1,1,88,0,1.082868," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{45 \, {\left(A + B\right)} a d x + {\left(24 \, B a \cos\left(d x + c\right)^{4} + 30 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 4 \, B\right)} a \cos\left(d x + c\right)^{2} + 45 \, {\left(A + B\right)} a \cos\left(d x + c\right) + 16 \, {\left(5 \, A + 4 \, B\right)} a\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(45*(A + B)*a*d*x + (24*B*a*cos(d*x + c)^4 + 30*(A + B)*a*cos(d*x + c)^3 + 8*(5*A + 4*B)*a*cos(d*x + c)^2 + 45*(A + B)*a*cos(d*x + c) + 16*(5*A + 4*B)*a)*sin(d*x + c))/d","A",0
2,1,74,0,0.976619," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A + 3 \, B\right)} a d x + {\left(6 \, B a \cos\left(d x + c\right)^{3} + 8 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, A + 3 \, B\right)} a \cos\left(d x + c\right) + 16 \, {\left(A + B\right)} a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*A + 3*B)*a*d*x + (6*B*a*cos(d*x + c)^3 + 8*(A + B)*a*cos(d*x + c)^2 + 3*(4*A + 3*B)*a*cos(d*x + c) + 16*(A + B)*a)*sin(d*x + c))/d","A",0
3,1,56,0,1.080143," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(A + B\right)} a d x + {\left(2 \, B a \cos\left(d x + c\right)^{2} + 3 \, {\left(A + B\right)} a \cos\left(d x + c\right) + 2 \, {\left(3 \, A + 2 \, B\right)} a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(A + B)*a*d*x + (2*B*a*cos(d*x + c)^2 + 3*(A + B)*a*cos(d*x + c) + 2*(3*A + 2*B)*a)*sin(d*x + c))/d","A",0
4,1,38,0,1.059470," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, A + B\right)} a d x + {\left(B a \cos\left(d x + c\right) + 2 \, {\left(A + B\right)} a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*A + B)*a*d*x + (B*a*cos(d*x + c) + 2*(A + B)*a)*sin(d*x + c))/d","A",0
5,1,51,0,0.936986," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{2 \, {\left(A + B\right)} a d x + A a \log\left(\sin\left(d x + c\right) + 1\right) - A a \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(A + B)*a*d*x + A*a*log(sin(d*x + c) + 1) - A*a*log(-sin(d*x + c) + 1) + 2*B*a*sin(d*x + c))/d","A",0
6,1,79,0,0.624556," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, B a d x \cos\left(d x + c\right) + {\left(A + B\right)} a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A + B\right)} a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, A a \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*B*a*d*x*cos(d*x + c) + (A + B)*a*cos(d*x + c)*log(sin(d*x + c) + 1) - (A + B)*a*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*A*a*sin(d*x + c))/(d*cos(d*x + c))","B",0
7,1,89,0,0.788360," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(A + 2 \, B\right)} a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A + 2 \, B\right)} a \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(A + B\right)} a \cos\left(d x + c\right) + A a\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((A + 2*B)*a*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A + 2*B)*a*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*(A + B)*a*cos(d*x + c) + A*a)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
8,1,105,0,0.732417," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(2 \, A + 3 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(A + B\right)} a \cos\left(d x + c\right) + 2 \, A a\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(A + B)*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(A + B)*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(2*A + 3*B)*a*cos(d*x + c)^2 + 3*(A + B)*a*cos(d*x + c) + 2*A*a)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
9,1,127,0,0.679205," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 4 \, B\right)} a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, A + 4 \, B\right)} a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 4 \, B\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(A + B\right)} a \cos\left(d x + c\right) + 6 \, A a\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(3*A + 4*B)*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*A + 4*B)*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(A + B)*a*cos(d*x + c)^3 + 3*(3*A + 4*B)*a*cos(d*x + c)^2 + 8*(A + B)*a*cos(d*x + c) + 6*A*a)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
10,1,130,0,0.556248," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(12 \, A + 11 \, B\right)} a^{2} d x + {\left(40 \, B a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(12 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 16 \, {\left(9 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(12 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right) + 32 \, {\left(9 \, A + 8 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(12*A + 11*B)*a^2*d*x + (40*B*a^2*cos(d*x + c)^5 + 48*(A + 2*B)*a^2*cos(d*x + c)^4 + 10*(12*A + 11*B)*a^2*cos(d*x + c)^3 + 16*(9*A + 8*B)*a^2*cos(d*x + c)^2 + 15*(12*A + 11*B)*a^2*cos(d*x + c) + 32*(9*A + 8*B)*a^2)*sin(d*x + c))/d","A",0
11,1,110,0,0.680712," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(7 \, A + 6 \, B\right)} a^{2} d x + {\left(24 \, B a^{2} \cos\left(d x + c\right)^{4} + 30 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(10 \, A + 9 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(7 \, A + 6 \, B\right)} a^{2} \cos\left(d x + c\right) + 16 \, {\left(10 \, A + 9 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(7*A + 6*B)*a^2*d*x + (24*B*a^2*cos(d*x + c)^4 + 30*(A + 2*B)*a^2*cos(d*x + c)^3 + 8*(10*A + 9*B)*a^2*cos(d*x + c)^2 + 15*(7*A + 6*B)*a^2*cos(d*x + c) + 16*(10*A + 9*B)*a^2)*sin(d*x + c))/d","A",0
12,1,90,0,0.753459," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, A + 7 \, B\right)} a^{2} d x + {\left(6 \, B a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 7 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(5 \, A + 4 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(8*A + 7*B)*a^2*d*x + (6*B*a^2*cos(d*x + c)^3 + 8*(A + 2*B)*a^2*cos(d*x + c)^2 + 3*(8*A + 7*B)*a^2*cos(d*x + c) + 8*(5*A + 4*B)*a^2)*sin(d*x + c))/d","A",0
13,1,70,0,0.912936," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 2 \, B\right)} a^{2} d x + {\left(2 \, B a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(6 \, A + 5 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(3*A + 2*B)*a^2*d*x + (2*B*a^2*cos(d*x + c)^2 + 3*(A + 2*B)*a^2*cos(d*x + c) + 2*(6*A + 5*B)*a^2)*sin(d*x + c))/d","A",0
14,1,79,0,0.888554," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{{\left(4 \, A + 3 \, B\right)} a^{2} d x + A a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - A a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(B a^{2} \cos\left(d x + c\right) + 2 \, {\left(A + 2 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((4*A + 3*B)*a^2*d*x + A*a^2*log(sin(d*x + c) + 1) - A*a^2*log(-sin(d*x + c) + 1) + (B*a^2*cos(d*x + c) + 2*(A + 2*B)*a^2)*sin(d*x + c))/d","A",0
15,1,108,0,0.665030," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(A + 2 \, B\right)} a^{2} d x \cos\left(d x + c\right) + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(A + 2*B)*a^2*d*x*cos(d*x + c) + (2*A + B)*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) - (2*A + B)*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(B*a^2*cos(d*x + c) + A*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
16,1,119,0,0.846729," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, B a^{2} d x \cos\left(d x + c\right)^{2} + {\left(3 \, A + 4 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, A + 4 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*B*a^2*d*x*cos(d*x + c)^2 + (3*A + 4*B)*a^2*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (3*A + 4*B)*a^2*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*(2*A + B)*a^2*cos(d*x + c) + A*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
17,1,125,0,0.603438," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(5 \, A + 6 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + 2 \, A a^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(2*A + 3*B)*a^2*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*A + 3*B)*a^2*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(5*A + 6*B)*a^2*cos(d*x + c)^2 + 3*(2*A + B)*a^2*cos(d*x + c) + 2*A*a^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
18,1,145,0,0.626443," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(7 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(4 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + 6 \, A a^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(7*A + 8*B)*a^2*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(7*A + 8*B)*a^2*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(4*A + 5*B)*a^2*cos(d*x + c)^3 + 3*(7*A + 8*B)*a^2*cos(d*x + c)^2 + 8*(2*A + B)*a^2*cos(d*x + c) + 6*A*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
19,1,130,0,0.832352," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(26 \, A + 23 \, B\right)} a^{3} d x + {\left(40 \, B a^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} + 10 \, {\left(18 \, A + 23 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(19 \, A + 17 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(26 \, A + 23 \, B\right)} a^{3} \cos\left(d x + c\right) + 32 \, {\left(19 \, A + 17 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(26*A + 23*B)*a^3*d*x + (40*B*a^3*cos(d*x + c)^5 + 48*(A + 3*B)*a^3*cos(d*x + c)^4 + 10*(18*A + 23*B)*a^3*cos(d*x + c)^3 + 16*(19*A + 17*B)*a^3*cos(d*x + c)^2 + 15*(26*A + 23*B)*a^3*cos(d*x + c) + 32*(19*A + 17*B)*a^3)*sin(d*x + c))/d","A",0
20,1,110,0,0.867721," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(15 \, A + 13 \, B\right)} a^{3} d x + {\left(24 \, B a^{3} \cos\left(d x + c\right)^{4} + 30 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, A + 19 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(15 \, A + 13 \, B\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(45 \, A + 38 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(15*A + 13*B)*a^3*d*x + (24*B*a^3*cos(d*x + c)^4 + 30*(A + 3*B)*a^3*cos(d*x + c)^3 + 8*(15*A + 19*B)*a^3*cos(d*x + c)^2 + 15*(15*A + 13*B)*a^3*cos(d*x + c) + 8*(45*A + 38*B)*a^3)*sin(d*x + c))/d","A",0
21,1,90,0,0.806681," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, B\right)} a^{3} d x + {\left(6 \, B a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 9 \, {\left(4 \, A + 5 \, B\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(11 \, A + 9 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(15*(4*A + 3*B)*a^3*d*x + (6*B*a^3*cos(d*x + c)^3 + 8*(A + 3*B)*a^3*cos(d*x + c)^2 + 9*(4*A + 5*B)*a^3*cos(d*x + c) + 8*(11*A + 9*B)*a^3)*sin(d*x + c))/d","A",0
22,1,102,0,0.810521," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A + 5 \, B\right)} a^{3} d x + 3 \, A a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, A a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, B a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right) + 2 \, {\left(9 \, A + 11 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(7*A + 5*B)*a^3*d*x + 3*A*a^3*log(sin(d*x + c) + 1) - 3*A*a^3*log(-sin(d*x + c) + 1) + (2*B*a^3*cos(d*x + c)^2 + 3*(A + 3*B)*a^3*cos(d*x + c) + 2*(9*A + 11*B)*a^3)*sin(d*x + c))/d","A",0
23,1,127,0,0.712944," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(6 \, A + 7 \, B\right)} a^{3} d x \cos\left(d x + c\right) + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(B a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right) + 2 \, A a^{3}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((6*A + 7*B)*a^3*d*x*cos(d*x + c) + (3*A + B)*a^3*cos(d*x + c)*log(sin(d*x + c) + 1) - (3*A + B)*a^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + (B*a^3*cos(d*x + c)^2 + 2*(A + 3*B)*a^3*cos(d*x + c) + 2*A*a^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
24,1,137,0,0.626959," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(A + 3 \, B\right)} a^{3} d x \cos\left(d x + c\right)^{2} + {\left(7 \, A + 6 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(7 \, A + 6 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*(A + 3*B)*a^3*d*x*cos(d*x + c)^2 + (7*A + 6*B)*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (7*A + 6*B)*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*B*a^3*cos(d*x + c)^2 + 2*(3*A + B)*a^3*cos(d*x + c) + A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
25,1,141,0,0.651263," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{12 \, B a^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 7 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, A + 7 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(11 \, A + 9 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + 2 \, A a^{3}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*B*a^3*d*x*cos(d*x + c)^3 + 3*(5*A + 7*B)*a^3*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(5*A + 7*B)*a^3*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(11*A + 9*B)*a^3*cos(d*x + c)^2 + 3*(3*A + B)*a^3*cos(d*x + c) + 2*A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
26,1,145,0,0.764803," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, A + 4 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, A + 4 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(9 \, A + 11 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 9 \, {\left(5 \, A + 4 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + 6 \, A a^{3}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(15*(3*A + 4*B)*a^3*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 15*(3*A + 4*B)*a^3*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(9*A + 11*B)*a^3*cos(d*x + c)^3 + 9*(5*A + 4*B)*a^3*cos(d*x + c)^2 + 8*(3*A + B)*a^3*cos(d*x + c) + 6*A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
27,1,165,0,0.732328," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, A + 15 \, B\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(13 \, A + 15 \, B\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(38 \, A + 45 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} + 15 \, {\left(13 \, A + 15 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(19 \, A + 15 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 30 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + 24 \, A a^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(13*A + 15*B)*a^3*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(13*A + 15*B)*a^3*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(38*A + 45*B)*a^3*cos(d*x + c)^4 + 15*(13*A + 15*B)*a^3*cos(d*x + c)^3 + 8*(19*A + 15*B)*a^3*cos(d*x + c)^2 + 30*(3*A + B)*a^3*cos(d*x + c) + 24*A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
28,1,150,0,0.877276," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, {\left(49 \, A + 44 \, B\right)} a^{4} d x + {\left(240 \, B a^{4} \cos\left(d x + c\right)^{6} + 280 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right)^{5} + 192 \, {\left(7 \, A + 12 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(41 \, A + 44 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} + 16 \, {\left(252 \, A + 227 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(49 \, A + 44 \, B\right)} a^{4} \cos\left(d x + c\right) + 32 \, {\left(252 \, A + 227 \, B\right)} a^{4}\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(105*(49*A + 44*B)*a^4*d*x + (240*B*a^4*cos(d*x + c)^6 + 280*(A + 4*B)*a^4*cos(d*x + c)^5 + 192*(7*A + 12*B)*a^4*cos(d*x + c)^4 + 70*(41*A + 44*B)*a^4*cos(d*x + c)^3 + 16*(252*A + 227*B)*a^4*cos(d*x + c)^2 + 105*(49*A + 44*B)*a^4*cos(d*x + c) + 32*(252*A + 227*B)*a^4)*sin(d*x + c))/d","A",0
29,1,130,0,0.700161," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, {\left(8 \, A + 7 \, B\right)} a^{4} d x + {\left(40 \, B a^{4} \cos\left(d x + c\right)^{5} + 48 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} + 10 \, {\left(24 \, A + 41 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} + 32 \, {\left(17 \, A + 18 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(8 \, A + 7 \, B\right)} a^{4} \cos\left(d x + c\right) + 16 \, {\left(83 \, A + 72 \, B\right)} a^{4}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(105*(8*A + 7*B)*a^4*d*x + (40*B*a^4*cos(d*x + c)^5 + 48*(A + 4*B)*a^4*cos(d*x + c)^4 + 10*(24*A + 41*B)*a^4*cos(d*x + c)^3 + 32*(17*A + 18*B)*a^4*cos(d*x + c)^2 + 105*(8*A + 7*B)*a^4*cos(d*x + c) + 16*(83*A + 72*B)*a^4)*sin(d*x + c))/d","A",0
30,1,110,0,0.621414," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, {\left(5 \, A + 4 \, B\right)} a^{4} d x + {\left(24 \, B a^{4} \cos\left(d x + c\right)^{4} + 30 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} + 16 \, {\left(10 \, A + 17 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 15 \, {\left(27 \, A + 28 \, B\right)} a^{4} \cos\left(d x + c\right) + 8 \, {\left(100 \, A + 83 \, B\right)} a^{4}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(105*(5*A + 4*B)*a^4*d*x + (24*B*a^4*cos(d*x + c)^4 + 30*(A + 4*B)*a^4*cos(d*x + c)^3 + 16*(10*A + 17*B)*a^4*cos(d*x + c)^2 + 15*(27*A + 28*B)*a^4*cos(d*x + c) + 8*(100*A + 83*B)*a^4)*sin(d*x + c))/d","A",0
31,1,118,0,0.649085," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left(48 \, A + 35 \, B\right)} a^{4} d x + 12 \, A a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, A a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, B a^{4} \cos\left(d x + c\right)^{3} + 8 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 3 \, {\left(16 \, A + 27 \, B\right)} a^{4} \cos\left(d x + c\right) + 160 \, {\left(A + B\right)} a^{4}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(48*A + 35*B)*a^4*d*x + 12*A*a^4*log(sin(d*x + c) + 1) - 12*A*a^4*log(-sin(d*x + c) + 1) + (6*B*a^4*cos(d*x + c)^3 + 8*(A + 4*B)*a^4*cos(d*x + c)^2 + 3*(16*A + 27*B)*a^4*cos(d*x + c) + 160*(A + B)*a^4)*sin(d*x + c))/d","A",0
32,1,150,0,0.954362," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(13 \, A + 12 \, B\right)} a^{4} d x \cos\left(d x + c\right) + 3 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, B a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, A + 5 \, B\right)} a^{4} \cos\left(d x + c\right) + 6 \, A a^{4}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(3*(13*A + 12*B)*a^4*d*x*cos(d*x + c) + 3*(4*A + B)*a^4*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*(4*A + B)*a^4*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*B*a^4*cos(d*x + c)^3 + 3*(A + 4*B)*a^4*cos(d*x + c)^2 + 8*(3*A + 5*B)*a^4*cos(d*x + c) + 6*A*a^4)*sin(d*x + c))/(d*cos(d*x + c))","A",0
33,1,156,0,0.670177," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, A + 13 \, B\right)} a^{4} d x \cos\left(d x + c\right)^{2} + {\left(13 \, A + 8 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(13 \, A + 8 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(A + 4 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) + A a^{4}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*(8*A + 13*B)*a^4*d*x*cos(d*x + c)^2 + (13*A + 8*B)*a^4*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (13*A + 8*B)*a^4*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(B*a^4*cos(d*x + c)^3 + 2*(A + 4*B)*a^4*cos(d*x + c)^2 + 2*(4*A + B)*a^4*cos(d*x + c) + A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
34,1,159,0,0.937372," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{12 \, {\left(A + 4 \, B\right)} a^{4} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(12 \, A + 13 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(12 \, A + 13 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, B a^{4} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 3 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) + 2 \, A a^{4}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*(A + 4*B)*a^4*d*x*cos(d*x + c)^3 + 3*(12*A + 13*B)*a^4*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(12*A + 13*B)*a^4*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*B*a^4*cos(d*x + c)^3 + 8*(5*A + 3*B)*a^4*cos(d*x + c)^2 + 3*(4*A + B)*a^4*cos(d*x + c) + 2*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
35,1,157,0,0.655400," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{48 \, B a^{4} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(35 \, A + 48 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(35 \, A + 48 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(160 \, {\left(A + B\right)} a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(27 \, A + 16 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 8 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) + 6 \, A a^{4}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(48*B*a^4*d*x*cos(d*x + c)^4 + 3*(35*A + 48*B)*a^4*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(35*A + 48*B)*a^4*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(160*(A + B)*a^4*cos(d*x + c)^3 + 3*(27*A + 16*B)*a^4*cos(d*x + c)^2 + 8*(4*A + B)*a^4*cos(d*x + c) + 6*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
36,1,165,0,1.242472," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{105 \, {\left(4 \, A + 5 \, B\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(4 \, A + 5 \, B\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(83 \, A + 100 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} + 15 \, {\left(28 \, A + 27 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} + 16 \, {\left(17 \, A + 10 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 30 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) + 24 \, A a^{4}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(105*(4*A + 5*B)*a^4*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 105*(4*A + 5*B)*a^4*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(83*A + 100*B)*a^4*cos(d*x + c)^4 + 15*(28*A + 27*B)*a^4*cos(d*x + c)^3 + 16*(17*A + 10*B)*a^4*cos(d*x + c)^2 + 30*(4*A + B)*a^4*cos(d*x + c) + 24*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
37,1,185,0,0.729578," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{105 \, {\left(7 \, A + 8 \, B\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(7 \, A + 8 \, B\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(72 \, A + 83 \, B\right)} a^{4} \cos\left(d x + c\right)^{5} + 105 \, {\left(7 \, A + 8 \, B\right)} a^{4} \cos\left(d x + c\right)^{4} + 32 \, {\left(18 \, A + 17 \, B\right)} a^{4} \cos\left(d x + c\right)^{3} + 10 \, {\left(41 \, A + 24 \, B\right)} a^{4} \cos\left(d x + c\right)^{2} + 48 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) + 40 \, A a^{4}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(105*(7*A + 8*B)*a^4*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 105*(7*A + 8*B)*a^4*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(72*A + 83*B)*a^4*cos(d*x + c)^5 + 105*(7*A + 8*B)*a^4*cos(d*x + c)^4 + 32*(18*A + 17*B)*a^4*cos(d*x + c)^3 + 10*(41*A + 24*B)*a^4*cos(d*x + c)^2 + 48*(4*A + B)*a^4*cos(d*x + c) + 40*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
38,1,120,0,0.617812," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{9 \, {\left(4 \, A - 5 \, B\right)} d x \cos\left(d x + c\right) + 9 \, {\left(4 \, A - 5 \, B\right)} d x - {\left(6 \, B \cos\left(d x + c\right)^{4} + 2 \, {\left(4 \, A - B\right)} \cos\left(d x + c\right)^{3} - {\left(4 \, A - 13 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(28 \, A - 19 \, B\right)} \cos\left(d x + c\right) + 64 \, A - 64 \, B\right)} \sin\left(d x + c\right)}{24 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/24*(9*(4*A - 5*B)*d*x*cos(d*x + c) + 9*(4*A - 5*B)*d*x - (6*B*cos(d*x + c)^4 + 2*(4*A - B)*cos(d*x + c)^3 - (4*A - 13*B)*cos(d*x + c)^2 + (28*A - 19*B)*cos(d*x + c) + 64*A - 64*B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
39,1,98,0,0.649406," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left(A - B\right)} d x \cos\left(d x + c\right) + 9 \, {\left(A - B\right)} d x + {\left(2 \, B \cos\left(d x + c\right)^{3} + {\left(3 \, A - B\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, A - 7 \, B\right)} \cos\left(d x + c\right) - 12 \, A + 16 \, B\right)} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/6*(9*(A - B)*d*x*cos(d*x + c) + 9*(A - B)*d*x + (2*B*cos(d*x + c)^3 + (3*A - B)*cos(d*x + c)^2 - (3*A - 7*B)*cos(d*x + c) - 12*A + 16*B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
40,1,83,0,0.559184," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(2 \, A - 3 \, B\right)} d x \cos\left(d x + c\right) + {\left(2 \, A - 3 \, B\right)} d x - {\left(B \cos\left(d x + c\right)^{2} + {\left(2 \, A - B\right)} \cos\left(d x + c\right) + 4 \, A - 4 \, B\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/2*((2*A - 3*B)*d*x*cos(d*x + c) + (2*A - 3*B)*d*x - (B*cos(d*x + c)^2 + (2*A - B)*cos(d*x + c) + 4*A - 4*B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
41,1,61,0,0.659015," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(A - B\right)} d x \cos\left(d x + c\right) + {\left(A - B\right)} d x + {\left(B \cos\left(d x + c\right) - A + 2 \, B\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"((A - B)*d*x*cos(d*x + c) + (A - B)*d*x + (B*cos(d*x + c) - A + 2*B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
42,1,43,0,0.711411," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{B d x \cos\left(d x + c\right) + B d x + {\left(A - B\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"(B*d*x*cos(d*x + c) + B*d*x + (A - B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
43,1,74,0,0.653487," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(A \cos\left(d x + c\right) + A\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A \cos\left(d x + c\right) + A\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A - B\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*((A*cos(d*x + c) + A)*log(sin(d*x + c) + 1) - (A*cos(d*x + c) + A)*log(-sin(d*x + c) + 1) - 2*(A - B)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
44,1,127,0,0.567159," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left({\left(A - B\right)} \cos\left(d x + c\right)^{2} + {\left(A - B\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A - B\right)} \cos\left(d x + c\right)^{2} + {\left(A - B\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(2 \, A - B\right)} \cos\left(d x + c\right) + A\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}"," ",0,"-1/2*(((A - B)*cos(d*x + c)^2 + (A - B)*cos(d*x + c))*log(sin(d*x + c) + 1) - ((A - B)*cos(d*x + c)^2 + (A - B)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*((2*A - B)*cos(d*x + c) + A)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
45,1,156,0,0.656926," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(A - B\right)} \cos\left(d x + c\right)^{2} + {\left(A - 2 \, B\right)} \cos\left(d x + c\right) - A\right)} \sin\left(d x + c\right)}{4 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/4*(((3*A - 2*B)*cos(d*x + c)^3 + (3*A - 2*B)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((3*A - 2*B)*cos(d*x + c)^3 + (3*A - 2*B)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(A - B)*cos(d*x + c)^2 + (A - 2*B)*cos(d*x + c) - A)*sin(d*x + c))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
46,1,168,0,0.552075," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{9 \, {\left({\left(A - B\right)} \cos\left(d x + c\right)^{4} + {\left(A - B\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, {\left({\left(A - B\right)} \cos\left(d x + c\right)^{4} + {\left(A - B\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(4 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(A - 3 \, B\right)} \cos\left(d x + c\right) + 2 \, A\right)} \sin\left(d x + c\right)}{12 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/12*(9*((A - B)*cos(d*x + c)^4 + (A - B)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 9*((A - B)*cos(d*x + c)^4 + (A - B)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(4*(4*A - 3*B)*cos(d*x + c)^3 + (7*A - 3*B)*cos(d*x + c)^2 - (A - 3*B)*cos(d*x + c) + 2*A)*sin(d*x + c))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
47,1,154,0,1.031808," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A - 10 \, B\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(7 \, A - 10 \, B\right)} d x \cos\left(d x + c\right) + 3 \, {\left(7 \, A - 10 \, B\right)} d x + {\left(2 \, B \cos\left(d x + c\right)^{4} + {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(43 \, A - 66 \, B\right)} \cos\left(d x + c\right) - 32 \, A + 48 \, B\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(7*A - 10*B)*d*x*cos(d*x + c)^2 + 6*(7*A - 10*B)*d*x*cos(d*x + c) + 3*(7*A - 10*B)*d*x + (2*B*cos(d*x + c)^4 + (3*A - 2*B)*cos(d*x + c)^3 - 6*(A - 2*B)*cos(d*x + c)^2 - (43*A - 66*B)*cos(d*x + c) - 32*A + 48*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
48,1,138,0,0.785209," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(4 \, A - 7 \, B\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(4 \, A - 7 \, B\right)} d x \cos\left(d x + c\right) + 3 \, {\left(4 \, A - 7 \, B\right)} d x - {\left(3 \, B \cos\left(d x + c\right)^{3} + 6 \, {\left(A - B\right)} \cos\left(d x + c\right)^{2} + {\left(28 \, A - 43 \, B\right)} \cos\left(d x + c\right) + 20 \, A - 32 \, B\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/6*(3*(4*A - 7*B)*d*x*cos(d*x + c)^2 + 6*(4*A - 7*B)*d*x*cos(d*x + c) + 3*(4*A - 7*B)*d*x - (3*B*cos(d*x + c)^3 + 6*(A - B)*cos(d*x + c)^2 + (28*A - 43*B)*cos(d*x + c) + 20*A - 32*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
49,1,117,0,0.753418," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(A - 2 \, B\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(A - 2 \, B\right)} d x \cos\left(d x + c\right) + 3 \, {\left(A - 2 \, B\right)} d x + {\left(3 \, B \cos\left(d x + c\right)^{2} - {\left(5 \, A - 14 \, B\right)} \cos\left(d x + c\right) - 4 \, A + 10 \, B\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(3*(A - 2*B)*d*x*cos(d*x + c)^2 + 6*(A - 2*B)*d*x*cos(d*x + c) + 3*(A - 2*B)*d*x + (3*B*cos(d*x + c)^2 - (5*A - 14*B)*cos(d*x + c) - 4*A + 10*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
50,1,91,0,0.805490," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, B d x \cos\left(d x + c\right)^{2} + 6 \, B d x \cos\left(d x + c\right) + 3 \, B d x + {\left({\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right) + A - 4 \, B\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(3*B*d*x*cos(d*x + c)^2 + 6*B*d*x*cos(d*x + c) + 3*B*d*x + ((2*A - 5*B)*cos(d*x + c) + A - 4*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
51,1,58,0,0.767437," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left({\left(A + 2 \, B\right)} \cos\left(d x + c\right) + 2 \, A + B\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*((A + 2*B)*cos(d*x + c) + 2*A + B)*sin(d*x + c)/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
52,1,131,0,0.804602," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + A\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + A\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(4 \, A - B\right)} \cos\left(d x + c\right) + 5 \, A - 2 \, B\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + A)*log(sin(d*x + c) + 1) - 3*(A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + A)*log(-sin(d*x + c) + 1) - 2*((4*A - B)*cos(d*x + c) + 5*A - 2*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
53,1,207,0,0.754233," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(2 \, A - B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, A - B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A - B\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(2 \, A - B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, A - B\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, A - B\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(14 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 3 \, A\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/6*(3*((2*A - B)*cos(d*x + c)^3 + 2*(2*A - B)*cos(d*x + c)^2 + (2*A - B)*cos(d*x + c))*log(sin(d*x + c) + 1) - 3*((2*A - B)*cos(d*x + c)^3 + 2*(2*A - B)*cos(d*x + c)^2 + (2*A - B)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*(5*A - 2*B)*cos(d*x + c)^2 + (14*A - 5*B)*cos(d*x + c) + 3*A)*sin(d*x + c))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))","B",0
54,1,228,0,0.871401," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(7 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(7 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(8 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(43 \, A - 28 \, B\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(A - B\right)} \cos\left(d x + c\right) - 3 \, A\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/12*(3*((7*A - 4*B)*cos(d*x + c)^4 + 2*(7*A - 4*B)*cos(d*x + c)^3 + (7*A - 4*B)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*((7*A - 4*B)*cos(d*x + c)^4 + 2*(7*A - 4*B)*cos(d*x + c)^3 + (7*A - 4*B)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(8*A - 5*B)*cos(d*x + c)^3 + (43*A - 28*B)*cos(d*x + c)^2 + 6*(A - B)*cos(d*x + c) - 3*A)*sin(d*x + c))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)","A",0
