 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 320 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1280 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1920 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2880 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1920 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 400 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4320 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2880 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1280 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1920 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2880 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1920 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 300 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(120*(d*x + c)*C*b^4 + 15*(3*B*a^4 + 12*A*a^3*b + 16*C*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 32*C*a*b^3 + 8*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*B*a^4 + 12*A*a^3*b + 16*C*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 32*C*a*b^3 + 8*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 75*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 120*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 300*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 480*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 240*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 240*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 480*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 160*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 30*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 320*C*a^4*tan(1/2*d*x + 1/2*c)^7 + 120*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 1280*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 480*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 1920*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 2880*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 1920*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 480*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 400*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 1600*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 2400*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 4320*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 2880*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 720*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 160*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 30*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 320*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 120*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1280*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 480*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1920*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 2880*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 1920*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 480*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^4*tan(1/2*d*x + 1/2*c) + 75*B*a^4*tan(1/2*d*x + 1/2*c) + 120*C*a^4*tan(1/2*d*x + 1/2*c) + 300*A*a^3*b*tan(1/2*d*x + 1/2*c) + 480*B*a^3*b*tan(1/2*d*x + 1/2*c) + 240*C*a^3*b*tan(1/2*d*x + 1/2*c) + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 240*A*a*b^3*tan(1/2*d*x + 1/2*c) + 480*B*a*b^3*tan(1/2*d*x + 1/2*c) + 120*A*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
972,1,1658,0,0.410727," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{15 \, {\left(5 \, A a^{4} + 6 \, C a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4} + 16 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(5 \, A a^{4} + 6 \, C a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 48 \, C a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4} + 16 \, C b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 150 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1440 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 560 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 210 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 840 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5280 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2160 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1440 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1248 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8640 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9600 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1248 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5760 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8640 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9600 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 560 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 840 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5280 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2160 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1440 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1440 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*A*a^4 + 6*C*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 48*C*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4 + 16*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(5*A*a^4 + 6*C*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 48*C*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4 + 16*C*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(165*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 240*B*a^4*tan(1/2*d*x + 1/2*c)^11 + 150*C*a^4*tan(1/2*d*x + 1/2*c)^11 - 960*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 600*B*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 960*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 1440*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 960*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 480*B*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 960*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^11 - 240*B*b^4*tan(1/2*d*x + 1/2*c)^11 + 25*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 560*B*a^4*tan(1/2*d*x + 1/2*c)^9 - 210*C*a^4*tan(1/2*d*x + 1/2*c)^9 + 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 840*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 5280*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 2160*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 1440*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 4800*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 360*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 1200*B*b^4*tan(1/2*d*x + 1/2*c)^9 + 450*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 1248*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 60*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 240*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 8640*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 1440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 960*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 9600*C*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 2400*B*b^4*tan(1/2*d*x + 1/2*c)^7 + 450*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 1248*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 60*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 240*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 5760*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 8640*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 1440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 960*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 9600*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 240*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 2400*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 25*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 560*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 210*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 840*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 3520*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 5280*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 2160*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 1440*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 4800*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 360*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 1200*B*b^4*tan(1/2*d*x + 1/2*c)^3 + 165*A*a^4*tan(1/2*d*x + 1/2*c) + 240*B*a^4*tan(1/2*d*x + 1/2*c) + 150*C*a^4*tan(1/2*d*x + 1/2*c) + 960*A*a^3*b*tan(1/2*d*x + 1/2*c) + 600*B*a^3*b*tan(1/2*d*x + 1/2*c) + 960*C*a^3*b*tan(1/2*d*x + 1/2*c) + 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 1440*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 720*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 960*A*a*b^3*tan(1/2*d*x + 1/2*c) + 480*B*a*b^3*tan(1/2*d*x + 1/2*c) + 960*C*a*b^3*tan(1/2*d*x + 1/2*c) + 120*A*b^4*tan(1/2*d*x + 1/2*c) + 240*B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
973,1,1888,0,0.420075," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^8,x, algorithm=""giac"")","\frac{105 \, {\left(5 \, B a^{4} + 20 \, A a^{3} b + 24 \, C a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 32 \, C a b^{3} + 8 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(5 \, B a^{4} + 20 \, A a^{3} b + 24 \, C a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 32 \, C a b^{3} + 8 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(1680 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1155 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4620 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 6720 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4200 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 10080 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 6300 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 10080 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4200 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 6720 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 3360 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 840 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 3360 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 980 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 5600 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3920 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 22400 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 10080 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 33600 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 15120 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 47040 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 10080 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 31360 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 13440 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 7840 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3360 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 10080 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 14448 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2975 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 12656 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 11900 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 50624 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 7560 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 75936 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 11340 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 97440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 7560 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 64960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 16800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 16240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25200 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 10176 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17472 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 69888 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 104832 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 120960 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80640 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 20160 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 33600 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 14448 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2975 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12656 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 11900 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 50624 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7560 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 75936 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 11340 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 97440 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7560 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 64960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16800 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25200 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3360 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 980 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5600 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3920 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 22400 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10080 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 33600 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15120 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 47040 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10080 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 31360 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 13440 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7840 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3360 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10080 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1680 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1155 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4620 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6720 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4200 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10080 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6300 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10080 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4200 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6720 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3360 \, C a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 840 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(5*B*a^4 + 20*A*a^3*b + 24*C*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 32*C*a*b^3 + 8*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(5*B*a^4 + 20*A*a^3*b + 24*C*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 32*C*a*b^3 + 8*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(1680*A*a^4*tan(1/2*d*x + 1/2*c)^13 - 1155*B*a^4*tan(1/2*d*x + 1/2*c)^13 + 1680*C*a^4*tan(1/2*d*x + 1/2*c)^13 - 4620*A*a^3*b*tan(1/2*d*x + 1/2*c)^13 + 6720*B*a^3*b*tan(1/2*d*x + 1/2*c)^13 - 4200*C*a^3*b*tan(1/2*d*x + 1/2*c)^13 + 10080*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 - 6300*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 + 10080*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^13 - 