55,1,247,0,1.584186," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(10 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(10 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(10 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(10 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(10 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(10 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(66 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(2 \, A - B\right)} \cos\left(d x + c\right)^{2} - {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 2 \, A\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} + 2 \, a^{2} d \cos\left(d x + c\right)^{4} + a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/12*(3*((10*A - 7*B)*cos(d*x + c)^5 + 2*(10*A - 7*B)*cos(d*x + c)^4 + (10*A - 7*B)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((10*A - 7*B)*cos(d*x + c)^5 + 2*(10*A - 7*B)*cos(d*x + c)^4 + (10*A - 7*B)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(16*(3*A - 2*B)*cos(d*x + c)^4 + (66*A - 43*B)*cos(d*x + c)^3 + 6*(2*A - B)*cos(d*x + c)^2 - (2*A - 3*B)*cos(d*x + c) + 2*A)*sin(d*x + c))/(a^2*d*cos(d*x + c)^5 + 2*a^2*d*cos(d*x + c)^4 + a^2*d*cos(d*x + c)^3)","A",0
56,1,205,0,0.653683," ","integrate(cos(d*x+c)^5*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, A - 23 \, B\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(13 \, A - 23 \, B\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(13 \, A - 23 \, B\right)} d x \cos\left(d x + c\right) + 15 \, {\left(13 \, A - 23 \, B\right)} d x + {\left(10 \, B \cos\left(d x + c\right)^{5} + 15 \, {\left(A - B\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(9 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} - {\left(479 \, A - 869 \, B\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(239 \, A - 429 \, B\right)} \cos\left(d x + c\right) - 304 \, A + 544 \, B\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(15*(13*A - 23*B)*d*x*cos(d*x + c)^3 + 45*(13*A - 23*B)*d*x*cos(d*x + c)^2 + 45*(13*A - 23*B)*d*x*cos(d*x + c) + 15*(13*A - 23*B)*d*x + (10*B*cos(d*x + c)^5 + 15*(A - B)*cos(d*x + c)^4 - 5*(9*A - 19*B)*cos(d*x + c)^3 - (479*A - 869*B)*cos(d*x + c)^2 - 3*(239*A - 429*B)*cos(d*x + c) - 304*A + 544*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
57,1,190,0,0.586679," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(6 \, A - 13 \, B\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(6 \, A - 13 \, B\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(6 \, A - 13 \, B\right)} d x \cos\left(d x + c\right) + 15 \, {\left(6 \, A - 13 \, B\right)} d x - {\left(15 \, B \cos\left(d x + c\right)^{4} + 15 \, {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(234 \, A - 479 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(114 \, A - 239 \, B\right)} \cos\left(d x + c\right) + 144 \, A - 304 \, B\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/30*(15*(6*A - 13*B)*d*x*cos(d*x + c)^3 + 45*(6*A - 13*B)*d*x*cos(d*x + c)^2 + 45*(6*A - 13*B)*d*x*cos(d*x + c) + 15*(6*A - 13*B)*d*x - (15*B*cos(d*x + c)^4 + 15*(2*A - 3*B)*cos(d*x + c)^3 + (234*A - 479*B)*cos(d*x + c)^2 + 3*(114*A - 239*B)*cos(d*x + c) + 144*A - 304*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
58,1,165,0,0.624100," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(A - 3 \, B\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(A - 3 \, B\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(A - 3 \, B\right)} d x \cos\left(d x + c\right) + 15 \, {\left(A - 3 \, B\right)} d x + {\left(15 \, B \cos\left(d x + c\right)^{3} - {\left(32 \, A - 117 \, B\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(17 \, A - 57 \, B\right)} \cos\left(d x + c\right) - 22 \, A + 72 \, B\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(15*(A - 3*B)*d*x*cos(d*x + c)^3 + 45*(A - 3*B)*d*x*cos(d*x + c)^2 + 45*(A - 3*B)*d*x*cos(d*x + c) + 15*(A - 3*B)*d*x + (15*B*cos(d*x + c)^3 - (32*A - 117*B)*cos(d*x + c)^2 - 3*(17*A - 57*B)*cos(d*x + c) - 22*A + 72*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
59,1,137,0,0.882902," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, B d x \cos\left(d x + c\right)^{3} + 45 \, B d x \cos\left(d x + c\right)^{2} + 45 \, B d x \cos\left(d x + c\right) + 15 \, B d x + {\left({\left(7 \, A - 32 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A - 17 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 22 \, B\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(15*B*d*x*cos(d*x + c)^3 + 45*B*d*x*cos(d*x + c)^2 + 45*B*d*x*cos(d*x + c) + 15*B*d*x + ((7*A - 32*B)*cos(d*x + c)^2 + 3*(2*A - 17*B)*cos(d*x + c) + 2*A - 22*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
60,1,93,0,0.759341," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(3 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 2 \, B\right)} \cos\left(d x + c\right) + 3 \, A + 2 \, B\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*((3*A + 7*B)*cos(d*x + c)^2 + 3*(3*A + 2*B)*cos(d*x + c) + 3*A + 2*B)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
61,1,93,0,0.539016," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 7 \, A + 3 \, B\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*((2*A + 3*B)*cos(d*x + c)^2 + 3*(2*A + 3*B)*cos(d*x + c) + 7*A + 3*B)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
62,1,185,0,0.724642," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + A\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + A\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(11 \, A - B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(17 \, A - 2 \, B\right)} \cos\left(d x + c\right) + 32 \, A - 7 \, B\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(15*(A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 + 3*A*cos(d*x + c) + A)*log(sin(d*x + c) + 1) - 15*(A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 + 3*A*cos(d*x + c) + A)*log(-sin(d*x + c) + 1) - 2*(2*(11*A - B)*cos(d*x + c)^2 + 3*(17*A - 2*B)*cos(d*x + c) + 32*A - 7*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
63,1,272,0,0.663946," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(3 \, A - B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, A - B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - B\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - B\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(3 \, A - B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, A - B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - B\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - B\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(36 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(57 \, A - 17 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(117 \, A - 32 \, B\right)} \cos\left(d x + c\right) + 15 \, A\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/30*(15*((3*A - B)*cos(d*x + c)^4 + 3*(3*A - B)*cos(d*x + c)^3 + 3*(3*A - B)*cos(d*x + c)^2 + (3*A - B)*cos(d*x + c))*log(sin(d*x + c) + 1) - 15*((3*A - B)*cos(d*x + c)^4 + 3*(3*A - B)*cos(d*x + c)^3 + 3*(3*A - B)*cos(d*x + c)^2 + (3*A - B)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*(36*A - 11*B)*cos(d*x + c)^3 + 3*(57*A - 17*B)*cos(d*x + c)^2 + (117*A - 32*B)*cos(d*x + c) + 15*A)*sin(d*x + c))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))","A",0
64,1,295,0,0.821853," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(13 \, A - 6 \, B\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(13 \, A - 6 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(13 \, A - 6 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, A - 6 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(13 \, A - 6 \, B\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(13 \, A - 6 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(13 \, A - 6 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, A - 6 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(19 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(239 \, A - 114 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(479 \, A - 234 \, B\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right) - 15 \, A\right)} \sin\left(d x + c\right)}{60 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/60*(15*((13*A - 6*B)*cos(d*x + c)^5 + 3*(13*A - 6*B)*cos(d*x + c)^4 + 3*(13*A - 6*B)*cos(d*x + c)^3 + (13*A - 6*B)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 15*((13*A - 6*B)*cos(d*x + c)^5 + 3*(13*A - 6*B)*cos(d*x + c)^4 + 3*(13*A - 6*B)*cos(d*x + c)^3 + (13*A - 6*B)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(16*(19*A - 9*B)*cos(d*x + c)^4 + 3*(239*A - 114*B)*cos(d*x + c)^3 + (479*A - 234*B)*cos(d*x + c)^2 + 15*(3*A - 2*B)*cos(d*x + c) - 15*A)*sin(d*x + c))/(a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2)","A",0
65,1,238,0,0.775489," ","integrate(cos(d*x+c)^5*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","-\frac{105 \, {\left(8 \, A - 21 \, B\right)} d x \cos\left(d x + c\right)^{4} + 420 \, {\left(8 \, A - 21 \, B\right)} d x \cos\left(d x + c\right)^{3} + 630 \, {\left(8 \, A - 21 \, B\right)} d x \cos\left(d x + c\right)^{2} + 420 \, {\left(8 \, A - 21 \, B\right)} d x \cos\left(d x + c\right) + 105 \, {\left(8 \, A - 21 \, B\right)} d x - {\left(105 \, B \cos\left(d x + c\right)^{5} + 210 \, {\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(592 \, A - 1509 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(1318 \, A - 3411 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4472 \, A - 11619 \, B\right)} \cos\left(d x + c\right) + 1328 \, A - 3456 \, B\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/210*(105*(8*A - 21*B)*d*x*cos(d*x + c)^4 + 420*(8*A - 21*B)*d*x*cos(d*x + c)^3 + 630*(8*A - 21*B)*d*x*cos(d*x + c)^2 + 420*(8*A - 21*B)*d*x*cos(d*x + c) + 105*(8*A - 21*B)*d*x - (105*B*cos(d*x + c)^5 + 210*(A - 2*B)*cos(d*x + c)^4 + 4*(592*A - 1509*B)*cos(d*x + c)^3 + 4*(1318*A - 3411*B)*cos(d*x + c)^2 + (4472*A - 11619*B)*cos(d*x + c) + 1328*A - 3456*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
66,1,213,0,0.753667," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(A - 4 \, B\right)} d x \cos\left(d x + c\right)^{4} + 420 \, {\left(A - 4 \, B\right)} d x \cos\left(d x + c\right)^{3} + 630 \, {\left(A - 4 \, B\right)} d x \cos\left(d x + c\right)^{2} + 420 \, {\left(A - 4 \, B\right)} d x \cos\left(d x + c\right) + 105 \, {\left(A - 4 \, B\right)} d x + {\left(105 \, B \cos\left(d x + c\right)^{4} - 4 \, {\left(65 \, A - 296 \, B\right)} \cos\left(d x + c\right)^{3} - 4 \, {\left(155 \, A - 659 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(535 \, A - 2236 \, B\right)} \cos\left(d x + c\right) - 160 \, A + 664 \, B\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(105*(A - 4*B)*d*x*cos(d*x + c)^4 + 420*(A - 4*B)*d*x*cos(d*x + c)^3 + 630*(A - 4*B)*d*x*cos(d*x + c)^2 + 420*(A - 4*B)*d*x*cos(d*x + c) + 105*(A - 4*B)*d*x + (105*B*cos(d*x + c)^4 - 4*(65*A - 296*B)*cos(d*x + c)^3 - 4*(155*A - 659*B)*cos(d*x + c)^2 - (535*A - 2236*B)*cos(d*x + c) - 160*A + 664*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
67,1,180,0,0.906763," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, B d x \cos\left(d x + c\right)^{4} + 420 \, B d x \cos\left(d x + c\right)^{3} + 630 \, B d x \cos\left(d x + c\right)^{2} + 420 \, B d x \cos\left(d x + c\right) + 105 \, B d x + {\left(4 \, {\left(9 \, A - 65 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A - 620 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(24 \, A - 535 \, B\right)} \cos\left(d x + c\right) + 6 \, A - 160 \, B\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(105*B*d*x*cos(d*x + c)^4 + 420*B*d*x*cos(d*x + c)^3 + 630*B*d*x*cos(d*x + c)^2 + 420*B*d*x*cos(d*x + c) + 105*B*d*x + (4*(9*A - 65*B)*cos(d*x + c)^3 + (39*A - 620*B)*cos(d*x + c)^2 + (24*A - 535*B)*cos(d*x + c) + 6*A - 160*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
68,1,124,0,0.743791," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(13 \, A + 36 \, B\right)} \cos\left(d x + c\right)^{3} + 13 \, {\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 8 \, A + 6 \, B\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*((13*A + 36*B)*cos(d*x + c)^3 + 13*(4*A + 3*B)*cos(d*x + c)^2 + 8*(4*A + 3*B)*cos(d*x + c) + 8*A + 6*B)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
69,1,124,0,0.620889," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(8 \, A + 13 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(8 \, A + 13 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(13 \, A + 8 \, B\right)} \cos\left(d x + c\right) + 13 \, A + 8 \, B\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*((8*A + 13*B)*cos(d*x + c)^3 + 4*(8*A + 13*B)*cos(d*x + c)^2 + 4*(13*A + 8*B)*cos(d*x + c) + 13*A + 8*B)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
70,1,125,0,0.538476," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right)^{2} + 13 \, {\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right) + 36 \, A + 13 \, B\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(2*(3*A + 4*B)*cos(d*x + c)^3 + 8*(3*A + 4*B)*cos(d*x + c)^2 + 13*(3*A + 4*B)*cos(d*x + c) + 36*A + 13*B)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
71,1,236,0,0.783467," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(A \cos\left(d x + c\right)^{4} + 4 \, A \cos\left(d x + c\right)^{3} + 6 \, A \cos\left(d x + c\right)^{2} + 4 \, A \cos\left(d x + c\right) + A\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(A \cos\left(d x + c\right)^{4} + 4 \, A \cos\left(d x + c\right)^{3} + 6 \, A \cos\left(d x + c\right)^{2} + 4 \, A \cos\left(d x + c\right) + A\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(80 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(535 \, A - 24 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(620 \, A - 39 \, B\right)} \cos\left(d x + c\right) + 260 \, A - 36 \, B\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/210*(105*(A*cos(d*x + c)^4 + 4*A*cos(d*x + c)^3 + 6*A*cos(d*x + c)^2 + 4*A*cos(d*x + c) + A)*log(sin(d*x + c) + 1) - 105*(A*cos(d*x + c)^4 + 4*A*cos(d*x + c)^3 + 6*A*cos(d*x + c)^2 + 4*A*cos(d*x + c) + A)*log(-sin(d*x + c) + 1) - 2*(2*(80*A - 3*B)*cos(d*x + c)^3 + (535*A - 24*B)*cos(d*x + c)^2 + (620*A - 39*B)*cos(d*x + c) + 260*A - 36*B)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
72,1,337,0,0.957325," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","-\frac{105 \, {\left({\left(4 \, A - B\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(4 \, A - B\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(4 \, A - B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(4 \, A - B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A - B\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(4 \, A - B\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(4 \, A - B\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(4 \, A - B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(4 \, A - B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A - B\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(8 \, {\left(83 \, A - 20 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(2236 \, A - 535 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(659 \, A - 155 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(296 \, A - 65 \, B\right)} \cos\left(d x + c\right) + 105 \, A\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} + 4 \, a^{4} d \cos\left(d x + c\right)^{4} + 6 \, a^{4} d \cos\left(d x + c\right)^{3} + 4 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/210*(105*((4*A - B)*cos(d*x + c)^5 + 4*(4*A - B)*cos(d*x + c)^4 + 6*(4*A - B)*cos(d*x + c)^3 + 4*(4*A - B)*cos(d*x + c)^2 + (4*A - B)*cos(d*x + c))*log(sin(d*x + c) + 1) - 105*((4*A - B)*cos(d*x + c)^5 + 4*(4*A - B)*cos(d*x + c)^4 + 6*(4*A - B)*cos(d*x + c)^3 + 4*(4*A - B)*cos(d*x + c)^2 + (4*A - B)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(8*(83*A - 20*B)*cos(d*x + c)^4 + (2236*A - 535*B)*cos(d*x + c)^3 + 4*(659*A - 155*B)*cos(d*x + c)^2 + 4*(296*A - 65*B)*cos(d*x + c) + 105*A)*sin(d*x + c))/(a^4*d*cos(d*x + c)^5 + 4*a^4*d*cos(d*x + c)^4 + 6*a^4*d*cos(d*x + c)^3 + 4*a^4*d*cos(d*x + c)^2 + a^4*d*cos(d*x + c))","B",0
73,1,360,0,0.587518," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left({\left(21 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(21 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(21 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(21 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(21 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(21 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(21 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(21 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(21 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(21 \, A - 8 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(216 \, A - 83 \, B\right)} \cos\left(d x + c\right)^{5} + {\left(11619 \, A - 4472 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(3411 \, A - 1318 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(1509 \, A - 592 \, B\right)} \cos\left(d x + c\right)^{2} + 210 \, {\left(2 \, A - B\right)} \cos\left(d x + c\right) - 105 \, A\right)} \sin\left(d x + c\right)}{420 \, {\left(a^{4} d \cos\left(d x + c\right)^{6} + 4 \, a^{4} d \cos\left(d x + c\right)^{5} + 6 \, a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + a^{4} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/420*(105*((21*A - 8*B)*cos(d*x + c)^6 + 4*(21*A - 8*B)*cos(d*x + c)^5 + 6*(21*A - 8*B)*cos(d*x + c)^4 + 4*(21*A - 8*B)*cos(d*x + c)^3 + (21*A - 8*B)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 105*((21*A - 8*B)*cos(d*x + c)^6 + 4*(21*A - 8*B)*cos(d*x + c)^5 + 6*(21*A - 8*B)*cos(d*x + c)^4 + 4*(21*A - 8*B)*cos(d*x + c)^3 + (21*A - 8*B)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(16*(216*A - 83*B)*cos(d*x + c)^5 + (11619*A - 4472*B)*cos(d*x + c)^4 + 4*(3411*A - 1318*B)*cos(d*x + c)^3 + 4*(1509*A - 592*B)*cos(d*x + c)^2 + 210*(2*A - B)*cos(d*x + c) - 105*A)*sin(d*x + c))/(a^4*d*cos(d*x + c)^6 + 4*a^4*d*cos(d*x + c)^5 + 6*a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + a^4*d*cos(d*x + c)^2)","A",0
74,1,99,0,0.608844," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B \cos\left(d x + c\right)^{4} + 5 \, {\left(9 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(9 \, A + 8 \, B\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(9 \, A + 8 \, B\right)} \cos\left(d x + c\right) + 144 \, A + 128 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*B*cos(d*x + c)^4 + 5*(9*A + 8*B)*cos(d*x + c)^3 + 6*(9*A + 8*B)*cos(d*x + c)^2 + 8*(9*A + 8*B)*cos(d*x + c) + 144*A + 128*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
75,1,82,0,0.628720," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, A + 6 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(7 \, A + 6 \, B\right)} \cos\left(d x + c\right) + 56 \, A + 48 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/105*(15*B*cos(d*x + c)^3 + 3*(7*A + 6*B)*cos(d*x + c)^2 + 4*(7*A + 6*B)*cos(d*x + c) + 56*A + 48*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
76,1,64,0,0.803316," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B \cos\left(d x + c\right)^{2} + {\left(5 \, A + 4 \, B\right)} \cos\left(d x + c\right) + 10 \, A + 8 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/15*(3*B*cos(d*x + c)^2 + (5*A + 4*B)*cos(d*x + c) + 10*A + 8*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
77,1,47,0,0.671601," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(B \cos\left(d x + c\right) + 3 \, A + 2 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/3*(B*cos(d*x + c) + 3*A + 2*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
78,1,127,0,0.662372," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{{\left(A \cos\left(d x + c\right) + A\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} B \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/2*((A*cos(d*x + c) + A)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*B*sin(d*x + c))/(d*cos(d*x + c) + d)","B",0
79,1,153,0,0.800928," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left({\left(A + 2 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(A + 2 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} A \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*(((A + 2*B)*cos(d*x + c)^2 + (A + 2*B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*A*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","B",0
80,1,178,0,0.777306," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left({\left(3 \, A + 4 \, B\right)} \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(((3*A + 4*B)*cos(d*x + c)^3 + (3*A + 4*B)*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*((3*A + 4*B)*cos(d*x + c) + 2*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
81,1,197,0,0.775056," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(5 \, A + 6 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, A + 6 \, B\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(3 \, {\left(5 \, A + 6 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A + 6 \, B\right)} \cos\left(d x + c\right) + 8 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/96*(3*((5*A + 6*B)*cos(d*x + c)^4 + (5*A + 6*B)*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*(5*A + 6*B)*cos(d*x + c)^2 + 2*(5*A + 6*B)*cos(d*x + c) + 8*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
82,1,125,0,1.153693," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B a \cos\left(d x + c\right)^{5} + 35 \, {\left(11 \, A + 21 \, B\right)} a \cos\left(d x + c\right)^{4} + 5 \, {\left(187 \, A + 168 \, B\right)} a \cos\left(d x + c\right)^{3} + 6 \, {\left(187 \, A + 168 \, B\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(187 \, A + 168 \, B\right)} a \cos\left(d x + c\right) + 16 \, {\left(187 \, A + 168 \, B\right)} a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{3465 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/3465*(315*B*a*cos(d*x + c)^5 + 35*(11*A + 21*B)*a*cos(d*x + c)^4 + 5*(187*A + 168*B)*a*cos(d*x + c)^3 + 6*(187*A + 168*B)*a*cos(d*x + c)^2 + 8*(187*A + 168*B)*a*cos(d*x + c) + 16*(187*A + 168*B)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
83,1,107,0,0.588925," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B a \cos\left(d x + c\right)^{4} + 5 \, {\left(9 \, A + 17 \, B\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(39 \, A + 34 \, B\right)} a \cos\left(d x + c\right)^{2} + 4 \, {\left(39 \, A + 34 \, B\right)} a \cos\left(d x + c\right) + 8 \, {\left(39 \, A + 34 \, B\right)} a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*B*a*cos(d*x + c)^4 + 5*(9*A + 17*B)*a*cos(d*x + c)^3 + 3*(39*A + 34*B)*a*cos(d*x + c)^2 + 4*(39*A + 34*B)*a*cos(d*x + c) + 8*(39*A + 34*B)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
84,1,88,0,0.831849," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B a \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, A + 13 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(63 \, A + 52 \, B\right)} a \cos\left(d x + c\right) + 2 \, {\left(63 \, A + 52 \, B\right)} a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/105*(15*B*a*cos(d*x + c)^3 + 3*(7*A + 13*B)*a*cos(d*x + c)^2 + (63*A + 52*B)*a*cos(d*x + c) + 2*(63*A + 52*B)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
85,1,69,0,0.603714," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B a \cos\left(d x + c\right)^{2} + {\left(5 \, A + 9 \, B\right)} a \cos\left(d x + c\right) + {\left(25 \, A + 18 \, B\right)} a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/15*(3*B*a*cos(d*x + c)^2 + (5*A + 9*B)*a*cos(d*x + c) + (25*A + 18*B)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
86,1,149,0,0.627460," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left(A a \cos\left(d x + c\right) + A a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(B a \cos\left(d x + c\right) + {\left(3 \, A + 5 \, B\right)} a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/6*(3*(A*a*cos(d*x + c) + A*a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(B*a*cos(d*x + c) + (3*A + 5*B)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
87,1,172,0,0.655957," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left({\left(3 \, A + 2 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(3 \, A + 2 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(2 \, B a \cos\left(d x + c\right) + A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*(((3*A + 2*B)*a*cos(d*x + c)^2 + (3*A + 2*B)*a*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(2*B*a*cos(d*x + c) + A*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
88,1,182,0,0.621407," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(7 \, A + 12 \, B\right)} a \cos\left(d x + c\right)^{3} + {\left(7 \, A + 12 \, B\right)} a \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left({\left(7 \, A + 4 \, B\right)} a \cos\left(d x + c\right) + 2 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(((7*A + 12*B)*a*cos(d*x + c)^3 + (7*A + 12*B)*a*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*((7*A + 4*B)*a*cos(d*x + c) + 2*A*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
89,1,202,0,0.594112," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(11 \, A + 14 \, B\right)} a \cos\left(d x + c\right)^{4} + {\left(11 \, A + 14 \, B\right)} a \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(3 \, {\left(11 \, A + 14 \, B\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A + 6 \, B\right)} a \cos\left(d x + c\right) + 8 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/96*(3*((11*A + 14*B)*a*cos(d*x + c)^4 + (11*A + 14*B)*a*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*(11*A + 14*B)*a*cos(d*x + c)^2 + 2*(11*A + 6*B)*a*cos(d*x + c) + 8*A*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
90,1,220,0,0.863403," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(75 \, A + 88 \, B\right)} a \cos\left(d x + c\right)^{5} + {\left(75 \, A + 88 \, B\right)} a \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(3 \, {\left(75 \, A + 88 \, B\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(75 \, A + 88 \, B\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(15 \, A + 8 \, B\right)} a \cos\left(d x + c\right) + 48 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{768 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/768*(3*((75*A + 88*B)*a*cos(d*x + c)^5 + (75*A + 88*B)*a*cos(d*x + c)^4)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*(75*A + 88*B)*a*cos(d*x + c)^3 + 2*(75*A + 88*B)*a*cos(d*x + c)^2 + 8*(15*A + 8*B)*a*cos(d*x + c) + 48*A*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
91,1,137,0,0.671876," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B a^{2} \cos\left(d x + c\right)^{5} + 35 \, {\left(11 \, A + 32 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(286 \, A + 355 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(803 \, A + 710 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 4 \, {\left(803 \, A + 710 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(803 \, A + 710 \, B\right)} a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{3465 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/3465*(315*B*a^2*cos(d*x + c)^5 + 35*(11*A + 32*B)*a^2*cos(d*x + c)^4 + 5*(286*A + 355*B)*a^2*cos(d*x + c)^3 + 3*(803*A + 710*B)*a^2*cos(d*x + c)^2 + 4*(803*A + 710*B)*a^2*cos(d*x + c) + 8*(803*A + 710*B)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
92,1,116,0,0.809450," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(9 \, A + 26 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(60 \, A + 73 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(345 \, A + 292 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(345 \, A + 292 \, B\right)} a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*B*a^2*cos(d*x + c)^4 + 5*(9*A + 26*B)*a^2*cos(d*x + c)^3 + 3*(60*A + 73*B)*a^2*cos(d*x + c)^2 + (345*A + 292*B)*a^2*cos(d*x + c) + 2*(345*A + 292*B)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
93,1,95,0,0.472177," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, A + 20 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(98 \, A + 115 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(301 \, A + 230 \, B\right)} a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/105*(15*B*a^2*cos(d*x + c)^3 + 3*(7*A + 20*B)*a^2*cos(d*x + c)^2 + (98*A + 115*B)*a^2*cos(d*x + c) + (301*A + 230*B)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
94,1,177,0,0.441278," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{15 \, {\left(A a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(3 \, B a^{2} \cos\left(d x + c\right)^{2} + {\left(5 \, A + 14 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(40 \, A + 43 \, B\right)} a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{30 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/30*(15*(A*a^2*cos(d*x + c) + A*a^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*B*a^2*cos(d*x + c)^2 + (5*A + 14*B)*a^2*cos(d*x + c) + (40*A + 43*B)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
95,1,202,0,1.206574," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(5 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(5 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(2 \, B a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/12*(3*((5*A + 2*B)*a^2*cos(d*x + c)^2 + (5*A + 2*B)*a^2*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(2*B*a^2*cos(d*x + c)^2 + 2*(3*A + 8*B)*a^2*cos(d*x + c) + 3*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
96,1,204,0,0.607919," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(19 \, A + 20 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(19 \, A + 20 \, B\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(8 \, B a^{2} \cos\left(d x + c\right)^{2} + {\left(11 \, A + 4 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(((19*A + 20*B)*a^2*cos(d*x + c)^3 + (19*A + 20*B)*a^2*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(8*B*a^2*cos(d*x + c)^2 + (11*A + 4*B)*a^2*cos(d*x + c) + 2*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
97,1,212,0,0.616167," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(25 \, A + 38 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(25 \, A + 38 \, B\right)} a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(3 \, {\left(25 \, A + 22 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(17 \, A + 6 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/96*(3*((25*A + 38*B)*a^2*cos(d*x + c)^4 + (25*A + 38*B)*a^2*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*(25*A + 22*B)*a^2*cos(d*x + c)^2 + 2*(17*A + 6*B)*a^2*cos(d*x + c) + 8*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
98,1,232,0,0.717760," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(163 \, A + 200 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(163 \, A + 200 \, B\right)} a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(3 \, {\left(163 \, A + 200 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(163 \, A + 136 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(23 \, A + 8 \, B\right)} a^{2} \cos\left(d x + c\right) + 48 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{768 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/768*(3*((163*A + 200*B)*a^2*cos(d*x + c)^5 + (163*A + 200*B)*a^2*cos(d*x + c)^4)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(3*(163*A + 200*B)*a^2*cos(d*x + c)^3 + 2*(163*A + 136*B)*a^2*cos(d*x + c)^2 + 8*(23*A + 8*B)*a^2*cos(d*x + c) + 48*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
99,1,252,0,1.117647," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(283 \, A + 326 \, B\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(283 \, A + 326 \, B\right)} a^{2} \cos\left(d x + c\right)^{5}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(15 \, {\left(283 \, A + 326 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(283 \, A + 326 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(283 \, A + 230 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 48 \, {\left(29 \, A + 10 \, B\right)} a^{2} \cos\left(d x + c\right) + 384 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{7680 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"1/7680*(15*((283*A + 326*B)*a^2*cos(d*x + c)^6 + (283*A + 326*B)*a^2*cos(d*x + c)^5)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(15*(283*A + 326*B)*a^2*cos(d*x + c)^4 + 10*(283*A + 326*B)*a^2*cos(d*x + c)^3 + 8*(283*A + 230*B)*a^2*cos(d*x + c)^2 + 48*(29*A + 10*B)*a^2*cos(d*x + c) + 384*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^6 + d*cos(d*x + c)^5)","A",0
100,1,184,0,0.605363," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(15 \, B \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, A - B\right)} \cos\left(d x + c\right)^{2} - {\left(7 \, A - 31 \, B\right)} \cos\left(d x + c\right) + 91 \, A - 43 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) - \frac{105 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{210 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/210*(4*(15*B*cos(d*x + c)^3 + 3*(7*A - B)*cos(d*x + c)^2 - (7*A - 31*B)*cos(d*x + c) + 91*A - 43*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) - 105*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
101,1,166,0,0.685663," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, B \cos\left(d x + c\right)^{2} + {\left(5 \, A - B\right)} \cos\left(d x + c\right) - 5 \, A + 13 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) - \frac{15 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{30 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/30*(4*(3*B*cos(d*x + c)^2 + (5*A - B)*cos(d*x + c) - 5*A + 13*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) - 15*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
102,1,149,0,0.633955," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(B \cos\left(d x + c\right) + 3 \, A - B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) - \frac{3 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/6*(4*(B*cos(d*x + c) + 3*A - B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) - 3*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
103,1,135,0,0.759332," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{a \cos\left(d x + c\right) + a} B \sin\left(d x + c\right) - \frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*(4*sqrt(a*cos(d*x + c) + a)*B*sin(d*x + c) - sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","B",0
104,1,171,0,0.678860," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(A - B\right)} \sqrt{a} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - A \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{2 \, a d}"," ",0,"-1/2*(sqrt(2)*(A - B)*sqrt(a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - A*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a*d)","B",0
105,1,259,0,0.930158," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(A - 2 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - 4 \, \sqrt{a \cos\left(d x + c\right) + a} A \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B\right)} a \cos\left(d x + c\right)\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{4 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}"," ",0,"-1/4*(((A - 2*B)*cos(d*x + c)^2 + (A - 2*B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*sqrt(a*cos(d*x + c) + a)*A*sin(d*x + c) + 2*sqrt(2)*((A - B)*a*cos(d*x + c)^2 + (A - B)*a*cos(d*x + c))*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","B",0
106,1,284,0,0.814067," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(7 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A - 4 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left({\left(A - 4 \, B\right)} \cos\left(d x + c\right) - 2 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{8 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B\right)} a \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{16 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/16*(((7*A - 4*B)*cos(d*x + c)^3 + (7*A - 4*B)*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*((A - 4*B)*cos(d*x + c) - 2*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 8*sqrt(2)*((A - B)*a*cos(d*x + c)^3 + (A - B)*a*cos(d*x + c)^2)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","B",0
107,1,241,0,0.959857," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{2} {\left({\left(15 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A - 19 \, B\right)} \cos\left(d x + c\right) + 15 \, A - 19 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(60 \, B \cos\left(d x + c\right)^{4} + 12 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} - 28 \, {\left(3 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(63 \, A - 67 \, B\right)} \cos\left(d x + c\right) + 1029 \, A - 1201 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{840 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/840*(105*sqrt(2)*((15*A - 19*B)*cos(d*x + c)^2 + 2*(15*A - 19*B)*cos(d*x + c) + 15*A - 19*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(60*B*cos(d*x + c)^4 + 12*(7*A - 3*B)*cos(d*x + c)^3 - 28*(3*A - 7*B)*cos(d*x + c)^2 + 12*(63*A - 67*B)*cos(d*x + c) + 1029*A - 1201*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
108,1,224,0,0.896665," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{2} {\left({\left(11 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A - 15 \, B\right)} \cos\left(d x + c\right) + 11 \, A - 15 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(12 \, B \cos\left(d x + c\right)^{3} + 4 \, {\left(5 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right) - 95 \, A + 147 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{120 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/120*(15*sqrt(2)*((11*A - 15*B)*cos(d*x + c)^2 + 2*(11*A - 15*B)*cos(d*x + c) + 11*A - 15*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(12*B*cos(d*x + c)^3 + 4*(5*A - 3*B)*cos(d*x + c)^2 - 12*(5*A - 9*B)*cos(d*x + c) - 95*A + 147*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
109,1,205,0,0.719843," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(7 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 11 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 11 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(4 \, B \cos\left(d x + c\right)^{2} + 12 \, {\left(A - B\right)} \cos\left(d x + c\right) + 15 \, A - 19 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{24 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/24*(3*sqrt(2)*((7*A - 11*B)*cos(d*x + c)^2 + 2*(7*A - 11*B)*cos(d*x + c) + 7*A - 11*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(4*B*cos(d*x + c)^2 + 12*(A - B)*cos(d*x + c) + 15*A - 19*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
110,1,189,0,0.603346," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 7 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(4 \, B \cos\left(d x + c\right) - A + 5 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/8*(sqrt(2)*((3*A - 7*B)*cos(d*x + c)^2 + 2*(3*A - 7*B)*cos(d*x + c) + 3*A - 7*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(4*B*cos(d*x + c) - A + 5*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
111,1,172,0,0.844225," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 3 \, B\right)} \cos\left(d x + c\right) + A + 3 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(A - B\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/8*(sqrt(2)*((A + 3*B)*cos(d*x + c)^2 + 2*(A + 3*B)*cos(d*x + c) + A + 3*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*sqrt(a*cos(d*x + c) + a)*(A - B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","B",0
112,1,281,0,0.849626," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(5 \, A - B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - B\right)} \cos\left(d x + c\right) + 5 \, A - B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(A - B\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/8*(sqrt(2)*((5*A - B)*cos(d*x + c)^2 + 2*(5*A - B)*cos(d*x + c) + 5*A - B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + A)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*(A - B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","B",0
113,1,339,0,1.311198," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 2 \, {\left({\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - 2 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - 4 \, {\left({\left(3 \, A - B\right)} \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/8*(sqrt(2)*((9*A - 5*B)*cos(d*x + c)^3 + 2*(9*A - 5*B)*cos(d*x + c)^2 + (9*A - 5*B)*cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 2*((3*A - 2*B)*cos(d*x + c)^3 + 2*(3*A - 2*B)*cos(d*x + c)^2 + (3*A - 2*B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*((3*A - B)*cos(d*x + c) + 2*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))","B",0
114,1,361,0,0.733435," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left({\left(13 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(13 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + {\left({\left(19 \, A - 12 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(19 \, A - 12 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(19 \, A - 12 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left({\left(7 \, A - 6 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - 4 \, B\right)} \cos\left(d x + c\right) - 2 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{16 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/16*(2*sqrt(2)*((13*A - 9*B)*cos(d*x + c)^4 + 2*(13*A - 9*B)*cos(d*x + c)^3 + (13*A - 9*B)*cos(d*x + c)^2)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + ((19*A - 12*B)*cos(d*x + c)^4 + 2*(19*A - 12*B)*cos(d*x + c)^3 + (19*A - 12*B)*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*((7*A - 6*B)*cos(d*x + c)^2 + (3*A - 4*B)*cos(d*x + c) - 2*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)","A",0
115,1,270,0,0.797317," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{2} {\left({\left(163 \, A - 283 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 283 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(163 \, A - 283 \, B\right)} \cos\left(d x + c\right) + 163 \, A - 283 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(96 \, B \cos\left(d x + c\right)^{4} + 160 \, {\left(A - B\right)} \cos\left(d x + c\right)^{3} - 32 \, {\left(25 \, A - 49 \, B\right)} \cos\left(d x + c\right)^{2} - 5 \, {\left(503 \, A - 911 \, B\right)} \cos\left(d x + c\right) - 1495 \, A + 2671 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{960 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/960*(15*sqrt(2)*((163*A - 283*B)*cos(d*x + c)^3 + 3*(163*A - 283*B)*cos(d*x + c)^2 + 3*(163*A - 283*B)*cos(d*x + c) + 163*A - 283*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(96*B*cos(d*x + c)^4 + 160*(A - B)*cos(d*x + c)^3 - 32*(25*A - 49*B)*cos(d*x + c)^2 - 5*(503*A - 911*B)*cos(d*x + c) - 1495*A + 2671*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
116,1,254,0,0.682524," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 163 \, B\right)} \cos\left(d x + c\right) + 75 \, A - 163 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(32 \, B \cos\left(d x + c\right)^{3} + 32 \, {\left(3 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(255 \, A - 503 \, B\right)} \cos\left(d x + c\right) + 147 \, A - 299 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{192 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/192*(3*sqrt(2)*((75*A - 163*B)*cos(d*x + c)^3 + 3*(75*A - 163*B)*cos(d*x + c)^2 + 3*(75*A - 163*B)*cos(d*x + c) + 75*A - 163*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(32*B*cos(d*x + c)^3 + 32*(3*A - 5*B)*cos(d*x + c)^2 + (255*A - 503*B)*cos(d*x + c) + 147*A - 299*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
117,1,237,0,0.736237," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(19 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A - 75 \, B\right)} \cos\left(d x + c\right) + 19 \, A - 75 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(32 \, B \cos\left(d x + c\right)^{2} - {\left(13 \, A - 85 \, B\right)} \cos\left(d x + c\right) - 9 \, A + 49 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/64*(sqrt(2)*((19*A - 75*B)*cos(d*x + c)^3 + 3*(19*A - 75*B)*cos(d*x + c)^2 + 3*(19*A - 75*B)*cos(d*x + c) + 19*A - 75*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(32*B*cos(d*x + c)^2 - (13*A - 85*B)*cos(d*x + c) - 9*A + 49*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
118,1,223,0,0.772469," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(5 \, A + 19 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 19 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 19 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 19 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left({\left(5 \, A - 13 \, B\right)} \cos\left(d x + c\right) + A - 9 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/64*(sqrt(2)*((5*A + 19*B)*cos(d*x + c)^3 + 3*(5*A + 19*B)*cos(d*x + c)^2 + 3*(5*A + 19*B)*cos(d*x + c) + 5*A + 19*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((5*A - 13*B)*cos(d*x + c) + A - 9*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
119,1,223,0,0.543390," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 3 \, A + 5 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left({\left(3 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 7 \, A + B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/64*(sqrt(2)*((3*A + 5*B)*cos(d*x + c)^3 + 3*(3*A + 5*B)*cos(d*x + c)^2 + 3*(3*A + 5*B)*cos(d*x + c) + 3*A + 5*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((3*A + 5*B)*cos(d*x + c) + 7*A + B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
120,1,339,0,0.810563," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(43 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 43 \, A - 3 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 32 \, {\left(A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + A\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left({\left(11 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 15 \, A - 7 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/64*(sqrt(2)*((43*A - 3*B)*cos(d*x + c)^3 + 3*(43*A - 3*B)*cos(d*x + c)^2 + 3*(43*A - 3*B)*cos(d*x + c) + 43*A - 3*B)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 32*(A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 + 3*A*cos(d*x + c) + A)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*((11*A - 3*B)*cos(d*x + c) + 15*A - 7*B)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
121,1,404,0,1.478424," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(115 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(115 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(115 \, A - 43 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 16 \, {\left({\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 2 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - 4 \, {\left({\left(35 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(11 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 16 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/64*(sqrt(2)*((115*A - 43*B)*cos(d*x + c)^4 + 3*(115*A - 43*B)*cos(d*x + c)^3 + 3*(115*A - 43*B)*cos(d*x + c)^2 + (115*A - 43*B)*cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 16*((5*A - 2*B)*cos(d*x + c)^4 + 3*(5*A - 2*B)*cos(d*x + c)^3 + 3*(5*A - 2*B)*cos(d*x + c)^2 + (5*A - 2*B)*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*((35*A - 11*B)*cos(d*x + c)^2 + 5*(11*A - 3*B)*cos(d*x + c) + 16*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))","B",0
122,1,428,0,0.664994," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(219 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(219 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(219 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(219 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left({\left(39 \, A - 20 \, B\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(39 \, A - 20 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(39 \, A - 20 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A - 20 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(7 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(19 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(5 \, A - 4 \, B\right)} \cos\left(d x + c\right) - 8 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/64*(sqrt(2)*((219*A - 115*B)*cos(d*x + c)^5 + 3*(219*A - 115*B)*cos(d*x + c)^4 + 3*(219*A - 115*B)*cos(d*x + c)^3 + (219*A - 115*B)*cos(d*x + c)^2)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*((39*A - 20*B)*cos(d*x + c)^5 + 3*(39*A - 20*B)*cos(d*x + c)^4 + 3*(39*A - 20*B)*cos(d*x + c)^3 + (39*A - 20*B)*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(7*(9*A - 5*B)*cos(d*x + c)^3 + 5*(19*A - 11*B)*cos(d*x + c)^2 + 4*(5*A - 4*B)*cos(d*x + c) - 8*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2)","A",0
123,0,0,0,0.803126," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \cos\left(d x + c\right)^{4} + {\left(A + B\right)} a \cos\left(d x + c\right)^{3} + A a \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^4 + (A + B)*a*cos(d*x + c)^3 + A*a*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
124,0,0,0,1.138231," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \cos\left(d x + c\right)^{3} + {\left(A + B\right)} a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^3 + (A + B)*a*cos(d*x + c)^2 + A*a*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
125,0,0,0,0.894058," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sqrt(cos(d*x + c)), x)","F",0
126,0,0,0,0.916662," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/sqrt(cos(d*x + c)), x)","F",0
127,0,0,0,0.705447," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/cos(d*x + c)^(3/2), x)","F",0
128,0,0,0,0.836849," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/cos(d*x + c)^(5/2), x)","F",0
129,0,0,0,0.883676," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/cos(d*x + c)^(7/2), x)","F",0
130,0,0,0,0.714325," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \cos\left(d x + c\right)^{4} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{2} + A a^{2} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^4 + (A + 2*B)*a^2*cos(d*x + c)^3 + (2*A + B)*a^2*cos(d*x + c)^2 + A*a^2*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
131,0,0,0,1.103127," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)*sqrt(cos(d*x + c)), x)","F",0
132,0,0,0,0.841864," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)/sqrt(cos(d*x + c)), x)","F",0
133,0,0,0,0.845180," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)/cos(d*x + c)^(3/2), x)","F",0
134,0,0,0,0.613835," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)/cos(d*x + c)^(5/2), x)","F",0
135,0,0,0,1.021902," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)/cos(d*x + c)^(7/2), x)","F",0
136,0,0,0,0.877316," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)/cos(d*x + c)^(9/2), x)","F",0
137,0,0,0,1.047775," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{3} \cos\left(d x + c\right)^{5} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + A a^{3} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^5 + (A + 3*B)*a^3*cos(d*x + c)^4 + 3*(A + B)*a^3*cos(d*x + c)^3 + (3*A + B)*a^3*cos(d*x + c)^2 + A*a^3*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
138,0,0,0,0.933631," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)*sqrt(cos(d*x + c)), x)","F",0
139,0,0,0,0.980544," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)/sqrt(cos(d*x + c)), x)","F",0
140,0,0,0,0.857612," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(3/2), x)","F",0
141,0,0,0,0.732902," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(5/2), x)","F",0
142,0,0,0,0.825009," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(7/2), x)","F",0
143,0,0,0,0.851591," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(9/2), x)","F",0
144,0,0,0,0.679794," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(11/2), x)","F",0
145,0,0,0,0.936350," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
146,0,0,0,0.838641," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
147,0,0,0,0.783207," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
148,0,0,0,0.840727," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)^2 + a*cos(d*x + c)), x)","F",0
149,0,0,0,0.649579," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)^3 + a*cos(d*x + c)^2), x)","F",0
150,0,0,0,0.890646," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)^4 + a*cos(d*x + c)^3), x)","F",0
151,0,0,0,0.900122," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{4} + A \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^4 + A*cos(d*x + c)^3)*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
152,0,0,0,1.164015," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
153,0,0,0,1.214405," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
154,0,0,0,1.085660," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
155,0,0,0,0.849487," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{3} + 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^3 + 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c)), x)","F",0
156,0,0,0,0.996936," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{3} + a^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^3 + a^2*cos(d*x + c)^2), x)","F",0
157,0,0,0,0.953825," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{5} + 2 \, a^{2} \cos\left(d x + c\right)^{4} + a^{2} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^5 + 2*a^2*cos(d*x + c)^4 + a^2*cos(d*x + c)^3), x)","F",0
158,0,0,0,1.219916," ","integrate(cos(d*x+c)^(9/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{5} + A \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^5 + A*cos(d*x + c)^4)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
159,0,0,0,0.942769," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{4} + A \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^4 + A*cos(d*x + c)^3)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
160,0,0,0,0.947586," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
161,0,0,0,1.182855," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
162,0,0,0,1.078851," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
163,0,0,0,0.758178," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + a^3*cos(d*x + c)), x)","F",0
164,0,0,0,1.159802," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{5} + 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^5 + 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2), x)","F",0
165,0,0,0,1.011108," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{6} + 3 \, a^{3} \cos\left(d x + c\right)^{5} + 3 \, a^{3} \cos\left(d x + c\right)^{4} + a^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^6 + 3*a^3*cos(d*x + c)^5 + 3*a^3*cos(d*x + c)^4 + a^3*cos(d*x + c)^3), x)","F",0
166,1,151,0,0.997593," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(48 \, B \cos\left(d x + c\right)^{3} + 8 \, {\left(8 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{2} + 10 \, {\left(8 \, A + 7 \, B\right)} \cos\left(d x + c\right) + 120 \, A + 105 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 15 \, {\left({\left(8 \, A + 7 \, B\right)} \cos\left(d x + c\right) + 8 \, A + 7 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/192*((48*B*cos(d*x + c)^3 + 8*(8*A + 7*B)*cos(d*x + c)^2 + 10*(8*A + 7*B)*cos(d*x + c) + 120*A + 105*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*((8*A + 7*B)*cos(d*x + c) + 8*A + 7*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
167,1,134,0,0.995813," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(8 \, B \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 18 \, A + 15 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left({\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 6 \, A + 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/24*((8*B*cos(d*x + c)^2 + 2*(6*A + 5*B)*cos(d*x + c) + 18*A + 15*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((6*A + 5*B)*cos(d*x + c) + 6*A + 5*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
168,1,117,0,1.025760," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, B \cos\left(d x + c\right) + 4 \, A + 3 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 4 \, A + 3 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/4*((2*B*cos(d*x + c) + 4*A + 3*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((4*A + 3*B)*cos(d*x + c) + 4*A + 3*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
169,1,97,0,1.009992," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(2 \, A + B\right)} \cos\left(d x + c\right) + 2 \, A + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{d \cos\left(d x + c\right) + d}"," ",0,"(sqrt(a*cos(d*x + c) + a)*B*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*A + B)*cos(d*x + c) + 2*A + B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
170,1,109,0,1.070642," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{a \cos\left(d x + c\right) + a} A \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left(B \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)\right)}}{d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)}"," ",0,"2*(sqrt(a*cos(d*x + c) + a)*A*sqrt(cos(d*x + c))*sin(d*x + c) - (B*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
171,1,67,0,0.784472," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(2 \, A + 3 \, B\right)} \cos\left(d x + c\right) + A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"2/3*((2*A + 3*B)*cos(d*x + c) + A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
172,1,86,0,1.022801," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(4 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 3 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/15*(2*(4*A + 5*B)*cos(d*x + c)^2 + (4*A + 5*B)*cos(d*x + c) + 3*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
173,1,104,0,0.963152," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right) + 15 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"2/105*(8*(6*A + 7*B)*cos(d*x + c)^3 + 4*(6*A + 7*B)*cos(d*x + c)^2 + 3*(6*A + 7*B)*cos(d*x + c) + 15*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
174,1,162,0,1.165890," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(48 \, B a \cos\left(d x + c\right)^{3} + 8 \, {\left(8 \, A + 15 \, B\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right) + 3 \, {\left(88 \, A + 75 \, B\right)} a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left({\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right) + {\left(88 \, A + 75 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/192*((48*B*a*cos(d*x + c)^3 + 8*(8*A + 15*B)*a*cos(d*x + c)^2 + 2*(88*A + 75*B)*a*cos(d*x + c) + 3*(88*A + 75*B)*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((88*A + 75*B)*a*cos(d*x + c) + (88*A + 75*B)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
175,1,144,0,1.348074," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(8 \, B a \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 11 \, B\right)} a \cos\left(d x + c\right) + 3 \, {\left(14 \, A + 11 \, B\right)} a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left({\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right) + {\left(14 \, A + 11 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/24*((8*B*a*cos(d*x + c)^2 + 2*(6*A + 11*B)*a*cos(d*x + c) + 3*(14*A + 11*B)*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((14*A + 11*B)*a*cos(d*x + c) + (14*A + 11*B)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
176,1,125,0,1.240831," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, B a \cos\left(d x + c\right) + {\left(4 \, A + 7 \, B\right)} a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(12 \, A + 7 \, B\right)} a \cos\left(d x + c\right) + {\left(12 \, A + 7 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/4*((2*B*a*cos(d*x + c) + (4*A + 7*B)*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((12*A + 7*B)*a*cos(d*x + c) + (12*A + 7*B)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
177,1,135,0,1.150666," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(B a \cos\left(d x + c\right) + 2 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(2 \, A + 3 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(2 \, A + 3 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)}"," ",0,"((B*a*cos(d*x + c) + 2*A*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*A + 3*B)*a*cos(d*x + c)^2 + (2*A + 3*B)*a*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
178,1,133,0,0.877334," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left({\left(5 \, A + 3 \, B\right)} a \cos\left(d x + c\right) + A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left(B a \cos\left(d x + c\right)^{3} + B a \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)\right)}}{3 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"2/3*(((5*A + 3*B)*a*cos(d*x + c) + A*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*(B*a*cos(d*x + c)^3 + B*a*cos(d*x + c)^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
179,1,88,0,1.354626," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(18 \, A + 25 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(9 \, A + 5 \, B\right)} a \cos\left(d x + c\right) + 3 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/15*((18*A + 25*B)*a*cos(d*x + c)^2 + (9*A + 5*B)*a*cos(d*x + c) + 3*A*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
180,1,107,0,0.689031," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(52 \, A + 63 \, B\right)} a \cos\left(d x + c\right)^{3} + {\left(52 \, A + 63 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(13 \, A + 7 \, B\right)} a \cos\left(d x + c\right) + 15 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"2/105*(2*(52*A + 63*B)*a*cos(d*x + c)^3 + (52*A + 63*B)*a*cos(d*x + c)^2 + 3*(13*A + 7*B)*a*cos(d*x + c) + 15*A*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
181,1,126,0,0.850909," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right)^{4} + 4 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right)^{2} + 5 \, {\left(17 \, A + 9 \, B\right)} a \cos\left(d x + c\right) + 35 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"2/315*(8*(34*A + 39*B)*a*cos(d*x + c)^4 + 4*(34*A + 39*B)*a*cos(d*x + c)^3 + 3*(34*A + 39*B)*a*cos(d*x + c)^2 + 5*(17*A + 9*B)*a*cos(d*x + c) + 35*A*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^6 + d*cos(d*x + c)^5)","A",0
182,1,194,0,1.195957," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(384 \, B a^{2} \cos\left(d x + c\right)^{4} + 48 \, {\left(10 \, A + 29 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(230 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 10 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right) + 15 \, {\left(326 \, A + 283 \, B\right)} a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 15 \, {\left({\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(326 \, A + 283 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{1920 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/1920*((384*B*a^2*cos(d*x + c)^4 + 48*(10*A + 29*B)*a^2*cos(d*x + c)^3 + 8*(230*A + 283*B)*a^2*cos(d*x + c)^2 + 10*(326*A + 283*B)*a^2*cos(d*x + c) + 15*(326*A + 283*B)*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*((326*A + 283*B)*a^2*cos(d*x + c) + (326*A + 283*B)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
183,1,174,0,1.282680," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(48 \, B a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(8 \, A + 23 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(136 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, {\left(200 \, A + 163 \, B\right)} a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left({\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(200 \, A + 163 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/192*((48*B*a^2*cos(d*x + c)^3 + 8*(8*A + 23*B)*a^2*cos(d*x + c)^2 + 2*(136*A + 163*B)*a^2*cos(d*x + c) + 3*(200*A + 163*B)*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((200*A + 163*B)*a^2*cos(d*x + c) + (200*A + 163*B)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
184,1,154,0,1.133860," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, B a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, A + 17 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, {\left(22 \, A + 25 \, B\right)} a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left({\left(38 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(38 \, A + 25 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/24*((8*B*a^2*cos(d*x + c)^2 + 2*(6*A + 17*B)*a^2*cos(d*x + c) + 3*(22*A + 25*B)*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((38*A + 25*B)*a^2*cos(d*x + c) + (38*A + 25*B)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
185,1,164,0,0.878290," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, B a^{2} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*((2*B*a^2*cos(d*x + c)^2 + (4*A + 11*B)*a^2*cos(d*x + c) + 8*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((20*A + 19*B)*a^2*cos(d*x + c)^2 + (20*A + 19*B)*a^2*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
186,1,169,0,1.011981," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left({\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{3 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/3*((3*B*a^2*cos(d*x + c)^2 + 2*(8*A + 3*B)*a^2*cos(d*x + c) + 2*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((2*A + 5*B)*a^2*cos(d*x + c)^3 + (2*A + 5*B)*a^2*cos(d*x + c)^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
187,1,161,0,0.988164," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left({\left(43 \, A + 40 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 15 \, {\left(B a^{2} \cos\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)\right)}}{15 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/15*(((43*A + 40*B)*a^2*cos(d*x + c)^2 + (14*A + 5*B)*a^2*cos(d*x + c) + 3*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*(B*a^2*cos(d*x + c)^4 + B*a^2*cos(d*x + c)^3)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