4200*A*a*b^3*tan(1/2*d*x + 1/2*c)^13 + 6720*B*a*b^3*tan(1/2*d*x + 1/2*c)^13 - 3360*C*a*b^3*tan(1/2*d*x + 1/2*c)^13 + 1680*A*b^4*tan(1/2*d*x + 1/2*c)^13 - 840*B*b^4*tan(1/2*d*x + 1/2*c)^13 + 1680*C*b^4*tan(1/2*d*x + 1/2*c)^13 - 3360*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 980*B*a^4*tan(1/2*d*x + 1/2*c)^11 - 5600*C*a^4*tan(1/2*d*x + 1/2*c)^11 + 3920*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 22400*B*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 10080*C*a^3*b*tan(1/2*d*x + 1/2*c)^11 - 33600*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 15120*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 47040*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 + 10080*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 31360*B*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 13440*C*a*b^3*tan(1/2*d*x + 1/2*c)^11 - 7840*A*b^4*tan(1/2*d*x + 1/2*c)^11 + 3360*B*b^4*tan(1/2*d*x + 1/2*c)^11 - 10080*C*b^4*tan(1/2*d*x + 1/2*c)^11 + 14448*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 2975*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 12656*C*a^4*tan(1/2*d*x + 1/2*c)^9 - 11900*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 50624*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 7560*C*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 75936*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 11340*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 97440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 7560*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 64960*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 16800*C*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 16240*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 4200*B*b^4*tan(1/2*d*x + 1/2*c)^9 + 25200*C*b^4*tan(1/2*d*x + 1/2*c)^9 - 10176*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 17472*C*a^4*tan(1/2*d*x + 1/2*c)^7 - 69888*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 104832*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 120960*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 80640*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 20160*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 33600*C*b^4*tan(1/2*d*x + 1/2*c)^7 + 14448*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 2975*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 12656*C*a^4*tan(1/2*d*x + 1/2*c)^5 + 11900*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 50624*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 7560*C*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 75936*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 11340*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 97440*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 7560*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 64960*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 16800*C*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 16240*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 4200*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 25200*C*b^4*tan(1/2*d*x + 1/2*c)^5 - 3360*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 980*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 5600*C*a^4*tan(1/2*d*x + 1/2*c)^3 - 3920*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 22400*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 10080*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 33600*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 15120*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 47040*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 10080*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 31360*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 13440*C*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 7840*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 3360*B*b^4*tan(1/2*d*x + 1/2*c)^3 - 10080*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 1680*A*a^4*tan(1/2*d*x + 1/2*c) + 1155*B*a^4*tan(1/2*d*x + 1/2*c) + 1680*C*a^4*tan(1/2*d*x + 1/2*c) + 4620*A*a^3*b*tan(1/2*d*x + 1/2*c) + 6720*B*a^3*b*tan(1/2*d*x + 1/2*c) + 4200*C*a^3*b*tan(1/2*d*x + 1/2*c) + 10080*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 6300*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 10080*C*a^2*b^2*tan(1/2*d*x + 1/2*c) + 4200*A*a*b^3*tan(1/2*d*x + 1/2*c) + 6720*B*a*b^3*tan(1/2*d*x + 1/2*c) + 3360*C*a*b^3*tan(1/2*d*x + 1/2*c) + 1680*A*b^4*tan(1/2*d*x + 1/2*c) + 840*B*b^4*tan(1/2*d*x + 1/2*c) + 1680*C*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","B",0
974,1,227,0,0.230799," ","integrate((a+b*cos(d*x+c))^3*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{5} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{1}{8} \, {\left(8 \, C a^{5} - 8 \, B a^{4} b + 8 \, C a^{3} b^{2} - 24 \, B a^{2} b^{3} - 9 \, C a b^{4} - 3 \, B b^{5}\right)} x + \frac{{\left(3 \, C a b^{4} + B b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(8 \, C a^{2} b^{3} + 16 \, B a b^{4} + 5 \, C b^{5}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{{\left(2 \, C a^{3} b^{2} - 6 \, B a^{2} b^{3} - 3 \, C a b^{4} - B b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} - \frac{{\left(24 \, C a^{4} b - 32 \, B a^{3} b^{2} - 12 \, C a^{2} b^{3} - 24 \, B a b^{4} - 5 \, C b^{5}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*C*b^5*sin(5*d*x + 5*c)/d - 1/8*(8*C*a^5 - 8*B*a^4*b + 8*C*a^3*b^2 - 24*B*a^2*b^3 - 9*C*a*b^4 - 3*B*b^5)*x + 1/32*(3*C*a*b^4 + B*b^5)*sin(4*d*x + 4*c)/d + 1/48*(8*C*a^2*b^3 + 16*B*a*b^4 + 5*C*b^5)*sin(3*d*x + 3*c)/d - 1/4*(2*C*a^3*b^2 - 6*B*a^2*b^3 - 3*C*a*b^4 - B*b^5)*sin(2*d*x + 2*c)/d - 1/8*(24*C*a^4*b - 32*B*a^3*b^2 - 12*C*a^2*b^3 - 24*B*a*b^4 - 5*C*b^5)*sin(d*x + c)/d","A",0
975,1,144,0,1.590082," ","integrate((a+b*cos(d*x+c))^2*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{4} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{1}{8} \, {\left(8 \, C a^{4} - 8 \, B a^{3} b - 12 \, B a b^{3} - 3 \, C b^{4}\right)} x + \frac{{\left(2 \, C a b^{3} + B b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(3 \, B a b^{3} + C b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} - \frac{{\left(8 \, C a^{3} b - 12 \, B a^{2} b^{2} - 6 \, C a b^{3} - 3 \, B b^{4}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/32*C*b^4*sin(4*d*x + 4*c)/d - 1/8*(8*C*a^4 - 8*B*a^3*b - 12*B*a*b^3 - 3*C*b^4)*x + 1/12*(2*C*a*b^3 + B*b^4)*sin(3*d*x + 3*c)/d + 1/4*(3*B*a*b^3 + C*b^4)*sin(2*d*x + 2*c)/d - 1/4*(8*C*a^3*b - 12*B*a^2*b^2 - 6*C*a*b^3 - 3*B*b^4)*sin(d*x + c)/d","A",0
976,1,107,0,0.184095," ","integrate((a+b*cos(d*x+c))*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""giac"")","\frac{C b^{3} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{1}{2} \, {\left(2 \, C a^{3} - 2 \, B a^{2} b - C a b^{2} - B b^{3}\right)} x + \frac{{\left(C a b^{2} + B b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} - \frac{{\left(4 \, C a^{2} b - 8 \, B a b^{2} - 3 \, C b^{3}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/12*C*b^3*sin(3*d*x + 3*c)/d - 1/2*(2*C*a^3 - 2*B*a^2*b - C*a*b^2 - B*b^3)*x + 1/4*(C*a*b^2 + B*b^3)*sin(2*d*x + 2*c)/d - 1/4*(4*C*a^2*b - 8*B*a*b^2 - 3*C*b^3)*sin(d*x + c)/d","A",0
977,1,801,0,0.253402," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, C a^{4} - 8 \, B a^{3} b + 8 \, A a^{2} b^{2} + 4 \, C a^{2} b^{2} - 4 \, B a b^{3} + 4 \, A b^{4} + 3 \, C b^{4}\right)} {\left(d x + c\right)}}{b^{5}} + \frac{48 \, {\left(C a^{5} - B a^{4} b + A a^{3} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{5}} - \frac{2 \, {\left(24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} b^{4}}}{24 \, d}"," ",0,"1/24*(3*(8*C*a^4 - 8*B*a^3*b + 8*A*a^2*b^2 + 4*C*a^2*b^2 - 4*B*a*b^3 + 4*A*b^4 + 3*C*b^4)*(d*x + c)/b^5 + 48*(C*a^5 - B*a^4*b + A*a^3*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^5) - 2*(24*C*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 24*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 12*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*C*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 24*B*b^3*tan(1/2*d*x + 1/2*c)^7 + 15*C*b^3*tan(1/2*d*x + 1/2*c)^7 + 72*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 72*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 72*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 40*C*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*A*b^3*tan(1/2*d*x + 1/2*c)^5 - 40*B*b^3*tan(1/2*d*x + 1/2*c)^5 - 9*C*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^3*tan(1/2*d*x + 1/2*c)^3 - 72*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 72*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 40*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 40*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 9*C*b^3*tan(1/2*d*x + 1/2*c)^3 + 24*C*a^3*tan(1/2*d*x + 1/2*c) - 24*B*a^2*b*tan(1/2*d*x + 1/2*c) - 12*C*a^2*b*tan(1/2*d*x + 1/2*c) + 24*A*a*b^2*tan(1/2*d*x + 1/2*c) + 12*B*a*b^2*tan(1/2*d*x + 1/2*c) + 24*C*a*b^2*tan(1/2*d*x + 1/2*c) - 12*A*b^3*tan(1/2*d*x + 1/2*c) - 24*B*b^3*tan(1/2*d*x + 1/2*c) - 15*C*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^4))/d","B",0
978,1,424,0,0.222414," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{3} - 2 \, B a^{2} b + 2 \, A a b^{2} + C a b^{2} - B b^{3}\right)} {\left(d x + c\right)}}{b^{4}} + \frac{12 \, {\left(C a^{4} - B a^{3} b + A a^{2} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} - \frac{2 \, {\left(6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*C*a^3 - 2*B*a^2*b + 2*A*a*b^2 + C*a*b^2 - B*b^3)*(d*x + c)/b^4 + 12*(C*a^4 - B*a^3*b + A*a^2*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) - 2*(6*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 6*B*a*b*tan(1/2*d*x + 1/2*c) - 3*C*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c) + 3*B*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^3))/d","B",0
979,1,239,0,0.199090," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, C a^{2} - 2 \, B a b + 2 \, A b^{2} + C b^{2}\right)} {\left(d x + c\right)}}{b^{3}} + \frac{4 \, {\left(C a^{3} - B a^{2} b + A a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{3}} - \frac{2 \, {\left(2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*((2*C*a^2 - 2*B*a*b + 2*A*b^2 + C*b^2)*(d*x + c)/b^3 + 4*(C*a^3 - B*a^2*b + A*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^3) - 2*(2*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 + 2*C*a*tan(1/2*d*x + 1/2*c) - 2*B*b*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^2))/d","A",0
980,1,147,0,0.393742," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(C a - B b\right)} {\left(d x + c\right)}}{b^{2}} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b} + \frac{2 \, {\left(C a^{2} - B a b + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{2}}}{d}"," ",0,"-((C*a - B*b)*(d*x + c)/b^2 - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b) + 2*(C*a^2 - B*a*b + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^2))/d","A",0
981,1,148,0,0.333066," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} C}{b} + \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(C a^{2} - B a b + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a b}}{d}"," ",0,"((d*x + c)*C/b + A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(C*a^2 - B*a*b + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a*b))/d","A",0
982,1,180,0,0.259949," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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)}{a^{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)}{a^{2}} - \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a} - \frac{2 \, {\left(C a^{2} - B a b + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{2}}}{d}"," ",0,"((B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - (B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a) - 2*(C*a^2 - B*a*b + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^2))/d","A",0
983,1,287,0,0.331748," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(A a^{2} + 2 \, C a^{2} - 2 \, B a b + 2 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{{\left(A a^{2} + 2 \, C a^{2} - 2 \, B a b + 2 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{4 \, {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3}} + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*((A*a^2 + 2*C*a^2 - 2*B*a*b + 2*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (A*a^2 + 2*C*a^2 - 2*B*a*b + 2*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 4*(C*a^2*b - B*a*b^2 + A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 2*A*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) + 2*B*a*tan(1/2*d*x + 1/2*c) - 2*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2))/d","B",0
984,1,483,0,1.820482," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(B a^{3} - A a^{2} b - 2 \, C a^{2} b + 2 \, B a b^{2} - 2 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3 \, {\left(B a^{3} - A a^{2} b - 2 \, C a^{2} b + 2 \, B a b^{2} - 2 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{12 \, {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4}} - \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a^3 - A*a^2*b - 2*C*a^2*b + 2*B*a*b^2 - 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3*(B*a^3 - A*a^2*b - 2*C*a^2*b + 2*B*a*b^2 - 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - 12*(C*a^2*b^2 - B*a*b^3 + A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4) - 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 3*A*a*b*tan(1/2*d*x + 1/2*c) - 6*B*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^3))/d","B",0
985,1,878,0,1.486860," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, A a^{4} + 4 \, C a^{4} - 4 \, B a^{3} b + 4 \, A a^{2} b^{2} + 8 \, C a^{2} b^{2} - 8 \, B a b^{3} + 8 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} - \frac{3 \, {\left(3 \, A a^{4} + 4 \, C a^{4} - 4 \, B a^{3} b + 4 \, A a^{2} b^{2} + 8 \, C a^{2} b^{2} - 8 \, B a b^{3} + 8 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}} + \frac{48 \, {\left(C a^{2} b^{3} - B a b^{4} + A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{5}} + \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4} a^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^4 + 4*C*a^4 - 4*B*a^3*b + 4*A*a^2*b^2 + 8*C*a^2*b^2 - 8*B*a*b^3 + 8*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 - 3*(3*A*a^4 + 4*C*a^4 - 4*B*a^3*b + 4*A*a^2*b^2 + 8*C*a^2*b^2 - 8*B*a*b^3 + 8*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5 + 48*(C*a^2*b^3 - B*a*b^4 + A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^5) + 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 12*C*a^3*tan(1/2*d*x + 1/2*c)^7 + 24*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 12*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 24*C*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 24*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 12*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 72*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 72*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^3*tan(1/2*d*x + 1/2*c) + 24*B*a^3*tan(1/2*d*x + 1/2*c) + 12*C*a^3*tan(1/2*d*x + 1/2*c) - 24*A*a^2*b*tan(1/2*d*x + 1/2*c) - 12*B*a^2*b*tan(1/2*d*x + 1/2*c) - 24*C*a^2*b*tan(1/2*d*x + 1/2*c) + 12*A*a*b^2*tan(1/2*d*x + 1/2*c) + 24*B*a*b^2*tan(1/2*d*x + 1/2*c) - 24*A*b^3*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^4*a^4))/d","B",0