188,1,114,0,0.988592," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(230 \, A + 301 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(115 \, A + 98 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, A + 7 \, B\right)} a^{2} \cos\left(d x + c\right) + 15 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"2/105*((230*A + 301*B)*a^2*cos(d*x + c)^3 + (115*A + 98*B)*a^2*cos(d*x + c)^2 + 3*(20*A + 7*B)*a^2*cos(d*x + c) + 15*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
189,1,135,0,1.034989," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(292 \, A + 345 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(292 \, A + 345 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(73 \, A + 60 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 5 \, {\left(26 \, A + 9 \, B\right)} a^{2} \cos\left(d x + c\right) + 35 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"2/315*(2*(292*A + 345*B)*a^2*cos(d*x + c)^4 + (292*A + 345*B)*a^2*cos(d*x + c)^3 + 3*(73*A + 60*B)*a^2*cos(d*x + c)^2 + 5*(26*A + 9*B)*a^2*cos(d*x + c) + 35*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^6 + d*cos(d*x + c)^5)","A",0
190,1,156,0,0.946896," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + 4 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 5 \, {\left(355 \, A + 286 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 35 \, {\left(32 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right) + 315 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{3465 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"2/3465*(8*(710*A + 803*B)*a^2*cos(d*x + c)^5 + 4*(710*A + 803*B)*a^2*cos(d*x + c)^4 + 3*(710*A + 803*B)*a^2*cos(d*x + c)^3 + 5*(355*A + 286*B)*a^2*cos(d*x + c)^2 + 35*(32*A + 11*B)*a^2*cos(d*x + c) + 315*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^7 + d*cos(d*x + c)^6)","A",0
191,1,184,0,8.757933," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, B \cos\left(d x + c\right) + 4 \, A - B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left({\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 4 \, A - 7 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{4 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{4 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/4*((2*B*cos(d*x + c) + 4*A - B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) + ((4*A - 7*B)*cos(d*x + c) + 4*A - 7*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 4*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
192,1,168,0,4.158638," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(2 \, A - B\right)} \cos\left(d x + c\right) + 2 \, A - B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{a d \cos\left(d x + c\right) + a d}"," ",0,"(sqrt(a*cos(d*x + c) + a)*B*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*A - B)*cos(d*x + c) + 2*A - B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
193,1,96,0,3.878563," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(A - B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, B \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{a d}"," ",0,"-(sqrt(2)*(A - B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*B*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a*d)","A",0
194,1,143,0,1.177743," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} A \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B\right)} a \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a}}\right)}{\sqrt{a}}}{a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)}"," ",0,"(2*sqrt(a*cos(d*x + c) + a)*A*sqrt(cos(d*x + c))*sin(d*x + c) - sqrt(2)*((A - B)*a*cos(d*x + c)^2 + (A - B)*a*cos(d*x + c))*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)))/sqrt(a))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
195,1,163,0,0.752821," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(A - 3 \, B\right)} \cos\left(d x + c\right) - A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{3 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B\right)} a \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a}}\right)}{\sqrt{a}}}{3 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/3*(2*((A - 3*B)*cos(d*x + c) - A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*sqrt(2)*((A - B)*a*cos(d*x + c)^3 + (A - B)*a*cos(d*x + c)^2)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)))/sqrt(a))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
196,1,180,0,1.166094," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(13 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(A - 5 \, B\right)} \cos\left(d x + c\right) + 3 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{15 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B\right)} a \cos\left(d x + c\right)^{3}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a}}\right)}{\sqrt{a}}}{15 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/15*(2*((13*A - 5*B)*cos(d*x + c)^2 - (A - 5*B)*cos(d*x + c) + 3*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*sqrt(2)*((A - B)*a*cos(d*x + c)^4 + (A - B)*a*cos(d*x + c)^3)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)))/sqrt(a))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
197,1,237,0,15.059941," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right) + 5 \, A - 9 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left(2 \, B \cos\left(d x + c\right) - A + 3 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 4 \, {\left({\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 3 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/4*(sqrt(2)*((5*A - 9*B)*cos(d*x + c)^2 + 2*(5*A - 9*B)*cos(d*x + c) + 5*A - 9*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(2*B*cos(d*x + c) - A + 3*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 4*((2*A - 3*B)*cos(d*x + c)^2 + 2*(2*A - 3*B)*cos(d*x + c) + 2*A - 3*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
198,1,203,0,10.313170," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 5 \, B\right)} \cos\left(d x + c\right) + A - 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(A - B\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, {\left(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/4*(sqrt(2)*((A - 5*B)*cos(d*x + c)^2 + 2*(A - 5*B)*cos(d*x + c) + A - 5*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(A - B)*sqrt(cos(d*x + c))*sin(d*x + c) + 8*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
199,1,164,0,0.922917," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right) + 3 \, A + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(A - B\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/4*(sqrt(2)*((3*A + B)*cos(d*x + c)^2 + 2*(3*A + B)*cos(d*x + c) + 3*A + B)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(A - B)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
200,1,201,0,1.055069," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left({\left(5 \, A - B\right)} \cos\left(d x + c\right) + 4 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/4*(sqrt(2)*((7*A - 3*B)*cos(d*x + c)^3 + 2*(7*A - 3*B)*cos(d*x + c)^2 + (7*A - 3*B)*cos(d*x + c))*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*((5*A - B)*cos(d*x + c) + 4*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))","A",0
201,1,221,0,0.983805," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left({\left(19 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(A - B\right)} \cos\left(d x + c\right) - 4 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/12*(3*sqrt(2)*((11*A - 7*B)*cos(d*x + c)^4 + 2*(11*A - 7*B)*cos(d*x + c)^3 + (11*A - 7*B)*cos(d*x + c)^2)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*((19*A - 15*B)*cos(d*x + c)^2 + 12*(A - B)*cos(d*x + c) - 4*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)","A",0
202,1,302,0,28.556490," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right) + 43 \, A - 115 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left(16 \, B \cos\left(d x + c\right)^{2} - 5 \, {\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right) - 11 \, A + 35 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 32 \, {\left({\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(sqrt(2)*((43*A - 115*B)*cos(d*x + c)^3 + 3*(43*A - 115*B)*cos(d*x + c)^2 + 3*(43*A - 115*B)*cos(d*x + c) + 43*A - 115*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(16*B*cos(d*x + c)^2 - 5*(3*A - 11*B)*cos(d*x + c) - 11*A + 35*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 32*((2*A - 5*B)*cos(d*x + c)^3 + 3*(2*A - 5*B)*cos(d*x + c)^2 + 3*(2*A - 5*B)*cos(d*x + c) + 2*A - 5*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
203,1,267,0,24.442189," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 43 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left({\left(7 \, A - 15 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 11 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 64 \, {\left(B \cos\left(d x + c\right)^{3} + 3 \, B \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/32*(sqrt(2)*((3*A - 43*B)*cos(d*x + c)^3 + 3*(3*A - 43*B)*cos(d*x + c)^2 + 3*(3*A - 43*B)*cos(d*x + c) + 3*A - 43*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*((7*A - 15*B)*cos(d*x + c) + 3*A - 11*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) + 64*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
204,1,215,0,0.887928," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) + 2 \, {\left({\left(A + 7 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(sqrt(2)*((5*A + 3*B)*cos(d*x + c)^3 + 3*(5*A + 3*B)*cos(d*x + c)^2 + 3*(5*A + 3*B)*cos(d*x + c) + 5*A + 3*B)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) + 2*((A + 7*B)*cos(d*x + c) + 5*A + 3*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
205,1,217,0,1.131508," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left({\left(9 \, A - B\right)} \cos\left(d x + c\right) + 13 \, A - 5 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(sqrt(2)*((19*A + 5*B)*cos(d*x + c)^3 + 3*(19*A + 5*B)*cos(d*x + c)^2 + 3*(19*A + 5*B)*cos(d*x + c) + 19*A + 5*B)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*((9*A - B)*cos(d*x + c) + 13*A - 5*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
206,1,248,0,0.840269," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left({\left(49 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(85 \, A - 13 \, B\right)} \cos\left(d x + c\right) + 32 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/32*(sqrt(2)*((75*A - 19*B)*cos(d*x + c)^4 + 3*(75*A - 19*B)*cos(d*x + c)^3 + 3*(75*A - 19*B)*cos(d*x + c)^2 + (75*A - 19*B)*cos(d*x + c))*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*((49*A - 9*B)*cos(d*x + c)^2 + (85*A - 13*B)*cos(d*x + c) + 32*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))","A",0
207,1,270,0,1.011803," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left({\left(299 \, A - 147 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(503 \, A - 255 \, B\right)} \cos\left(d x + c\right)^{2} + 32 \, {\left(5 \, A - 3 \, B\right)} \cos\left(d x + c\right) - 32 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{96 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/96*(3*sqrt(2)*((163*A - 75*B)*cos(d*x + c)^5 + 3*(163*A - 75*B)*cos(d*x + c)^4 + 3*(163*A - 75*B)*cos(d*x + c)^3 + (163*A - 75*B)*cos(d*x + c)^2)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*((299*A - 147*B)*cos(d*x + c)^3 + (503*A - 255*B)*cos(d*x + c)^2 + 32*(5*A - 3*B)*cos(d*x + c) - 32*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2)","A",0
208,1,368,0,43.470485," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(177 \, A - 637 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(177 \, A - 637 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(177 \, A - 637 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(177 \, A - 637 \, B\right)} \cos\left(d x + c\right) + 177 \, A - 637 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left(192 \, B \cos\left(d x + c\right)^{3} - {\left(247 \, A - 1099 \, B\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(181 \, A - 721 \, B\right)} \cos\left(d x + c\right) - 147 \, A + 567 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 384 \, {\left({\left(2 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(2 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(2 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(2 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 7 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(3*sqrt(2)*((177*A - 637*B)*cos(d*x + c)^4 + 4*(177*A - 637*B)*cos(d*x + c)^3 + 6*(177*A - 637*B)*cos(d*x + c)^2 + 4*(177*A - 637*B)*cos(d*x + c) + 177*A - 637*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(192*B*cos(d*x + c)^3 - (247*A - 1099*B)*cos(d*x + c)^2 - 2*(181*A - 721*B)*cos(d*x + c) - 147*A + 567*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 384*((2*A - 7*B)*cos(d*x + c)^4 + 4*(2*A - 7*B)*cos(d*x + c)^3 + 6*(2*A - 7*B)*cos(d*x + c)^2 + 4*(2*A - 7*B)*cos(d*x + c) + 2*A - 7*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
209,1,327,0,24.593372," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(5 \, A - 177 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(5 \, A - 177 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(5 \, A - 177 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(5 \, A - 177 \, B\right)} \cos\left(d x + c\right) + 5 \, A - 177 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left({\left(67 \, A - 247 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(25 \, A - 181 \, B\right)} \cos\left(d x + c\right) + 15 \, A - 147 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 768 \, {\left(B \cos\left(d x + c\right)^{4} + 4 \, B \cos\left(d x + c\right)^{3} + 6 \, B \cos\left(d x + c\right)^{2} + 4 \, B \cos\left(d x + c\right) + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(3*sqrt(2)*((5*A - 177*B)*cos(d*x + c)^4 + 4*(5*A - 177*B)*cos(d*x + c)^3 + 6*(5*A - 177*B)*cos(d*x + c)^2 + 4*(5*A - 177*B)*cos(d*x + c) + 5*A - 177*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*((67*A - 247*B)*cos(d*x + c)^2 + 2*(25*A - 181*B)*cos(d*x + c) + 15*A - 147*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) + 768*(B*cos(d*x + c)^4 + 4*B*cos(d*x + c)^3 + 6*B*cos(d*x + c)^2 + 4*B*cos(d*x + c) + B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
210,1,266,0,0.603116," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 7 \, A + 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) + 2 \, {\left({\left(17 \, A + 67 \, B\right)} \cos\left(d x + c\right)^{2} + 10 \, {\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 21 \, A + 15 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(3*sqrt(2)*((7*A + 5*B)*cos(d*x + c)^4 + 4*(7*A + 5*B)*cos(d*x + c)^3 + 6*(7*A + 5*B)*cos(d*x + c)^2 + 4*(7*A + 5*B)*cos(d*x + c) + 7*A + 5*B)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) + 2*((17*A + 67*B)*cos(d*x + c)^2 + 10*(7*A + 5*B)*cos(d*x + c) + 21*A + 15*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
211,1,264,0,1.745878," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(13 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(13 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(13 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(13 \, A + 7 \, B\right)} \cos\left(d x + c\right) + 13 \, A + 7 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left({\left(5 \, A - 17 \, B\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(A + 35 \, B\right)} \cos\left(d x + c\right) - 39 \, A - 21 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(3*sqrt(2)*((13*A + 7*B)*cos(d*x + c)^4 + 4*(13*A + 7*B)*cos(d*x + c)^3 + 6*(13*A + 7*B)*cos(d*x + c)^2 + 4*(13*A + 7*B)*cos(d*x + c) + 13*A + 7*B)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*((5*A - 17*B)*cos(d*x + c)^2 - 2*(A + 35*B)*cos(d*x + c) - 39*A - 21*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
212,1,266,0,1.054359," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(63 \, A + 13 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(63 \, A + 13 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(63 \, A + 13 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(63 \, A + 13 \, B\right)} \cos\left(d x + c\right) + 63 \, A + 13 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left({\left(103 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(133 \, A - B\right)} \cos\left(d x + c\right) + 195 \, A - 39 \, B\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(3*sqrt(2)*((63*A + 13*B)*cos(d*x + c)^4 + 4*(63*A + 13*B)*cos(d*x + c)^3 + 6*(63*A + 13*B)*cos(d*x + c)^2 + 4*(63*A + 13*B)*cos(d*x + c) + 63*A + 13*B)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*((103*A + 5*B)*cos(d*x + c)^2 + 2*(133*A - B)*cos(d*x + c) + 195*A - 39*B)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
213,1,298,0,0.818381," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{9 \, \sqrt{2} {\left({\left(121 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(121 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(121 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(121 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(121 \, A - 21 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left({\left(691 \, A - 103 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(937 \, A - 133 \, B\right)} \cos\left(d x + c\right)^{2} + 39 \, {\left(41 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 384 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} + 4 \, a^{4} d \cos\left(d x + c\right)^{4} + 6 \, a^{4} d \cos\left(d x + c\right)^{3} + 4 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/384*(9*sqrt(2)*((121*A - 21*B)*cos(d*x + c)^5 + 4*(121*A - 21*B)*cos(d*x + c)^4 + 6*(121*A - 21*B)*cos(d*x + c)^3 + 4*(121*A - 21*B)*cos(d*x + c)^2 + (121*A - 21*B)*cos(d*x + c))*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*((691*A - 103*B)*cos(d*x + c)^3 + 2*(937*A - 133*B)*cos(d*x + c)^2 + 39*(41*A - 5*B)*cos(d*x + c) + 384*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^5 + 4*a^4*d*cos(d*x + c)^4 + 6*a^4*d*cos(d*x + c)^3 + 4*a^4*d*cos(d*x + c)^2 + a^4*d*cos(d*x + c))","A",0
214,1,319,0,0.825937," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(1015 \, A - 363 \, B\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(1015 \, A - 363 \, B\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(1015 \, A - 363 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(1015 \, A - 363 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(1015 \, A - 363 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left({\left(1887 \, A - 691 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2541 \, A - 937 \, B\right)} \cos\left(d x + c\right)^{3} + 39 \, {\left(109 \, A - 41 \, B\right)} \cos\left(d x + c\right)^{2} + 128 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right) - 128 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{6} + 4 \, a^{4} d \cos\left(d x + c\right)^{5} + 6 \, a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + a^{4} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/384*(3*sqrt(2)*((1015*A - 363*B)*cos(d*x + c)^6 + 4*(1015*A - 363*B)*cos(d*x + c)^5 + 6*(1015*A - 363*B)*cos(d*x + c)^4 + 4*(1015*A - 363*B)*cos(d*x + c)^3 + (1015*A - 363*B)*cos(d*x + c)^2)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*((1887*A - 691*B)*cos(d*x + c)^4 + 2*(2541*A - 937*B)*cos(d*x + c)^3 + 39*(109*A - 41*B)*cos(d*x + c)^2 + 128*(7*A - 3*B)*cos(d*x + c) - 128*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^6 + 4*a^4*d*cos(d*x + c)^5 + 6*a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + a^4*d*cos(d*x + c)^2)","A",0
215,1,81,0,1.001316," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A a + 3 \, B b\right)} d x + {\left(6 \, B b \cos\left(d x + c\right)^{3} + 8 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{2} + 16 \, B a + 16 \, A b + 3 \, {\left(4 \, A a + 3 \, B b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*A*a + 3*B*b)*d*x + (6*B*b*cos(d*x + c)^3 + 8*(B*a + A*b)*cos(d*x + c)^2 + 16*B*a + 16*A*b + 3*(4*A*a + 3*B*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
216,1,60,0,1.033649," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(B a + A b\right)} d x + {\left(2 \, B b \cos\left(d x + c\right)^{2} + 6 \, A a + 4 \, B b + 3 \, {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(B*a + A*b)*d*x + (2*B*b*cos(d*x + c)^2 + 6*A*a + 4*B*b + 3*(B*a + A*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
217,1,42,0,0.794946," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, A a + B b\right)} d x + {\left(B b \cos\left(d x + c\right) + 2 \, B a + 2 \, A b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*A*a + B*b)*d*x + (B*b*cos(d*x + c) + 2*B*a + 2*A*b)*sin(d*x + c))/d","A",0
218,1,54,0,1.232994," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{2 \, {\left(B a + A b\right)} d x + A a \log\left(\sin\left(d x + c\right) + 1\right) - A a \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B b \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(B*a + A*b)*d*x + A*a*log(sin(d*x + c) + 1) - A*a*log(-sin(d*x + c) + 1) + 2*B*b*sin(d*x + c))/d","A",0
219,1,85,0,0.619822," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, B b d x \cos\left(d x + c\right) + {\left(B a + A b\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a + A b\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, A a \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*B*b*d*x*cos(d*x + c) + (B*a + A*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - (B*a + A*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*A*a*sin(d*x + c))/(d*cos(d*x + c))","B",0
220,1,96,0,0.527437," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(A a + 2 \, B b\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a + 2 \, B b\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a + 2 \, {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((A*a + 2*B*b)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A*a + 2*B*b)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a + 2*(B*a + A*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
221,1,115,0,0.993779," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(2 \, A a + 3 \, B b\right)} \cos\left(d x + c\right)^{2} + 2 \, A a + 3 \, {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(B*a + A*b)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B*a + A*b)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(2*A*a + 3*B*b)*cos(d*x + c)^2 + 2*A*a + 3*(B*a + A*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
222,1,136,0,0.651821," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A a + 4 \, B b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, A a + 4 \, B b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A a + 4 \, B b\right)} \cos\left(d x + c\right)^{2} + 6 \, A a + 8 \, {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(3*A*a + 4*B*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*A*a + 4*B*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(B*a + A*b)*cos(d*x + c)^3 + 3*(3*A*a + 4*B*b)*cos(d*x + c)^2 + 6*A*a + 8*(B*a + A*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
223,1,142,0,0.646579," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A a^{2} + 6 \, B a b + 3 \, A b^{2}\right)} d x + {\left(24 \, B b^{2} \cos\left(d x + c\right)^{4} + 30 \, {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{3} + 80 \, B a^{2} + 160 \, A a b + 64 \, B b^{2} + 8 \, {\left(5 \, B a^{2} + 10 \, A a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, A a^{2} + 6 \, B a b + 3 \, A b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*A*a^2 + 6*B*a*b + 3*A*b^2)*d*x + (24*B*b^2*cos(d*x + c)^4 + 30*(2*B*a*b + A*b^2)*cos(d*x + c)^3 + 80*B*a^2 + 160*A*a*b + 64*B*b^2 + 8*(5*B*a^2 + 10*A*a*b + 4*B*b^2)*cos(d*x + c)^2 + 15*(4*A*a^2 + 6*B*a*b + 3*A*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
224,1,114,0,0.748101," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, B a^{2} + 8 \, A a b + 3 \, B b^{2}\right)} d x + {\left(6 \, B b^{2} \cos\left(d x + c\right)^{3} + 24 \, A a^{2} + 32 \, B a b + 16 \, A b^{2} + 8 \, {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, B a^{2} + 8 \, A a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*B*a^2 + 8*A*a*b + 3*B*b^2)*d*x + (6*B*b^2*cos(d*x + c)^3 + 24*A*a^2 + 32*B*a*b + 16*A*b^2 + 8*(2*B*a*b + A*b^2)*cos(d*x + c)^2 + 3*(4*B*a^2 + 8*A*a*b + 3*B*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
225,1,85,0,0.657029," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A a^{2} + 2 \, B a b + A b^{2}\right)} d x + {\left(2 \, B b^{2} \cos\left(d x + c\right)^{2} + 6 \, B a^{2} + 12 \, A a b + 4 \, B b^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*A*a^2 + 2*B*a*b + A*b^2)*d*x + (2*B*b^2*cos(d*x + c)^2 + 6*B*a^2 + 12*A*a*b + 4*B*b^2 + 3*(2*B*a*b + A*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
226,1,87,0,0.726212," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{A a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - A a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, B a^{2} + 4 \, A a b + B b^{2}\right)} d x + {\left(B b^{2} \cos\left(d x + c\right) + 4 \, B a b + 2 \, A b^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(A*a^2*log(sin(d*x + c) + 1) - A*a^2*log(-sin(d*x + c) + 1) + (2*B*a^2 + 4*A*a*b + B*b^2)*d*x + (B*b^2*cos(d*x + c) + 4*B*a*b + 2*A*b^2)*sin(d*x + c))/d","A",0
227,1,117,0,0.610073," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, B a b + A b^{2}\right)} d x \cos\left(d x + c\right) + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B b^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(2*B*a*b + A*b^2)*d*x*cos(d*x + c) + (B*a^2 + 2*A*a*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - (B*a^2 + 2*A*a*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(B*b^2*cos(d*x + c) + A*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
228,1,136,0,0.614219," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, B b^{2} d x \cos\left(d x + c\right)^{2} + {\left(A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*B*b^2*d*x*cos(d*x + c)^2 + (A*a^2 + 4*B*a*b + 2*A*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A*a^2 + 4*B*a*b + 2*A*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a^2 + 2*(B*a^2 + 2*A*a*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
229,1,150,0,1.059190," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(B a^{2} + 2 \, A a b + 2 \, B b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B a^{2} + 2 \, A a b + 2 \, B b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{2} + 2 \, {\left(2 \, A a^{2} + 6 \, B a b + 3 \, A b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(B*a^2 + 2*A*a*b + 2*B*b^2)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B*a^2 + 2*A*a*b + 2*B*b^2)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*A*a^2 + 2*(2*A*a^2 + 6*B*a*b + 3*A*b^2)*cos(d*x + c)^2 + 3*(B*a^2 + 2*A*a*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
230,1,180,0,0.915389," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A a^{2} + 8 \, B a b + 4 \, A b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, A a^{2} + 8 \, B a b + 4 \, A b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(2 \, B a^{2} + 4 \, A a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, A a^{2} + 3 \, {\left(3 \, A a^{2} + 8 \, B a b + 4 \, A b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(3*A*a^2 + 8*B*a*b + 4*A*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*A*a^2 + 8*B*a*b + 4*A*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(2*B*a^2 + 4*A*a*b + 3*B*b^2)*cos(d*x + c)^3 + 6*A*a^2 + 3*(3*A*a^2 + 8*B*a*b + 4*A*b^2)*cos(d*x + c)^2 + 8*(B*a^2 + 2*A*a*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
231,1,211,0,0.955137," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, A a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2} + 5 \, B b^{3}\right)} d x + {\left(40 \, B b^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{4} + 160 \, B a^{3} + 480 \, A a^{2} b + 384 \, B a b^{2} + 128 \, A b^{3} + 10 \, {\left(18 \, B a^{2} b + 18 \, A a b^{2} + 5 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(5 \, B a^{3} + 15 \, A a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(8 \, A a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2} + 5 \, B b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(8*A*a^3 + 18*B*a^2*b + 18*A*a*b^2 + 5*B*b^3)*d*x + (40*B*b^3*cos(d*x + c)^5 + 48*(3*B*a*b^2 + A*b^3)*cos(d*x + c)^4 + 160*B*a^3 + 480*A*a^2*b + 384*B*a*b^2 + 128*A*b^3 + 10*(18*B*a^2*b + 18*A*a*b^2 + 5*B*b^3)*cos(d*x + c)^3 + 16*(5*B*a^3 + 15*A*a^2*b + 12*B*a*b^2 + 4*A*b^3)*cos(d*x + c)^2 + 15*(8*A*a^3 + 18*B*a^2*b + 18*A*a*b^2 + 5*B*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
232,1,174,0,0.696651," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, B a^{3} + 12 \, A a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} d x + {\left(24 \, B b^{3} \cos\left(d x + c\right)^{4} + 120 \, A a^{3} + 240 \, B a^{2} b + 240 \, A a b^{2} + 64 \, B b^{3} + 30 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, B a^{2} b + 15 \, A a b^{2} + 4 \, B b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, B a^{3} + 12 \, A a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*B*a^3 + 12*A*a^2*b + 9*B*a*b^2 + 3*A*b^3)*d*x + (24*B*b^3*cos(d*x + c)^4 + 120*A*a^3 + 240*B*a^2*b + 240*A*a*b^2 + 64*B*b^3 + 30*(3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 8*(15*B*a^2*b + 15*A*a*b^2 + 4*B*b^3)*cos(d*x + c)^2 + 15*(4*B*a^3 + 12*A*a^2*b + 9*B*a*b^2 + 3*A*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
233,1,136,0,1.164154," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 3 \, B b^{3}\right)} d x + {\left(6 \, B b^{3} \cos\left(d x + c\right)^{3} + 24 \, B a^{3} + 72 \, A a^{2} b + 48 \, B a b^{2} + 16 \, A b^{3} + 8 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(4 \, B a^{2} b + 4 \, A a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(8*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 3*B*b^3)*d*x + (6*B*b^3*cos(d*x + c)^3 + 24*B*a^3 + 72*A*a^2*b + 48*B*a*b^2 + 16*A*b^3 + 8*(3*B*a*b^2 + A*b^3)*cos(d*x + c)^2 + 9*(4*B*a^2*b + 4*A*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
234,1,131,0,0.537191," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, A a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, A a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, B a^{3} + 6 \, A a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d x + {\left(2 \, B b^{3} \cos\left(d x + c\right)^{2} + 18 \, B a^{2} b + 18 \, A a b^{2} + 4 \, B b^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*A*a^3*log(sin(d*x + c) + 1) - 3*A*a^3*log(-sin(d*x + c) + 1) + 3*(2*B*a^3 + 6*A*a^2*b + 3*B*a*b^2 + A*b^3)*d*x + (2*B*b^3*cos(d*x + c)^2 + 18*B*a^2*b + 18*A*a*b^2 + 4*B*b^3 + 3*(3*B*a*b^2 + A*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
235,1,152,0,0.965181," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(6 \, B a^{2} b + 6 \, A a b^{2} + B b^{3}\right)} d x \cos\left(d x + c\right) + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(B b^{3} \cos\left(d x + c\right)^{2} + 2 \, A a^{3} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((6*B*a^2*b + 6*A*a*b^2 + B*b^3)*d*x*cos(d*x + c) + (B*a^3 + 3*A*a^2*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - (B*a^3 + 3*A*a^2*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (B*b^3*cos(d*x + c)^2 + 2*A*a^3 + 2*(3*B*a*b^2 + A*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
236,1,167,0,0.902015," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d x \cos\left(d x + c\right)^{2} + {\left(A a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B b^{3} \cos\left(d x + c\right)^{2} + A a^{3} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*(3*B*a*b^2 + A*b^3)*d*x*cos(d*x + c)^2 + (A*a^3 + 6*B*a^2*b + 6*A*a*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A*a^3 + 6*B*a^2*b + 6*A*a*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*B*b^3*cos(d*x + c)^2 + A*a^3 + 2*(B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
237,1,189,0,0.521113," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{12 \, B b^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B a^{3} + 3 \, A a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{3} + 2 \, {\left(2 \, A a^{3} + 9 \, B a^{2} b + 9 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*B*b^3*d*x*cos(d*x + c)^3 + 3*(B*a^3 + 3*A*a^2*b + 6*B*a*b^2 + 2*A*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B*a^3 + 3*A*a^2*b + 6*B*a*b^2 + 2*A*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*A*a^3 + 2*(2*A*a^3 + 9*B*a^2*b + 9*A*a*b^2)*cos(d*x + c)^2 + 3*(B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
238,1,211,0,0.901394," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 8 \, B b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 8 \, B b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, A a^{3} + 8 \, {\left(2 \, B a^{3} + 6 \, A a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} + 9 \, {\left(A a^{3} + 4 \, B a^{2} b + 4 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(3*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 8*B*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 8*B*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(6*A*a^3 + 8*(2*B*a^3 + 6*A*a^2*b + 9*B*a*b^2 + 3*A*b^3)*cos(d*x + c)^3 + 9*(A*a^3 + 4*B*a^2*b + 4*A*a*b^2)*cos(d*x + c)^2 + 8*(B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
239,1,249,0,0.858627," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(8 \, A a^{3} + 30 \, B a^{2} b + 30 \, A a b^{2} + 15 \, B b^{3}\right)} \cos\left(d x + c\right)^{4} + 24 \, A a^{3} + 15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, A a^{3} + 15 \, B a^{2} b + 15 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(3*B*a^3 + 9*A*a^2*b + 12*B*a*b^2 + 4*A*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*B*a^3 + 9*A*a^2*b + 12*B*a*b^2 + 4*A*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(8*A*a^3 + 30*B*a^2*b + 30*A*a*b^2 + 15*B*b^3)*cos(d*x + c)^4 + 24*A*a^3 + 15*(3*B*a^3 + 9*A*a^2*b + 12*B*a*b^2 + 4*A*b^3)*cos(d*x + c)^3 + 8*(4*A*a^3 + 15*B*a^2*b + 15*A*a*b^2)*cos(d*x + c)^2 + 30*(B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
240,1,289,0,1.602859," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, {\left(8 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 20 \, B a b^{3} + 5 \, A b^{4}\right)} d x + {\left(240 \, B b^{4} \cos\left(d x + c\right)^{6} + 280 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{5} + 1120 \, B a^{4} + 4480 \, A a^{3} b + 5376 \, B a^{2} b^{2} + 3584 \, A a b^{3} + 768 \, B b^{4} + 96 \, {\left(21 \, B a^{2} b^{2} + 14 \, A a b^{3} + 3 \, B b^{4}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left(24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 20 \, B a b^{3} + 5 \, A b^{4}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(35 \, B a^{4} + 140 \, A a^{3} b + 168 \, B a^{2} b^{2} + 112 \, A a b^{3} + 24 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} + 105 \, {\left(8 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 20 \, B a b^{3} + 5 \, A b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(105*(8*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 20*B*a*b^3 + 5*A*b^4)*d*x + (240*B*b^4*cos(d*x + c)^6 + 280*(4*B*a*b^3 + A*b^4)*cos(d*x + c)^5 + 1120*B*a^4 + 4480*A*a^3*b + 5376*B*a^2*b^2 + 3584*A*a*b^3 + 768*B*b^4 + 96*(21*B*a^2*b^2 + 14*A*a*b^3 + 3*B*b^4)*cos(d*x + c)^4 + 70*(24*B*a^3*b + 36*A*a^2*b^2 + 20*B*a*b^3 + 5*A*b^4)*cos(d*x + c)^3 + 16*(35*B*a^4 + 140*A*a^3*b + 168*B*a^2*b^2 + 112*A*a*b^3 + 24*B*b^4)*cos(d*x + c)^2 + 105*(8*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 20*B*a*b^3 + 5*A*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
241,1,243,0,0.854343," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} d x + {\left(40 \, B b^{4} \cos\left(d x + c\right)^{5} + 240 \, A a^{4} + 640 \, B a^{3} b + 960 \, A a^{2} b^{2} + 512 \, B a b^{3} + 128 \, A b^{4} + 48 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 10 \, {\left(36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(10 \, B a^{3} b + 15 \, A a^{2} b^{2} + 8 \, B a b^{3} + 2 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(8*B*a^4 + 32*A*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*d*x + (40*B*b^4*cos(d*x + c)^5 + 240*A*a^4 + 640*B*a^3*b + 960*A*a^2*b^2 + 512*B*a*b^3 + 128*A*b^4 + 48*(4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 10*(36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*cos(d*x + c)^3 + 32*(10*B*a^3*b + 15*A*a^2*b^2 + 8*B*a*b^3 + 2*A*b^4)*cos(d*x + c)^2 + 15*(8*B*a^4 + 32*A*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
242,1,197,0,1.136396," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 12 \, B a b^{3} + 3 \, A b^{4}\right)} d x + {\left(24 \, B b^{4} \cos\left(d x + c\right)^{4} + 120 \, B a^{4} + 480 \, A a^{3} b + 480 \, B a^{2} b^{2} + 320 \, A a b^{3} + 64 \, B b^{4} + 30 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(15 \, B a^{2} b^{2} + 10 \, A a b^{3} + 2 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 12 \, B a b^{3} + 3 \, A b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(8*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 12*B*a*b^3 + 3*A*b^4)*d*x + (24*B*b^4*cos(d*x + c)^4 + 120*B*a^4 + 480*A*a^3*b + 480*B*a^2*b^2 + 320*A*a*b^3 + 64*B*b^4 + 30*(4*B*a*b^3 + A*b^4)*cos(d*x + c)^3 + 16*(15*B*a^2*b^2 + 10*A*a*b^3 + 2*B*b^4)*cos(d*x + c)^2 + 15*(16*B*a^3*b + 24*A*a^2*b^2 + 12*B*a*b^3 + 3*A*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
243,1,183,0,1.521272," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{12 \, A a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, A a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 3 \, B b^{4}\right)} d x + {\left(6 \, B b^{4} \cos\left(d x + c\right)^{3} + 96 \, B a^{3} b + 144 \, A a^{2} b^{2} + 64 \, B a b^{3} + 16 \, A b^{4} + 8 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 3 \, B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(12*A*a^4*log(sin(d*x + c) + 1) - 12*A*a^4*log(-sin(d*x + c) + 1) + 3*(8*B*a^4 + 32*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 3*B*b^4)*d*x + (6*B*b^4*cos(d*x + c)^3 + 96*B*a^3*b + 144*A*a^2*b^2 + 64*B*a*b^3 + 16*A*b^4 + 8*(4*B*a*b^3 + A*b^4)*cos(d*x + c)^2 + 3*(24*B*a^2*b^2 + 16*A*a*b^3 + 3*B*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
244,1,196,0,1.587712," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, B a^{3} b + 12 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, B b^{4} \cos\left(d x + c\right)^{3} + 6 \, A a^{4} + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(9 \, B a^{2} b^{2} + 6 \, A a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(3*(8*B*a^3*b + 12*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*d*x*cos(d*x + c) + 3*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*B*b^4*cos(d*x + c)^3 + 6*A*a^4 + 3*(4*B*a*b^3 + A*b^4)*cos(d*x + c)^2 + 4*(9*B*a^2*b^2 + 6*A*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
245,1,202,0,0.697998," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(12 \, B a^{2} b^{2} + 8 \, A a b^{3} + B b^{4}\right)} d x \cos\left(d x + c\right)^{2} + {\left(A a^{4} + 8 \, B a^{3} b + 12 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{4} + 8 \, B a^{3} b + 12 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B b^{4} \cos\left(d x + c\right)^{3} + A a^{4} + 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*(12*B*a^2*b^2 + 8*A*a*b^3 + B*b^4)*d*x*cos(d*x + c)^2 + (A*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(B*b^4*cos(d*x + c)^3 + A*a^4 + 2*(4*B*a*b^3 + A*b^4)*cos(d*x + c)^2 + 2*(B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
246,1,219,0,1.619930," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B a^{4} + 4 \, A a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, B b^{4} \cos\left(d x + c\right)^{3} + 2 \, A a^{4} + 4 \, {\left(A a^{4} + 6 \, B a^{3} b + 9 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*(4*B*a*b^3 + A*b^4)*d*x*cos(d*x + c)^3 + 3*(B*a^4 + 4*A*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B*a^4 + 4*A*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*B*b^4*cos(d*x + c)^3 + 2*A*a^4 + 4*(A*a^4 + 6*B*a^3*b + 9*A*a^2*b^2)*cos(d*x + c)^2 + 3*(B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
247,1,250,0,0.843805," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{48 \, B b^{4} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, A a^{4} + 16 \, {\left(B a^{4} + 4 \, A a^{3} b + 9 \, B a^{2} b^{2} + 6 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(48*B*b^4*d*x*cos(d*x + c)^4 + 3*(3*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(6*A*a^4 + 16*(B*a^4 + 4*A*a^3*b + 9*B*a^2*b^2 + 6*A*a*b^3)*cos(d*x + c)^3 + 3*(3*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2)*cos(d*x + c)^2 + 8*(B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
248,1,281,0,0.656650," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 8 \, B b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 8 \, B b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, A a^{4} + 8 \, {\left(8 \, A a^{4} + 40 \, B a^{3} b + 60 \, A a^{2} b^{2} + 60 \, B a b^{3} + 15 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(2 \, A a^{4} + 10 \, B a^{3} b + 15 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(3*B*a^4 + 12*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 8*B*b^4)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*B*a^4 + 12*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 8*B*b^4)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(24*A*a^4 + 8*(8*A*a^4 + 40*B*a^3*b + 60*A*a^2*b^2 + 60*B*a*b^3 + 15*A*b^4)*cos(d*x + c)^4 + 15*(3*B*a^4 + 12*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3)*cos(d*x + c)^3 + 16*(2*A*a^4 + 10*B*a^3*b + 15*A*a^2*b^2)*cos(d*x + c)^2 + 30*(B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
249,1,327,0,1.100129," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left(5 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(5 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 60 \, B a^{2} b^{2} + 40 \, A a b^{3} + 15 \, B b^{4}\right)} \cos\left(d x + c\right)^{5} + 40 \, A a^{4} + 15 \, {\left(5 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} + 32 \, {\left(2 \, B a^{4} + 8 \, A a^{3} b + 15 \, B a^{2} b^{2} + 10 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(5 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 48 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(5*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(5*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(8*B*a^4 + 32*A*a^3*b + 60*B*a^2*b^2 + 40*A*a*b^3 + 15*B*b^4)*cos(d*x + c)^5 + 40*A*a^4 + 15*(5*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c)^4 + 32*(2*B*a^4 + 8*A*a^3*b + 15*B*a^2*b^2 + 10*A*a*b^3)*cos(d*x + c)^3 + 10*(5*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2)*cos(d*x + c)^2 + 48*(B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
250,1,541,0,1.106037," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, B a^{5} - 2 \, A a^{4} b - B a^{3} b^{2} + A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} d x - 3 \, {\left(B a^{4} - A a^{3} b\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(6 \, B a^{4} b - 6 \, A a^{3} b^{2} - 2 \, B a^{2} b^{3} + 6 \, A a b^{4} - 4 \, B b^{5} + 2 \, {\left(B a^{2} b^{3} - B b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(B a^{3} b^{2} - A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} - b^{6}\right)} d}, -\frac{3 \, {\left(2 \, B a^{5} - 2 \, A a^{4} b - B a^{3} b^{2} + A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} d x - 6 \, {\left(B a^{4} - A a^{3} b\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(6 \, B a^{4} b - 6 \, A a^{3} b^{2} - 2 \, B a^{2} b^{3} + 6 \, A a b^{4} - 4 \, B b^{5} + 2 \, {\left(B a^{2} b^{3} - B b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(B a^{3} b^{2} - A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} - b^{6}\right)} d}\right]"," ",0,"[-1/6*(3*(2*B*a^5 - 2*A*a^4*b - B*a^3*b^2 + A*a^2*b^3 - B*a*b^4 + A*b^5)*d*x - 3*(B*a^4 - A*a^3*b)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (6*B*a^4*b - 6*A*a^3*b^2 - 2*B*a^2*b^3 + 6*A*a*b^4 - 4*B*b^5 + 2*(B*a^2*b^3 - B*b^5)*cos(d*x + c)^2 - 3*(B*a^3*b^2 - A*a^2*b^3 - B*a*b^4 + A*b^5)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d), -1/6*(3*(2*B*a^5 - 2*A*a^4*b - B*a^3*b^2 + A*a^2*b^3 - B*a*b^4 + A*b^5)*d*x - 6*(B*a^4 - A*a^3*b)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*B*a^4*b - 6*A*a^3*b^2 - 2*B*a^2*b^3 + 6*A*a*b^4 - 4*B*b^5 + 2*(B*a^2*b^3 - B*b^5)*cos(d*x + c)^2 - 3*(B*a^3*b^2 - A*a^2*b^3 - B*a*b^4 + A*b^5)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d)]","A",0
251,1,426,0,1.147980," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a^{4} - 2 \, A a^{3} b - B a^{2} b^{2} + 2 \, A a b^{3} - B b^{4}\right)} d x + {\left(B a^{3} - A a^{2} b\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(2 \, B a^{3} b - 2 \, A a^{2} b^{2} - 2 \, B a b^{3} + 2 \, A b^{4} - {\left(B a^{2} b^{2} - B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} - b^{5}\right)} d}, \frac{{\left(2 \, B a^{4} - 2 \, A a^{3} b - B a^{2} b^{2} + 2 \, A a b^{3} - B b^{4}\right)} d x - 2 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, B a^{3} b - 2 \, A a^{2} b^{2} - 2 \, B a b^{3} + 2 \, A b^{4} - {\left(B a^{2} b^{2} - B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} - b^{5}\right)} d}\right]"," ",0,"[1/2*((2*B*a^4 - 2*A*a^3*b - B*a^2*b^2 + 2*A*a*b^3 - B*b^4)*d*x + (B*a^3 - A*a^2*b)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (2*B*a^3*b - 2*A*a^2*b^2 - 2*B*a*b^3 + 2*A*b^4 - (B*a^2*b^2 - B*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d), 1/2*((2*B*a^4 - 2*A*a^3*b - B*a^2*b^2 + 2*A*a*b^3 - B*b^4)*d*x - 2*(B*a^3 - A*a^2*b)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*B*a^3*b - 2*A*a^2*b^2 - 2*B*a*b^3 + 2*A*b^4 - (B*a^2*b^2 - B*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d)]","A",0
252,1,322,0,0.944089," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} d x - {\left(B a^{2} - A a b\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(B a^{2} b - B b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d}, -\frac{{\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} d x - {\left(B a^{2} - A a b\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(B a^{2} b - B b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d}\right]"," ",0,"[-1/2*(2*(B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*d*x - (B*a^2 - A*a*b)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(B*a^2*b - B*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d), -((B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*d*x - (B*a^2 - A*a*b)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (B*a^2*b - B*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d)]","A",0
253,1,242,0,0.720409," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a^{2} - B b^{2}\right)} d x + {\left(B a - A b\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right)}{2 \, {\left(a^{2} b - b^{3}\right)} d}, \frac{{\left(B a^{2} - B b^{2}\right)} d x - {\left(B a - A b\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right)}{{\left(a^{2} b - b^{3}\right)} d}\right]"," ",0,"[1/2*(2*(B*a^2 - B*b^2)*d*x + (B*a - A*b)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)))/((a^2*b - b^3)*d), ((B*a^2 - B*b^2)*d*x - (B*a - A*b)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))))/((a^2*b - b^3)*d)]","A",0
254,1,304,0,1.910670," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(B a - A b\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + {\left(A a^{2} - A b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{2} - A b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}, \frac{2 \, {\left(B a - A b\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(A a^{2} - A b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{2} - A b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[1/2*((B*a - A*b)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + (A*a^2 - A*b^2)*log(sin(d*x + c) + 1) - (A*a^2 - A*b^2)*log(-sin(d*x + c) + 1))/((a^3 - a*b^2)*d), 1/2*(2*(B*a - A*b)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (A*a^2 - A*b^2)*log(sin(d*x + c) + 1) - (A*a^2 - A*b^2)*log(-sin(d*x + c) + 1))/((a^3 - a*b^2)*d)]","A",0
255,1,460,0,0.949638," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(B a b - A b^{2}\right)} \sqrt{-a^{2} + b^{2}} \cos\left(d x + c\right) \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{3} - A a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(d x + c\right)}, -\frac{2 \, {\left(B a b - A b^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right) - {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A a^{3} - A a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*((B*a*b - A*b^2)*sqrt(-a^2 + b^2)*cos(d*x + c)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + (B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) - (B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(A*a^3 - A*a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d*cos(d*x + c)), -1/2*(2*(B*a*b - A*b^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))*cos(d*x + c) - (B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) + (B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) - 2*(A*a^3 - A*a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d*cos(d*x + c))]","B",0
256,1,589,0,8.205276," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a b^{2} - A b^{3}\right)} \sqrt{-a^{2} + b^{2}} \cos\left(d x + c\right)^{2} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + {\left(A a^{4} - 2 \, B a^{3} b + A a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{4} - 2 \, B a^{3} b + A a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{4} - A a^{2} b^{2} + 2 \, {\left(B a^{4} - A a^{3} b - B a^{2} b^{2} + A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} - a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2}}, \frac{4 \, {\left(B a b^{2} - A b^{3}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right)^{2} + {\left(A a^{4} - 2 \, B a^{3} b + A a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{4} - 2 \, B a^{3} b + A a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{4} - A a^{2} b^{2} + 2 \, {\left(B a^{4} - A a^{3} b - B a^{2} b^{2} + A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} - a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[1/4*(2*(B*a*b^2 - A*b^3)*sqrt(-a^2 + b^2)*cos(d*x + c)^2*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + (A*a^4 - 2*B*a^3*b + A*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A*a^4 - 2*B*a^3*b + A*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a^4 - A*a^2*b^2 + 2*(B*a^4 - A*a^3*b - B*a^2*b^2 + A*a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d*cos(d*x + c)^2), 1/4*(4*(B*a*b^2 - A*b^3)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))*cos(d*x + c)^2 + (A*a^4 - 2*B*a^3*b + A*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A*a^4 - 2*B*a^3*b + A*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a^4 - A*a^2*b^2 + 2*(B*a^4 - A*a^3*b - B*a^2*b^2 + A*a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d*cos(d*x + c)^2)]","B",0
257,1,729,0,2.716660," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(B a b^{3} - A b^{4}\right)} \sqrt{-a^{2} + b^{2}} \cos\left(d x + c\right)^{3} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 3 \, {\left(B a^{5} - A a^{4} b + B a^{3} b^{2} - A a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B a^{5} - A a^{4} b + B a^{3} b^{2} - A a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{5} - 2 \, A a^{3} b^{2} + 2 \, {\left(2 \, A a^{5} - 3 \, B a^{4} b + A a^{3} b^{2} + 3 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{5} - A a^{4} b - B a^{3} b^{2} + A a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(d x + c\right)^{3}}, -\frac{12 \, {\left(B a b^{3} - A b^{4}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} - 3 \, {\left(B a^{5} - A a^{4} b + B a^{3} b^{2} - A a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(B a^{5} - A a^{4} b + B a^{3} b^{2} - A a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, A a^{5} - 2 \, A a^{3} b^{2} + 2 \, {\left(2 \, A a^{5} - 3 \, B a^{4} b + A a^{3} b^{2} + 3 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{5} - A a^{4} b - B a^{3} b^{2} + A a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[1/12*(6*(B*a*b^3 - A*b^4)*sqrt(-a^2 + b^2)*cos(d*x + c)^3*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 3*(B*a^5 - A*a^4*b + B*a^3*b^2 - A*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B*a^5 - A*a^4*b + B*a^3*b^2 - A*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*A*a^5 - 2*A*a^3*b^2 + 2*(2*A*a^5 - 3*B*a^4*b + A*a^3*b^2 + 3*B*a^2*b^3 - 3*A*a*b^4)*cos(d*x + c)^2 + 3*(B*a^5 - A*a^4*b - B*a^3*b^2 + A*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d*cos(d*x + c)^3), -1/12*(12*(B*a*b^3 - A*b^4)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))*cos(d*x + c)^3 - 3*(B*a^5 - A*a^4*b + B*a^3*b^2 - A*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(B*a^5 - A*a^4*b + B*a^3*b^2 - A*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - 2*(2*A*a^5 - 2*A*a^3*b^2 + 2*(2*A*a^5 - 3*B*a^4*b + A*a^3*b^2 + 3*B*a^2*b^3 - 3*A*a*b^4)*cos(d*x + c)^2 + 3*(B*a^5 - A*a^4*b - B*a^3*b^2 + A*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d*cos(d*x + c)^3)]","A",0
258,1,965,0,1.566190," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(6 \, B a^{6} b - 4 \, A a^{5} b^{2} - 11 \, B a^{4} b^{3} + 8 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 4 \, A a b^{6} + B b^{7}\right)} d x \cos\left(d x + c\right) + {\left(6 \, B a^{7} - 4 \, A a^{6} b - 11 \, B a^{5} b^{2} + 8 \, A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 4 \, A a^{2} b^{5} + B a b^{6}\right)} d x - {\left(3 \, B a^{6} - 2 \, A a^{5} b - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} + {\left(3 \, B a^{5} b - 2 \, A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(6 \, B a^{6} b - 4 \, A a^{5} b^{2} - 10 \, B a^{4} b^{3} + 6 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 2 \, A a b^{6} - {\left(B a^{4} b^{3} - 2 \, B a^{2} b^{5} + B b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B a^{5} b^{2} - 2 \, A a^{4} b^{3} - 6 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} + 3 \, B a b^{6} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d\right)}}, \frac{{\left(6 \, B a^{6} b - 4 \, A a^{5} b^{2} - 11 \, B a^{4} b^{3} + 8 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 4 \, A a b^{6} + B b^{7}\right)} d x \cos\left(d x + c\right) + {\left(6 \, B a^{7} - 4 \, A a^{6} b - 11 \, B a^{5} b^{2} + 8 \, A a^{4} b^{3} + 4 \, B a^{3} b^{4} - 4 \, A a^{2} b^{5} + B a b^{6}\right)} d x - 2 \, {\left(3 \, B a^{6} - 2 \, A a^{5} b - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} + {\left(3 \, B a^{5} b - 2 \, A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(6 \, B a^{6} b - 4 \, A a^{5} b^{2} - 10 \, B a^{4} b^{3} + 6 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 2 \, A a b^{6} - {\left(B a^{4} b^{3} - 2 \, B a^{2} b^{5} + B b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B a^{5} b^{2} - 2 \, A a^{4} b^{3} - 6 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} + 3 \, B a b^{6} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d\right)}}\right]"," ",0,"[1/2*((6*B*a^6*b - 4*A*a^5*b^2 - 11*B*a^4*b^3 + 8*A*a^3*b^4 + 4*B*a^2*b^5 - 4*A*a*b^6 + B*b^7)*d*x*cos(d*x + c) + (6*B*a^7 - 4*A*a^6*b - 11*B*a^5*b^2 + 8*A*a^4*b^3 + 4*B*a^3*b^4 - 4*A*a^2*b^5 + B*a*b^6)*d*x - (3*B*a^6 - 2*A*a^5*b - 4*B*a^4*b^2 + 3*A*a^3*b^3 + (3*B*a^5*b - 2*A*a^4*b^2 - 4*B*a^3*b^3 + 3*A*a^2*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (6*B*a^6*b - 4*A*a^5*b^2 - 10*B*a^4*b^3 + 6*A*a^3*b^4 + 4*B*a^2*b^5 - 2*A*a*b^6 - (B*a^4*b^3 - 2*B*a^2*b^5 + B*b^7)*cos(d*x + c)^2 + (3*B*a^5*b^2 - 2*A*a^4*b^3 - 6*B*a^3*b^4 + 4*A*a^2*b^5 + 3*B*a*b^6 - 2*A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c) + (a^5*b^4 - 2*a^3*b^6 + a*b^8)*d), 1/2*((6*B*a^6*b - 4*A*a^5*b^2 - 11*B*a^4*b^3 + 8*A*a^3*b^4 + 4*B*a^2*b^5 - 4*A*a*b^6 + B*b^7)*d*x*cos(d*x + c) + (6*B*a^7 - 4*A*a^6*b - 11*B*a^5*b^2 + 8*A*a^4*b^3 + 4*B*a^3*b^4 - 4*A*a^2*b^5 + B*a*b^6)*d*x - 2*(3*B*a^6 - 2*A*a^5*b - 4*B*a^4*b^2 + 3*A*a^3*b^3 + (3*B*a^5*b - 2*A*a^4*b^2 - 4*B*a^3*b^3 + 3*A*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*B*a^6*b - 4*A*a^5*b^2 - 10*B*a^4*b^3 + 6*A*a^3*b^4 + 4*B*a^2*b^5 - 2*A*a*b^6 - (B*a^4*b^3 - 2*B*a^2*b^5 + B*b^7)*cos(d*x + c)^2 + (3*B*a^5*b^2 - 2*A*a^4*b^3 - 6*B*a^3*b^4 + 4*A*a^2*b^5 + 3*B*a*b^6 - 2*A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c) + (a^5*b^4 - 2*a^3*b^6 + a*b^8)*d)]","A",0
259,1,788,0,1.254577," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(2 \, B a^{5} b - A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4} + 2 \, B a b^{5} - A b^{6}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(2 \, B a^{6} - A a^{5} b - 4 \, B a^{4} b^{2} + 2 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - A a b^{5}\right)} d x + {\left(2 \, B a^{5} - A a^{4} b - 3 \, B a^{3} b^{2} + 2 \, A a^{2} b^{3} + {\left(2 \, B a^{4} b - A a^{3} b^{2} - 3 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(2 \, B a^{5} b - A a^{4} b^{2} - 3 \, B a^{3} b^{3} + A a^{2} b^{4} + B a b^{5} + {\left(B a^{4} b^{2} - 2 \, B a^{2} b^{4} + B b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} d\right)}}, -\frac{{\left(2 \, B a^{5} b - A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4} + 2 \, B a b^{5} - A b^{6}\right)} d x \cos\left(d x + c\right) + {\left(2 \, B a^{6} - A a^{5} b - 4 \, B a^{4} b^{2} + 2 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - A a b^{5}\right)} d x - {\left(2 \, B a^{5} - A a^{4} b - 3 \, B a^{3} b^{2} + 2 \, A a^{2} b^{3} + {\left(2 \, B a^{4} b - A a^{3} b^{2} - 3 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, B a^{5} b - A a^{4} b^{2} - 3 \, B a^{3} b^{3} + A a^{2} b^{4} + B a b^{5} + {\left(B a^{4} b^{2} - 2 \, B a^{2} b^{4} + B b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} d}\right]"," ",0,"[-1/2*(2*(2*B*a^5*b - A*a^4*b^2 - 4*B*a^3*b^3 + 2*A*a^2*b^4 + 2*B*a*b^5 - A*b^6)*d*x*cos(d*x + c) + 2*(2*B*a^6 - A*a^5*b - 4*B*a^4*b^2 + 2*A*a^3*b^3 + 2*B*a^2*b^4 - A*a*b^5)*d*x + (2*B*a^5 - A*a^4*b - 3*B*a^3*b^2 + 2*A*a^2*b^3 + (2*B*a^4*b - A*a^3*b^2 - 3*B*a^2*b^3 + 2*A*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(2*B*a^5*b - A*a^4*b^2 - 3*B*a^3*b^3 + A*a^2*b^4 + B*a*b^5 + (B*a^4*b^2 - 2*B*a^2*b^4 + B*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*d*cos(d*x + c) + (a^5*b^3 - 2*a^3*b^5 + a*b^7)*d), -((2*B*a^5*b - A*a^4*b^2 - 4*B*a^3*b^3 + 2*A*a^2*b^4 + 2*B*a*b^5 - A*b^6)*d*x*cos(d*x + c) + (2*B*a^6 - A*a^5*b - 4*B*a^4*b^2 + 2*A*a^3*b^3 + 2*B*a^2*b^4 - A*a*b^5)*d*x - (2*B*a^5 - A*a^4*b - 3*B*a^3*b^2 + 2*A*a^2*b^3 + (2*B*a^4*b - A*a^3*b^2 - 3*B*a^2*b^3 + 2*A*a*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*B*a^5*b - A*a^4*b^2 - 3*B*a^3*b^3 + A*a^2*b^4 + B*a*b^5 + (B*a^4*b^2 - 2*B*a^2*b^4 + B*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*d*cos(d*x + c) + (a^5*b^3 - 2*a^3*b^5 + a*b^7)*d)]","B",0
260,1,552,0,0.731155," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4}\right)} d x - {\left(B a^{4} - 2 \, B a^{2} b^{2} + A a b^{3} + {\left(B a^{3} b - 2 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(B a^{4} b - A a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d\right)}}, \frac{{\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5}\right)} d x \cos\left(d x + c\right) + {\left(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4}\right)} d x - {\left(B a^{4} - 2 \, B a^{2} b^{2} + A a b^{3} + {\left(B a^{3} b - 2 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(B a^{4} b - A a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} \sin\left(d x + c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d}\right]"," ",0,"[1/2*(2*(B*a^4*b - 2*B*a^2*b^3 + B*b^5)*d*x*cos(d*x + c) + 2*(B*a^5 - 2*B*a^3*b^2 + B*a*b^4)*d*x - (B*a^4 - 2*B*a^2*b^2 + A*a*b^3 + (B*a^3*b - 2*B*a*b^3 + A*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(B*a^4*b - A*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*sin(d*x + c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*d*cos(d*x + c) + (a^5*b^2 - 2*a^3*b^4 + a*b^6)*d), ((B*a^4*b - 2*B*a^2*b^3 + B*b^5)*d*x*cos(d*x + c) + (B*a^5 - 2*B*a^3*b^2 + B*a*b^4)*d*x - (B*a^4 - 2*B*a^2*b^2 + A*a*b^3 + (B*a^3*b - 2*B*a*b^3 + A*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (B*a^4*b - A*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*sin(d*x + c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*d*cos(d*x + c) + (a^5*b^2 - 2*a^3*b^4 + a*b^6)*d)]","B",0
261,1,379,0,0.782759," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(A a^{2} - B a b + {\left(A a b - B b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}, \frac{{\left(A a^{2} - B a b + {\left(A a b - B b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d}\right]"," ",0,"[-1/2*((A*a^2 - B*a*b + (A*a*b - B*b^2)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*sin(d*x + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d), ((A*a^2 - B*a*b + (A*a*b - B*b^2)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*sin(d*x + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d)]","A",0
262,1,684,0,7.686752," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(B a^{4} - 2 \, A a^{3} b + A a b^{3} + {\left(B a^{3} b - 2 \, A a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + {\left(A a^{5} - 2 \, A a^{3} b^{2} + A a b^{4} + {\left(A a^{4} b - 2 \, A a^{2} b^{3} + A b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{5} - 2 \, A a^{3} b^{2} + A a b^{4} + {\left(A a^{4} b - 2 \, A a^{2} b^{3} + A b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{4} b - A a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d\right)}}, \frac{2 \, {\left(B a^{4} - 2 \, A a^{3} b + A a b^{3} + {\left(B a^{3} b - 2 \, A a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(A a^{5} - 2 \, A a^{3} b^{2} + A a b^{4} + {\left(A a^{4} b - 2 \, A a^{2} b^{3} + A b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{5} - 2 \, A a^{3} b^{2} + A a b^{4} + {\left(A a^{4} b - 2 \, A a^{2} b^{3} + A b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{4} b - A a^{3} b^{2} - B a^{2} b^{3} + A a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d\right)}}\right]"," ",0,"[1/2*((B*a^4 - 2*A*a^3*b + A*a*b^3 + (B*a^3*b - 2*A*a^2*b^2 + A*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + (A*a^5 - 2*A*a^3*b^2 + A*a*b^4 + (A*a^4*b - 2*A*a^2*b^3 + A*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) - (A*a^5 - 2*A*a^3*b^2 + A*a*b^4 + (A*a^4*b - 2*A*a^2*b^3 + A*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(B*a^4*b - A*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*sin(d*x + c))/((a^6*b - 2*a^4*b^3 + a^2*b^5)*d*cos(d*x + c) + (a^7 - 2*a^5*b^2 + a^3*b^4)*d), 1/2*(2*(B*a^4 - 2*A*a^3*b + A*a*b^3 + (B*a^3*b - 2*A*a^2*b^2 + A*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (A*a^5 - 2*A*a^3*b^2 + A*a*b^4 + (A*a^4*b - 2*A*a^2*b^3 + A*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) - (A*a^5 - 2*A*a^3*b^2 + A*a*b^4 + (A*a^4*b - 2*A*a^2*b^3 + A*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(B*a^4*b - A*a^3*b^2 - B*a^2*b^3 + A*a*b^4)*sin(d*x + c))/((a^6*b - 2*a^4*b^3 + a^2*b^5)*d*cos(d*x + c) + (a^7 - 2*a^5*b^2 + a^3*b^4)*d)]","B",0
263,1,1088,0,21.473795," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - B a b^{4} + 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{4} b - 3 \, A a^{3} b^{2} - B a^{2} b^{3} + 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left({\left(B a^{5} b - 2 \, A a^{4} b^{2} - 2 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} + B a b^{5} - 2 \, A b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{6} - 2 \, A a^{5} b - 2 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(B a^{5} b - 2 \, A a^{4} b^{2} - 2 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} + B a b^{5} - 2 \, A b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{6} - 2 \, A a^{5} b - 2 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A a^{6} - 2 \, A a^{4} b^{2} + A a^{2} b^{4} + {\left(A a^{5} b + B a^{4} b^{2} - 3 \, A a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{2 \, {\left({\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - B a b^{4} + 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{4} b - 3 \, A a^{3} b^{2} - B a^{2} b^{3} + 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left({\left(B a^{5} b - 2 \, A a^{4} b^{2} - 2 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} + B a b^{5} - 2 \, A b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{6} - 2 \, A a^{5} b - 2 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(B a^{5} b - 2 \, A a^{4} b^{2} - 2 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} + B a b^{5} - 2 \, A b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{6} - 2 \, A a^{5} b - 2 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} + B a^{2} b^{4} - 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A a^{6} - 2 \, A a^{4} b^{2} + A a^{2} b^{4} + {\left(A a^{5} b + B a^{4} b^{2} - 3 \, A a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/2*(((2*B*a^3*b^2 - 3*A*a^2*b^3 - B*a*b^4 + 2*A*b^5)*cos(d*x + c)^2 + (2*B*a^4*b - 3*A*a^3*b^2 - B*a^2*b^3 + 2*A*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - ((B*a^5*b - 2*A*a^4*b^2 - 2*B*a^3*b^3 + 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*cos(d*x + c)^2 + (B*a^6 - 2*A*a^5*b - 2*B*a^4*b^2 + 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((B*a^5*b - 2*A*a^4*b^2 - 2*B*a^3*b^3 + 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*cos(d*x + c)^2 + (B*a^6 - 2*A*a^5*b - 2*B*a^4*b^2 + 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(A*a^6 - 2*A*a^4*b^2 + A*a^2*b^4 + (A*a^5*b + B*a^4*b^2 - 3*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^7*b - 2*a^5*b^3 + a^3*b^5)*d*cos(d*x + c)^2 + (a^8 - 2*a^6*b^2 + a^4*b^4)*d*cos(d*x + c)), -1/2*(2*((2*B*a^3*b^2 - 3*A*a^2*b^3 - B*a*b^4 + 2*A*b^5)*cos(d*x + c)^2 + (2*B*a^4*b - 3*A*a^3*b^2 - B*a^2*b^3 + 2*A*a*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - ((B*a^5*b - 2*A*a^4*b^2 - 2*B*a^3*b^3 + 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*cos(d*x + c)^2 + (B*a^6 - 2*A*a^5*b - 2*B*a^4*b^2 + 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((B*a^5*b - 2*A*a^4*b^2 - 2*B*a^3*b^3 + 4*A*a^2*b^4 + B*a*b^5 - 2*A*b^6)*cos(d*x + c)^2 + (B*a^6 - 2*A*a^5*b - 2*B*a^4*b^2 + 4*A*a^3*b^3 + B*a^2*b^4 - 2*A*a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(A*a^6 - 2*A*a^4*b^2 + A*a^2*b^4 + (A*a^5*b + B*a^4*b^2 - 3*A*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^7*b - 2*a^5*b^3 + a^3*b^5)*d*cos(d*x + c)^2 + (a^8 - 2*a^6*b^2 + a^4*b^4)*d*cos(d*x + c))]","B",0