986,1,563,0,0.249812," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(4 \, C a^{6} - 3 \, B a^{5} b + 2 \, A a^{4} b^{2} - 5 \, C a^{4} b^{2} + 4 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{5} - b^{7}\right)} \sqrt{a^{2} - b^{2}}} - \frac{12 \, {\left(C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} + \frac{3 \, {\left(8 \, C a^{3} - 6 \, B a^{2} b + 4 \, A a b^{2} + 2 \, C a b^{2} - B b^{3}\right)} {\left(d x + c\right)}}{b^{5}} - \frac{2 \, {\left(18 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{4}}}{6 \, d}"," ",0,"-1/6*(12*(4*C*a^6 - 3*B*a^5*b + 2*A*a^4*b^2 - 5*C*a^4*b^2 + 4*B*a^3*b^3 - 3*A*a^2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^5 - b^7)*sqrt(a^2 - b^2)) - 12*(C*a^5*tan(1/2*d*x + 1/2*c) - B*a^4*b*tan(1/2*d*x + 1/2*c) + A*a^3*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) + 3*(8*C*a^3 - 6*B*a^2*b + 4*A*a*b^2 + 2*C*a*b^2 - B*b^3)*(d*x + c)/b^5 - 2*(18*C*a^2*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*b^2*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*b^2*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^2*tan(1/2*d*x + 1/2*c) - 12*B*a*b*tan(1/2*d*x + 1/2*c) - 6*C*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c) + 3*B*b^2*tan(1/2*d*x + 1/2*c) + 6*C*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^4))/d","A",0
987,1,376,0,1.115911," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(3 \, C a^{5} - 2 \, B a^{4} b + A a^{3} b^{2} - 4 \, C a^{3} b^{2} + 3 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{4 \, {\left(C a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} + \frac{{\left(6 \, C a^{2} - 4 \, B a b + 2 \, A b^{2} + C b^{2}\right)} {\left(d x + c\right)}}{b^{4}} - \frac{2 \, {\left(4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{3}}}{2 \, d}"," ",0,"1/2*(4*(3*C*a^5 - 2*B*a^4*b + A*a^3*b^2 - 4*C*a^3*b^2 + 3*B*a^2*b^3 - 2*A*a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - 4*(C*a^4*tan(1/2*d*x + 1/2*c) - B*a^3*b*tan(1/2*d*x + 1/2*c) + A*a^2*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b^3 - b^5)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) + (6*C*a^2 - 4*B*a*b + 2*A*b^2 + C*b^2)*(d*x + c)/b^4 - 2*(4*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 + 4*C*a*tan(1/2*d*x + 1/2*c) - 2*B*b*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^3))/d","A",0
988,1,1249,0,2.942463," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(4 \, C a^{6} b^{2} - 2 \, B a^{5} b^{3} - 2 \, C a^{5} b^{3} + B a^{4} b^{4} - 9 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 4 \, C a^{3} b^{5} - A a^{2} b^{6} - 2 \, B a^{2} b^{6} + 5 \, C a^{2} b^{6} - 3 \, B a b^{7} - 2 \, C a b^{7} + A b^{8} + B b^{8} + 2 \, C a^{3} {\left| -a^{2} b^{3} + b^{5} \right|} - B a^{2} b {\left| -a^{2} b^{3} + b^{5} \right|} - C a^{2} b {\left| -a^{2} b^{3} + b^{5} \right|} + B a b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} - 2 \, C a b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} - A b^{3} {\left| -a^{2} b^{3} + b^{5} \right|} + B b^{3} {\left| -a^{2} b^{3} + b^{5} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a^{3} b^{2} - 2 \, a b^{4} + \sqrt{-4 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)}^{2}}}{a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}}}}\right)\right)}}{a^{3} b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} - a b^{4} {\left| -a^{2} b^{3} + b^{5} \right|} + {\left(a^{2} b^{3} - b^{5}\right)}^{2}} + \frac{{\left(\sqrt{a^{2} - b^{2}} A b^{3} {\left| -a^{2} b^{3} + b^{5} \right|} {\left| -a + b \right|} + {\left(a^{2} b - a b^{2} - b^{3}\right)} \sqrt{a^{2} - b^{2}} B {\left| -a^{2} b^{3} + b^{5} \right|} {\left| -a + b \right|} - {\left(2 \, a^{3} - a^{2} b - 2 \, a b^{2}\right)} \sqrt{a^{2} - b^{2}} C {\left| -a^{2} b^{3} + b^{5} \right|} {\left| -a + b \right|} - {\left(a^{2} b^{6} - b^{8}\right)} \sqrt{a^{2} - b^{2}} A {\left| -a + b \right|} - {\left(2 \, a^{5} b^{3} - a^{4} b^{4} - 5 \, a^{3} b^{5} + 2 \, a^{2} b^{6} + 3 \, a b^{7} - b^{8}\right)} \sqrt{a^{2} - b^{2}} B {\left| -a + b \right|} + {\left(4 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 9 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + 5 \, a^{2} b^{6} - 2 \, a b^{7}\right)} \sqrt{a^{2} - b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a^{3} b^{2} - 2 \, a b^{4} - \sqrt{-4 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)}^{2}}}{a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} {\left| -a^{2} b^{3} + b^{5} \right|}} + \frac{2 \, {\left(2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} {\left(a^{2} b^{2} - b^{4}\right)}}}{d}"," ",0,"((4*C*a^6*b^2 - 2*B*a^5*b^3 - 2*C*a^5*b^3 + B*a^4*b^4 - 9*C*a^4*b^4 + 5*B*a^3*b^5 + 4*C*a^3*b^5 - A*a^2*b^6 - 2*B*a^2*b^6 + 5*C*a^2*b^6 - 3*B*a*b^7 - 2*C*a*b^7 + A*b^8 + B*b^8 + 2*C*a^3*abs(-a^2*b^3 + b^5) - B*a^2*b*abs(-a^2*b^3 + b^5) - C*a^2*b*abs(-a^2*b^3 + b^5) + B*a*b^2*abs(-a^2*b^3 + b^5) - 2*C*a*b^2*abs(-a^2*b^3 + b^5) - A*b^3*abs(-a^2*b^3 + b^5) + B*b^3*abs(-a^2*b^3 + b^5))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a^3*b^2 - 2*a*b^4 + sqrt(-4*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5) + 4*(a^3*b^2 - a*b^4)^2))/(a^3*b^2 - a^2*b^3 - a*b^4 + b^5))))/(a^3*b^2*abs(-a^2*b^3 + b^5) - a*b^4*abs(-a^2*b^3 + b^5) + (a^2*b^3 - b^5)^2) + (sqrt(a^2 - b^2)*A*b^3*abs(-a^2*b^3 + b^5)*abs(-a + b) + (a^2*b - a*b^2 - b^3)*sqrt(a^2 - b^2)*B*abs(-a^2*b^3 + b^5)*abs(-a + b) - (2*a^3 - a^2*b - 2*a*b^2)*sqrt(a^2 - b^2)*C*abs(-a^2*b^3 + b^5)*abs(-a + b) - (a^2*b^6 - b^8)*sqrt(a^2 - b^2)*A*abs(-a + b) - (2*a^5*b^3 - a^4*b^4 - 5*a^3*b^5 + 2*a^2*b^6 + 3*a*b^7 - b^8)*sqrt(a^2 - b^2)*B*abs(-a + b) + (4*a^6*b^2 - 2*a^5*b^3 - 9*a^4*b^4 + 4*a^3*b^5 + 5*a^2*b^6 - 2*a*b^7)*sqrt(a^2 - b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a^3*b^2 - 2*a*b^4 - sqrt(-4*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5) + 4*(a^3*b^2 - a*b^4)^2))/(a^3*b^2 - a^2*b^3 - a*b^4 + b^5))))/((a^2*b^3 - b^5)^2*(a^2 - 2*a*b + b^2) - (a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*abs(-a^2*b^3 + b^5)) + 2*(2*C*a^3*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + C*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^3*tan(1/2*d*x + 1/2*c) - B*a^2*b*tan(1/2*d*x + 1/2*c) + C*a^2*b*tan(1/2*d*x + 1/2*c) + A*a*b^2*tan(1/2*d*x + 1/2*c) - C*a*b^2*tan(1/2*d*x + 1/2*c) - C*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)*(a^2*b^2 - b^4)))/d","B",0
989,1,220,0,2.109526," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(C a^{3} - A a b^{2} - 2 \, C a b^{2} + B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{{\left(d x + c\right)} C}{b^{2}} - \frac{2 \, {\left(C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b - b^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}}}{d}"," ",0,"(2*(C*a^3 - A*a*b^2 - 2*C*a*b^2 + B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^2 - b^4)*sqrt(a^2 - b^2)) + (d*x + c)*C/b^2 - 2*(C*a^2*tan(1/2*d*x + 1/2*c) - B*a*b*tan(1/2*d*x + 1/2*c) + A*b^2*tan(1/2*d*x + 1/2*c))/((a^2*b - b^3)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)))/d","A",0
990,1,244,0,0.241663," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a^{3} - 2 \, A a^{2} b - C a^{2} b + A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}}}{d}"," ",0,"(2*(B*a^3 - 2*A*a^2*b - C*a^2*b + A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - a^2*b^2)*sqrt(a^2 - b^2)) + A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 2*(C*a^2*tan(1/2*d*x + 1/2*c) - B*a*b*tan(1/2*d*x + 1/2*c) + A*b^2*tan(1/2*d*x + 1/2*c))/((a^3 - a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)))/d","A",0
991,1,442,0,0.288727," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(C a^{4} - 2 \, B a^{3} b + 3 \, A a^{2} b^{2} + B a b^{3} - 2 \, A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{4} - a^{2} b^{2}\right)}} - \frac{{\left(B a - 2 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} + \frac{{\left(B a - 2 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}}}{d}"," ",0,"-(2*(C*a^4 - 2*B*a^3*b + 3*A*a^2*b^2 + B*a*b^3 - 2*A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^5 - a^3*b^2)*sqrt(a^2 - b^2)) + 2*(A*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + C*a^2*b*tan(1/2*d*x + 1/2*c)^3 - A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^3*tan(1/2*d*x + 1/2*c)^3 + A*a^3*tan(1/2*d*x + 1/2*c) + A*a^2*b*tan(1/2*d*x + 1/2*c) - C*a^2*b*tan(1/2*d*x + 1/2*c) - A*a*b^2*tan(1/2*d*x + 1/2*c) + B*a*b^2*tan(1/2*d*x + 1/2*c) - 2*A*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^4 - a^2*b^2)) - (B*a - 2*A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 + (B*a - 2*A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3)/d","B",0
992,1,423,0,1.502472," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(2 \, C a^{4} b - 3 \, B a^{3} b^{2} + 4 \, A a^{2} b^{3} - C a^{2} b^{3} + 2 \, B a b^{4} - 3 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{4 \, {\left(C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} + \frac{{\left(A a^{2} + 2 \, C a^{2} - 4 \, B a b + 6 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{{\left(A a^{2} + 2 \, C a^{2} - 4 \, B a b + 6 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}}}{2 \, d}"," ",0,"1/2*(4*(2*C*a^4*b - 3*B*a^3*b^2 + 4*A*a^2*b^3 - C*a^2*b^3 + 2*B*a*b^4 - 3*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - a^4*b^2)*sqrt(a^2 - b^2)) + 4*(C*a^2*b^2*tan(1/2*d*x + 1/2*c) - B*a*b^3*tan(1/2*d*x + 1/2*c) + A*b^4*tan(1/2*d*x + 1/2*c))/((a^5 - a^3*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) + (A*a^2 + 2*C*a^2 - 4*B*a*b + 6*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - (A*a^2 + 2*C*a^2 - 4*B*a*b + 6*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/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
993,1,619,0,0.320547," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(3 \, C a^{4} b^{2} - 4 \, B a^{3} b^{3} + 5 \, A a^{2} b^{4} - 2 \, C a^{2} b^{4} + 3 \, B a b^{5} - 4 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{7} - a^{5} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{12 \, {\left(C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} - \frac{3 \, {\left(B a^{3} - 2 \, A a^{2} b - 4 \, C a^{2} b + 6 \, B a b^{2} - 8 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} + \frac{3 \, {\left(B a^{3} - 2 \, A a^{2} b - 4 \, C a^{2} b + 6 \, B a b^{2} - 8 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}} + \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{4}}}{6 \, d}"," ",0,"-1/6*(12*(3*C*a^4*b^2 - 4*B*a^3*b^3 + 5*A*a^2*b^4 - 2*C*a^2*b^4 + 3*B*a*b^5 - 4*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^7 - a^5*b^2)*sqrt(a^2 - b^2)) + 12*(C*a^2*b^3*tan(1/2*d*x + 1/2*c) - B*a*b^4*tan(1/2*d*x + 1/2*c) + A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - a^4*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) - 3*(B*a^3 - 2*A*a^2*b - 4*C*a^2*b + 6*B*a*b^2 - 8*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 + 3*(B*a^3 - 2*A*a^2*b - 4*C*a^2*b + 6*B*a*b^2 - 8*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5 + 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 36*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) + 6*C*a^2*tan(1/2*d*x + 1/2*c) - 6*A*a*b*tan(1/2*d*x + 1/2*c) - 12*B*a*b*tan(1/2*d*x + 1/2*c) + 18*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^4))/d","A",0
994,1,3417,0,2.744107," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left({\left(2 \, a^{4} b^{2} - a^{3} b^{3} - 4 \, a^{2} b^{4} + 4 \, a b^{5} + 2 \, b^{6}\right)} \sqrt{a^{2} - b^{2}} A {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} {\left| -a + b \right|} - 3 \, {\left(2 \, a^{5} b - a^{4} b^{2} - 4 \, a^{3} b^{3} + 2 \, a^{2} b^{4} + 2 \, a b^{5}\right)} \sqrt{a^{2} - b^{2}} B {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} {\left| -a + b \right|} + {\left(12 \, a^{6} - 6 \, a^{5} b - 23 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} - a b^{5} + b^{6}\right)} \sqrt{a^{2} - b^{2}} C {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} {\left| -a + b \right|} + {\left(4 \, a^{9} b^{6} - 2 \, a^{8} b^{7} - 17 \, a^{7} b^{8} + 8 \, a^{6} b^{9} + 30 \, a^{5} b^{10} - 12 \, a^{4} b^{11} - 25 \, a^{3} b^{12} + 8 \, a^{2} b^{13} + 8 \, a b^{14} - 2 \, b^{15}\right)} \sqrt{a^{2} - b^{2}} A {\left| -a + b \right|} - 3 \, {\left(4 \, a^{10} b^{5} - 2 \, a^{9} b^{6} - 17 \, a^{8} b^{7} + 8 \, a^{7} b^{8} + 28 \, a^{6} b^{9} - 12 \, a^{5} b^{10} - 21 \, a^{4} b^{11} + 8 \, a^{3} b^{12} + 6 \, a^{2} b^{13} - 2 \, a b^{14}\right)} \sqrt{a^{2} - b^{2}} B {\left| -a + b \right|} + {\left(24 \, a^{11} b^{4} - 12 \, a^{10} b^{5} - 100 \, a^{9} b^{6} + 47 \, a^{8} b^{7} + 158 \, a^{7} b^{8} - 68 \, a^{6} b^{9} - 111 \, a^{5} b^{10} + 42 \, a^{4} b^{11} + 28 \, a^{3} b^{12} - 8 \, a^{2} b^{13} + a b^{14} - b^{15}\right)} \sqrt{a^{2} - b^{2}} C {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{4 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 4 \, a b^{8} + \sqrt{-16 \, {\left(a^{5} b^{4} + a^{4} b^{5} - 2 \, a^{3} b^{6} - 2 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} {\left(a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} + 16 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)}^{2}}}{a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}}}}\right)\right)}}{{\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} + {\left(a^{7} b^{4} - 2 \, a^{6} b^{5} - a^{5} b^{6} + 4 \, a^{4} b^{7} - a^{3} b^{8} - 2 \, a^{2} b^{9} + a b^{10}\right)} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|}} - \frac{{\left(24 \, C a^{11} b^{4} - 12 \, B a^{10} b^{5} - 12 \, C a^{10} b^{5} + 4 \, A a^{9} b^{6} + 6 \, B a^{9} b^{6} - 100 \, C a^{9} b^{6} - 2 \, A a^{8} b^{7} + 51 \, B a^{8} b^{7} + 47 \, C a^{8} b^{7} - 17 \, A a^{7} b^{8} - 24 \, B a^{7} b^{8} + 158 \, C a^{7} b^{8} + 8 \, A a^{6} b^{9} - 84 \, B a^{6} b^{9} - 68 \, C a^{6} b^{9} + 30 \, A a^{5} b^{10} + 36 \, B a^{5} b^{10} - 111 \, C a^{5} b^{10} - 12 \, A a^{4} b^{11} + 63 \, B a^{4} b^{11} + 42 \, C a^{4} b^{11} - 25 \, A a^{3} b^{12} - 24 \, B a^{3} b^{12} + 28 \, C a^{3} b^{12} + 8 \, A a^{2} b^{13} - 18 \, B a^{2} b^{13} - 8 \, C a^{2} b^{13} + 8 \, A a b^{14} + 6 \, B a b^{14} + C a b^{14} - 2 \, A b^{15} - C b^{15} - 12 \, C a^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, B a^{5} b {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, C a^{5} b {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 2 \, A a^{4} b^{2} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 3 \, B a^{4} b^{2} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 23 \, C a^{4} b^{2} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + A a^{3} b^{3} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 12 \, B a^{3} b^{3} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 10 \, C a^{3} b^{3} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 4 \, A a^{2} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, B a^{2} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 10 \, C a^{2} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 4 \, A a b^{5} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, B a b^{5} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + C a b^{5} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 2 \, A b^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - C b^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{4 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 4 \, a b^{8} - \sqrt{-16 \, {\left(a^{5} b^{4} + a^{4} b^{5} - 2 \, a^{3} b^{6} - 2 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} {\left(a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} + 