264,1,1329,0,33.863680," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left({\left(3 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4} - 2 \, B a b^{5} + 3 \, A b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, B a^{4} b^{2} - 4 \, A a^{3} b^{3} - 2 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left({\left(A a^{6} b - 4 \, B a^{5} b^{2} + 4 \, A a^{4} b^{3} + 8 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(A a^{7} - 4 \, B a^{6} b + 4 \, A a^{5} b^{2} + 8 \, B a^{4} b^{3} - 11 \, A a^{3} b^{4} - 4 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(A a^{6} b - 4 \, B a^{5} b^{2} + 4 \, A a^{4} b^{3} + 8 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(A a^{7} - 4 \, B a^{6} b + 4 \, A a^{5} b^{2} + 8 \, B a^{4} b^{3} - 11 \, A a^{3} b^{4} - 4 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A a^{7} - 2 \, A a^{5} b^{2} + A a^{3} b^{4} + 2 \, {\left(B a^{6} b - 2 \, A a^{5} b^{2} - 3 \, B a^{4} b^{3} + 5 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} - 3 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{7} - 3 \, A a^{6} b - 4 \, B a^{5} b^{2} + 6 \, A a^{4} b^{3} + 2 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)}}, \frac{4 \, {\left({\left(3 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4} - 2 \, B a b^{5} + 3 \, A b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, B a^{4} b^{2} - 4 \, A a^{3} b^{3} - 2 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left({\left(A a^{6} b - 4 \, B a^{5} b^{2} + 4 \, A a^{4} b^{3} + 8 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(A a^{7} - 4 \, B a^{6} b + 4 \, A a^{5} b^{2} + 8 \, B a^{4} b^{3} - 11 \, A a^{3} b^{4} - 4 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A a^{6} b - 4 \, B a^{5} b^{2} + 4 \, A a^{4} b^{3} + 8 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(A a^{7} - 4 \, B a^{6} b + 4 \, A a^{5} b^{2} + 8 \, B a^{4} b^{3} - 11 \, A a^{3} b^{4} - 4 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{7} - 2 \, A a^{5} b^{2} + A a^{3} b^{4} + 2 \, {\left(B a^{6} b - 2 \, A a^{5} b^{2} - 3 \, B a^{4} b^{3} + 5 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} - 3 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B a^{7} - 3 \, A a^{6} b - 4 \, B a^{5} b^{2} + 6 \, A a^{4} b^{3} + 2 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/4*(2*((3*B*a^3*b^3 - 4*A*a^2*b^4 - 2*B*a*b^5 + 3*A*b^6)*cos(d*x + c)^3 + (3*B*a^4*b^2 - 4*A*a^3*b^3 - 2*B*a^2*b^4 + 3*A*a*b^5)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - ((A*a^6*b - 4*B*a^5*b^2 + 4*A*a^4*b^3 + 8*B*a^3*b^4 - 11*A*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*cos(d*x + c)^3 + (A*a^7 - 4*B*a^6*b + 4*A*a^5*b^2 + 8*B*a^4*b^3 - 11*A*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((A*a^6*b - 4*B*a^5*b^2 + 4*A*a^4*b^3 + 8*B*a^3*b^4 - 11*A*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*cos(d*x + c)^3 + (A*a^7 - 4*B*a^6*b + 4*A*a^5*b^2 + 8*B*a^4*b^3 - 11*A*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(A*a^7 - 2*A*a^5*b^2 + A*a^3*b^4 + 2*(B*a^6*b - 2*A*a^5*b^2 - 3*B*a^4*b^3 + 5*A*a^3*b^4 + 2*B*a^2*b^5 - 3*A*a*b^6)*cos(d*x + c)^2 + (2*B*a^7 - 3*A*a^6*b - 4*B*a^5*b^2 + 6*A*a^4*b^3 + 2*B*a^3*b^4 - 3*A*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*b - 2*a^6*b^3 + a^4*b^5)*d*cos(d*x + c)^3 + (a^9 - 2*a^7*b^2 + a^5*b^4)*d*cos(d*x + c)^2), 1/4*(4*((3*B*a^3*b^3 - 4*A*a^2*b^4 - 2*B*a*b^5 + 3*A*b^6)*cos(d*x + c)^3 + (3*B*a^4*b^2 - 4*A*a^3*b^3 - 2*B*a^2*b^4 + 3*A*a*b^5)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + ((A*a^6*b - 4*B*a^5*b^2 + 4*A*a^4*b^3 + 8*B*a^3*b^4 - 11*A*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*cos(d*x + c)^3 + (A*a^7 - 4*B*a^6*b + 4*A*a^5*b^2 + 8*B*a^4*b^3 - 11*A*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((A*a^6*b - 4*B*a^5*b^2 + 4*A*a^4*b^3 + 8*B*a^3*b^4 - 11*A*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*cos(d*x + c)^3 + (A*a^7 - 4*B*a^6*b + 4*A*a^5*b^2 + 8*B*a^4*b^3 - 11*A*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(A*a^7 - 2*A*a^5*b^2 + A*a^3*b^4 + 2*(B*a^6*b - 2*A*a^5*b^2 - 3*B*a^4*b^3 + 5*A*a^3*b^4 + 2*B*a^2*b^5 - 3*A*a*b^6)*cos(d*x + c)^2 + (2*B*a^7 - 3*A*a^6*b - 4*B*a^5*b^2 + 6*A*a^4*b^3 + 2*B*a^3*b^4 - 3*A*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*b - 2*a^6*b^3 + a^4*b^5)*d*cos(d*x + c)^3 + (a^9 - 2*a^7*b^2 + a^5*b^4)*d*cos(d*x + c)^2)]","B",0
265,1,1812,0,1.226658," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(12 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} - 35 \, B a^{6} b^{4} + 18 \, A a^{5} b^{5} + 33 \, B a^{4} b^{6} - 18 \, A a^{3} b^{7} - 9 \, B a^{2} b^{8} + 6 \, A a b^{9} - B b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(12 \, B a^{9} b - 6 \, A a^{8} b^{2} - 35 \, B a^{7} b^{3} + 18 \, A a^{6} b^{4} + 33 \, B a^{5} b^{5} - 18 \, A a^{4} b^{6} - 9 \, B a^{3} b^{7} + 6 \, A a^{2} b^{8} - B a b^{9}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(12 \, B a^{10} - 6 \, A a^{9} b - 35 \, B a^{8} b^{2} + 18 \, A a^{7} b^{3} + 33 \, B a^{6} b^{4} - 18 \, A a^{5} b^{5} - 9 \, B a^{4} b^{6} + 6 \, A a^{3} b^{7} - B a^{2} b^{8}\right)} d x + {\left(12 \, B a^{9} - 6 \, A a^{8} b - 29 \, B a^{7} b^{2} + 15 \, A a^{6} b^{3} + 20 \, B a^{5} b^{4} - 12 \, A a^{4} b^{5} + {\left(12 \, B a^{7} b^{2} - 6 \, A a^{6} b^{3} - 29 \, B a^{5} b^{4} + 15 \, A a^{4} b^{5} + 20 \, B a^{3} b^{6} - 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, B a^{8} b - 6 \, A a^{7} b^{2} - 29 \, B a^{6} b^{3} + 15 \, A a^{5} b^{4} + 20 \, B a^{4} b^{5} - 12 \, A a^{3} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(12 \, B a^{9} b - 6 \, A a^{8} b^{2} - 33 \, B a^{7} b^{3} + 17 \, A a^{6} b^{4} + 27 \, B a^{5} b^{5} - 13 \, A a^{4} b^{6} - 6 \, B a^{3} b^{7} + 2 \, A a^{2} b^{8} - {\left(B a^{6} b^{4} - 3 \, B a^{4} b^{6} + 3 \, B a^{2} b^{8} - B b^{10}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, B a^{7} b^{3} - A a^{6} b^{4} - 6 \, B a^{5} b^{5} + 3 \, A a^{4} b^{6} + 6 \, B a^{3} b^{7} - 3 \, A a^{2} b^{8} - 2 \, B a b^{9} + A b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, B a^{8} b^{2} - 9 \, A a^{7} b^{3} - 50 \, B a^{6} b^{4} + 25 \, A a^{5} b^{5} + 43 \, B a^{4} b^{6} - 20 \, A a^{3} b^{7} - 11 \, B a^{2} b^{8} + 4 \, A a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b^{7} - 3 \, a^{4} b^{9} + 3 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{6} - 3 \, a^{5} b^{8} + 3 \, a^{3} b^{10} - a b^{12}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{5} - 3 \, a^{6} b^{7} + 3 \, a^{4} b^{9} - a^{2} b^{11}\right)} d\right)}}, \frac{{\left(12 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} - 35 \, B a^{6} b^{4} + 18 \, A a^{5} b^{5} + 33 \, B a^{4} b^{6} - 18 \, A a^{3} b^{7} - 9 \, B a^{2} b^{8} + 6 \, A a b^{9} - B b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, B a^{9} b - 6 \, A a^{8} b^{2} - 35 \, B a^{7} b^{3} + 18 \, A a^{6} b^{4} + 33 \, B a^{5} b^{5} - 18 \, A a^{4} b^{6} - 9 \, B a^{3} b^{7} + 6 \, A a^{2} b^{8} - B a b^{9}\right)} d x \cos\left(d x + c\right) + {\left(12 \, B a^{10} - 6 \, A a^{9} b - 35 \, B a^{8} b^{2} + 18 \, A a^{7} b^{3} + 33 \, B a^{6} b^{4} - 18 \, A a^{5} b^{5} - 9 \, B a^{4} b^{6} + 6 \, A a^{3} b^{7} - B a^{2} b^{8}\right)} d x - {\left(12 \, B a^{9} - 6 \, A a^{8} b - 29 \, B a^{7} b^{2} + 15 \, A a^{6} b^{3} + 20 \, B a^{5} b^{4} - 12 \, A a^{4} b^{5} + {\left(12 \, B a^{7} b^{2} - 6 \, A a^{6} b^{3} - 29 \, B a^{5} b^{4} + 15 \, A a^{4} b^{5} + 20 \, B a^{3} b^{6} - 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, B a^{8} b - 6 \, A a^{7} b^{2} - 29 \, B a^{6} b^{3} + 15 \, A a^{5} b^{4} + 20 \, B a^{4} b^{5} - 12 \, A a^{3} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(12 \, B a^{9} b - 6 \, A a^{8} b^{2} - 33 \, B a^{7} b^{3} + 17 \, A a^{6} b^{4} + 27 \, B a^{5} b^{5} - 13 \, A a^{4} b^{6} - 6 \, B a^{3} b^{7} + 2 \, A a^{2} b^{8} - {\left(B a^{6} b^{4} - 3 \, B a^{4} b^{6} + 3 \, B a^{2} b^{8} - B b^{10}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, B a^{7} b^{3} - A a^{6} b^{4} - 6 \, B a^{5} b^{5} + 3 \, A a^{4} b^{6} + 6 \, B a^{3} b^{7} - 3 \, A a^{2} b^{8} - 2 \, B a b^{9} + A b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, B a^{8} b^{2} - 9 \, A a^{7} b^{3} - 50 \, B a^{6} b^{4} + 25 \, A a^{5} b^{5} + 43 \, B a^{4} b^{6} - 20 \, A a^{3} b^{7} - 11 \, B a^{2} b^{8} + 4 \, A a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{7} - 3 \, a^{4} b^{9} + 3 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{6} - 3 \, a^{5} b^{8} + 3 \, a^{3} b^{10} - a b^{12}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{5} - 3 \, a^{6} b^{7} + 3 \, a^{4} b^{9} - a^{2} b^{11}\right)} d\right)}}\right]"," ",0,"[1/4*(2*(12*B*a^8*b^2 - 6*A*a^7*b^3 - 35*B*a^6*b^4 + 18*A*a^5*b^5 + 33*B*a^4*b^6 - 18*A*a^3*b^7 - 9*B*a^2*b^8 + 6*A*a*b^9 - B*b^10)*d*x*cos(d*x + c)^2 + 4*(12*B*a^9*b - 6*A*a^8*b^2 - 35*B*a^7*b^3 + 18*A*a^6*b^4 + 33*B*a^5*b^5 - 18*A*a^4*b^6 - 9*B*a^3*b^7 + 6*A*a^2*b^8 - B*a*b^9)*d*x*cos(d*x + c) + 2*(12*B*a^10 - 6*A*a^9*b - 35*B*a^8*b^2 + 18*A*a^7*b^3 + 33*B*a^6*b^4 - 18*A*a^5*b^5 - 9*B*a^4*b^6 + 6*A*a^3*b^7 - B*a^2*b^8)*d*x + (12*B*a^9 - 6*A*a^8*b - 29*B*a^7*b^2 + 15*A*a^6*b^3 + 20*B*a^5*b^4 - 12*A*a^4*b^5 + (12*B*a^7*b^2 - 6*A*a^6*b^3 - 29*B*a^5*b^4 + 15*A*a^4*b^5 + 20*B*a^3*b^6 - 12*A*a^2*b^7)*cos(d*x + c)^2 + 2*(12*B*a^8*b - 6*A*a^7*b^2 - 29*B*a^6*b^3 + 15*A*a^5*b^4 + 20*B*a^4*b^5 - 12*A*a^3*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(12*B*a^9*b - 6*A*a^8*b^2 - 33*B*a^7*b^3 + 17*A*a^6*b^4 + 27*B*a^5*b^5 - 13*A*a^4*b^6 - 6*B*a^3*b^7 + 2*A*a^2*b^8 - (B*a^6*b^4 - 3*B*a^4*b^6 + 3*B*a^2*b^8 - B*b^10)*cos(d*x + c)^3 + 2*(2*B*a^7*b^3 - A*a^6*b^4 - 6*B*a^5*b^5 + 3*A*a^4*b^6 + 6*B*a^3*b^7 - 3*A*a^2*b^8 - 2*B*a*b^9 + A*b^10)*cos(d*x + c)^2 + (18*B*a^8*b^2 - 9*A*a^7*b^3 - 50*B*a^6*b^4 + 25*A*a^5*b^5 + 43*B*a^4*b^6 - 20*A*a^3*b^7 - 11*B*a^2*b^8 + 4*A*a*b^9)*cos(d*x + c))*sin(d*x + c))/((a^6*b^7 - 3*a^4*b^9 + 3*a^2*b^11 - b^13)*d*cos(d*x + c)^2 + 2*(a^7*b^6 - 3*a^5*b^8 + 3*a^3*b^10 - a*b^12)*d*cos(d*x + c) + (a^8*b^5 - 3*a^6*b^7 + 3*a^4*b^9 - a^2*b^11)*d), 1/2*((12*B*a^8*b^2 - 6*A*a^7*b^3 - 35*B*a^6*b^4 + 18*A*a^5*b^5 + 33*B*a^4*b^6 - 18*A*a^3*b^7 - 9*B*a^2*b^8 + 6*A*a*b^9 - B*b^10)*d*x*cos(d*x + c)^2 + 2*(12*B*a^9*b - 6*A*a^8*b^2 - 35*B*a^7*b^3 + 18*A*a^6*b^4 + 33*B*a^5*b^5 - 18*A*a^4*b^6 - 9*B*a^3*b^7 + 6*A*a^2*b^8 - B*a*b^9)*d*x*cos(d*x + c) + (12*B*a^10 - 6*A*a^9*b - 35*B*a^8*b^2 + 18*A*a^7*b^3 + 33*B*a^6*b^4 - 18*A*a^5*b^5 - 9*B*a^4*b^6 + 6*A*a^3*b^7 - B*a^2*b^8)*d*x - (12*B*a^9 - 6*A*a^8*b - 29*B*a^7*b^2 + 15*A*a^6*b^3 + 20*B*a^5*b^4 - 12*A*a^4*b^5 + (12*B*a^7*b^2 - 6*A*a^6*b^3 - 29*B*a^5*b^4 + 15*A*a^4*b^5 + 20*B*a^3*b^6 - 12*A*a^2*b^7)*cos(d*x + c)^2 + 2*(12*B*a^8*b - 6*A*a^7*b^2 - 29*B*a^6*b^3 + 15*A*a^5*b^4 + 20*B*a^4*b^5 - 12*A*a^3*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (12*B*a^9*b - 6*A*a^8*b^2 - 33*B*a^7*b^3 + 17*A*a^6*b^4 + 27*B*a^5*b^5 - 13*A*a^4*b^6 - 6*B*a^3*b^7 + 2*A*a^2*b^8 - (B*a^6*b^4 - 3*B*a^4*b^6 + 3*B*a^2*b^8 - B*b^10)*cos(d*x + c)^3 + 2*(2*B*a^7*b^3 - A*a^6*b^4 - 6*B*a^5*b^5 + 3*A*a^4*b^6 + 6*B*a^3*b^7 - 3*A*a^2*b^8 - 2*B*a*b^9 + A*b^10)*cos(d*x + c)^2 + (18*B*a^8*b^2 - 9*A*a^7*b^3 - 50*B*a^6*b^4 + 25*A*a^5*b^5 + 43*B*a^4*b^6 - 20*A*a^3*b^7 - 11*B*a^2*b^8 + 4*A*a*b^9)*cos(d*x + c))*sin(d*x + c))/((a^6*b^7 - 3*a^4*b^9 + 3*a^2*b^11 - b^13)*d*cos(d*x + c)^2 + 2*(a^7*b^6 - 3*a^5*b^8 + 3*a^3*b^10 - a*b^12)*d*cos(d*x + c) + (a^8*b^5 - 3*a^6*b^7 + 3*a^4*b^9 - a^2*b^11)*d)]","B",0
266,1,1561,0,0.869248," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(3 \, B a^{7} b^{2} - A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 3 \, A a^{4} b^{5} + 9 \, B a^{3} b^{6} - 3 \, A a^{2} b^{7} - 3 \, B a b^{8} + A b^{9}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, B a^{8} b - A a^{7} b^{2} - 9 \, B a^{6} b^{3} + 3 \, A a^{5} b^{4} + 9 \, B a^{4} b^{5} - 3 \, A a^{3} b^{6} - 3 \, B a^{2} b^{7} + A a b^{8}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(3 \, B a^{9} - A a^{8} b - 9 \, B a^{7} b^{2} + 3 \, A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 3 \, A a^{4} b^{5} - 3 \, B a^{3} b^{6} + A a^{2} b^{7}\right)} d x - {\left(6 \, B a^{8} - 2 \, A a^{7} b - 15 \, B a^{6} b^{2} + 5 \, A a^{5} b^{3} + 12 \, B a^{4} b^{4} - 6 \, A a^{3} b^{5} + {\left(6 \, B a^{6} b^{2} - 2 \, A a^{5} b^{3} - 15 \, B a^{4} b^{4} + 5 \, A a^{3} b^{5} + 12 \, B a^{2} b^{6} - 6 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B a^{7} b - 2 \, A a^{6} b^{2} - 15 \, B a^{5} b^{3} + 5 \, A a^{4} b^{4} + 12 \, B a^{3} b^{5} - 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(6 \, B a^{8} b - 2 \, A a^{7} b^{2} - 17 \, B a^{6} b^{3} + 7 \, A a^{5} b^{4} + 13 \, B a^{4} b^{5} - 5 \, A a^{3} b^{6} - 2 \, B a^{2} b^{7} + 2 \, {\left(B a^{6} b^{3} - 3 \, B a^{4} b^{5} + 3 \, B a^{2} b^{7} - B b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, B a^{7} b^{2} - 3 \, A a^{6} b^{3} - 25 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} + 20 \, B a^{3} b^{6} - 6 \, A a^{2} b^{7} - 4 \, B a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{5} - 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{4} - 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d\right)}}, -\frac{2 \, {\left(3 \, B a^{7} b^{2} - A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 3 \, A a^{4} b^{5} + 9 \, B a^{3} b^{6} - 3 \, A a^{2} b^{7} - 3 \, B a b^{8} + A b^{9}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(3 \, B a^{8} b - A a^{7} b^{2} - 9 \, B a^{6} b^{3} + 3 \, A a^{5} b^{4} + 9 \, B a^{4} b^{5} - 3 \, A a^{3} b^{6} - 3 \, B a^{2} b^{7} + A a b^{8}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(3 \, B a^{9} - A a^{8} b - 9 \, B a^{7} b^{2} + 3 \, A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 3 \, A a^{4} b^{5} - 3 \, B a^{3} b^{6} + A a^{2} b^{7}\right)} d x - {\left(6 \, B a^{8} - 2 \, A a^{7} b - 15 \, B a^{6} b^{2} + 5 \, A a^{5} b^{3} + 12 \, B a^{4} b^{4} - 6 \, A a^{3} b^{5} + {\left(6 \, B a^{6} b^{2} - 2 \, A a^{5} b^{3} - 15 \, B a^{4} b^{4} + 5 \, A a^{3} b^{5} + 12 \, B a^{2} b^{6} - 6 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B a^{7} b - 2 \, A a^{6} b^{2} - 15 \, B a^{5} b^{3} + 5 \, A a^{4} b^{4} + 12 \, B a^{3} b^{5} - 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(6 \, B a^{8} b - 2 \, A a^{7} b^{2} - 17 \, B a^{6} b^{3} + 7 \, A a^{5} b^{4} + 13 \, B a^{4} b^{5} - 5 \, A a^{3} b^{6} - 2 \, B a^{2} b^{7} + 2 \, {\left(B a^{6} b^{3} - 3 \, B a^{4} b^{5} + 3 \, B a^{2} b^{7} - B b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, B a^{7} b^{2} - 3 \, A a^{6} b^{3} - 25 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} + 20 \, B a^{3} b^{6} - 6 \, A a^{2} b^{7} - 4 \, B a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{5} - 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{4} - 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d\right)}}\right]"," ",0,"[-1/4*(4*(3*B*a^7*b^2 - A*a^6*b^3 - 9*B*a^5*b^4 + 3*A*a^4*b^5 + 9*B*a^3*b^6 - 3*A*a^2*b^7 - 3*B*a*b^8 + A*b^9)*d*x*cos(d*x + c)^2 + 8*(3*B*a^8*b - A*a^7*b^2 - 9*B*a^6*b^3 + 3*A*a^5*b^4 + 9*B*a^4*b^5 - 3*A*a^3*b^6 - 3*B*a^2*b^7 + A*a*b^8)*d*x*cos(d*x + c) + 4*(3*B*a^9 - A*a^8*b - 9*B*a^7*b^2 + 3*A*a^6*b^3 + 9*B*a^5*b^4 - 3*A*a^4*b^5 - 3*B*a^3*b^6 + A*a^2*b^7)*d*x - (6*B*a^8 - 2*A*a^7*b - 15*B*a^6*b^2 + 5*A*a^5*b^3 + 12*B*a^4*b^4 - 6*A*a^3*b^5 + (6*B*a^6*b^2 - 2*A*a^5*b^3 - 15*B*a^4*b^4 + 5*A*a^3*b^5 + 12*B*a^2*b^6 - 6*A*a*b^7)*cos(d*x + c)^2 + 2*(6*B*a^7*b - 2*A*a^6*b^2 - 15*B*a^5*b^3 + 5*A*a^4*b^4 + 12*B*a^3*b^5 - 6*A*a^2*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(6*B*a^8*b - 2*A*a^7*b^2 - 17*B*a^6*b^3 + 7*A*a^5*b^4 + 13*B*a^4*b^5 - 5*A*a^3*b^6 - 2*B*a^2*b^7 + 2*(B*a^6*b^3 - 3*B*a^4*b^5 + 3*B*a^2*b^7 - B*b^9)*cos(d*x + c)^2 + (9*B*a^7*b^2 - 3*A*a^6*b^3 - 25*B*a^5*b^4 + 9*A*a^4*b^5 + 20*B*a^3*b^6 - 6*A*a^2*b^7 - 4*B*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12)*d*cos(d*x + c)^2 + 2*(a^7*b^5 - 3*a^5*b^7 + 3*a^3*b^9 - a*b^11)*d*cos(d*x + c) + (a^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10)*d), -1/2*(2*(3*B*a^7*b^2 - A*a^6*b^3 - 9*B*a^5*b^4 + 3*A*a^4*b^5 + 9*B*a^3*b^6 - 3*A*a^2*b^7 - 3*B*a*b^8 + A*b^9)*d*x*cos(d*x + c)^2 + 4*(3*B*a^8*b - A*a^7*b^2 - 9*B*a^6*b^3 + 3*A*a^5*b^4 + 9*B*a^4*b^5 - 3*A*a^3*b^6 - 3*B*a^2*b^7 + A*a*b^8)*d*x*cos(d*x + c) + 2*(3*B*a^9 - A*a^8*b - 9*B*a^7*b^2 + 3*A*a^6*b^3 + 9*B*a^5*b^4 - 3*A*a^4*b^5 - 3*B*a^3*b^6 + A*a^2*b^7)*d*x - (6*B*a^8 - 2*A*a^7*b - 15*B*a^6*b^2 + 5*A*a^5*b^3 + 12*B*a^4*b^4 - 6*A*a^3*b^5 + (6*B*a^6*b^2 - 2*A*a^5*b^3 - 15*B*a^4*b^4 + 5*A*a^3*b^5 + 12*B*a^2*b^6 - 6*A*a*b^7)*cos(d*x + c)^2 + 2*(6*B*a^7*b - 2*A*a^6*b^2 - 15*B*a^5*b^3 + 5*A*a^4*b^4 + 12*B*a^3*b^5 - 6*A*a^2*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*B*a^8*b - 2*A*a^7*b^2 - 17*B*a^6*b^3 + 7*A*a^5*b^4 + 13*B*a^4*b^5 - 5*A*a^3*b^6 - 2*B*a^2*b^7 + 2*(B*a^6*b^3 - 3*B*a^4*b^5 + 3*B*a^2*b^7 - B*b^9)*cos(d*x + c)^2 + (9*B*a^7*b^2 - 3*A*a^6*b^3 - 25*B*a^5*b^4 + 9*A*a^4*b^5 + 20*B*a^3*b^6 - 6*A*a^2*b^7 - 4*B*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12)*d*cos(d*x + c)^2 + 2*(a^7*b^5 - 3*a^5*b^7 + 3*a^3*b^9 - a*b^11)*d*cos(d*x + c) + (a^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10)*d)]","B",0
267,1,1152,0,0.892517," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6}\right)} d x + {\left(2 \, B a^{7} - 5 \, B a^{5} b^{2} - A a^{4} b^{3} + 6 \, B a^{3} b^{4} - 2 \, A a^{2} b^{5} + {\left(2 \, B a^{5} b^{2} - 5 \, B a^{3} b^{4} - A a^{2} b^{5} + 6 \, B a b^{6} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{6} b - 5 \, B a^{4} b^{3} - A a^{3} b^{4} + 6 \, B a^{2} b^{5} - 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(2 \, B a^{7} b - 7 \, B a^{5} b^{3} + 3 \, A a^{4} b^{4} + 5 \, B a^{3} b^{5} - 3 \, A a^{2} b^{6} + {\left(3 \, B a^{6} b^{2} - A a^{5} b^{3} - 9 \, B a^{4} b^{4} + 5 \, A a^{3} b^{5} + 6 \, B a^{2} b^{6} - 4 \, A a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{4} - 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{3} - 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} - a^{2} b^{9}\right)} d\right)}}, \frac{2 \, {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6}\right)} d x - {\left(2 \, B a^{7} - 5 \, B a^{5} b^{2} - A a^{4} b^{3} + 6 \, B a^{3} b^{4} - 2 \, A a^{2} b^{5} + {\left(2 \, B a^{5} b^{2} - 5 \, B a^{3} b^{4} - A a^{2} b^{5} + 6 \, B a b^{6} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{6} b - 5 \, B a^{4} b^{3} - A a^{3} b^{4} + 6 \, B a^{2} b^{5} - 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, B a^{7} b - 7 \, B a^{5} b^{3} + 3 \, A a^{4} b^{4} + 5 \, B a^{3} b^{5} - 3 \, A a^{2} b^{6} + {\left(3 \, B a^{6} b^{2} - A a^{5} b^{3} - 9 \, B a^{4} b^{4} + 5 \, A a^{3} b^{5} + 6 \, B a^{2} b^{6} - 4 \, A a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{4} - 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{3} - 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} - a^{2} b^{9}\right)} d\right)}}\right]"," ",0,"[1/4*(4*(B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8)*d*x*cos(d*x + c)^2 + 8*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*d*x*cos(d*x + c) + 4*(B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6)*d*x + (2*B*a^7 - 5*B*a^5*b^2 - A*a^4*b^3 + 6*B*a^3*b^4 - 2*A*a^2*b^5 + (2*B*a^5*b^2 - 5*B*a^3*b^4 - A*a^2*b^5 + 6*B*a*b^6 - 2*A*b^7)*cos(d*x + c)^2 + 2*(2*B*a^6*b - 5*B*a^4*b^3 - A*a^3*b^4 + 6*B*a^2*b^5 - 2*A*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(2*B*a^7*b - 7*B*a^5*b^3 + 3*A*a^4*b^4 + 5*B*a^3*b^5 - 3*A*a^2*b^6 + (3*B*a^6*b^2 - A*a^5*b^3 - 9*B*a^4*b^4 + 5*A*a^3*b^5 + 6*B*a^2*b^6 - 4*A*a*b^7)*cos(d*x + c))*sin(d*x + c))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*d*cos(d*x + c)^2 + 2*(a^7*b^4 - 3*a^5*b^6 + 3*a^3*b^8 - a*b^10)*d*cos(d*x + c) + (a^8*b^3 - 3*a^6*b^5 + 3*a^4*b^7 - a^2*b^9)*d), 1/2*(2*(B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8)*d*x*cos(d*x + c)^2 + 4*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*d*x*cos(d*x + c) + 2*(B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6)*d*x - (2*B*a^7 - 5*B*a^5*b^2 - A*a^4*b^3 + 6*B*a^3*b^4 - 2*A*a^2*b^5 + (2*B*a^5*b^2 - 5*B*a^3*b^4 - A*a^2*b^5 + 6*B*a*b^6 - 2*A*b^7)*cos(d*x + c)^2 + 2*(2*B*a^6*b - 5*B*a^4*b^3 - A*a^3*b^4 + 6*B*a^2*b^5 - 2*A*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*B*a^7*b - 7*B*a^5*b^3 + 3*A*a^4*b^4 + 5*B*a^3*b^5 - 3*A*a^2*b^6 + (3*B*a^6*b^2 - A*a^5*b^3 - 9*B*a^4*b^4 + 5*A*a^3*b^5 + 6*B*a^2*b^6 - 4*A*a*b^7)*cos(d*x + c))*sin(d*x + c))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*d*cos(d*x + c)^2 + 2*(a^7*b^4 - 3*a^5*b^6 + 3*a^3*b^8 - a*b^10)*d*cos(d*x + c) + (a^8*b^3 - 3*a^6*b^5 + 3*a^4*b^7 - a^2*b^9)*d)]","B",0
268,1,740,0,0.775352," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{4} - 3 \, A a^{3} b + 2 \, B a^{2} b^{2} + {\left(B a^{2} b^{2} - 3 \, A a b^{3} + 2 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2} + 2 \, B a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(2 \, A a^{5} - 3 \, B a^{4} b - A a^{3} b^{2} + 3 \, B a^{2} b^{3} - A a b^{4} + {\left(B a^{5} + A a^{4} b - 5 \, B a^{3} b^{2} + A a^{2} b^{3} + 4 \, B a b^{4} - 2 \, A b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}, \frac{{\left(B a^{4} - 3 \, A a^{3} b + 2 \, B a^{2} b^{2} + {\left(B a^{2} b^{2} - 3 \, A a b^{3} + 2 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2} + 2 \, B a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(2 \, A a^{5} - 3 \, B a^{4} b - A a^{3} b^{2} + 3 \, B a^{2} b^{3} - A a b^{4} + {\left(B a^{5} + A a^{4} b - 5 \, B a^{3} b^{2} + A a^{2} b^{3} + 4 \, B a b^{4} - 2 \, A b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}\right]"," ",0,"[-1/4*((B*a^4 - 3*A*a^3*b + 2*B*a^2*b^2 + (B*a^2*b^2 - 3*A*a*b^3 + 2*B*b^4)*cos(d*x + c)^2 + 2*(B*a^3*b - 3*A*a^2*b^2 + 2*B*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(2*A*a^5 - 3*B*a^4*b - A*a^3*b^2 + 3*B*a^2*b^3 - A*a*b^4 + (B*a^5 + A*a^4*b - 5*B*a^3*b^2 + A*a^2*b^3 + 4*B*a*b^4 - 2*A*b^5)*cos(d*x + c))*sin(d*x + c))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*cos(d*x + c) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d), 1/2*((B*a^4 - 3*A*a^3*b + 2*B*a^2*b^2 + (B*a^2*b^2 - 3*A*a*b^3 + 2*B*b^4)*cos(d*x + c)^2 + 2*(B*a^3*b - 3*A*a^2*b^2 + 2*B*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (2*A*a^5 - 3*B*a^4*b - A*a^3*b^2 + 3*B*a^2*b^3 - A*a*b^4 + (B*a^5 + A*a^4*b - 5*B*a^3*b^2 + A*a^2*b^3 + 4*B*a*b^4 - 2*A*b^5)*cos(d*x + c))*sin(d*x + c))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*cos(d*x + c) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d)]","B",0
269,1,742,0,0.676387," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, A a^{4} - 3 \, B a^{3} b + A a^{2} b^{2} + {\left(2 \, A a^{2} b^{2} - 3 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A a^{3} b - 3 \, B a^{2} b^{2} + A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(2 \, B a^{5} - 4 \, A a^{4} b - B a^{3} b^{2} + 5 \, A a^{2} b^{3} - B a b^{4} - A b^{5} + {\left(B a^{4} b - 3 \, A a^{3} b^{2} + B a^{2} b^{3} + 3 \, A a b^{4} - 2 \, B b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}, \frac{{\left(2 \, A a^{4} - 3 \, B a^{3} b + A a^{2} b^{2} + {\left(2 \, A a^{2} b^{2} - 3 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A a^{3} b - 3 \, B a^{2} b^{2} + A a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(2 \, B a^{5} - 4 \, A a^{4} b - B a^{3} b^{2} + 5 \, A a^{2} b^{3} - B a b^{4} - A b^{5} + {\left(B a^{4} b - 3 \, A a^{3} b^{2} + B a^{2} b^{3} + 3 \, A a b^{4} - 2 \, B b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}\right]"," ",0,"[-1/4*((2*A*a^4 - 3*B*a^3*b + A*a^2*b^2 + (2*A*a^2*b^2 - 3*B*a*b^3 + A*b^4)*cos(d*x + c)^2 + 2*(2*A*a^3*b - 3*B*a^2*b^2 + A*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(2*B*a^5 - 4*A*a^4*b - B*a^3*b^2 + 5*A*a^2*b^3 - B*a*b^4 - A*b^5 + (B*a^4*b - 3*A*a^3*b^2 + B*a^2*b^3 + 3*A*a*b^4 - 2*B*b^5)*cos(d*x + c))*sin(d*x + c))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*cos(d*x + c) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d), 1/2*((2*A*a^4 - 3*B*a^3*b + A*a^2*b^2 + (2*A*a^2*b^2 - 3*B*a*b^3 + A*b^4)*cos(d*x + c)^2 + 2*(2*A*a^3*b - 3*B*a^2*b^2 + A*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (2*B*a^5 - 4*A*a^4*b - B*a^3*b^2 + 5*A*a^2*b^3 - B*a*b^4 - A*b^5 + (B*a^4*b - 3*A*a^3*b^2 + B*a^2*b^3 + 3*A*a*b^4 - 2*B*b^5)*cos(d*x + c))*sin(d*x + c))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*cos(d*x + c) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d)]","B",0
270,1,1400,0,37.506110," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a^{7} - 6 \, A a^{6} b + B a^{5} b^{2} + 5 \, A a^{4} b^{3} - 2 \, A a^{2} b^{5} + {\left(2 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} + B a^{3} b^{4} + 5 \, A a^{2} b^{5} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{6} b - 6 \, A a^{5} b^{2} + B a^{4} b^{3} + 5 \, A a^{3} b^{4} - 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 2 \, {\left(A a^{8} - 3 \, A a^{6} b^{2} + 3 \, A a^{4} b^{4} - A a^{2} b^{6} + {\left(A a^{6} b^{2} - 3 \, A a^{4} b^{4} + 3 \, A a^{2} b^{6} - A b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A a^{7} b - 3 \, A a^{5} b^{3} + 3 \, A a^{3} b^{5} - A a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A a^{8} - 3 \, A a^{6} b^{2} + 3 \, A a^{4} b^{4} - A a^{2} b^{6} + {\left(A a^{6} b^{2} - 3 \, A a^{4} b^{4} + 3 \, A a^{2} b^{6} - A b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A a^{7} b - 3 \, A a^{5} b^{3} + 3 \, A a^{3} b^{5} - A a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, B a^{7} b - 6 \, A a^{6} b^{2} - 5 \, B a^{5} b^{3} + 9 \, A a^{4} b^{4} + B a^{3} b^{5} - 3 \, A a^{2} b^{6} + {\left(3 \, B a^{6} b^{2} - 5 \, A a^{5} b^{3} - 3 \, B a^{4} b^{4} + 7 \, A a^{3} b^{5} - 2 \, A a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{9} b^{2} - 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} - a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d\right)}}, \frac{{\left(2 \, B a^{7} - 6 \, A a^{6} b + B a^{5} b^{2} + 5 \, A a^{4} b^{3} - 2 \, A a^{2} b^{5} + {\left(2 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} + B a^{3} b^{4} + 5 \, A a^{2} b^{5} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{6} b - 6 \, A a^{5} b^{2} + B a^{4} b^{3} + 5 \, A a^{3} b^{4} - 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(A a^{8} - 3 \, A a^{6} b^{2} + 3 \, A a^{4} b^{4} - A a^{2} b^{6} + {\left(A a^{6} b^{2} - 3 \, A a^{4} b^{4} + 3 \, A a^{2} b^{6} - A b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A a^{7} b - 3 \, A a^{5} b^{3} + 3 \, A a^{3} b^{5} - A a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{8} - 3 \, A a^{6} b^{2} + 3 \, A a^{4} b^{4} - A a^{2} b^{6} + {\left(A a^{6} b^{2} - 3 \, A a^{4} b^{4} + 3 \, A a^{2} b^{6} - A b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A a^{7} b - 3 \, A a^{5} b^{3} + 3 \, A a^{3} b^{5} - A a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(4 \, B a^{7} b - 6 \, A a^{6} b^{2} - 5 \, B a^{5} b^{3} + 9 \, A a^{4} b^{4} + B a^{3} b^{5} - 3 \, A a^{2} b^{6} + {\left(3 \, B a^{6} b^{2} - 5 \, A a^{5} b^{3} - 3 \, B a^{4} b^{4} + 7 \, A a^{3} b^{5} - 2 \, A a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{9} b^{2} - 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} - a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d\right)}}\right]"," ",0,"[1/4*((2*B*a^7 - 6*A*a^6*b + B*a^5*b^2 + 5*A*a^4*b^3 - 2*A*a^2*b^5 + (2*B*a^5*b^2 - 6*A*a^4*b^3 + B*a^3*b^4 + 5*A*a^2*b^5 - 2*A*b^7)*cos(d*x + c)^2 + 2*(2*B*a^6*b - 6*A*a^5*b^2 + B*a^4*b^3 + 5*A*a^3*b^4 - 2*A*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 2*(A*a^8 - 3*A*a^6*b^2 + 3*A*a^4*b^4 - A*a^2*b^6 + (A*a^6*b^2 - 3*A*a^4*b^4 + 3*A*a^2*b^6 - A*b^8)*cos(d*x + c)^2 + 2*(A*a^7*b - 3*A*a^5*b^3 + 3*A*a^3*b^5 - A*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) - 2*(A*a^8 - 3*A*a^6*b^2 + 3*A*a^4*b^4 - A*a^2*b^6 + (A*a^6*b^2 - 3*A*a^4*b^4 + 3*A*a^2*b^6 - A*b^8)*cos(d*x + c)^2 + 2*(A*a^7*b - 3*A*a^5*b^3 + 3*A*a^3*b^5 - A*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(4*B*a^7*b - 6*A*a^6*b^2 - 5*B*a^5*b^3 + 9*A*a^4*b^4 + B*a^3*b^5 - 3*A*a^2*b^6 + (3*B*a^6*b^2 - 5*A*a^5*b^3 - 3*B*a^4*b^4 + 7*A*a^3*b^5 - 2*A*a*b^7)*cos(d*x + c))*sin(d*x + c))/((a^9*b^2 - 3*a^7*b^4 + 3*a^5*b^6 - a^3*b^8)*d*cos(d*x + c)^2 + 2*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cos(d*x + c) + (a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d), 1/2*((2*B*a^7 - 6*A*a^6*b + B*a^5*b^2 + 5*A*a^4*b^3 - 2*A*a^2*b^5 + (2*B*a^5*b^2 - 6*A*a^4*b^3 + B*a^3*b^4 + 5*A*a^2*b^5 - 2*A*b^7)*cos(d*x + c)^2 + 2*(2*B*a^6*b - 6*A*a^5*b^2 + B*a^4*b^3 + 5*A*a^3*b^4 - 2*A*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (A*a^8 - 3*A*a^6*b^2 + 3*A*a^4*b^4 - A*a^2*b^6 + (A*a^6*b^2 - 3*A*a^4*b^4 + 3*A*a^2*b^6 - A*b^8)*cos(d*x + c)^2 + 2*(A*a^7*b - 3*A*a^5*b^3 + 3*A*a^3*b^5 - A*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) - (A*a^8 - 3*A*a^6*b^2 + 3*A*a^4*b^4 - A*a^2*b^6 + (A*a^6*b^2 - 3*A*a^4*b^4 + 3*A*a^2*b^6 - A*b^8)*cos(d*x + c)^2 + 2*(A*a^7*b - 3*A*a^5*b^3 + 3*A*a^3*b^5 - A*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) - (4*B*a^7*b - 6*A*a^6*b^2 - 5*B*a^5*b^3 + 9*A*a^4*b^4 + B*a^3*b^5 - 3*A*a^2*b^6 + (3*B*a^6*b^2 - 5*A*a^5*b^3 - 3*B*a^4*b^4 + 7*A*a^3*b^5 - 2*A*a*b^7)*cos(d*x + c))*sin(d*x + c))/((a^9*b^2 - 3*a^7*b^4 + 3*a^5*b^6 - a^3*b^8)*d*cos(d*x + c)^2 + 2*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cos(d*x + c) + (a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d)]","B",0