16 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)}^{2}}}{a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}}}}\right)\right)}}{a^{5} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 2 \, a^{3} b^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + a b^{8} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)}^{2}} + \frac{2 \, {\left(12 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 67 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 35 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 29 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 26 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 17 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, C a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(((2*a^4*b^2 - a^3*b^3 - 4*a^2*b^4 + 4*a*b^5 + 2*b^6)*sqrt(a^2 - b^2)*A*abs(a^4*b^5 - 2*a^2*b^7 + b^9)*abs(-a + b) - 3*(2*a^5*b - a^4*b^2 - 4*a^3*b^3 + 2*a^2*b^4 + 2*a*b^5)*sqrt(a^2 - b^2)*B*abs(a^4*b^5 - 2*a^2*b^7 + b^9)*abs(-a + b) + (12*a^6 - 6*a^5*b - 23*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 - a*b^5 + b^6)*sqrt(a^2 - b^2)*C*abs(a^4*b^5 - 2*a^2*b^7 + b^9)*abs(-a + b) + (4*a^9*b^6 - 2*a^8*b^7 - 17*a^7*b^8 + 8*a^6*b^9 + 30*a^5*b^10 - 12*a^4*b^11 - 25*a^3*b^12 + 8*a^2*b^13 + 8*a*b^14 - 2*b^15)*sqrt(a^2 - b^2)*A*abs(-a + b) - 3*(4*a^10*b^5 - 2*a^9*b^6 - 17*a^8*b^7 + 8*a^7*b^8 + 28*a^6*b^9 - 12*a^5*b^10 - 21*a^4*b^11 + 8*a^3*b^12 + 6*a^2*b^13 - 2*a*b^14)*sqrt(a^2 - b^2)*B*abs(-a + b) + (24*a^11*b^4 - 12*a^10*b^5 - 100*a^9*b^6 + 47*a^8*b^7 + 158*a^7*b^8 - 68*a^6*b^9 - 111*a^5*b^10 + 42*a^4*b^11 + 28*a^3*b^12 - 8*a^2*b^13 + a*b^14 - b^15)*sqrt(a^2 - b^2)*C*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*tan(1/2*d*x + 1/2*c)/sqrt((4*a^5*b^4 - 8*a^3*b^6 + 4*a*b^8 + sqrt(-16*(a^5*b^4 + a^4*b^5 - 2*a^3*b^6 - 2*a^2*b^7 + a*b^8 + b^9)*(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9) + 16*(a^5*b^4 - 2*a^3*b^6 + a*b^8)^2))/(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9))))/((a^4*b^5 - 2*a^2*b^7 + b^9)^2*(a^2 - 2*a*b + b^2) + (a^7*b^4 - 2*a^6*b^5 - a^5*b^6 + 4*a^4*b^7 - a^3*b^8 - 2*a^2*b^9 + a*b^10)*abs(a^4*b^5 - 2*a^2*b^7 + b^9)) - (24*C*a^11*b^4 - 12*B*a^10*b^5 - 12*C*a^10*b^5 + 4*A*a^9*b^6 + 6*B*a^9*b^6 - 100*C*a^9*b^6 - 2*A*a^8*b^7 + 51*B*a^8*b^7 + 47*C*a^8*b^7 - 17*A*a^7*b^8 - 24*B*a^7*b^8 + 158*C*a^7*b^8 + 8*A*a^6*b^9 - 84*B*a^6*b^9 - 68*C*a^6*b^9 + 30*A*a^5*b^10 + 36*B*a^5*b^10 - 111*C*a^5*b^10 - 12*A*a^4*b^11 + 63*B*a^4*b^11 + 42*C*a^4*b^11 - 25*A*a^3*b^12 - 24*B*a^3*b^12 + 28*C*a^3*b^12 + 8*A*a^2*b^13 - 18*B*a^2*b^13 - 8*C*a^2*b^13 + 8*A*a*b^14 + 6*B*a*b^14 + C*a*b^14 - 2*A*b^15 - C*b^15 - 12*C*a^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*B*a^5*b*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*C*a^5*b*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 2*A*a^4*b^2*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 3*B*a^4*b^2*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 23*C*a^4*b^2*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + A*a^3*b^3*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 12*B*a^3*b^3*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 10*C*a^3*b^3*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 4*A*a^2*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*B*a^2*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 10*C*a^2*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 4*A*a*b^5*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*B*a*b^5*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + C*a*b^5*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 2*A*b^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - C*b^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*tan(1/2*d*x + 1/2*c)/sqrt((4*a^5*b^4 - 8*a^3*b^6 + 4*a*b^8 - sqrt(-16*(a^5*b^4 + a^4*b^5 - 2*a^3*b^6 - 2*a^2*b^7 + a*b^8 + b^9)*(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9) + 16*(a^5*b^4 - 2*a^3*b^6 + a*b^8)^2))/(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9))))/(a^5*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 2*a^3*b^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + a*b^8*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - (a^4*b^5 - 2*a^2*b^7 + b^9)^2) + 2*(12*C*a^7*tan(1/2*d*x + 1/2*c)^7 - 6*B*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 2*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 17*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 5*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 2*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 2*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 13*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^7 - 2*B*b^7*tan(1/2*d*x + 1/2*c)^7 + C*b^7*tan(1/2*d*x + 1/2*c)^7 + 36*C*a^7*tan(1/2*d*x + 1/2*c)^5 - 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 67*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 35*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 29*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 15*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 26*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 10*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 5*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 2*B*b^7*tan(1/2*d*x + 1/2*c)^5 - 3*C*b^7*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^7*tan(1/2*d*x + 1/2*c)^3 - 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 67*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 35*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 26*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 10*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 5*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^3 - 4*C*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 2*B*b^7*tan(1/2*d*x + 1/2*c)^3 + 3*C*b^7*tan(1/2*d*x + 1/2*c)^3 + 12*C*a^7*tan(1/2*d*x + 1/2*c) - 6*B*a^6*b*tan(1/2*d*x + 1/2*c) + 18*C*a^6*b*tan(1/2*d*x + 1/2*c) + 2*A*a^5*b^2*tan(1/2*d*x + 1/2*c) - 9*B*a^5*b^2*tan(1/2*d*x + 1/2*c) - 17*C*a^5*b^2*tan(1/2*d*x + 1/2*c) + 3*A*a^4*b^3*tan(1/2*d*x + 1/2*c) + 9*B*a^4*b^3*tan(1/2*d*x + 1/2*c) - 33*C*a^4*b^3*tan(1/2*d*x + 1/2*c) - 5*A*a^3*b^4*tan(1/2*d*x + 1/2*c) + 16*B*a^3*b^4*tan(1/2*d*x + 1/2*c) - 2*C*a^3*b^4*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^5*tan(1/2*d*x + 1/2*c) + 2*B*a^2*b^5*tan(1/2*d*x + 1/2*c) + 13*C*a^2*b^5*tan(1/2*d*x + 1/2*c) - 4*B*a*b^6*tan(1/2*d*x + 1/2*c) + 4*C*a*b^6*tan(1/2*d*x + 1/2*c) - 2*B*b^7*tan(1/2*d*x + 1/2*c) - C*b^7*tan(1/2*d*x + 1/2*c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
995,1,666,0,0.329154," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, C a^{6} - 2 \, B a^{5} b - 15 \, C a^{4} b^{2} + 5 \, B a^{3} b^{3} + A a^{2} b^{4} + 12 \, C a^{2} b^{4} - 6 \, B a b^{5} + 2 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} - b^{2}}} - \frac{4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} + \frac{{\left(3 \, C a - B b\right)} {\left(d x + c\right)}}{b^{4}} - \frac{2 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b^{3}}}{d}"," ",0,"-((6*C*a^6 - 2*B*a^5*b - 15*C*a^4*b^2 + 5*B*a^3*b^3 + A*a^2*b^4 + 12*C*a^2*b^4 - 6*B*a*b^5 + 2*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(a^2 - b^2)) - (4*C*a^6*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*A*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*C*a^6*tan(1/2*d*x + 1/2*c) - 2*B*a^5*b*tan(1/2*d*x + 1/2*c) + 5*C*a^5*b*tan(1/2*d*x + 1/2*c) - 3*B*a^4*b^2*tan(1/2*d*x + 1/2*c) - 7*C*a^4*b^2*tan(1/2*d*x + 1/2*c) + A*a^3*b^3*tan(1/2*d*x + 1/2*c) + 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c) - 8*C*a^3*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a^2*b^4*tan(1/2*d*x + 1/2*c) + 6*B*a^2*b^4*tan(1/2*d*x + 1/2*c) - 4*A*a*b^5*tan(1/2*d*x + 1/2*c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) + (3*C*a - B*b)*(d*x + c)/b^4 - 2*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b^3))/d","B",0
996,1,603,0,0.282403," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, C a^{5} - 5 \, C a^{3} b^{2} - B a^{2} b^{3} + 3 \, A a b^{4} + 6 \, C a b^{4} - 2 \, B b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{a^{2} - b^{2}}} - \frac{{\left(d x + c\right)} C}{b^{3}} + \frac{2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"-((2*C*a^5 - 5*C*a^3*b^2 - B*a^2*b^3 + 3*A*a*b^4 + 6*C*a*b^4 - 2*B*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(a^2 - b^2)) - (d*x + c)*C/b^3 + (2*C*a^5*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 2*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - A*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^5*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^5*tan(1/2*d*x + 1/2*c) + 3*C*a^4*b*tan(1/2*d*x + 1/2*c) - 2*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - B*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*C*a^3*b^2*tan(1/2*d*x + 1/2*c) - A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 3*B*a^2*b^3*tan(1/2*d*x + 1/2*c) - 6*C*a^2*b^3*tan(1/2*d*x + 1/2*c) - A*a*b^4*tan(1/2*d*x + 1/2*c) + 4*B*a*b^4*tan(1/2*d*x + 1/2*c) - 2*A*b^5*tan(1/2*d*x + 1/2*c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
997,1,500,0,0.268203," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, A a^{2} + C a^{2} - 3 \, B a b + A b^{2} + 2 \, C b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, C a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"((2*A*a^2 + C*a^2 - 3*B*a*b + A*b^2 + 2*C*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - C*a^3*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*C*a*b^2*tan(1/2*d*x + 1/2*c)^3 + A*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^3*tan(1/2*d*x + 1/2*c) + C*a^3*tan(1/2*d*x + 1/2*c) - 4*A*a^2*b*tan(1/2*d*x + 1/2*c) + B*a^2*b*tan(1/2*d*x + 1/2*c) - 3*C*a^2*b*tan(1/2*d*x + 1/2*c) - 3*A*a*b^2*tan(1/2*d*x + 1/2*c) + B*a*b^2*tan(1/2*d*x + 1/2*c) - 4*C*a*b^2*tan(1/2*d*x + 1/2*c) + A*b^3*tan(1/2*d*x + 1/2*c) + 2*B*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
998,1,624,0,0.371216," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, B a^{5} - 6 \, A a^{4} b - 3 \, C a^{4} b + B a^{3} b^{2} + 5 \, A a^{2} b^{3} - 2 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"((2*B*a^5 - 6*A*a^4*b - 3*C*a^4*b + B*a^3*b^2 + 5*A*a^2*b^3 - 2*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(a^2 - b^2)) + A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + (2*C*a^5*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^4*b*tan(1/2*d*x + 1/2*c)^3 - C*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^5*tan(1/2*d*x + 1/2*c)^3 + 2*C*a^5*tan(1/2*d*x + 1/2*c) - 4*B*a^4*b*tan(1/2*d*x + 1/2*c) + C*a^4*b*tan(1/2*d*x + 1/2*c) + 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - 3*B*a^3*b^2*tan(1/2*d*x + 1/2*c) + C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 2*C*a^2*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a*b^4*tan(1/2*d*x + 1/2*c) - 2*A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
999,1,699,0,0.354135," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, C a^{6} - 6 \, B a^{5} b + 12 \, A a^{4} b^{2} + C a^{4} b^{2} + 5 \, B a^{3} b^{3} - 15 \, A a^{2} b^{4} - 2 \, B a b^{5} + 6 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{4 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} - \frac{{\left(B a - 3 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} + \frac{{\left(B a - 3 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}}}{d}"," ",0,"-((2*C*a^6 - 6*B*a^5*b + 12*A*a^4*b^2 + C*a^4*b^2 + 5*B*a^3*b^3 - 15*A*a^2*b^4 - 2*B*a*b^5 + 6*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(a^2 - b^2)) + (4*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 6*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 5*A*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*A*b^6*tan(1/2*d*x + 1/2*c)^3 + 4*C*a^5*b*tan(1/2*d*x + 1/2*c) - 6*B*a^4*b^2*tan(1/2*d*x + 1/2*c) + 3*C*a^4*b^2*tan(1/2*d*x + 1/2*c) + 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c) - 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c) - C*a^3*b^3*tan(1/2*d*x + 1/2*c) + 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c) + 3*B*a^2*b^4*tan(1/2*d*x + 1/2*c) - 5*A*a*b^5*tan(1/2*d*x + 1/2*c) + 2*B*a*b^5*tan(1/2*d*x + 1/2*c) - 4*A*b^6*tan(1/2*d*x + 1/2*c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) - (B*a - 3*A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 + (B*a - 3*A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3))/d","B",0
1000,1,1744,0,0.404408," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(6 \, C a^{6} b - 12 \, B a^{5} b^{2} + 20 \, A a^{4} b^{3} - 5 \, C a^{4} b^{3} + 15 \, B a^{3} b^{4} - 29 \, A a^{2} b^{5} + 2 \, C a^{2} b^{5} - 6 \, B a b^{6} + 12 \, 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^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, C a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, C a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} + \frac{{\left(A a^{2} + 2 \, C a^{2} - 6 \, B a b + 12 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} - \frac{{\left(A a^{2} + 2 \, C a^{2} - 6 \, B a b + 12 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}}}{2 \, d}"," ",0,"1/2*(2*(6*C*a^6*b - 12*B*a^5*b^2 + 20*A*a^4*b^3 - 5*C*a^4*b^3 + 15*B*a^3*b^4 - 29*A*a^2*b^5 + 2*C*a^2*b^5 - 6*B*a*b^6 + 12*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^9 - 2*a^7*b^2 + a^5*b^4)*sqrt(a^2 - b^2)) + 2*(A*a^7*tan(1/2*d*x + 1/2*c)^7 - 2*B*a^7*tan(1/2*d*x + 1/2*c)^7 + 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 2*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 5*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 2*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^7 - 6*B*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^7*tan(1/2*d*x + 1/2*c)^7 + 3*A*a^7*tan(1/2*d*x + 1/2*c)^5 - 2*B*a^7*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 10*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 15*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 35*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 18*B*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 36*A*b^7*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^7*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^7*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 10*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*C*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 35*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^3 - 18*B*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^7*tan(1/2*d*x + 1/2*c)^3 + A*a^7*tan(1/2*d*x + 1/2*c) + 2*B*a^7*tan(1/2*d*x + 1/2*c) - 4*A*a^6*b*tan(1/2*d*x + 1/2*c) + 4*B*a^6*b*tan(1/2*d*x + 1/2*c) - 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c) - 2*B*a^5*b^2*tan(1/2*d*x + 1/2*c) + 6*C*a^5*b^2*tan(1/2*d*x + 1/2*c) + 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c) - 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c) + 5*C*a^4*b^3*tan(1/2*d*x + 1/2*c) + 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c) - 9*B*a^3*b^4*tan(1/2*d*x + 1/2*c) - 3*C*a^3*b^4*tan(1/2*d*x + 1/2*c) + 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c) + 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c) - 2*C*a^2*b^5*tan(1/2*d*x + 1/2*c) - 18*A*a*b^6*tan(1/2*d*x + 1/2*c) + 6*B*a*b^6*tan(1/2*d*x + 1/2*c) - 12*A*b^7*tan(1/2*d*x + 1/2*c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) + (A*a^2 + 2*C*a^2 - 6*B*a*b + 12*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 - (A*a^2 + 2*C*a^2 - 6*B*a*b + 12*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5)/d","B",0
1001,1,1436,0,3.843254," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(20 \, C a^{9} - 8 \, B a^{8} b + 2 \, A a^{7} b^{2} - 69 \, C a^{7} b^{2} + 28 \, B a^{6} b^{3} - 7 \, A a^{5} b^{4} + 84 \, C a^{5} b^{4} - 35 \, B a^{4} b^{5} + 8 \, A a^{3} b^{6} - 40 \, C a^{3} b^{6} + 20 \, B a^{2} b^{7} - 8 \, A a b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - b^{12}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(36 \, C a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 81 \, C a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 42 \, B a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, A a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 213 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 117 \, B a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, 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} - 162 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, B a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 90 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 284 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 392 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 236 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 180 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 81 \, C a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 42 \, B a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, A a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 213 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 117 \, B a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, 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) + 162 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 90 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\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(20 \, C a^{2} - 8 \, B a b + 2 \, A b^{2} + C b^{2}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{6 \, {\left(8 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, C a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{5}}}{6 \, d}"," ",0,"1/6*(6*(20*C*a^9 - 8*B*a^8*b + 2*A*a^7*b^2 - 69*C*a^7*b^2 + 28*B*a^6*b^3 - 7*A*a^5*b^4 + 84*C*a^5*b^4 - 35*B*a^4*b^5 + 8*A*a^3*b^6 - 40*C*a^3*b^6 + 20*B*a^2*b^7 - 8*A*a*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12)*sqrt(a^2 - b^2)) - 2*(36*C*a^10*tan(1/2*d*x + 1/2*c)^5 - 18*B*a^9*b*tan(1/2*d*x + 1/2*c)^5 - 81*C*a^9*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^8*b^2*tan(1/2*d*x + 1/2*c)^5 + 42*B*a^8*b^2*tan(1/2*d*x + 1/2*c)^5 - 48*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^5 - 15*A*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 + 24*B*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 + 213*C*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 117*B*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 48*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 + 45*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 - 162*C*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 + 105*B*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 + 90*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 60*A*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 60*B*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^10*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^9*b*tan(1/2*d*x + 1/2*c)^3 + 12*A*a^8*b^2*tan(1/2*d*x + 1/2*c)^3 - 284*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^3 + 152*B*a^7*b^3*tan(1/2*d*x + 1/2*c)^3 - 56*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 + 392*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 - 236*B*a^5*b^5*tan(1/2*d*x + 1/2*c)^3 + 116*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 - 180*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 + 120*B*a^3*b^7*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^10*tan(1/2*d*x + 1/2*c) - 18*B*a^9*b*tan(1/2*d*x + 1/2*c) + 81*C*a^9*b*tan(1/2*d*x + 1/2*c) + 6*A*a^8*b^2*tan(1/2*d*x + 1/2*c) - 42*B*a^8*b^2*tan(1/2*d*x + 1/2*c) - 48*C*a^8*b^2*tan(1/2*d*x + 1/2*c) + 15*A*a^7*b^3*tan(1/2*d*x + 1/2*c) + 24*B*a^7*b^3*tan(1/2*d*x + 1/2*c) - 213*C*a^7*b^3*tan(1/2*d*x + 1/2*c) - 6*A*a^6*b^4*tan(1/2*d*x + 1/2*c) + 117*B*a^6*b^4*tan(1/2*d*x + 1/2*c) - 48*C*a^6*b^4*tan(1/2*d*x + 1/2*c) - 45*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) + 162*C*a^5*b^5*tan(1/2*d*x + 1/2*c) - 6*A*a^4*b^6*tan(1/2*d*x + 1/2*c) - 105*B*a^4*b^6*tan(1/2*d*x + 1/2*c) + 90*C*a^4*b^6*tan(1/2*d*x + 1/2*c) + 60*A*a^3*b^7*tan(1/2*d*x + 1/2*c) - 60*B*a^3*b^7*tan(1/2*d*x + 1/2*c) + 36*A*a^2*b^8*tan(1/2*d*x + 1/2*c))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) + 3*(20*C*a^2 - 8*B*a*b + 2*A*b^2 + C*b^2)*(d*x + c)/b^6 - 6*(8*C*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*b*tan(1/2*d*x + 1/2*c)^3 + C*b*tan(1/2*d*x + 1/2*c)^3 + 8*C*a*tan(1/2*d*x + 1/2*c) - 2*B*b*tan(1/2*d*x + 1/2*c) - C*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^5))/d","B",0
1002,1,1225,0,0.346305," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, C a^{8} - 2 \, B a^{7} b - 28 \, C a^{6} b^{2} + 7 \, B a^{5} b^{3} + 35 \, C a^{4} b^{4} - 8 \, B a^{3} b^{5} - 3 \, A a^{2} b^{6} - 20 \, C a^{2} b^{6} + 8 \, B a b^{7} - 2 \, A b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} \sqrt{a^{2} - b^{2}}} - \frac{18 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 152 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 236 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}} + \frac{3 \, {\left(4 \, C a - B b\right)} {\left(d x + c\right)}}{b^{5}} - \frac{6 \, C \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b^{4}}}{3 \, d}"," ",0,"-1/3*(3*(8*C*a^8 - 2*B*a^7*b - 28*C*a^6*b^2 + 7*B*a^5*b^3 + 35*C*a^4*b^4 - 8*B*a^3*b^5 - 3*A*a^2*b^6 - 20*C*a^2*b^6 + 8*B*a*b^7 - 2*A*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*sqrt(a^2 - b^2)) - (18*C*a^9*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 42*C*a^8*b*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 - 24*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 117*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 45*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 105*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 60*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 60*C*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^8*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^9*tan(1/2*d*x + 1/2*c)^3 - 12*B*a^8*b*tan(1/2*d*x + 1/2*c)^3 - 152*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 + 56*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 + 236*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 - 116*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 + 32*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 - 120*C*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 72*B*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^8*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^9*tan(1/2*d*x + 1/2*c) - 6*B*a^8*b*tan(1/2*d*x + 1/2*c) + 42*C*a^8*b*tan(1/2*d*x + 1/2*c) - 15*B*a^7*b^2*tan(1/2*d*x + 1/2*c) - 24*C*a^7*b^2*tan(1/2*d*x + 1/2*c) + 6*B*a^6*b^3*tan(1/2*d*x + 1/2*c) - 117*C*a^6*b^3*tan(1/2*d*x + 1/2*c) + 6*A*a^5*b^4*tan(1/2*d*x + 1/2*c) + 45*B*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*C*a^5*b^4*tan(1/2*d*x + 1/2*c) + 3*A*a^4*b^5*tan(1/2*d*x + 1/2*c) + 6*B*a^4*b^5*tan(1/2*d*x + 1/2*c) + 105*C*a^4*b^5*tan(1/2*d*x + 1/2*c) + 6*A*a^3*b^6*tan(1/2*d*x + 1/2*c) - 60*B*a^3*b^6*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b^6*tan(1/2*d*x + 1/2*c) + 27*A*a^2*b^7*tan(1/2*d*x + 1/2*c) - 36*B*a^2*b^7*tan(1/2*d*x + 1/2*c) + 18*A*a*b^8*tan(1/2*d*x + 1/2*c))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) + 3*(4*C*a - B*b)*(d*x + c)/b^5 - 6*C*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b^4))/d","B",0
1003,1,1104,0,0.314758," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, C a^{7} - 7 \, C a^{5} b^{2} - A a^{3} b^{4} + 8 \, C a^{3} b^{4} + 3 \, B a^{2} b^{5} - 4 \, A a b^{6} - 8 \, C a b^{6} + 2 \, B b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, {\left(d x + c\right)} C}{b^{4}} - \frac{6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, C a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(2*C*a^7 - 7*C*a^5*b^2 - A*a^3*b^4 + 8*C*a^3*b^4 + 3*B*a^2*b^5 - 4*A*a*b^6 - 8*C*a*b^6 + 2*B*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*sqrt(a^2 - b^2)) + 3*(d*x + c)*C/b^4 - (6*C*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 45*C*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 - 18*B*a*b^7*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^8*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^8*tan(1/2*d*x + 1/2*c)^3 - 56*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^3 + 28*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 116*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 32*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^3 - 16*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 72*C*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^7*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^8*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^8*tan(1/2*d*x + 1/2*c) + 15*C*a^7*b*tan(1/2*d*x + 1/2*c) - 6*C*a^6*b^2*tan(1/2*d*x + 1/2*c) - 3*A*a^5*b^3*tan(1/2*d*x + 1/2*c) - 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c) - 45*C*a^5*b^3*tan(1/2*d*x + 1/2*c) + 12*A*a^4*b^4*tan(1/2*d*x + 1/2*c) - 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c) - 6*C*a^4*b^4*tan(1/2*d*x + 1/2*c) + 27*A*a^3*b^5*tan(1/2*d*x + 1/2*c) - 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c) + 60*C*a^3*b^5*tan(1/2*d*x + 1/2*c) + 12*A*a^2*b^6*tan(1/2*d*x + 1/2*c) - 27*B*a^2*b^6*tan(1/2*d*x + 1/2*c) + 36*C*a^2*b^6*tan(1/2*d*x + 1/2*c) + 6*A*a*b^7*tan(1/2*d*x + 1/2*c) - 18*B*a*b^7*tan(1/2*d*x + 1/2*c) + 6*A*b^8*tan(1/2*d*x + 1/2*c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
1004,1,966,0,0.332019," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(B a^{3} - 4 \, A a^{2} b - 3 \, C a^{2} b + 4 \, B a b^{2} - A b^{3} - 2 \, C b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(B*a^3 - 4*A*a^2*b - 3*C*a^2*b + 4*B*a*b^2 - A*b^3 - 2*C*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - (6*A*a^5*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 18*C*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*b^5*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^5*tan(1/2*d*x + 1/2*c)^3 + 4*C*a^5*tan(1/2*d*x + 1/2*c)^3 - 28*B*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 16*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 32*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 28*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 36*C*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 12*B*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^5*tan(1/2*d*x + 1/2*c) + 3*B*a^5*tan(1/2*d*x + 1/2*c) + 6*C*a^5*tan(1/2*d*x + 1/2*c) + 6*A*a^4*b*tan(1/2*d*x + 1/2*c) - 12*B*a^4*b*tan(1/2*d*x + 1/2*c) + 3*C*a^4*b*tan(1/2*d*x + 1/2*c) + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - 27*B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 6*C*a^3*b^2*tan(1/2*d*x + 1/2*c) + 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c) - 12*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 27*C*a^2*b^3*tan(1/2*d*x + 1/2*c) + 12*A*a*b^4*tan(1/2*d*x + 1/2*c) - 6*B*a*b^4*tan(1/2*d*x + 1/2*c) + 18*C*a*b^4*tan(1/2*d*x + 1/2*c) - 3*A*b^5*tan(1/2*d*x + 1/2*c) - 6*B*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
1005,1,966,0,0.295274," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, A a^{3} + C a^{3} - 4 \, B a^{2} b + 3 \, A a b^{2} + 4 \, C a b^{2} - B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(2*A*a^3 + C*a^3 - 4*B*a^2*b + 3*A*a*b^2 + 4*C*a*b^2 - B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - (6*B*a^5*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^5*tan(1/2*d*x + 1/2*c)^5 - 18*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 27*C*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*C*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*B*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*C*b^5*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^5*tan(1/2*d*x + 1/2*c)^3 - 36*A*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 28*C*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 32*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 16*C*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 28*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*A*b^5*tan(1/2*d*x + 1/2*c)^3 + 12*C*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^5*tan(1/2*d*x + 1/2*c) + 3*C*a^5*tan(1/2*d*x + 1/2*c) - 18*A*a^4*b*tan(1/2*d*x + 1/2*c) + 6*B*a^4*b*tan(1/2*d*x + 1/2*c) - 12*C*a^4*b*tan(1/2*d*x + 1/2*c) - 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 12*B*a^3*b^2*tan(1/2*d*x + 1/2*c) - 27*C*a^3*b^2*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c) - 12*C*a^2*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a*b^4*tan(1/2*d*x + 1/2*c) + 12*B*a*b^4*tan(1/2*d*x + 1/2*c) - 6*C*a*b^4*tan(1/2*d*x + 1/2*c) - 6*A*b^5*tan(1/2*d*x + 1/2*c) - 3*B*b^5*tan(1/2*d*x + 1/2*c) - 6*C*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
1006,1,1127,0,0.374216," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, B a^{7} - 8 \, A a^{6} b - 4 \, C a^{6} b + 3 \, B a^{5} b^{2} + 8 \, A a^{4} b^{3} - C a^{4} b^{3} - 7 \, A a^{2} b^{5} + 2 \, A b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, C a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(2*B*a^7 - 8*A*a^6*b - 4*C*a^6*b + 3*B*a^5*b^2 + 8*A*a^4*b^3 - C*a^4*b^3 - 7*A*a^2*b^5 + 2*A*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*sqrt(a^2 - b^2)) + 3*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + (6*C*a^8*tan(1/2*d*x + 1/2*c)^5 - 18*B*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^7*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*C*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 15*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^8*tan(1/2*d*x + 1/2*c)^5 + 12*C*a^8*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^7*b*tan(1/2*d*x + 1/2*c)^3 + 72*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 16*C*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 32*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^3 - 116*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 28*C*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^3 + 56*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^8*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^8*tan(1/2*d*x + 1/2*c) - 18*B*a^7*b*tan(1/2*d*x + 1/2*c) + 6*C*a^7*b*tan(1/2*d*x + 1/2*c) + 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c) - 27*B*a^6*b^2*tan(1/2*d*x + 1/2*c) + 12*C*a^6*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c) - 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c) + 27*C*a^5*b^3*tan(1/2*d*x + 1/2*c) - 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c) - 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c) + 12*C*a^4*b^4*tan(1/2*d*x + 1/2*c) - 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c) - 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c) - 3*C*a^3*b^5*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c) + 15*A*a*b^7*tan(1/2*d*x + 1/2*c) + 6*A*b^8*tan(1/2*d*x + 1/2*c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