271,1,2100,0,76.797416," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(6 \, B a^{5} b^{3} - 12 \, A a^{4} b^{4} - 5 \, B a^{3} b^{5} + 15 \, A a^{2} b^{6} + 2 \, B a b^{7} - 6 \, A b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, B a^{6} b^{2} - 12 \, A a^{5} b^{3} - 5 \, B a^{4} b^{4} + 15 \, A a^{3} b^{5} + 2 \, B a^{2} b^{6} - 6 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, B a^{7} b - 12 \, A a^{6} b^{2} - 5 \, B a^{5} b^{3} + 15 \, A a^{4} b^{4} + 2 \, B a^{3} b^{5} - 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 2 \, {\left({\left(B a^{7} b^{2} - 3 \, A a^{6} b^{3} - 3 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} - B a b^{8} + 3 \, A b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(B a^{8} b - 3 \, A a^{7} b^{2} - 3 \, B a^{6} b^{3} + 9 \, A a^{5} b^{4} + 3 \, B a^{4} b^{5} - 9 \, A a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{9} - 3 \, A a^{8} b - 3 \, B a^{7} b^{2} + 9 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} - B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(B a^{7} b^{2} - 3 \, A a^{6} b^{3} - 3 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} - B a b^{8} + 3 \, A b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(B a^{8} b - 3 \, A a^{7} b^{2} - 3 \, B a^{6} b^{3} + 9 \, A a^{5} b^{4} + 3 \, B a^{4} b^{5} - 9 \, A a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{9} - 3 \, A a^{8} b - 3 \, B a^{7} b^{2} + 9 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} - B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{9} - 6 \, A a^{7} b^{2} + 6 \, A a^{5} b^{4} - 2 \, A a^{3} b^{6} + {\left(2 \, A a^{7} b^{2} + 5 \, B a^{6} b^{3} - 13 \, A a^{5} b^{4} - 7 \, B a^{4} b^{5} + 17 \, A a^{3} b^{6} + 2 \, B a^{2} b^{7} - 6 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A a^{8} b + 6 \, B a^{7} b^{2} - 20 \, A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 25 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{10} b^{2} - 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} - a^{4} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{11} b - 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} - a^{5} b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{{\left({\left(6 \, B a^{5} b^{3} - 12 \, A a^{4} b^{4} - 5 \, B a^{3} b^{5} + 15 \, A a^{2} b^{6} + 2 \, B a b^{7} - 6 \, A b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, B a^{6} b^{2} - 12 \, A a^{5} b^{3} - 5 \, B a^{4} b^{4} + 15 \, A a^{3} b^{5} + 2 \, B a^{2} b^{6} - 6 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, B a^{7} b - 12 \, A a^{6} b^{2} - 5 \, B a^{5} b^{3} + 15 \, A a^{4} b^{4} + 2 \, B a^{3} b^{5} - 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left({\left(B a^{7} b^{2} - 3 \, A a^{6} b^{3} - 3 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} - B a b^{8} + 3 \, A b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(B a^{8} b - 3 \, A a^{7} b^{2} - 3 \, B a^{6} b^{3} + 9 \, A a^{5} b^{4} + 3 \, B a^{4} b^{5} - 9 \, A a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{9} - 3 \, A a^{8} b - 3 \, B a^{7} b^{2} + 9 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} - B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(B a^{7} b^{2} - 3 \, A a^{6} b^{3} - 3 \, B a^{5} b^{4} + 9 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} - B a b^{8} + 3 \, A b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(B a^{8} b - 3 \, A a^{7} b^{2} - 3 \, B a^{6} b^{3} + 9 \, A a^{5} b^{4} + 3 \, B a^{4} b^{5} - 9 \, A a^{3} b^{6} - B a^{2} b^{7} + 3 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{9} - 3 \, A a^{8} b - 3 \, B a^{7} b^{2} + 9 \, A a^{6} b^{3} + 3 \, B a^{5} b^{4} - 9 \, A a^{4} b^{5} - B a^{3} b^{6} + 3 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(2 \, A a^{9} - 6 \, A a^{7} b^{2} + 6 \, A a^{5} b^{4} - 2 \, A a^{3} b^{6} + {\left(2 \, A a^{7} b^{2} + 5 \, B a^{6} b^{3} - 13 \, A a^{5} b^{4} - 7 \, B a^{4} b^{5} + 17 \, A a^{3} b^{6} + 2 \, B a^{2} b^{7} - 6 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A a^{8} b + 6 \, B a^{7} b^{2} - 20 \, A a^{6} b^{3} - 9 \, B a^{5} b^{4} + 25 \, A a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{10} b^{2} - 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} - a^{4} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{11} b - 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} - a^{5} b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(((6*B*a^5*b^3 - 12*A*a^4*b^4 - 5*B*a^3*b^5 + 15*A*a^2*b^6 + 2*B*a*b^7 - 6*A*b^8)*cos(d*x + c)^3 + 2*(6*B*a^6*b^2 - 12*A*a^5*b^3 - 5*B*a^4*b^4 + 15*A*a^3*b^5 + 2*B*a^2*b^6 - 6*A*a*b^7)*cos(d*x + c)^2 + (6*B*a^7*b - 12*A*a^6*b^2 - 5*B*a^5*b^3 + 15*A*a^4*b^4 + 2*B*a^3*b^5 - 6*A*a^2*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 2*((B*a^7*b^2 - 3*A*a^6*b^3 - 3*B*a^5*b^4 + 9*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7 - B*a*b^8 + 3*A*b^9)*cos(d*x + c)^3 + 2*(B*a^8*b - 3*A*a^7*b^2 - 3*B*a^6*b^3 + 9*A*a^5*b^4 + 3*B*a^4*b^5 - 9*A*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8)*cos(d*x + c)^2 + (B*a^9 - 3*A*a^8*b - 3*B*a^7*b^2 + 9*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 - B*a^3*b^6 + 3*A*a^2*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) - 2*((B*a^7*b^2 - 3*A*a^6*b^3 - 3*B*a^5*b^4 + 9*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7 - B*a*b^8 + 3*A*b^9)*cos(d*x + c)^3 + 2*(B*a^8*b - 3*A*a^7*b^2 - 3*B*a^6*b^3 + 9*A*a^5*b^4 + 3*B*a^4*b^5 - 9*A*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8)*cos(d*x + c)^2 + (B*a^9 - 3*A*a^8*b - 3*B*a^7*b^2 + 9*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 - B*a^3*b^6 + 3*A*a^2*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(2*A*a^9 - 6*A*a^7*b^2 + 6*A*a^5*b^4 - 2*A*a^3*b^6 + (2*A*a^7*b^2 + 5*B*a^6*b^3 - 13*A*a^5*b^4 - 7*B*a^4*b^5 + 17*A*a^3*b^6 + 2*B*a^2*b^7 - 6*A*a*b^8)*cos(d*x + c)^2 + (4*A*a^8*b + 6*B*a^7*b^2 - 20*A*a^6*b^3 - 9*B*a^5*b^4 + 25*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^10*b^2 - 3*a^8*b^4 + 3*a^6*b^6 - a^4*b^8)*d*cos(d*x + c)^3 + 2*(a^11*b - 3*a^9*b^3 + 3*a^7*b^5 - a^5*b^7)*d*cos(d*x + c)^2 + (a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*d*cos(d*x + c)), -1/2*(((6*B*a^5*b^3 - 12*A*a^4*b^4 - 5*B*a^3*b^5 + 15*A*a^2*b^6 + 2*B*a*b^7 - 6*A*b^8)*cos(d*x + c)^3 + 2*(6*B*a^6*b^2 - 12*A*a^5*b^3 - 5*B*a^4*b^4 + 15*A*a^3*b^5 + 2*B*a^2*b^6 - 6*A*a*b^7)*cos(d*x + c)^2 + (6*B*a^7*b - 12*A*a^6*b^2 - 5*B*a^5*b^3 + 15*A*a^4*b^4 + 2*B*a^3*b^5 - 6*A*a^2*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - ((B*a^7*b^2 - 3*A*a^6*b^3 - 3*B*a^5*b^4 + 9*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7 - B*a*b^8 + 3*A*b^9)*cos(d*x + c)^3 + 2*(B*a^8*b - 3*A*a^7*b^2 - 3*B*a^6*b^3 + 9*A*a^5*b^4 + 3*B*a^4*b^5 - 9*A*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8)*cos(d*x + c)^2 + (B*a^9 - 3*A*a^8*b - 3*B*a^7*b^2 + 9*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 - B*a^3*b^6 + 3*A*a^2*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((B*a^7*b^2 - 3*A*a^6*b^3 - 3*B*a^5*b^4 + 9*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7 - B*a*b^8 + 3*A*b^9)*cos(d*x + c)^3 + 2*(B*a^8*b - 3*A*a^7*b^2 - 3*B*a^6*b^3 + 9*A*a^5*b^4 + 3*B*a^4*b^5 - 9*A*a^3*b^6 - B*a^2*b^7 + 3*A*a*b^8)*cos(d*x + c)^2 + (B*a^9 - 3*A*a^8*b - 3*B*a^7*b^2 + 9*A*a^6*b^3 + 3*B*a^5*b^4 - 9*A*a^4*b^5 - B*a^3*b^6 + 3*A*a^2*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) - (2*A*a^9 - 6*A*a^7*b^2 + 6*A*a^5*b^4 - 2*A*a^3*b^6 + (2*A*a^7*b^2 + 5*B*a^6*b^3 - 13*A*a^5*b^4 - 7*B*a^4*b^5 + 17*A*a^3*b^6 + 2*B*a^2*b^7 - 6*A*a*b^8)*cos(d*x + c)^2 + (4*A*a^8*b + 6*B*a^7*b^2 - 20*A*a^6*b^3 - 9*B*a^5*b^4 + 25*A*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^10*b^2 - 3*a^8*b^4 + 3*a^6*b^6 - a^4*b^8)*d*cos(d*x + c)^3 + 2*(a^11*b - 3*a^9*b^3 + 3*a^7*b^5 - a^5*b^7)*d*cos(d*x + c)^2 + (a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*d*cos(d*x + c))]","B",0
272,1,2416,0,121.638218," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(12 \, B a^{5} b^{4} - 20 \, A a^{4} b^{5} - 15 \, B a^{3} b^{6} + 29 \, A a^{2} b^{7} + 6 \, B a b^{8} - 12 \, A b^{9}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, B a^{6} b^{3} - 20 \, A a^{5} b^{4} - 15 \, B a^{4} b^{5} + 29 \, A a^{3} b^{6} + 6 \, B a^{2} b^{7} - 12 \, A a b^{8}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, B a^{7} b^{2} - 20 \, A a^{6} b^{3} - 15 \, B a^{5} b^{4} + 29 \, A a^{4} b^{5} + 6 \, B a^{3} b^{6} - 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + {\left({\left(A a^{8} b^{2} - 6 \, B a^{7} b^{3} + 9 \, A a^{6} b^{4} + 18 \, B a^{5} b^{5} - 33 \, A a^{4} b^{6} - 18 \, B a^{3} b^{7} + 35 \, A a^{2} b^{8} + 6 \, B a b^{9} - 12 \, A b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(A a^{9} b - 6 \, B a^{8} b^{2} + 9 \, A a^{7} b^{3} + 18 \, B a^{6} b^{4} - 33 \, A a^{5} b^{5} - 18 \, B a^{4} b^{6} + 35 \, A a^{3} b^{7} + 6 \, B a^{2} b^{8} - 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(A a^{10} - 6 \, B a^{9} b + 9 \, A a^{8} b^{2} + 18 \, B a^{7} b^{3} - 33 \, A a^{6} b^{4} - 18 \, B a^{5} b^{5} + 35 \, A a^{4} b^{6} + 6 \, B a^{3} b^{7} - 12 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A a^{8} b^{2} - 6 \, B a^{7} b^{3} + 9 \, A a^{6} b^{4} + 18 \, B a^{5} b^{5} - 33 \, A a^{4} b^{6} - 18 \, B a^{3} b^{7} + 35 \, A a^{2} b^{8} + 6 \, B a b^{9} - 12 \, A b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(A a^{9} b - 6 \, B a^{8} b^{2} + 9 \, A a^{7} b^{3} + 18 \, B a^{6} b^{4} - 33 \, A a^{5} b^{5} - 18 \, B a^{4} b^{6} + 35 \, A a^{3} b^{7} + 6 \, B a^{2} b^{8} - 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(A a^{10} - 6 \, B a^{9} b + 9 \, A a^{8} b^{2} + 18 \, B a^{7} b^{3} - 33 \, A a^{6} b^{4} - 18 \, B a^{5} b^{5} + 35 \, A a^{4} b^{6} + 6 \, B a^{3} b^{7} - 12 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{10} - 3 \, A a^{8} b^{2} + 3 \, A a^{6} b^{4} - A a^{4} b^{6} + {\left(2 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} - 13 \, B a^{6} b^{4} + 27 \, A a^{5} b^{5} + 17 \, B a^{4} b^{6} - 33 \, A a^{3} b^{7} - 6 \, B a^{2} b^{8} + 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, B a^{9} b - 11 \, A a^{8} b^{2} - 20 \, B a^{7} b^{3} + 43 \, A a^{6} b^{4} + 25 \, B a^{5} b^{5} - 50 \, A a^{4} b^{6} - 9 \, B a^{3} b^{7} + 18 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{10} - 2 \, A a^{9} b - 3 \, B a^{8} b^{2} + 6 \, A a^{7} b^{3} + 3 \, B a^{6} b^{4} - 6 \, A a^{5} b^{5} - B a^{4} b^{6} + 2 \, A a^{3} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{11} b^{2} - 3 \, a^{9} b^{4} + 3 \, a^{7} b^{6} - a^{5} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{12} b - 3 \, a^{10} b^{3} + 3 \, a^{8} b^{5} - a^{6} b^{7}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{13} - 3 \, a^{11} b^{2} + 3 \, a^{9} b^{4} - a^{7} b^{6}\right)} d \cos\left(d x + c\right)^{2}\right)}}, \frac{2 \, {\left({\left(12 \, B a^{5} b^{4} - 20 \, A a^{4} b^{5} - 15 \, B a^{3} b^{6} + 29 \, A a^{2} b^{7} + 6 \, B a b^{8} - 12 \, A b^{9}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(12 \, B a^{6} b^{3} - 20 \, A a^{5} b^{4} - 15 \, B a^{4} b^{5} + 29 \, A a^{3} b^{6} + 6 \, B a^{2} b^{7} - 12 \, A a b^{8}\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, B a^{7} b^{2} - 20 \, A a^{6} b^{3} - 15 \, B a^{5} b^{4} + 29 \, A a^{4} b^{5} + 6 \, B a^{3} b^{6} - 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left({\left(A a^{8} b^{2} - 6 \, B a^{7} b^{3} + 9 \, A a^{6} b^{4} + 18 \, B a^{5} b^{5} - 33 \, A a^{4} b^{6} - 18 \, B a^{3} b^{7} + 35 \, A a^{2} b^{8} + 6 \, B a b^{9} - 12 \, A b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(A a^{9} b - 6 \, B a^{8} b^{2} + 9 \, A a^{7} b^{3} + 18 \, B a^{6} b^{4} - 33 \, A a^{5} b^{5} - 18 \, B a^{4} b^{6} + 35 \, A a^{3} b^{7} + 6 \, B a^{2} b^{8} - 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(A a^{10} - 6 \, B a^{9} b + 9 \, A a^{8} b^{2} + 18 \, B a^{7} b^{3} - 33 \, A a^{6} b^{4} - 18 \, B a^{5} b^{5} + 35 \, A a^{4} b^{6} + 6 \, B a^{3} b^{7} - 12 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A a^{8} b^{2} - 6 \, B a^{7} b^{3} + 9 \, A a^{6} b^{4} + 18 \, B a^{5} b^{5} - 33 \, A a^{4} b^{6} - 18 \, B a^{3} b^{7} + 35 \, A a^{2} b^{8} + 6 \, B a b^{9} - 12 \, A b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(A a^{9} b - 6 \, B a^{8} b^{2} + 9 \, A a^{7} b^{3} + 18 \, B a^{6} b^{4} - 33 \, A a^{5} b^{5} - 18 \, B a^{4} b^{6} + 35 \, A a^{3} b^{7} + 6 \, B a^{2} b^{8} - 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(A a^{10} - 6 \, B a^{9} b + 9 \, A a^{8} b^{2} + 18 \, B a^{7} b^{3} - 33 \, A a^{6} b^{4} - 18 \, B a^{5} b^{5} + 35 \, A a^{4} b^{6} + 6 \, B a^{3} b^{7} - 12 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{10} - 3 \, A a^{8} b^{2} + 3 \, A a^{6} b^{4} - A a^{4} b^{6} + {\left(2 \, B a^{8} b^{2} - 6 \, A a^{7} b^{3} - 13 \, B a^{6} b^{4} + 27 \, A a^{5} b^{5} + 17 \, B a^{4} b^{6} - 33 \, A a^{3} b^{7} - 6 \, B a^{2} b^{8} + 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, B a^{9} b - 11 \, A a^{8} b^{2} - 20 \, B a^{7} b^{3} + 43 \, A a^{6} b^{4} + 25 \, B a^{5} b^{5} - 50 \, A a^{4} b^{6} - 9 \, B a^{3} b^{7} + 18 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{10} - 2 \, A a^{9} b - 3 \, B a^{8} b^{2} + 6 \, A a^{7} b^{3} + 3 \, B a^{6} b^{4} - 6 \, A a^{5} b^{5} - B a^{4} b^{6} + 2 \, A a^{3} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{11} b^{2} - 3 \, a^{9} b^{4} + 3 \, a^{7} b^{6} - a^{5} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{12} b - 3 \, a^{10} b^{3} + 3 \, a^{8} b^{5} - a^{6} b^{7}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{13} - 3 \, a^{11} b^{2} + 3 \, a^{9} b^{4} - a^{7} b^{6}\right)} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/4*(((12*B*a^5*b^4 - 20*A*a^4*b^5 - 15*B*a^3*b^6 + 29*A*a^2*b^7 + 6*B*a*b^8 - 12*A*b^9)*cos(d*x + c)^4 + 2*(12*B*a^6*b^3 - 20*A*a^5*b^4 - 15*B*a^4*b^5 + 29*A*a^3*b^6 + 6*B*a^2*b^7 - 12*A*a*b^8)*cos(d*x + c)^3 + (12*B*a^7*b^2 - 20*A*a^6*b^3 - 15*B*a^5*b^4 + 29*A*a^4*b^5 + 6*B*a^3*b^6 - 12*A*a^2*b^7)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + ((A*a^8*b^2 - 6*B*a^7*b^3 + 9*A*a^6*b^4 + 18*B*a^5*b^5 - 33*A*a^4*b^6 - 18*B*a^3*b^7 + 35*A*a^2*b^8 + 6*B*a*b^9 - 12*A*b^10)*cos(d*x + c)^4 + 2*(A*a^9*b - 6*B*a^8*b^2 + 9*A*a^7*b^3 + 18*B*a^6*b^4 - 33*A*a^5*b^5 - 18*B*a^4*b^6 + 35*A*a^3*b^7 + 6*B*a^2*b^8 - 12*A*a*b^9)*cos(d*x + c)^3 + (A*a^10 - 6*B*a^9*b + 9*A*a^8*b^2 + 18*B*a^7*b^3 - 33*A*a^6*b^4 - 18*B*a^5*b^5 + 35*A*a^4*b^6 + 6*B*a^3*b^7 - 12*A*a^2*b^8)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((A*a^8*b^2 - 6*B*a^7*b^3 + 9*A*a^6*b^4 + 18*B*a^5*b^5 - 33*A*a^4*b^6 - 18*B*a^3*b^7 + 35*A*a^2*b^8 + 6*B*a*b^9 - 12*A*b^10)*cos(d*x + c)^4 + 2*(A*a^9*b - 6*B*a^8*b^2 + 9*A*a^7*b^3 + 18*B*a^6*b^4 - 33*A*a^5*b^5 - 18*B*a^4*b^6 + 35*A*a^3*b^7 + 6*B*a^2*b^8 - 12*A*a*b^9)*cos(d*x + c)^3 + (A*a^10 - 6*B*a^9*b + 9*A*a^8*b^2 + 18*B*a^7*b^3 - 33*A*a^6*b^4 - 18*B*a^5*b^5 + 35*A*a^4*b^6 + 6*B*a^3*b^7 - 12*A*a^2*b^8)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(A*a^10 - 3*A*a^8*b^2 + 3*A*a^6*b^4 - A*a^4*b^6 + (2*B*a^8*b^2 - 6*A*a^7*b^3 - 13*B*a^6*b^4 + 27*A*a^5*b^5 + 17*B*a^4*b^6 - 33*A*a^3*b^7 - 6*B*a^2*b^8 + 12*A*a*b^9)*cos(d*x + c)^3 + (4*B*a^9*b - 11*A*a^8*b^2 - 20*B*a^7*b^3 + 43*A*a^6*b^4 + 25*B*a^5*b^5 - 50*A*a^4*b^6 - 9*B*a^3*b^7 + 18*A*a^2*b^8)*cos(d*x + c)^2 + 2*(B*a^10 - 2*A*a^9*b - 3*B*a^8*b^2 + 6*A*a^7*b^3 + 3*B*a^6*b^4 - 6*A*a^5*b^5 - B*a^4*b^6 + 2*A*a^3*b^7)*cos(d*x + c))*sin(d*x + c))/((a^11*b^2 - 3*a^9*b^4 + 3*a^7*b^6 - a^5*b^8)*d*cos(d*x + c)^4 + 2*(a^12*b - 3*a^10*b^3 + 3*a^8*b^5 - a^6*b^7)*d*cos(d*x + c)^3 + (a^13 - 3*a^11*b^2 + 3*a^9*b^4 - a^7*b^6)*d*cos(d*x + c)^2), 1/4*(2*((12*B*a^5*b^4 - 20*A*a^4*b^5 - 15*B*a^3*b^6 + 29*A*a^2*b^7 + 6*B*a*b^8 - 12*A*b^9)*cos(d*x + c)^4 + 2*(12*B*a^6*b^3 - 20*A*a^5*b^4 - 15*B*a^4*b^5 + 29*A*a^3*b^6 + 6*B*a^2*b^7 - 12*A*a*b^8)*cos(d*x + c)^3 + (12*B*a^7*b^2 - 20*A*a^6*b^3 - 15*B*a^5*b^4 + 29*A*a^4*b^5 + 6*B*a^3*b^6 - 12*A*a^2*b^7)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + ((A*a^8*b^2 - 6*B*a^7*b^3 + 9*A*a^6*b^4 + 18*B*a^5*b^5 - 33*A*a^4*b^6 - 18*B*a^3*b^7 + 35*A*a^2*b^8 + 6*B*a*b^9 - 12*A*b^10)*cos(d*x + c)^4 + 2*(A*a^9*b - 6*B*a^8*b^2 + 9*A*a^7*b^3 + 18*B*a^6*b^4 - 33*A*a^5*b^5 - 18*B*a^4*b^6 + 35*A*a^3*b^7 + 6*B*a^2*b^8 - 12*A*a*b^9)*cos(d*x + c)^3 + (A*a^10 - 6*B*a^9*b + 9*A*a^8*b^2 + 18*B*a^7*b^3 - 33*A*a^6*b^4 - 18*B*a^5*b^5 + 35*A*a^4*b^6 + 6*B*a^3*b^7 - 12*A*a^2*b^8)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((A*a^8*b^2 - 6*B*a^7*b^3 + 9*A*a^6*b^4 + 18*B*a^5*b^5 - 33*A*a^4*b^6 - 18*B*a^3*b^7 + 35*A*a^2*b^8 + 6*B*a*b^9 - 12*A*b^10)*cos(d*x + c)^4 + 2*(A*a^9*b - 6*B*a^8*b^2 + 9*A*a^7*b^3 + 18*B*a^6*b^4 - 33*A*a^5*b^5 - 18*B*a^4*b^6 + 35*A*a^3*b^7 + 6*B*a^2*b^8 - 12*A*a*b^9)*cos(d*x + c)^3 + (A*a^10 - 6*B*a^9*b + 9*A*a^8*b^2 + 18*B*a^7*b^3 - 33*A*a^6*b^4 - 18*B*a^5*b^5 + 35*A*a^4*b^6 + 6*B*a^3*b^7 - 12*A*a^2*b^8)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(A*a^10 - 3*A*a^8*b^2 + 3*A*a^6*b^4 - A*a^4*b^6 + (2*B*a^8*b^2 - 6*A*a^7*b^3 - 13*B*a^6*b^4 + 27*A*a^5*b^5 + 17*B*a^4*b^6 - 33*A*a^3*b^7 - 6*B*a^2*b^8 + 12*A*a*b^9)*cos(d*x + c)^3 + (4*B*a^9*b - 11*A*a^8*b^2 - 20*B*a^7*b^3 + 43*A*a^6*b^4 + 25*B*a^5*b^5 - 50*A*a^4*b^6 - 9*B*a^3*b^7 + 18*A*a^2*b^8)*cos(d*x + c)^2 + 2*(B*a^10 - 2*A*a^9*b - 3*B*a^8*b^2 + 6*A*a^7*b^3 + 3*B*a^6*b^4 - 6*A*a^5*b^5 - B*a^4*b^6 + 2*A*a^3*b^7)*cos(d*x + c))*sin(d*x + c))/((a^11*b^2 - 3*a^9*b^4 + 3*a^7*b^6 - a^5*b^8)*d*cos(d*x + c)^4 + 2*(a^12*b - 3*a^10*b^3 + 3*a^8*b^5 - a^6*b^7)*d*cos(d*x + c)^3 + (a^13 - 3*a^11*b^2 + 3*a^9*b^4 - a^7*b^6)*d*cos(d*x + c)^2)]","B",0
273,1,2567,0,1.403555," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(4 \, B a^{9} b^{3} - A a^{8} b^{4} - 16 \, B a^{7} b^{5} + 4 \, A a^{6} b^{6} + 24 \, B a^{5} b^{7} - 6 \, A a^{4} b^{8} - 16 \, B a^{3} b^{9} + 4 \, A a^{2} b^{10} + 4 \, B a b^{11} - A b^{12}\right)} d x \cos\left(d x + c\right)^{3} + 36 \, {\left(4 \, B a^{10} b^{2} - A a^{9} b^{3} - 16 \, B a^{8} b^{4} + 4 \, A a^{7} b^{5} + 24 \, B a^{6} b^{6} - 6 \, A a^{5} b^{7} - 16 \, B a^{4} b^{8} + 4 \, A a^{3} b^{9} + 4 \, B a^{2} b^{10} - A a b^{11}\right)} d x \cos\left(d x + c\right)^{2} + 36 \, {\left(4 \, B a^{11} b - A a^{10} b^{2} - 16 \, B a^{9} b^{3} + 4 \, A a^{8} b^{4} + 24 \, B a^{7} b^{5} - 6 \, A a^{6} b^{6} - 16 \, B a^{5} b^{7} + 4 \, A a^{4} b^{8} + 4 \, B a^{3} b^{9} - A a^{2} b^{10}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(4 \, B a^{12} - A a^{11} b - 16 \, B a^{10} b^{2} + 4 \, A a^{9} b^{3} + 24 \, B a^{8} b^{4} - 6 \, A a^{7} b^{5} - 16 \, B a^{6} b^{6} + 4 \, A a^{5} b^{7} + 4 \, B a^{4} b^{8} - A a^{3} b^{9}\right)} d x - 3 \, {\left(8 \, B a^{11} - 2 \, A a^{10} b - 28 \, B a^{9} b^{2} + 7 \, A a^{8} b^{3} + 35 \, B a^{7} b^{4} - 8 \, A a^{6} b^{5} - 20 \, B a^{5} b^{6} + 8 \, A a^{4} b^{7} + {\left(8 \, B a^{8} b^{3} - 2 \, A a^{7} b^{4} - 28 \, B a^{6} b^{5} + 7 \, A a^{5} b^{6} + 35 \, B a^{4} b^{7} - 8 \, A a^{3} b^{8} - 20 \, B a^{2} b^{9} + 8 \, A a b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, B a^{9} b^{2} - 2 \, A a^{8} b^{3} - 28 \, B a^{7} b^{4} + 7 \, A a^{6} b^{5} + 35 \, B a^{5} b^{6} - 8 \, A a^{4} b^{7} - 20 \, B a^{3} b^{8} + 8 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, B a^{10} b - 2 \, A a^{9} b^{2} - 28 \, B a^{8} b^{3} + 7 \, A a^{7} b^{4} + 35 \, B a^{6} b^{5} - 8 \, A a^{5} b^{6} - 20 \, B a^{4} b^{7} + 8 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(24 \, B a^{11} b - 6 \, A a^{10} b^{2} - 92 \, B a^{9} b^{3} + 23 \, A a^{8} b^{4} + 133 \, B a^{7} b^{5} - 43 \, A a^{6} b^{6} - 71 \, B a^{5} b^{7} + 26 \, A a^{4} b^{8} + 6 \, B a^{3} b^{9} + 6 \, {\left(B a^{8} b^{4} - 4 \, B a^{6} b^{6} + 6 \, B a^{4} b^{8} - 4 \, B a^{2} b^{10} + B b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(44 \, B a^{9} b^{3} - 11 \, A a^{8} b^{4} - 169 \, B a^{7} b^{5} + 43 \, A a^{6} b^{6} + 239 \, B a^{5} b^{7} - 68 \, A a^{4} b^{8} - 132 \, B a^{3} b^{9} + 36 \, A a^{2} b^{10} + 18 \, B a b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, B a^{10} b^{2} - 5 \, A a^{9} b^{3} - 77 \, B a^{8} b^{4} + 20 \, A a^{7} b^{5} + 110 \, B a^{6} b^{6} - 35 \, A a^{5} b^{7} - 59 \, B a^{4} b^{8} + 20 \, A a^{3} b^{9} + 6 \, B a^{2} b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{8} - 4 \, a^{6} b^{10} + 6 \, a^{4} b^{12} - 4 \, a^{2} b^{14} + b^{16}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{7} - 4 \, a^{7} b^{9} + 6 \, a^{5} b^{11} - 4 \, a^{3} b^{13} + a b^{15}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{6} - 4 \, a^{8} b^{8} + 6 \, a^{6} b^{10} - 4 \, a^{4} b^{12} + a^{2} b^{14}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{5} - 4 \, a^{9} b^{7} + 6 \, a^{7} b^{9} - 4 \, a^{5} b^{11} + a^{3} b^{13}\right)} d\right)}}, -\frac{6 \, {\left(4 \, B a^{9} b^{3} - A a^{8} b^{4} - 16 \, B a^{7} b^{5} + 4 \, A a^{6} b^{6} + 24 \, B a^{5} b^{7} - 6 \, A a^{4} b^{8} - 16 \, B a^{3} b^{9} + 4 \, A a^{2} b^{10} + 4 \, B a b^{11} - A b^{12}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(4 \, B a^{10} b^{2} - A a^{9} b^{3} - 16 \, B a^{8} b^{4} + 4 \, A a^{7} b^{5} + 24 \, B a^{6} b^{6} - 6 \, A a^{5} b^{7} - 16 \, B a^{4} b^{8} + 4 \, A a^{3} b^{9} + 4 \, B a^{2} b^{10} - A a b^{11}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(4 \, B a^{11} b - A a^{10} b^{2} - 16 \, B a^{9} b^{3} + 4 \, A a^{8} b^{4} + 24 \, B a^{7} b^{5} - 6 \, A a^{6} b^{6} - 16 \, B a^{5} b^{7} + 4 \, A a^{4} b^{8} + 4 \, B a^{3} b^{9} - A a^{2} b^{10}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(4 \, B a^{12} - A a^{11} b - 16 \, B a^{10} b^{2} + 4 \, A a^{9} b^{3} + 24 \, B a^{8} b^{4} - 6 \, A a^{7} b^{5} - 16 \, B a^{6} b^{6} + 4 \, A a^{5} b^{7} + 4 \, B a^{4} b^{8} - A a^{3} b^{9}\right)} d x - 3 \, {\left(8 \, B a^{11} - 2 \, A a^{10} b - 28 \, B a^{9} b^{2} + 7 \, A a^{8} b^{3} + 35 \, B a^{7} b^{4} - 8 \, A a^{6} b^{5} - 20 \, B a^{5} b^{6} + 8 \, A a^{4} b^{7} + {\left(8 \, B a^{8} b^{3} - 2 \, A a^{7} b^{4} - 28 \, B a^{6} b^{5} + 7 \, A a^{5} b^{6} + 35 \, B a^{4} b^{7} - 8 \, A a^{3} b^{8} - 20 \, B a^{2} b^{9} + 8 \, A a b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, B a^{9} b^{2} - 2 \, A a^{8} b^{3} - 28 \, B a^{7} b^{4} + 7 \, A a^{6} b^{5} + 35 \, B a^{5} b^{6} - 8 \, A a^{4} b^{7} - 20 \, B a^{3} b^{8} + 8 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, B a^{10} b - 2 \, A a^{9} b^{2} - 28 \, B a^{8} b^{3} + 7 \, A a^{7} b^{4} + 35 \, B a^{6} b^{5} - 8 \, A a^{5} b^{6} - 20 \, B a^{4} b^{7} + 8 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(24 \, B a^{11} b - 6 \, A a^{10} b^{2} - 92 \, B a^{9} b^{3} + 23 \, A a^{8} b^{4} + 133 \, B a^{7} b^{5} - 43 \, A a^{6} b^{6} - 71 \, B a^{5} b^{7} + 26 \, A a^{4} b^{8} + 6 \, B a^{3} b^{9} + 6 \, {\left(B a^{8} b^{4} - 4 \, B a^{6} b^{6} + 6 \, B a^{4} b^{8} - 4 \, B a^{2} b^{10} + B b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(44 \, B a^{9} b^{3} - 11 \, A a^{8} b^{4} - 169 \, B a^{7} b^{5} + 43 \, A a^{6} b^{6} + 239 \, B a^{5} b^{7} - 68 \, A a^{4} b^{8} - 132 \, B a^{3} b^{9} + 36 \, A a^{2} b^{10} + 18 \, B a b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, B a^{10} b^{2} - 5 \, A a^{9} b^{3} - 77 \, B a^{8} b^{4} + 20 \, A a^{7} b^{5} + 110 \, B a^{6} b^{6} - 35 \, A a^{5} b^{7} - 59 \, B a^{4} b^{8} + 20 \, A a^{3} b^{9} + 6 \, B a^{2} b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{8} - 4 \, a^{6} b^{10} + 6 \, a^{4} b^{12} - 4 \, a^{2} b^{14} + b^{16}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{7} - 4 \, a^{7} b^{9} + 6 \, a^{5} b^{11} - 4 \, a^{3} b^{13} + a b^{15}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{6} - 4 \, a^{8} b^{8} + 6 \, a^{6} b^{10} - 4 \, a^{4} b^{12} + a^{2} b^{14}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{5} - 4 \, a^{9} b^{7} + 6 \, a^{7} b^{9} - 4 \, a^{5} b^{11} + a^{3} b^{13}\right)} d\right)}}\right]"," ",0,"[-1/12*(12*(4*B*a^9*b^3 - A*a^8*b^4 - 16*B*a^7*b^5 + 4*A*a^6*b^6 + 24*B*a^5*b^7 - 6*A*a^4*b^8 - 16*B*a^3*b^9 + 4*A*a^2*b^10 + 4*B*a*b^11 - A*b^12)*d*x*cos(d*x + c)^3 + 36*(4*B*a^10*b^2 - A*a^9*b^3 - 16*B*a^8*b^4 + 4*A*a^7*b^5 + 24*B*a^6*b^6 - 6*A*a^5*b^7 - 16*B*a^4*b^8 + 4*A*a^3*b^9 + 4*B*a^2*b^10 - A*a*b^11)*d*x*cos(d*x + c)^2 + 36*(4*B*a^11*b - A*a^10*b^2 - 16*B*a^9*b^3 + 4*A*a^8*b^4 + 24*B*a^7*b^5 - 6*A*a^6*b^6 - 16*B*a^5*b^7 + 4*A*a^4*b^8 + 4*B*a^3*b^9 - A*a^2*b^10)*d*x*cos(d*x + c) + 12*(4*B*a^12 - A*a^11*b - 16*B*a^10*b^2 + 4*A*a^9*b^3 + 24*B*a^8*b^4 - 6*A*a^7*b^5 - 16*B*a^6*b^6 + 4*A*a^5*b^7 + 4*B*a^4*b^8 - A*a^3*b^9)*d*x - 3*(8*B*a^11 - 2*A*a^10*b - 28*B*a^9*b^2 + 7*A*a^8*b^3 + 35*B*a^7*b^4 - 8*A*a^6*b^5 - 20*B*a^5*b^6 + 8*A*a^4*b^7 + (8*B*a^8*b^3 - 2*A*a^7*b^4 - 28*B*a^6*b^5 + 7*A*a^5*b^6 + 35*B*a^4*b^7 - 8*A*a^3*b^8 - 20*B*a^2*b^9 + 8*A*a*b^10)*cos(d*x + c)^3 + 3*(8*B*a^9*b^2 - 2*A*a^8*b^3 - 28*B*a^7*b^4 + 7*A*a^6*b^5 + 35*B*a^5*b^6 - 8*A*a^4*b^7 - 20*B*a^3*b^8 + 8*A*a^2*b^9)*cos(d*x + c)^2 + 3*(8*B*a^10*b - 2*A*a^9*b^2 - 28*B*a^8*b^3 + 7*A*a^7*b^4 + 35*B*a^6*b^5 - 8*A*a^5*b^6 - 20*B*a^4*b^7 + 8*A*a^3*b^8)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(24*B*a^11*b - 6*A*a^10*b^2 - 92*B*a^9*b^3 + 23*A*a^8*b^4 + 133*B*a^7*b^5 - 43*A*a^6*b^6 - 71*B*a^5*b^7 + 26*A*a^4*b^8 + 6*B*a^3*b^9 + 6*(B*a^8*b^4 - 4*B*a^6*b^6 + 6*B*a^4*b^8 - 4*B*a^2*b^10 + B*b^12)*cos(d*x + c)^3 + (44*B*a^9*b^3 - 11*A*a^8*b^4 - 169*B*a^7*b^5 + 43*A*a^6*b^6 + 239*B*a^5*b^7 - 68*A*a^4*b^8 - 132*B*a^3*b^9 + 36*A*a^2*b^10 + 18*B*a*b^11)*cos(d*x + c)^2 + 3*(20*B*a^10*b^2 - 5*A*a^9*b^3 - 77*B*a^8*b^4 + 20*A*a^7*b^5 + 110*B*a^6*b^6 - 35*A*a^5*b^7 - 59*B*a^4*b^8 + 20*A*a^3*b^9 + 6*B*a^2*b^10)*cos(d*x + c))*sin(d*x + c))/((a^8*b^8 - 4*a^6*b^10 + 6*a^4*b^12 - 4*a^2*b^14 + b^16)*d*cos(d*x + c)^3 + 3*(a^9*b^7 - 4*a^7*b^9 + 6*a^5*b^11 - 4*a^3*b^13 + a*b^15)*d*cos(d*x + c)^2 + 3*(a^10*b^6 - 4*a^8*b^8 + 6*a^6*b^10 - 4*a^4*b^12 + a^2*b^14)*d*cos(d*x + c) + (a^11*b^5 - 4*a^9*b^7 + 6*a^7*b^9 - 4*a^5*b^11 + a^3*b^13)*d), -1/6*(6*(4*B*a^9*b^3 - A*a^8*b^4 - 16*B*a^7*b^5 + 4*A*a^6*b^6 + 24*B*a^5*b^7 - 6*A*a^4*b^8 - 16*B*a^3*b^9 + 4*A*a^2*b^10 + 4*B*a*b^11 - A*b^12)*d*x*cos(d*x + c)^3 + 18*(4*B*a^10*b^2 - A*a^9*b^3 - 16*B*a^8*b^4 + 4*A*a^7*b^5 + 24*B*a^6*b^6 - 6*A*a^5*b^7 - 16*B*a^4*b^8 + 4*A*a^3*b^9 + 4*B*a^2*b^10 - A*a*b^11)*d*x*cos(d*x + c)^2 + 18*(4*B*a^11*b - A*a^10*b^2 - 16*B*a^9*b^3 + 4*A*a^8*b^4 + 24*B*a^7*b^5 - 6*A*a^6*b^6 - 16*B*a^5*b^7 + 4*A*a^4*b^8 + 4*B*a^3*b^9 - A*a^2*b^10)*d*x*cos(d*x + c) + 6*(4*B*a^12 - A*a^11*b - 16*B*a^10*b^2 + 4*A*a^9*b^3 + 24*B*a^8*b^4 - 6*A*a^7*b^5 - 16*B*a^6*b^6 + 4*A*a^5*b^7 + 4*B*a^4*b^8 - A*a^3*b^9)*d*x - 3*(8*B*a^11 - 2*A*a^10*b - 28*B*a^9*b^2 + 7*A*a^8*b^3 + 35*B*a^7*b^4 - 8*A*a^6*b^5 - 20*B*a^5*b^6 + 8*A*a^4*b^7 + (8*B*a^8*b^3 - 2*A*a^7*b^4 - 28*B*a^6*b^5 + 7*A*a^5*b^6 + 35*B*a^4*b^7 - 8*A*a^3*b^8 - 20*B*a^2*b^9 + 8*A*a*b^10)*cos(d*x + c)^3 + 3*(8*B*a^9*b^2 - 2*A*a^8*b^3 - 28*B*a^7*b^4 + 7*A*a^6*b^5 + 35*B*a^5*b^6 - 8*A*a^4*b^7 - 20*B*a^3*b^8 + 8*A*a^2*b^9)*cos(d*x + c)^2 + 3*(8*B*a^10*b - 2*A*a^9*b^2 - 28*B*a^8*b^3 + 7*A*a^7*b^4 + 35*B*a^6*b^5 - 8*A*a^5*b^6 - 20*B*a^4*b^7 + 8*A*a^3*b^8)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (24*B*a^11*b - 6*A*a^10*b^2 - 92*B*a^9*b^3 + 23*A*a^8*b^4 + 133*B*a^7*b^5 - 43*A*a^6*b^6 - 71*B*a^5*b^7 + 26*A*a^4*b^8 + 6*B*a^3*b^9 + 6*(B*a^8*b^4 - 4*B*a^6*b^6 + 6*B*a^4*b^8 - 4*B*a^2*b^10 + B*b^12)*cos(d*x + c)^3 + (44*B*a^9*b^3 - 11*A*a^8*b^4 - 169*B*a^7*b^5 + 43*A*a^6*b^6 + 239*B*a^5*b^7 - 68*A*a^4*b^8 - 132*B*a^3*b^9 + 36*A*a^2*b^10 + 18*B*a*b^11)*cos(d*x + c)^2 + 3*(20*B*a^10*b^2 - 5*A*a^9*b^3 - 77*B*a^8*b^4 + 20*A*a^7*b^5 + 110*B*a^6*b^6 - 35*A*a^5*b^7 - 59*B*a^4*b^8 + 20*A*a^3*b^9 + 6*B*a^2*b^10)*cos(d*x + c))*sin(d*x + c))/((a^8*b^8 - 4*a^6*b^10 + 6*a^4*b^12 - 4*a^2*b^14 + b^16)*d*cos(d*x + c)^3 + 3*(a^9*b^7 - 4*a^7*b^9 + 6*a^5*b^11 - 4*a^3*b^13 + a*b^15)*d*cos(d*x + c)^2 + 3*(a^10*b^6 - 4*a^8*b^8 + 6*a^6*b^10 - 4*a^4*b^12 + a^2*b^14)*d*cos(d*x + c) + (a^11*b^5 - 4*a^9*b^7 + 6*a^7*b^9 - 4*a^5*b^11 + a^3*b^13)*d)]","B",0
274,1,1857,0,1.307686," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(B a^{8} b^{3} - 4 \, B a^{6} b^{5} + 6 \, B a^{4} b^{7} - 4 \, B a^{2} b^{9} + B b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 36 \, {\left(B a^{9} b^{2} - 4 \, B a^{7} b^{4} + 6 \, B a^{5} b^{6} - 4 \, B a^{3} b^{8} + B a b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 36 \, {\left(B a^{10} b - 4 \, B a^{8} b^{3} + 6 \, B a^{6} b^{5} - 4 \, B a^{4} b^{7} + B a^{2} b^{9}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(B a^{11} - 4 \, B a^{9} b^{2} + 6 \, B a^{7} b^{4} - 4 \, B a^{5} b^{6} + B a^{3} b^{8}\right)} d x + 3 \, {\left(2 \, B a^{10} - 7 \, B a^{8} b^{2} + 8 \, B a^{6} b^{4} + 3 \, A a^{5} b^{5} - 8 \, B a^{4} b^{6} + 2 \, A a^{3} b^{7} + {\left(2 \, B a^{7} b^{3} - 7 \, B a^{5} b^{5} + 8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8} - 8 \, B a b^{9} + 2 \, A b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{8} b^{2} - 7 \, B a^{6} b^{4} + 8 \, B a^{4} b^{6} + 3 \, A a^{3} b^{7} - 8 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{9} b - 7 \, B a^{7} b^{3} + 8 \, B a^{5} b^{5} + 3 \, A a^{4} b^{6} - 8 \, B a^{3} b^{7} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(6 \, B a^{10} b - 23 \, B a^{8} b^{3} - 4 \, A a^{7} b^{4} + 43 \, B a^{6} b^{5} - 7 \, A a^{5} b^{6} - 26 \, B a^{4} b^{7} + 11 \, A a^{3} b^{8} + {\left(11 \, B a^{8} b^{3} - 2 \, A a^{7} b^{4} - 43 \, B a^{6} b^{5} + 7 \, A a^{5} b^{6} + 68 \, B a^{4} b^{7} - 23 \, A a^{3} b^{8} - 36 \, B a^{2} b^{9} + 18 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B a^{9} b^{2} - 20 \, B a^{7} b^{4} - A a^{6} b^{5} + 35 \, B a^{5} b^{6} - 8 \, A a^{4} b^{7} - 20 \, B a^{3} b^{8} + 9 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{7} - 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} - 4 \, a^{2} b^{13} + b^{15}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{6} - 4 \, a^{7} b^{8} + 6 \, a^{5} b^{10} - 4 \, a^{3} b^{12} + a b^{14}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{5} - 4 \, a^{8} b^{7} + 6 \, a^{6} b^{9} - 4 \, a^{4} b^{11} + a^{2} b^{13}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{4} - 4 \, a^{9} b^{6} + 6 \, a^{7} b^{8} - 4 \, a^{5} b^{10} + a^{3} b^{12}\right)} d\right)}}, \frac{6 \, {\left(B a^{8} b^{3} - 4 \, B a^{6} b^{5} + 6 \, B a^{4} b^{7} - 4 \, B a^{2} b^{9} + B b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(B a^{9} b^{2} - 4 \, B a^{7} b^{4} + 6 \, B a^{5} b^{6} - 4 \, B a^{3} b^{8} + B a b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(B a^{10} b - 4 \, B a^{8} b^{3} + 6 \, B a^{6} b^{5} - 4 \, B a^{4} b^{7} + B a^{2} b^{9}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(B a^{11} - 4 \, B a^{9} b^{2} + 6 \, B a^{7} b^{4} - 4 \, B a^{5} b^{6} + B a^{3} b^{8}\right)} d x - 3 \, {\left(2 \, B a^{10} - 7 \, B a^{8} b^{2} + 8 \, B a^{6} b^{4} + 3 \, A a^{5} b^{5} - 8 \, B a^{4} b^{6} + 2 \, A a^{3} b^{7} + {\left(2 \, B a^{7} b^{3} - 7 \, B a^{5} b^{5} + 8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8} - 8 \, B a b^{9} + 2 \, A b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{8} b^{2} - 7 \, B a^{6} b^{4} + 8 \, B a^{4} b^{6} + 3 \, A a^{3} b^{7} - 8 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{9} b - 7 \, B a^{7} b^{3} + 8 \, B a^{5} b^{5} + 3 \, A a^{4} b^{6} - 8 \, B a^{3} b^{7} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(6 \, B a^{10} b - 23 \, B a^{8} b^{3} - 4 \, A a^{7} b^{4} + 43 \, B a^{6} b^{5} - 7 \, A a^{5} b^{6} - 26 \, B a^{4} b^{7} + 11 \, A a^{3} b^{8} + {\left(11 \, B a^{8} b^{3} - 2 \, A a^{7} b^{4} - 43 \, B a^{6} b^{5} + 7 \, A a^{5} b^{6} + 68 \, B a^{4} b^{7} - 23 \, A a^{3} b^{8} - 36 \, B a^{2} b^{9} + 18 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B a^{9} b^{2} - 20 \, B a^{7} b^{4} - A a^{6} b^{5} + 35 \, B a^{5} b^{6} - 8 \, A a^{4} b^{7} - 20 \, B a^{3} b^{8} + 9 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{7} - 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} - 4 \, a^{2} b^{13} + b^{15}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{6} - 4 \, a^{7} b^{8} + 6 \, a^{5} b^{10} - 4 \, a^{3} b^{12} + a b^{14}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{5} - 4 \, a^{8} b^{7} + 6 \, a^{6} b^{9} - 4 \, a^{4} b^{11} + a^{2} b^{13}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{4} - 4 \, a^{9} b^{6} + 6 \, a^{7} b^{8} - 4 \, a^{5} b^{10} + a^{3} b^{12}\right)} d\right)}}\right]"," ",0,"[1/12*(12*(B*a^8*b^3 - 4*B*a^6*b^5 + 6*B*a^4*b^7 - 4*B*a^2*b^9 + B*b^11)*d*x*cos(d*x + c)^3 + 36*(B*a^9*b^2 - 4*B*a^7*b^4 + 6*B*a^5*b^6 - 4*B*a^3*b^8 + B*a*b^10)*d*x*cos(d*x + c)^2 + 36*(B*a^10*b - 4*B*a^8*b^3 + 6*B*a^6*b^5 - 4*B*a^4*b^7 + B*a^2*b^9)*d*x*cos(d*x + c) + 12*(B*a^11 - 4*B*a^9*b^2 + 6*B*a^7*b^4 - 4*B*a^5*b^6 + B*a^3*b^8)*d*x + 3*(2*B*a^10 - 7*B*a^8*b^2 + 8*B*a^6*b^4 + 3*A*a^5*b^5 - 8*B*a^4*b^6 + 2*A*a^3*b^7 + (2*B*a^7*b^3 - 7*B*a^5*b^5 + 8*B*a^3*b^7 + 3*A*a^2*b^8 - 8*B*a*b^9 + 2*A*b^10)*cos(d*x + c)^3 + 3*(2*B*a^8*b^2 - 7*B*a^6*b^4 + 8*B*a^4*b^6 + 3*A*a^3*b^7 - 8*B*a^2*b^8 + 2*A*a*b^9)*cos(d*x + c)^2 + 3*(2*B*a^9*b - 7*B*a^7*b^3 + 8*B*a^5*b^5 + 3*A*a^4*b^6 - 8*B*a^3*b^7 + 2*A*a^2*b^8)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(6*B*a^10*b - 23*B*a^8*b^3 - 4*A*a^7*b^4 + 43*B*a^6*b^5 - 7*A*a^5*b^6 - 26*B*a^4*b^7 + 11*A*a^3*b^8 + (11*B*a^8*b^3 - 2*A*a^7*b^4 - 43*B*a^6*b^5 + 7*A*a^5*b^6 + 68*B*a^4*b^7 - 23*A*a^3*b^8 - 36*B*a^2*b^9 + 18*A*a*b^10)*cos(d*x + c)^2 + 3*(5*B*a^9*b^2 - 20*B*a^7*b^4 - A*a^6*b^5 + 35*B*a^5*b^6 - 8*A*a^4*b^7 - 20*B*a^3*b^8 + 9*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^8*b^7 - 4*a^6*b^9 + 6*a^4*b^11 - 4*a^2*b^13 + b^15)*d*cos(d*x + c)^3 + 3*(a^9*b^6 - 4*a^7*b^8 + 6*a^5*b^10 - 4*a^3*b^12 + a*b^14)*d*cos(d*x + c)^2 + 3*(a^10*b^5 - 4*a^8*b^7 + 6*a^6*b^9 - 4*a^4*b^11 + a^2*b^13)*d*cos(d*x + c) + (a^11*b^4 - 4*a^9*b^6 + 6*a^7*b^8 - 4*a^5*b^10 + a^3*b^12)*d), 1/6*(6*(B*a^8*b^3 - 4*B*a^6*b^5 + 6*B*a^4*b^7 - 4*B*a^2*b^9 + B*b^11)*d*x*cos(d*x + c)^3 + 18*(B*a^9*b^2 - 4*B*a^7*b^4 + 6*B*a^5*b^6 - 4*B*a^3*b^8 + B*a*b^10)*d*x*cos(d*x + c)^2 + 18*(B*a^10*b - 4*B*a^8*b^3 + 6*B*a^6*b^5 - 4*B*a^4*b^7 + B*a^2*b^9)*d*x*cos(d*x + c) + 6*(B*a^11 - 4*B*a^9*b^2 + 6*B*a^7*b^4 - 4*B*a^5*b^6 + B*a^3*b^8)*d*x - 3*(2*B*a^10 - 7*B*a^8*b^2 + 8*B*a^6*b^4 + 3*A*a^5*b^5 - 8*B*a^4*b^6 + 2*A*a^3*b^7 + (2*B*a^7*b^3 - 7*B*a^5*b^5 + 8*B*a^3*b^7 + 3*A*a^2*b^8 - 8*B*a*b^9 + 2*A*b^10)*cos(d*x + c)^3 + 3*(2*B*a^8*b^2 - 7*B*a^6*b^4 + 8*B*a^4*b^6 + 3*A*a^3*b^7 - 8*B*a^2*b^8 + 2*A*a*b^9)*cos(d*x + c)^2 + 3*(2*B*a^9*b - 7*B*a^7*b^3 + 8*B*a^5*b^5 + 3*A*a^4*b^6 - 8*B*a^3*b^7 + 2*A*a^2*b^8)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*B*a^10*b - 23*B*a^8*b^3 - 4*A*a^7*b^4 + 43*B*a^6*b^5 - 7*A*a^5*b^6 - 26*B*a^4*b^7 + 11*A*a^3*b^8 + (11*B*a^8*b^3 - 2*A*a^7*b^4 - 43*B*a^6*b^5 + 7*A*a^5*b^6 + 68*B*a^4*b^7 - 23*A*a^3*b^8 - 36*B*a^2*b^9 + 18*A*a*b^10)*cos(d*x + c)^2 + 3*(5*B*a^9*b^2 - 20*B*a^7*b^4 - A*a^6*b^5 + 35*B*a^5*b^6 - 8*A*a^4*b^7 - 20*B*a^3*b^8 + 9*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^8*b^7 - 4*a^6*b^9 + 6*a^4*b^11 - 4*a^2*b^13 + b^15)*d*cos(d*x + c)^3 + 3*(a^9*b^6 - 4*a^7*b^8 + 6*a^5*b^10 - 4*a^3*b^12 + a*b^14)*d*cos(d*x + c)^2 + 3*(a^10*b^5 - 4*a^8*b^7 + 6*a^6*b^9 - 4*a^4*b^11 + a^2*b^13)*d*cos(d*x + c) + (a^11*b^4 - 4*a^9*b^6 + 6*a^7*b^8 - 4*a^5*b^10 + a^3*b^12)*d)]","B",0