1007,1,1255,0,0.379131," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{8} - 8 \, B a^{7} b + 20 \, A a^{6} b^{2} + 3 \, C a^{6} b^{2} + 8 \, B a^{5} b^{3} - 35 \, A a^{4} b^{4} - 7 \, B a^{3} b^{5} + 28 \, A a^{2} b^{6} + 2 \, B a b^{7} - 8 \, A b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{18 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 236 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, C a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, C a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}} - \frac{3 \, {\left(B a - 4 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} + \frac{3 \, {\left(B a - 4 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}} + \frac{6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{4}}}{3 \, d}"," ",0,"-1/3*(3*(2*C*a^8 - 8*B*a^7*b + 20*A*a^6*b^2 + 3*C*a^6*b^2 + 8*B*a^5*b^3 - 35*A*a^4*b^4 - 7*B*a^3*b^5 + 28*A*a^2*b^6 + 2*B*a*b^7 - 8*A*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*sqrt(a^2 - b^2)) + (18*C*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*C*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 60*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*C*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 45*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 42*A*a*b^8*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b^8*tan(1/2*d*x + 1/2*c)^5 + 18*A*b^9*tan(1/2*d*x + 1/2*c)^5 + 36*C*a^8*b*tan(1/2*d*x + 1/2*c)^3 - 72*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 - 32*C*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 + 116*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 - 236*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 - 56*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 152*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*b^8*tan(1/2*d*x + 1/2*c)^3 - 36*A*b^9*tan(1/2*d*x + 1/2*c)^3 + 18*C*a^8*b*tan(1/2*d*x + 1/2*c) - 36*B*a^7*b^2*tan(1/2*d*x + 1/2*c) + 27*C*a^7*b^2*tan(1/2*d*x + 1/2*c) + 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c) - 60*B*a^6*b^3*tan(1/2*d*x + 1/2*c) + 6*C*a^6*b^3*tan(1/2*d*x + 1/2*c) + 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c) + 6*B*a^5*b^4*tan(1/2*d*x + 1/2*c) + 3*C*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c) + 45*B*a^4*b^5*tan(1/2*d*x + 1/2*c) + 6*C*a^4*b^5*tan(1/2*d*x + 1/2*c) - 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c) + 6*B*a^3*b^6*tan(1/2*d*x + 1/2*c) - 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c) - 15*B*a^2*b^7*tan(1/2*d*x + 1/2*c) + 42*A*a*b^8*tan(1/2*d*x + 1/2*c) - 6*B*a*b^8*tan(1/2*d*x + 1/2*c) + 18*A*b^9*tan(1/2*d*x + 1/2*c))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) - 3*(B*a - 4*A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 + 3*(B*a - 4*A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/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
1008,1,1482,0,0.402749," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(8 \, C a^{8} b - 20 \, B a^{7} b^{2} + 40 \, A a^{6} b^{3} - 8 \, C a^{6} b^{3} + 35 \, B a^{5} b^{4} - 84 \, A a^{4} b^{5} + 7 \, C a^{4} b^{5} - 28 \, B a^{3} b^{6} + 69 \, A a^{2} b^{7} - 2 \, C a^{2} b^{7} + 8 \, B a b^{8} - 20 \, A b^{9}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(36 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, B a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 117 \, B a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, C a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 42 \, B a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 236 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 392 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 152 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 284 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, C a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, C a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, C a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 117 \, B a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, C a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, C a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 42 \, B a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, C a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}} + \frac{3 \, {\left(A a^{2} + 2 \, C a^{2} - 8 \, B a b + 20 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{6}} - \frac{3 \, {\left(A a^{2} + 2 \, C a^{2} - 8 \, B a b + 20 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{6}} + \frac{6 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{5}}}{6 \, d}"," ",0,"1/6*(6*(8*C*a^8*b - 20*B*a^7*b^2 + 40*A*a^6*b^3 - 8*C*a^6*b^3 + 35*B*a^5*b^4 - 84*A*a^4*b^5 + 7*C*a^4*b^5 - 28*B*a^3*b^6 + 69*A*a^2*b^7 - 2*C*a^2*b^7 + 8*B*a*b^8 - 20*A*b^9)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*sqrt(a^2 - b^2)) + 2*(36*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*B*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 - 60*C*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 + 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 + 105*B*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 + 24*B*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 + 45*C*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 - 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 117*B*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 6*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 + 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 + 24*B*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 15*C*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 + 42*B*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 + 6*C*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 - 81*A*a*b^9*tan(1/2*d*x + 1/2*c)^5 - 18*B*a*b^9*tan(1/2*d*x + 1/2*c)^5 + 36*A*b^10*tan(1/2*d*x + 1/2*c)^5 + 72*C*a^8*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*B*a^7*b^3*tan(1/2*d*x + 1/2*c)^3 + 180*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 - 116*C*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 + 236*B*a^5*b^5*tan(1/2*d*x + 1/2*c)^3 - 392*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 + 56*C*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 - 152*B*a^3*b^7*tan(1/2*d*x + 1/2*c)^3 + 284*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 - 12*C*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^9*tan(1/2*d*x + 1/2*c)^3 - 72*A*b^10*tan(1/2*d*x + 1/2*c)^3 + 36*C*a^8*b^2*tan(1/2*d*x + 1/2*c) - 60*B*a^7*b^3*tan(1/2*d*x + 1/2*c) + 60*C*a^7*b^3*tan(1/2*d*x + 1/2*c) + 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c) - 105*B*a^6*b^4*tan(1/2*d*x + 1/2*c) - 6*C*a^6*b^4*tan(1/2*d*x + 1/2*c) + 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c) + 24*B*a^5*b^5*tan(1/2*d*x + 1/2*c) - 45*C*a^5*b^5*tan(1/2*d*x + 1/2*c) - 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c) + 117*B*a^4*b^6*tan(1/2*d*x + 1/2*c) - 6*C*a^4*b^6*tan(1/2*d*x + 1/2*c) - 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c) + 24*B*a^3*b^7*tan(1/2*d*x + 1/2*c) + 15*C*a^3*b^7*tan(1/2*d*x + 1/2*c) - 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c) - 42*B*a^2*b^8*tan(1/2*d*x + 1/2*c) + 6*C*a^2*b^8*tan(1/2*d*x + 1/2*c) + 81*A*a*b^9*tan(1/2*d*x + 1/2*c) - 18*B*a*b^9*tan(1/2*d*x + 1/2*c) + 36*A*b^10*tan(1/2*d*x + 1/2*c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) + 3*(A*a^2 + 2*C*a^2 - 8*B*a*b + 20*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^6 - 3*(A*a^2 + 2*C*a^2 - 8*B*a*b + 20*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/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
1009,1,48,0,0.167618," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(C a - B b\right)} {\left(d x + c\right)} - \frac{2 \, C b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"-((C*a - B*b)*(d*x + c) - 2*C*b*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","A",0
1010,1,318,0,1.367148," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(\sqrt{a^{2} - b^{2}} B b^{2} {\left| a - b \right|} - \sqrt{a^{2} - b^{2}} C {\left(a + b\right)} {\left| a - b \right|} {\left| b \right|} + \sqrt{a^{2} - b^{2}} B b {\left| a - b \right|} {\left| b \right|} - \sqrt{a^{2} - b^{2}} {\left(3 \, a b - b^{2}\right)} C {\left| a - b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} - \frac{{\left(3 \, C a b - B b^{2} - C b^{2} - C a {\left| b \right|} + B b {\left| b \right|} - C b {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{b^{2} - a {\left| b \right|}}}{d}"," ",0,"((sqrt(a^2 - b^2)*B*b^2*abs(a - b) - sqrt(a^2 - b^2)*C*(a + b)*abs(a - b)*abs(b) + sqrt(a^2 - b^2)*B*b*abs(a - b)*abs(b) - sqrt(a^2 - b^2)*(3*a*b - b^2)*C*abs(a - b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) - (3*C*a*b - B*b^2 - C*b^2 - C*a*abs(b) + B*b*abs(b) - C*b*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/(b^2 - a*abs(b)))/d","B",0
1011,1,170,0,0.278960," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(C a^{2} - B a b + C b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, C a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\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*((C*a^2 - B*a*b + C*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(a^2 - b^2)^(3/2) - (2*C*a*b*tan(1/2*d*x + 1/2*c) - B*b^2*tan(1/2*d*x + 1/2*c))/((a*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
1012,1,381,0,0.279767," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, C a^{3} - 2 \, B a^{2} b + 4 \, C a b^{2} - B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{6 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, C b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, C a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, C a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, C b^{4} \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*C*a^3 - 2*B*a^2*b + 4*C*a*b^2 - B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) - (6*C*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*C*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + B*b^4*tan(1/2*d*x + 1/2*c)^3 - 2*C*b^4*tan(1/2*d*x + 1/2*c)^3 + 6*C*a^3*b*tan(1/2*d*x + 1/2*c) - 4*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 4*C*a^2*b^2*tan(1/2*d*x + 1/2*c) - 3*B*a*b^3*tan(1/2*d*x + 1/2*c) + B*b^4*tan(1/2*d*x + 1/2*c) + 2*C*b^4*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
1013,1,711,0,0.373472," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^5,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, C a^{4} - 2 \, B a^{3} b + 7 \, C a^{2} b^{2} - 3 \, B a b^{3} + C b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{24 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 33 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, C a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, C a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, C b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, C a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, C a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, C a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30 \, C a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, C a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, C b^{6} \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*C*a^4 - 2*B*a^3*b + 7*C*a^2*b^2 - 3*B*a*b^3 + C*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - (24*C*a^5*b*tan(1/2*d*x + 1/2*c)^5 - 18*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^5 - 33*C*a^4*b^2*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^5 + 18*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^5 - 30*C*a^2*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*B*a*b^5*tan(1/2*d*x + 1/2*c)^5 + 18*C*a*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*b^6*tan(1/2*d*x + 1/2*c)^5 + 3*C*b^6*tan(1/2*d*x + 1/2*c)^5 + 48*C*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 16*C*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 32*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 32*C*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*B*b^6*tan(1/2*d*x + 1/2*c)^3 + 24*C*a^5*b*tan(1/2*d*x + 1/2*c) - 18*B*a^4*b^2*tan(1/2*d*x + 1/2*c) + 33*C*a^4*b^2*tan(1/2*d*x + 1/2*c) - 27*B*a^3*b^3*tan(1/2*d*x + 1/2*c) + 18*C*a^3*b^3*tan(1/2*d*x + 1/2*c) - 6*B*a^2*b^4*tan(1/2*d*x + 1/2*c) + 30*C*a^2*b^4*tan(1/2*d*x + 1/2*c) - 3*B*a*b^5*tan(1/2*d*x + 1/2*c) + 18*C*a*b^5*tan(1/2*d*x + 1/2*c) - 6*B*b^6*tan(1/2*d*x + 1/2*c) - 3*C*b^6*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
1014,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
1015,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*cos(d*x + c), x)","F",0
1016,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a), x)","F",0
1017,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
1018,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
1019,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
1020,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
1021,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
1022,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
1023,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2), x)","F",0
1024,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
1025,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
1026,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
1027,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
1028,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^5, x)","F",0
1029,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
1030,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
1031,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2), x)","F",0
1032,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
1033,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
1034,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
1035,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
1036,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^5, x)","F",0
1037,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^6, x)","F",0
1038,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)*(b*cos(d*x + c) + a)^(3/2), x)","F",0
1039,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)*sqrt(b*cos(d*x + c) + a), x)","F",0
1040,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
1041,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
1042,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sqrt(b*cos(d*x + c) + a), x)","F",0
1043,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
1044,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
1045,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
1046,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{4}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^4/sqrt(b*cos(d*x + c) + a), x)","F",0
1047,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1048,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1049,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1050,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1051,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1052,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^3/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1053,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^3/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1054,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1055,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1056,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1057,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1058,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1059,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^3/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1060,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(7/2), x)","F",0
1061,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)/sqrt(b*cos(d*x + c) + a), x)","F",0
1062,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1063,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1064,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)/(b*cos(d*x + c) + a)^(7/2), x)","F",0
1065,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1066,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1067,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1068,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1069,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
1070,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
1071,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
1072,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
1073,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
1074,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
1075,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
1076,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
1077,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
1078,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
1079,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(11/2), x)","F",0
1080,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
1081,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
1082,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
1083,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
1084,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
1085,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
1086,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
1087,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sqrt(cos(d*x + c)), x)","F",0
1088,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/sqrt(cos(d*x + c)), x)","F",0
1089,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(3/2), x)","F",0
1090,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(5/2), x)","F",0
1091,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(7/2), x)","F",0
1092,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(9/2), x)","F",0
1093,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(11/2), x)","F",0
1094,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(13/2), x)","F",0
1095,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
1096,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
1097,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
1098,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1099,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1100,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
1101,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
1102,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
1103,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
1104,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
1105,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
1106,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
1107,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
1108,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
1109,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(7/2)/(b*cos(d*x + c) + a)^3, x)","F",0
1110,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^3, x)","F",0
1111,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^3, x)","F",0
1112,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^3, x)","F",0
1113,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
1114,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
1115,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
1116,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1117,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1118,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1119,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
1120,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
1121,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
1122,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1123,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1124,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1125,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1126,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1127,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1128,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1129,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1130,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1131,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1132,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1133,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1134,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1135,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1136,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1137,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1138,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1139,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1140,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
1141,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
1142,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1143,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1144,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c)+2*b*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{2 \, b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) + a}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((2*b*cos(d*x + c)^2 + a*cos(d*x + c) + a)/(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1145,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1146,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1147,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1148,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1149,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1150,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1151,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1152,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1153,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1154,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1155,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1156,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*cos(d*x + c)^m, x)","F",0
1157,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^m, x)","F",0
1158,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{m}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^m/(b*cos(d*x + c) + a), x)","F",0
1159,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{m}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^m/(b*cos(d*x + c) + a)^2, x)","F",0
1160,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1161,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1162,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1163,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1164,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1165,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1166,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1167,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(11/2), x)","F",0
1168,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(9/2), x)","F",0
1169,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
1170,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
1171,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
1172,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
1173,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
1174,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
1175,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(13/2), x)","F",0
1176,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(11/2), x)","F",0
1177,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
1178,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
1179,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
1180,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
1181,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
1182,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
1183,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
1184,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a), x)","F",0
1185,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
1186,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
1187,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
1188,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1189,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1190,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1191,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^2, x)","F",0
1192,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^2, x)","F",0
1193,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
1194,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
1195,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
1196,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
1197,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^3, x)","F",0
1198,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^3, x)","F",0
1199,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^3, x)","F",0
1200,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
1201,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
1202,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
1203,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2)), x)","F",0
1204,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1205,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1206,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1207,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1208,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1209,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1210,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1211,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1212,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1213,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1214,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1215,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1216,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1217,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1218,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1219,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1220,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1221,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(15/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1222,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1223,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1224,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1225,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1226,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1227,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1228,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1229,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1230,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1231,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1232,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1233,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1234,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1235,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/sqrt(a*cos(d*x + c) + a), x)","F",0
1236,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/sqrt(a*cos(d*x + c) + a), x)","F",0
1237,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1238,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{a \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1239,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(9/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1240,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1241,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1242,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1243,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1244,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
1245,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
1246,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
1247,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
1248,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
1249,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
1250,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
1251,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
1252,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
1253,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(9/2), x)","F",0
1254,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(7/2), x)","F",0
1255,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(5/2), x)","F",0
1256,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(3/2), x)","F",0
1257,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
1258,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
1259,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/sec(d*x + c)^(3/2), x)","F",0
1260,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2), x)","F",0
1261,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2), x)","F",0
1262,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2), x)","F",0
1263,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c)), x)","F",0
1264,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sqrt(sec(d*x + c)), x)","F",0
1265,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sec(d*x + c)^(3/2), x)","F",0
1266,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1267,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1268,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1269,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1270,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1271,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1272,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1273,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(11/2), x)","F",0
1274,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(9/2), x)","F",0
1275,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
1276,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
1277,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
1278,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
1279,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
1280,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
1281,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(13/2), x)","F",0
1282,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(11/2), x)","F",0
1283,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
1284,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
1285,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
1286,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
1287,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
1288,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
1289,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
1290,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a), x)","F",0
1291,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
1292,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
1293,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
1294,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1295,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1296,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1297,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^2, x)","F",0
1298,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^2, x)","F",0
1299,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
1300,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
1301,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
1302,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
1303,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^3, x)","F",0
1304,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^3, x)","F",0
1305,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^3, x)","F",0
1306,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
1307,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
1308,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
1309,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2)), x)","F",0
1310,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1311,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1312,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1313,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1314,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1315,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1316,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1317,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1318,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1319,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1320,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1321,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1322,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1323,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1324,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1325,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1326,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1327,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(15/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1328,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1329,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1330,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1331,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1332,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1333,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1334,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1335,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1336,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1337,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1338,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1339,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1340,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1341,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(a*cos(d*x + c) + a), x)","F",0
1342,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(a*cos(d*x + c) + a), x)","F",0
1343,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1344,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1345,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(sec(d*x + c))/sqrt(a*cos(d*x + c) + a), x)","F",0
1346,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(9/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1347,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1348,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1349,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1350,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1351,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
1352,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1353,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
1354,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
1355,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
1356,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
1357,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
1358,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
1359,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
1360,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1361,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1362,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1363,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1364,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1365,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1366,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1367,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(11/2), x)","F",0
1368,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(9/2), x)","F",0
1369,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
1370,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
1371,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
1372,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
1373,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
1374,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
1375,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(11/2), x)","F",0
1376,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
1377,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
1378,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
1379,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
1380,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
1381,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
1382,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
1383,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(13/2), x)","F",0
1384,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(11/2), x)","F",0
1385,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(9/2), x)","F",0
1386,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(7/2), x)","F",0
1387,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(5/2), x)","F",0
1388,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(3/2), x)","F",0
1389,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sqrt(sec(d*x + c)), x)","F",0
1390,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/sqrt(sec(d*x + c)), x)","F",0
1391,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/(b*cos(d*x + c) + a), x)","F",0
1392,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
1393,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
1394,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
1395,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1396,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1397,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1398,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
1399,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
1400,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
1401,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
1402,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
1403,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
1404,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^3, x)","F",0
1405,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^3, x)","F",0
1406,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^3, x)","F",0
1407,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
1408,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
1409,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
1410,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2)), x)","F",0
1411,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1412,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1413,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1414,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1415,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1416,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1417,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1418,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1419,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1420,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1421,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1422,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1423,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1424,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
1425,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1426,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1427,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1428,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1429,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1430,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1431,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1432,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1433,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1434,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(9/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1435,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1436,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1437,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1438,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1439,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1440,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1441,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1442,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1443,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1444,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1445,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1446,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1447,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1448,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1449,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1450,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1451,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1452,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1453,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1454,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1455,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1456,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1457,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1458,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(11/2), x)","F",0
1459,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(9/2), x)","F",0
1460,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
1461,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
1462,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
1463,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
1464,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
1465,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
1466,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(11/2), x)","F",0
1467,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
1468,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
1469,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
1470,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
1471,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
1472,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
1473,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
1474,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(13/2), x)","F",0
1475,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(11/2), x)","F",0
1476,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(9/2), x)","F",0
1477,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(7/2), x)","F",0
1478,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(5/2), x)","F",0
1479,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(3/2), x)","F",0
1480,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sqrt(sec(d*x + c)), x)","F",0
1481,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/sqrt(sec(d*x + c)), x)","F",0
1482,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/(b*cos(d*x + c) + a), x)","F",0
1483,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
1484,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
1485,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
1486,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1487,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1488,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1489,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
1490,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
1491,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
1492,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
1493,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
1494,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
1495,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^3, x)","F",0
1496,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^3, x)","F",0
1497,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^3, x)","F",0
1498,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
1499,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
1500,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
1501,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2)), x)","F",0
1502,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1503,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1504,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1505,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1506,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1507,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1508,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1509,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1510,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1511,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1512,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1513,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1514,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
1515,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1516,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1517,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1518,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1519,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1520,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1521,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1522,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1523,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1524,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1525,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(9/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1526,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1527,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1528,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1529,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1530,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1531,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1532,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1533,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1534,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1535,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1536,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1537,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1538,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1539,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1540,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1541,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