275,1,1220,0,0.872912," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(A a^{6} - 3 \, B a^{5} b + 4 \, A a^{4} b^{2} - 2 \, B a^{3} b^{3} + {\left(A a^{3} b^{3} - 3 \, B a^{2} b^{4} + 4 \, A a b^{5} - 2 \, B b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{4} b^{2} - 3 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} - 2 \, B a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{5} b - 3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} - 2 \, B a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(4 \, B a^{7} - 13 \, A a^{6} b + 7 \, B a^{5} b^{2} + 11 \, A a^{4} b^{3} - 11 \, B a^{3} b^{4} + 2 \, A a^{2} b^{5} + {\left(2 \, B a^{7} + A a^{6} b - 7 \, B a^{5} b^{2} - 11 \, A a^{4} b^{3} + 23 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} - 18 \, B a b^{6} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{7} + B a^{6} b - 10 \, A a^{5} b^{2} + 8 \, B a^{4} b^{3} + 7 \, A a^{3} b^{4} - 9 \, B a^{2} b^{5} + 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}, \frac{3 \, {\left(A a^{6} - 3 \, B a^{5} b + 4 \, A a^{4} b^{2} - 2 \, B a^{3} b^{3} + {\left(A a^{3} b^{3} - 3 \, B a^{2} b^{4} + 4 \, A a b^{5} - 2 \, B b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{4} b^{2} - 3 \, B a^{3} b^{3} + 4 \, A a^{2} b^{4} - 2 \, B a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{5} b - 3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3} - 2 \, B a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(4 \, B a^{7} - 13 \, A a^{6} b + 7 \, B a^{5} b^{2} + 11 \, A a^{4} b^{3} - 11 \, B a^{3} b^{4} + 2 \, A a^{2} b^{5} + {\left(2 \, B a^{7} + A a^{6} b - 7 \, B a^{5} b^{2} - 11 \, A a^{4} b^{3} + 23 \, B a^{3} b^{4} + 4 \, A a^{2} b^{5} - 18 \, B a b^{6} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{7} + B a^{6} b - 10 \, A a^{5} b^{2} + 8 \, B a^{4} b^{3} + 7 \, A a^{3} b^{4} - 9 \, B a^{2} b^{5} + 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}\right]"," ",0,"[-1/12*(3*(A*a^6 - 3*B*a^5*b + 4*A*a^4*b^2 - 2*B*a^3*b^3 + (A*a^3*b^3 - 3*B*a^2*b^4 + 4*A*a*b^5 - 2*B*b^6)*cos(d*x + c)^3 + 3*(A*a^4*b^2 - 3*B*a^3*b^3 + 4*A*a^2*b^4 - 2*B*a*b^5)*cos(d*x + c)^2 + 3*(A*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3 - 2*B*a^2*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(4*B*a^7 - 13*A*a^6*b + 7*B*a^5*b^2 + 11*A*a^4*b^3 - 11*B*a^3*b^4 + 2*A*a^2*b^5 + (2*B*a^7 + A*a^6*b - 7*B*a^5*b^2 - 11*A*a^4*b^3 + 23*B*a^3*b^4 + 4*A*a^2*b^5 - 18*B*a*b^6 + 6*A*b^7)*cos(d*x + c)^2 + 3*(A*a^7 + B*a^6*b - 10*A*a^5*b^2 + 8*B*a^4*b^3 + 7*A*a^3*b^4 - 9*B*a^2*b^5 + 2*A*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d), 1/6*(3*(A*a^6 - 3*B*a^5*b + 4*A*a^4*b^2 - 2*B*a^3*b^3 + (A*a^3*b^3 - 3*B*a^2*b^4 + 4*A*a*b^5 - 2*B*b^6)*cos(d*x + c)^3 + 3*(A*a^4*b^2 - 3*B*a^3*b^3 + 4*A*a^2*b^4 - 2*B*a*b^5)*cos(d*x + c)^2 + 3*(A*a^5*b - 3*B*a^4*b^2 + 4*A*a^3*b^3 - 2*B*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (4*B*a^7 - 13*A*a^6*b + 7*B*a^5*b^2 + 11*A*a^4*b^3 - 11*B*a^3*b^4 + 2*A*a^2*b^5 + (2*B*a^7 + A*a^6*b - 7*B*a^5*b^2 - 11*A*a^4*b^3 + 23*B*a^3*b^4 + 4*A*a^2*b^5 - 18*B*a*b^6 + 6*A*b^7)*cos(d*x + c)^2 + 3*(A*a^7 + B*a^6*b - 10*A*a^5*b^2 + 8*B*a^4*b^3 + 7*A*a^3*b^4 - 9*B*a^2*b^5 + 2*A*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d)]","B",0
276,1,1232,0,1.444355," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{6} - 4 \, A a^{5} b + 4 \, B a^{4} b^{2} - A a^{3} b^{3} + {\left(B a^{3} b^{3} - 4 \, A a^{2} b^{4} + 4 \, B a b^{5} - A b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{4} b^{2} - 4 \, A a^{3} b^{3} + 4 \, B a^{2} b^{4} - A a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{5} b - 4 \, A a^{4} b^{2} + 4 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(6 \, A a^{7} - 13 \, B a^{6} b + 4 \, A a^{5} b^{2} + 11 \, B a^{4} b^{3} - 11 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} + A a b^{6} + {\left(B a^{6} b + 2 \, A a^{5} b^{2} - 11 \, B a^{4} b^{3} + 11 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 13 \, A a b^{6} + 6 \, B b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{7} + 2 \, A a^{6} b - 10 \, B a^{5} b^{2} + 7 \, A a^{4} b^{3} + 7 \, B a^{3} b^{4} - 10 \, A a^{2} b^{5} + 2 \, B a b^{6} + A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}, \frac{3 \, {\left(B a^{6} - 4 \, A a^{5} b + 4 \, B a^{4} b^{2} - A a^{3} b^{3} + {\left(B a^{3} b^{3} - 4 \, A a^{2} b^{4} + 4 \, B a b^{5} - A b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{4} b^{2} - 4 \, A a^{3} b^{3} + 4 \, B a^{2} b^{4} - A a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{5} b - 4 \, A a^{4} b^{2} + 4 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(6 \, A a^{7} - 13 \, B a^{6} b + 4 \, A a^{5} b^{2} + 11 \, B a^{4} b^{3} - 11 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} + A a b^{6} + {\left(B a^{6} b + 2 \, A a^{5} b^{2} - 11 \, B a^{4} b^{3} + 11 \, A a^{3} b^{4} + 4 \, B a^{2} b^{5} - 13 \, A a b^{6} + 6 \, B b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{7} + 2 \, A a^{6} b - 10 \, B a^{5} b^{2} + 7 \, A a^{4} b^{3} + 7 \, B a^{3} b^{4} - 10 \, A a^{2} b^{5} + 2 \, B a b^{6} + A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}\right]"," ",0,"[-1/12*(3*(B*a^6 - 4*A*a^5*b + 4*B*a^4*b^2 - A*a^3*b^3 + (B*a^3*b^3 - 4*A*a^2*b^4 + 4*B*a*b^5 - A*b^6)*cos(d*x + c)^3 + 3*(B*a^4*b^2 - 4*A*a^3*b^3 + 4*B*a^2*b^4 - A*a*b^5)*cos(d*x + c)^2 + 3*(B*a^5*b - 4*A*a^4*b^2 + 4*B*a^3*b^3 - A*a^2*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(6*A*a^7 - 13*B*a^6*b + 4*A*a^5*b^2 + 11*B*a^4*b^3 - 11*A*a^3*b^4 + 2*B*a^2*b^5 + A*a*b^6 + (B*a^6*b + 2*A*a^5*b^2 - 11*B*a^4*b^3 + 11*A*a^3*b^4 + 4*B*a^2*b^5 - 13*A*a*b^6 + 6*B*b^7)*cos(d*x + c)^2 + 3*(B*a^7 + 2*A*a^6*b - 10*B*a^5*b^2 + 7*A*a^4*b^3 + 7*B*a^3*b^4 - 10*A*a^2*b^5 + 2*B*a*b^6 + A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d), 1/6*(3*(B*a^6 - 4*A*a^5*b + 4*B*a^4*b^2 - A*a^3*b^3 + (B*a^3*b^3 - 4*A*a^2*b^4 + 4*B*a*b^5 - A*b^6)*cos(d*x + c)^3 + 3*(B*a^4*b^2 - 4*A*a^3*b^3 + 4*B*a^2*b^4 - A*a*b^5)*cos(d*x + c)^2 + 3*(B*a^5*b - 4*A*a^4*b^2 + 4*B*a^3*b^3 - A*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (6*A*a^7 - 13*B*a^6*b + 4*A*a^5*b^2 + 11*B*a^4*b^3 - 11*A*a^3*b^4 + 2*B*a^2*b^5 + A*a*b^6 + (B*a^6*b + 2*A*a^5*b^2 - 11*B*a^4*b^3 + 11*A*a^3*b^4 + 4*B*a^2*b^5 - 13*A*a*b^6 + 6*B*b^7)*cos(d*x + c)^2 + 3*(B*a^7 + 2*A*a^6*b - 10*B*a^5*b^2 + 7*A*a^4*b^3 + 7*B*a^3*b^4 - 10*A*a^2*b^5 + 2*B*a*b^6 + A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d)]","B",0
277,1,1228,0,1.133049," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, A a^{6} - 4 \, B a^{5} b + 3 \, A a^{4} b^{2} - B a^{3} b^{3} + {\left(2 \, A a^{3} b^{3} - 4 \, B a^{2} b^{4} + 3 \, A a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A a^{5} b - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} - B a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(6 \, B a^{7} - 18 \, A a^{6} b + 4 \, B a^{5} b^{2} + 23 \, A a^{4} b^{3} - 11 \, B a^{3} b^{4} - 7 \, A a^{2} b^{5} + B a b^{6} + 2 \, A b^{7} + {\left(2 \, B a^{5} b^{2} - 11 \, A a^{4} b^{3} + 11 \, B a^{3} b^{4} + 7 \, A a^{2} b^{5} - 13 \, B a b^{6} + 4 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{6} b - 9 \, A a^{5} b^{2} + 7 \, B a^{4} b^{3} + 8 \, A a^{3} b^{4} - 10 \, B a^{2} b^{5} + A a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}, \frac{3 \, {\left(2 \, A a^{6} - 4 \, B a^{5} b + 3 \, A a^{4} b^{2} - B a^{3} b^{3} + {\left(2 \, A a^{3} b^{3} - 4 \, B a^{2} b^{4} + 3 \, A a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A a^{5} b - 4 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} - B a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(6 \, B a^{7} - 18 \, A a^{6} b + 4 \, B a^{5} b^{2} + 23 \, A a^{4} b^{3} - 11 \, B a^{3} b^{4} - 7 \, A a^{2} b^{5} + B a b^{6} + 2 \, A b^{7} + {\left(2 \, B a^{5} b^{2} - 11 \, A a^{4} b^{3} + 11 \, B a^{3} b^{4} + 7 \, A a^{2} b^{5} - 13 \, B a b^{6} + 4 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{6} b - 9 \, A a^{5} b^{2} + 7 \, B a^{4} b^{3} + 8 \, A a^{3} b^{4} - 10 \, B a^{2} b^{5} + A a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}\right]"," ",0,"[-1/12*(3*(2*A*a^6 - 4*B*a^5*b + 3*A*a^4*b^2 - B*a^3*b^3 + (2*A*a^3*b^3 - 4*B*a^2*b^4 + 3*A*a*b^5 - B*b^6)*cos(d*x + c)^3 + 3*(2*A*a^4*b^2 - 4*B*a^3*b^3 + 3*A*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + 3*(2*A*a^5*b - 4*B*a^4*b^2 + 3*A*a^3*b^3 - B*a^2*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(6*B*a^7 - 18*A*a^6*b + 4*B*a^5*b^2 + 23*A*a^4*b^3 - 11*B*a^3*b^4 - 7*A*a^2*b^5 + B*a*b^6 + 2*A*b^7 + (2*B*a^5*b^2 - 11*A*a^4*b^3 + 11*B*a^3*b^4 + 7*A*a^2*b^5 - 13*B*a*b^6 + 4*A*b^7)*cos(d*x + c)^2 + 3*(2*B*a^6*b - 9*A*a^5*b^2 + 7*B*a^4*b^3 + 8*A*a^3*b^4 - 10*B*a^2*b^5 + A*a*b^6 + B*b^7)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d), 1/6*(3*(2*A*a^6 - 4*B*a^5*b + 3*A*a^4*b^2 - B*a^3*b^3 + (2*A*a^3*b^3 - 4*B*a^2*b^4 + 3*A*a*b^5 - B*b^6)*cos(d*x + c)^3 + 3*(2*A*a^4*b^2 - 4*B*a^3*b^3 + 3*A*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + 3*(2*A*a^5*b - 4*B*a^4*b^2 + 3*A*a^3*b^3 - B*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (6*B*a^7 - 18*A*a^6*b + 4*B*a^5*b^2 + 23*A*a^4*b^3 - 11*B*a^3*b^4 - 7*A*a^2*b^5 + B*a*b^6 + 2*A*b^7 + (2*B*a^5*b^2 - 11*A*a^4*b^3 + 11*B*a^3*b^4 + 7*A*a^2*b^5 - 13*B*a*b^6 + 4*A*b^7)*cos(d*x + c)^2 + 3*(2*B*a^6*b - 9*A*a^5*b^2 + 7*B*a^4*b^3 + 8*A*a^3*b^4 - 10*B*a^2*b^5 + A*a*b^6 + B*b^7)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d)]","B",0
278,1,2269,0,136.531372," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B a^{10} - 8 \, A a^{9} b + 3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3} - 7 \, A a^{5} b^{5} + 2 \, A a^{3} b^{7} + {\left(2 \, B a^{7} b^{3} - 8 \, A a^{6} b^{4} + 3 \, B a^{5} b^{5} + 8 \, A a^{4} b^{6} - 7 \, A a^{2} b^{8} + 2 \, A b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{8} b^{2} - 8 \, A a^{7} b^{3} + 3 \, B a^{6} b^{4} + 8 \, A a^{5} b^{5} - 7 \, A a^{3} b^{7} + 2 \, A a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{9} b - 8 \, A a^{8} b^{2} + 3 \, B a^{7} b^{3} + 8 \, A a^{6} b^{4} - 7 \, A a^{4} b^{6} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 6 \, {\left(A a^{11} - 4 \, A a^{9} b^{2} + 6 \, A a^{7} b^{4} - 4 \, A a^{5} b^{6} + A a^{3} b^{8} + {\left(A a^{8} b^{3} - 4 \, A a^{6} b^{5} + 6 \, A a^{4} b^{7} - 4 \, A a^{2} b^{9} + A b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{9} b^{2} - 4 \, A a^{7} b^{4} + 6 \, A a^{5} b^{6} - 4 \, A a^{3} b^{8} + A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{10} b - 4 \, A a^{8} b^{3} + 6 \, A a^{6} b^{5} - 4 \, A a^{4} b^{7} + A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left(A a^{11} - 4 \, A a^{9} b^{2} + 6 \, A a^{7} b^{4} - 4 \, A a^{5} b^{6} + A a^{3} b^{8} + {\left(A a^{8} b^{3} - 4 \, A a^{6} b^{5} + 6 \, A a^{4} b^{7} - 4 \, A a^{2} b^{9} + A b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{9} b^{2} - 4 \, A a^{7} b^{4} + 6 \, A a^{5} b^{6} - 4 \, A a^{3} b^{8} + A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{10} b - 4 \, A a^{8} b^{3} + 6 \, A a^{6} b^{5} - 4 \, A a^{4} b^{7} + A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(18 \, B a^{10} b - 36 \, A a^{9} b^{2} - 23 \, B a^{8} b^{3} + 68 \, A a^{7} b^{4} + 7 \, B a^{6} b^{5} - 43 \, A a^{5} b^{6} - 2 \, B a^{4} b^{7} + 11 \, A a^{3} b^{8} + {\left(11 \, B a^{8} b^{3} - 26 \, A a^{7} b^{4} - 7 \, B a^{6} b^{5} + 43 \, A a^{5} b^{6} - 4 \, B a^{4} b^{7} - 23 \, A a^{3} b^{8} + 6 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(9 \, B a^{9} b^{2} - 20 \, A a^{8} b^{3} - 8 \, B a^{7} b^{4} + 35 \, A a^{6} b^{5} - B a^{5} b^{6} - 20 \, A a^{4} b^{7} + 5 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{12} b^{3} - 4 \, a^{10} b^{5} + 6 \, a^{8} b^{7} - 4 \, a^{6} b^{9} + a^{4} b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{13} b^{2} - 4 \, a^{11} b^{4} + 6 \, a^{9} b^{6} - 4 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{14} b - 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} - 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{15} - 4 \, a^{13} b^{2} + 6 \, a^{11} b^{4} - 4 \, a^{9} b^{6} + a^{7} b^{8}\right)} d\right)}}, \frac{3 \, {\left(2 \, B a^{10} - 8 \, A a^{9} b + 3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3} - 7 \, A a^{5} b^{5} + 2 \, A a^{3} b^{7} + {\left(2 \, B a^{7} b^{3} - 8 \, A a^{6} b^{4} + 3 \, B a^{5} b^{5} + 8 \, A a^{4} b^{6} - 7 \, A a^{2} b^{8} + 2 \, A b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{8} b^{2} - 8 \, A a^{7} b^{3} + 3 \, B a^{6} b^{4} + 8 \, A a^{5} b^{5} - 7 \, A a^{3} b^{7} + 2 \, A a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{9} b - 8 \, A a^{8} b^{2} + 3 \, B a^{7} b^{3} + 8 \, A a^{6} b^{4} - 7 \, A a^{4} b^{6} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + 3 \, {\left(A a^{11} - 4 \, A a^{9} b^{2} + 6 \, A a^{7} b^{4} - 4 \, A a^{5} b^{6} + A a^{3} b^{8} + {\left(A a^{8} b^{3} - 4 \, A a^{6} b^{5} + 6 \, A a^{4} b^{7} - 4 \, A a^{2} b^{9} + A b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{9} b^{2} - 4 \, A a^{7} b^{4} + 6 \, A a^{5} b^{6} - 4 \, A a^{3} b^{8} + A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{10} b - 4 \, A a^{8} b^{3} + 6 \, A a^{6} b^{5} - 4 \, A a^{4} b^{7} + A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A a^{11} - 4 \, A a^{9} b^{2} + 6 \, A a^{7} b^{4} - 4 \, A a^{5} b^{6} + A a^{3} b^{8} + {\left(A a^{8} b^{3} - 4 \, A a^{6} b^{5} + 6 \, A a^{4} b^{7} - 4 \, A a^{2} b^{9} + A b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{9} b^{2} - 4 \, A a^{7} b^{4} + 6 \, A a^{5} b^{6} - 4 \, A a^{3} b^{8} + A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A a^{10} b - 4 \, A a^{8} b^{3} + 6 \, A a^{6} b^{5} - 4 \, A a^{4} b^{7} + A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(18 \, B a^{10} b - 36 \, A a^{9} b^{2} - 23 \, B a^{8} b^{3} + 68 \, A a^{7} b^{4} + 7 \, B a^{6} b^{5} - 43 \, A a^{5} b^{6} - 2 \, B a^{4} b^{7} + 11 \, A a^{3} b^{8} + {\left(11 \, B a^{8} b^{3} - 26 \, A a^{7} b^{4} - 7 \, B a^{6} b^{5} + 43 \, A a^{5} b^{6} - 4 \, B a^{4} b^{7} - 23 \, A a^{3} b^{8} + 6 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(9 \, B a^{9} b^{2} - 20 \, A a^{8} b^{3} - 8 \, B a^{7} b^{4} + 35 \, A a^{6} b^{5} - B a^{5} b^{6} - 20 \, A a^{4} b^{7} + 5 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{12} b^{3} - 4 \, a^{10} b^{5} + 6 \, a^{8} b^{7} - 4 \, a^{6} b^{9} + a^{4} b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{13} b^{2} - 4 \, a^{11} b^{4} + 6 \, a^{9} b^{6} - 4 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{14} b - 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} - 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{15} - 4 \, a^{13} b^{2} + 6 \, a^{11} b^{4} - 4 \, a^{9} b^{6} + a^{7} b^{8}\right)} d\right)}}\right]"," ",0,"[1/12*(3*(2*B*a^10 - 8*A*a^9*b + 3*B*a^8*b^2 + 8*A*a^7*b^3 - 7*A*a^5*b^5 + 2*A*a^3*b^7 + (2*B*a^7*b^3 - 8*A*a^6*b^4 + 3*B*a^5*b^5 + 8*A*a^4*b^6 - 7*A*a^2*b^8 + 2*A*b^10)*cos(d*x + c)^3 + 3*(2*B*a^8*b^2 - 8*A*a^7*b^3 + 3*B*a^6*b^4 + 8*A*a^5*b^5 - 7*A*a^3*b^7 + 2*A*a*b^9)*cos(d*x + c)^2 + 3*(2*B*a^9*b - 8*A*a^8*b^2 + 3*B*a^7*b^3 + 8*A*a^6*b^4 - 7*A*a^4*b^6 + 2*A*a^2*b^8)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 6*(A*a^11 - 4*A*a^9*b^2 + 6*A*a^7*b^4 - 4*A*a^5*b^6 + A*a^3*b^8 + (A*a^8*b^3 - 4*A*a^6*b^5 + 6*A*a^4*b^7 - 4*A*a^2*b^9 + A*b^11)*cos(d*x + c)^3 + 3*(A*a^9*b^2 - 4*A*a^7*b^4 + 6*A*a^5*b^6 - 4*A*a^3*b^8 + A*a*b^10)*cos(d*x + c)^2 + 3*(A*a^10*b - 4*A*a^8*b^3 + 6*A*a^6*b^5 - 4*A*a^4*b^7 + A*a^2*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) - 6*(A*a^11 - 4*A*a^9*b^2 + 6*A*a^7*b^4 - 4*A*a^5*b^6 + A*a^3*b^8 + (A*a^8*b^3 - 4*A*a^6*b^5 + 6*A*a^4*b^7 - 4*A*a^2*b^9 + A*b^11)*cos(d*x + c)^3 + 3*(A*a^9*b^2 - 4*A*a^7*b^4 + 6*A*a^5*b^6 - 4*A*a^3*b^8 + A*a*b^10)*cos(d*x + c)^2 + 3*(A*a^10*b - 4*A*a^8*b^3 + 6*A*a^6*b^5 - 4*A*a^4*b^7 + A*a^2*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(18*B*a^10*b - 36*A*a^9*b^2 - 23*B*a^8*b^3 + 68*A*a^7*b^4 + 7*B*a^6*b^5 - 43*A*a^5*b^6 - 2*B*a^4*b^7 + 11*A*a^3*b^8 + (11*B*a^8*b^3 - 26*A*a^7*b^4 - 7*B*a^6*b^5 + 43*A*a^5*b^6 - 4*B*a^4*b^7 - 23*A*a^3*b^8 + 6*A*a*b^10)*cos(d*x + c)^2 + 3*(9*B*a^9*b^2 - 20*A*a^8*b^3 - 8*B*a^7*b^4 + 35*A*a^6*b^5 - B*a^5*b^6 - 20*A*a^4*b^7 + 5*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^12*b^3 - 4*a^10*b^5 + 6*a^8*b^7 - 4*a^6*b^9 + a^4*b^11)*d*cos(d*x + c)^3 + 3*(a^13*b^2 - 4*a^11*b^4 + 6*a^9*b^6 - 4*a^7*b^8 + a^5*b^10)*d*cos(d*x + c)^2 + 3*(a^14*b - 4*a^12*b^3 + 6*a^10*b^5 - 4*a^8*b^7 + a^6*b^9)*d*cos(d*x + c) + (a^15 - 4*a^13*b^2 + 6*a^11*b^4 - 4*a^9*b^6 + a^7*b^8)*d), 1/6*(3*(2*B*a^10 - 8*A*a^9*b + 3*B*a^8*b^2 + 8*A*a^7*b^3 - 7*A*a^5*b^5 + 2*A*a^3*b^7 + (2*B*a^7*b^3 - 8*A*a^6*b^4 + 3*B*a^5*b^5 + 8*A*a^4*b^6 - 7*A*a^2*b^8 + 2*A*b^10)*cos(d*x + c)^3 + 3*(2*B*a^8*b^2 - 8*A*a^7*b^3 + 3*B*a^6*b^4 + 8*A*a^5*b^5 - 7*A*a^3*b^7 + 2*A*a*b^9)*cos(d*x + c)^2 + 3*(2*B*a^9*b - 8*A*a^8*b^2 + 3*B*a^7*b^3 + 8*A*a^6*b^4 - 7*A*a^4*b^6 + 2*A*a^2*b^8)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + 3*(A*a^11 - 4*A*a^9*b^2 + 6*A*a^7*b^4 - 4*A*a^5*b^6 + A*a^3*b^8 + (A*a^8*b^3 - 4*A*a^6*b^5 + 6*A*a^4*b^7 - 4*A*a^2*b^9 + A*b^11)*cos(d*x + c)^3 + 3*(A*a^9*b^2 - 4*A*a^7*b^4 + 6*A*a^5*b^6 - 4*A*a^3*b^8 + A*a*b^10)*cos(d*x + c)^2 + 3*(A*a^10*b - 4*A*a^8*b^3 + 6*A*a^6*b^5 - 4*A*a^4*b^7 + A*a^2*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) - 3*(A*a^11 - 4*A*a^9*b^2 + 6*A*a^7*b^4 - 4*A*a^5*b^6 + A*a^3*b^8 + (A*a^8*b^3 - 4*A*a^6*b^5 + 6*A*a^4*b^7 - 4*A*a^2*b^9 + A*b^11)*cos(d*x + c)^3 + 3*(A*a^9*b^2 - 4*A*a^7*b^4 + 6*A*a^5*b^6 - 4*A*a^3*b^8 + A*a*b^10)*cos(d*x + c)^2 + 3*(A*a^10*b - 4*A*a^8*b^3 + 6*A*a^6*b^5 - 4*A*a^4*b^7 + A*a^2*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) - (18*B*a^10*b - 36*A*a^9*b^2 - 23*B*a^8*b^3 + 68*A*a^7*b^4 + 7*B*a^6*b^5 - 43*A*a^5*b^6 - 2*B*a^4*b^7 + 11*A*a^3*b^8 + (11*B*a^8*b^3 - 26*A*a^7*b^4 - 7*B*a^6*b^5 + 43*A*a^5*b^6 - 4*B*a^4*b^7 - 23*A*a^3*b^8 + 6*A*a*b^10)*cos(d*x + c)^2 + 3*(9*B*a^9*b^2 - 20*A*a^8*b^3 - 8*B*a^7*b^4 + 35*A*a^6*b^5 - B*a^5*b^6 - 20*A*a^4*b^7 + 5*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^12*b^3 - 4*a^10*b^5 + 6*a^8*b^7 - 4*a^6*b^9 + a^4*b^11)*d*cos(d*x + c)^3 + 3*(a^13*b^2 - 4*a^11*b^4 + 6*a^9*b^6 - 4*a^7*b^8 + a^5*b^10)*d*cos(d*x + c)^2 + 3*(a^14*b - 4*a^12*b^3 + 6*a^10*b^5 - 4*a^8*b^7 + a^6*b^9)*d*cos(d*x + c) + (a^15 - 4*a^13*b^2 + 6*a^11*b^4 - 4*a^9*b^6 + a^7*b^8)*d)]","B",0
279,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,1,25,0,0.686133," ","integrate(cos(d*x+c)^3*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(B \cos\left(d x + c\right)^{2} + 2 \, B\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(B*cos(d*x + c)^2 + 2*B)*sin(d*x + c)/d","A",0
282,1,24,0,0.843566," ","integrate(cos(d*x+c)^2*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{B d x + B \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*d*x + B*cos(d*x + c)*sin(d*x + c))/d","A",0
283,1,11,0,0.931913," ","integrate(cos(d*x+c)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{B \sin\left(d x + c\right)}{d}"," ",0,"B*sin(d*x + c)/d","A",0
284,1,3,0,0.510709," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","B x"," ",0,"B*x","A",0
285,1,31,0,1.091613," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{B \log\left(\sin\left(d x + c\right) + 1\right) - B \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, d}"," ",0,"1/2*(B*log(sin(d*x + c) + 1) - B*log(-sin(d*x + c) + 1))/d","B",0
286,1,19,0,0.693471," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{B \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}"," ",0,"B*sin(d*x + c)/(d*cos(d*x + c))","A",0
287,1,64,0,0.654849," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{B \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - B \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(B*cos(d*x + c)^2*log(sin(d*x + c) + 1) - B*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*B*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
288,1,32,0,1.146531," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, B \cos\left(d x + c\right)^{2} + B\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/3*(2*B*cos(d*x + c)^2 + B)*sin(d*x + c)/(d*cos(d*x + c)^3)","A",0
289,1,350,0,0.586893," ","integrate(cos(d*x+c)^3*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} B a^{3} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(2 \, B a^{4} - B a^{2} b^{2} - B b^{4}\right)} d x + {\left(2 \, B a^{3} b - 2 \, B a b^{3} - {\left(B a^{2} b^{2} - B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} - b^{5}\right)} d}, -\frac{2 \, \sqrt{a^{2} - b^{2}} B a^{3} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, B a^{4} - B a^{2} b^{2} - B b^{4}\right)} d x + {\left(2 \, B a^{3} b - 2 \, B a b^{3} - {\left(B a^{2} b^{2} - B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} - b^{5}\right)} d}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*B*a^3*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (2*B*a^4 - B*a^2*b^2 - B*b^4)*d*x + (2*B*a^3*b - 2*B*a*b^3 - (B*a^2*b^2 - B*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d), -1/2*(2*sqrt(a^2 - b^2)*B*a^3*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*B*a^4 - B*a^2*b^2 - B*b^4)*d*x + (2*B*a^3*b - 2*B*a*b^3 - (B*a^2*b^2 - B*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d)]","A",0
290,1,281,0,0.645070," ","integrate(cos(d*x+c)^2*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} B a^{2} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 2 \, {\left(B a^{3} - B a b^{2}\right)} d x - 2 \, {\left(B a^{2} b - B b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d}, \frac{\sqrt{a^{2} - b^{2}} B a^{2} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(B a^{3} - B a b^{2}\right)} d x + {\left(B a^{2} b - B b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*B*a^2*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 2*(B*a^3 - B*a*b^2)*d*x - 2*(B*a^2*b - B*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d), (sqrt(a^2 - b^2)*B*a^2*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (B*a^3 - B*a*b^2)*d*x + (B*a^2*b - B*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d)]","A",0
291,1,231,0,0.868804," ","integrate(cos(d*x+c)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} B a \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(B a^{2} - B b^{2}\right)} d x}{2 \, {\left(a^{2} b - b^{3}\right)} d}, -\frac{\sqrt{a^{2} - b^{2}} B a \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(B a^{2} - B b^{2}\right)} d x}{{\left(a^{2} b - b^{3}\right)} d}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*B*a*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(B*a^2 - B*b^2)*d*x)/((a^2*b - b^3)*d), -(sqrt(a^2 - b^2)*B*a*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (B*a^2 - B*b^2)*d*x)/((a^2*b - b^3)*d)]","A",0
292,1,177,0,0.717984," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} B \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right)}{2 \, {\left(a^{2} - b^{2}\right)} d}, \frac{B \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right)}{\sqrt{a^{2} - b^{2}} d}\right]"," ",0,"[-1/2*sqrt(-a^2 + b^2)*B*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2))/((a^2 - b^2)*d), B*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))/(sqrt(a^2 - b^2)*d)]","A",0
293,1,292,0,0.940695," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} B b \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(B a^{2} - B b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{2} - B b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}, -\frac{2 \, \sqrt{a^{2} - b^{2}} B b \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(B a^{2} - B b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{2} - B b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*B*b*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (B*a^2 - B*b^2)*log(sin(d*x + c) + 1) + (B*a^2 - B*b^2)*log(-sin(d*x + c) + 1))/((a^3 - a*b^2)*d), -1/2*(2*sqrt(a^2 - b^2)*B*b*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (B*a^2 - B*b^2)*log(sin(d*x + c) + 1) + (B*a^2 - B*b^2)*log(-sin(d*x + c) + 1))/((a^3 - a*b^2)*d)]","A",0
294,1,398,0,1.095401," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} B b^{2} \cos\left(d x + c\right) \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + {\left(B a^{2} b - B b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{2} b - B b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{3} - B a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(d x + c\right)}, \frac{2 \, \sqrt{a^{2} - b^{2}} B b^{2} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right) - {\left(B a^{2} b - B b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{2} b - B b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{3} - B a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*B*b^2*cos(d*x + c)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + (B*a^2*b - B*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) - (B*a^2*b - B*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) - 2*(B*a^3 - B*a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d*cos(d*x + c)), 1/2*(2*sqrt(a^2 - b^2)*B*b^2*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))*cos(d*x + c) - (B*a^2*b - B*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) + (B*a^2*b - B*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(B*a^3 - B*a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d*cos(d*x + c))]","B",0
295,1,487,0,0.892077," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{-a^{2} + b^{2}} B b^{3} \cos\left(d x + c\right)^{2} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(B a^{4} + B a^{2} b^{2} - 2 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{4} + B a^{2} b^{2} - 2 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{4} - B a^{2} b^{2} - 2 \, {\left(B a^{3} b - B a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} - a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2}}, -\frac{4 \, \sqrt{a^{2} - b^{2}} B b^{3} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right)^{2} - {\left(B a^{4} + B a^{2} b^{2} - 2 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(B a^{4} + B a^{2} b^{2} - 2 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{4} - B a^{2} b^{2} - 2 \, {\left(B a^{3} b - B a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} - a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[-1/4*(2*sqrt(-a^2 + b^2)*B*b^3*cos(d*x + c)^2*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (B*a^4 + B*a^2*b^2 - 2*B*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (B*a^4 + B*a^2*b^2 - 2*B*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(B*a^4 - B*a^2*b^2 - 2*(B*a^3*b - B*a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d*cos(d*x + c)^2), -1/4*(4*sqrt(a^2 - b^2)*B*b^3*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))*cos(d*x + c)^2 - (B*a^4 + B*a^2*b^2 - 2*B*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (B*a^4 + B*a^2*b^2 - 2*B*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(B*a^4 - B*a^2*b^2 - 2*(B*a^3*b - B*a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d*cos(d*x + c)^2)]","A",0
296,0,0,0,0.585507," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{4} + A \cos\left(d x + c\right)^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)^4 + A*cos(d*x + c)^3)*sqrt(b*cos(d*x + c) + a), x)","F",0
297,0,0,0,0.700066," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
298,0,0,0,0.714507," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
299,0,0,0,0.901145," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a), x)","F",0
300,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,0,0,0,1.043532," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{4} + A a \cos\left(d x + c\right)^{2} + {\left(B a + A b\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^4 + A*a*cos(d*x + c)^2 + (B*a + A*b)*cos(d*x + c)^3)*sqrt(b*cos(d*x + c) + a), x)","F",0
305,0,0,0,0.884012," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{3} + A a \cos\left(d x + c\right) + {\left(B a + A b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^3 + A*a*cos(d*x + c) + (B*a + A*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
306,0,0,0,0.737927," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\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{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
307,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,0,0,0,8.694197," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\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{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
309,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,0,0,0,1.109310," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{5} + A a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^5 + A*a^2*cos(d*x + c)^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^4 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^3)*sqrt(b*cos(d*x + c) + a), x)","F",0
312,0,0,0,1.368830," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{4} + A a^{2} \cos\left(d x + c\right) + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^4 + A*a^2*cos(d*x + c) + (2*B*a*b + A*b^2)*cos(d*x + c)^3 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
313,0,0,0,1.193362," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
314,0,0,0,3.344996," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right), x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
315,0,0,0,6.422349," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
316,0,0,0,8.148715," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
317,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,0,0,0,0.962079," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right)^{4} + A \cos\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*cos(d*x + c)^4 + A*cos(d*x + c)^3)/sqrt(b*cos(d*x + c) + a), x)","F",0
320,0,0,0,0.554742," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)/sqrt(b*cos(d*x + c) + a), x)","F",0
321,0,0,0,0.658181," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
322,0,0,0,0.633758," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/sqrt(b*cos(d*x + c) + a), x)","F",0
323,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,0,0,0,1.202502," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{4} + A \cos\left(d x + c\right)^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^4 + A*cos(d*x + c)^3)*sqrt(b*cos(d*x + c) + a)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
327,0,0,0,1.621637," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
328,0,0,0,1.195033," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
329,0,0,0,1.162599," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
330,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,0,0,0,1.634796," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{5} + A \cos\left(d x + c\right)^{4}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^5 + A*cos(d*x + c)^4)*sqrt(b*cos(d*x + c) + a)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
334,0,0,0,1.471250," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{4} + A \cos\left(d x + c\right)^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^4 + A*cos(d*x + c)^3)*sqrt(b*cos(d*x + c) + a)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
335,0,0,0,1.050489," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
336,0,0,0,0.782906," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
337,0,0,0,0.626753," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
338,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,0,0,0,0.419247," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(B/sqrt(b*cos(d*x + c) + a), x)","F",0
342,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,0,0,0,2.138554," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} B}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*B/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
344,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
345,0,0,0,0.898175," ","integrate(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{4} + A a \cos\left(d x + c\right)^{2} + {\left(B a + A b\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^4 + A*a*cos(d*x + c)^2 + (B*a + A*b)*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
346,0,0,0,0.527475," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{3} + A a \cos\left(d x + c\right) + {\left(B a + A b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^3 + A*a*cos(d*x + c) + (B*a + A*b)*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
347,0,0,0,0.755080," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\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)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
348,0,0,0,0.730964," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
349,0,0,0,0.697046," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
350,0,0,0,0.444455," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))/cos(d*x + c)^(5/2), x)","F",0
351,0,0,0,0.606848," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))/cos(d*x + c)^(7/2), x)","F",0
352,0,0,0,0.495530," ","integrate(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{5} + A a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^5 + A*a^2*cos(d*x + c)^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^4 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
353,0,0,0,0.630524," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{4} + A a^{2} \cos\left(d x + c\right) + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^4 + A*a^2*cos(d*x + c) + (2*B*a*b + A*b^2)*cos(d*x + c)^3 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
354,0,0,0,0.568279," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
355,0,0,0,0.482140," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
356,0,0,0,0.512147," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
357,0,0,0,0.455283," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))/cos(d*x + c)^(5/2), x)","F",0
358,0,0,0,0.444573," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))/cos(d*x + c)^(7/2), x)","F",0
359,0,0,0,0.758520," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \cos\left(d x + c\right)^{5} + A a^{3} \cos\left(d x + c\right) + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^5 + A*a^3*cos(d*x + c) + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^4 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^3 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
360,0,0,0,0.613412," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
361,0,0,0,0.692593," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
362,0,0,0,0.805604," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
363,0,0,0,0.732290," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))/cos(d*x + c)^(5/2), x)","F",0
364,0,0,0,0.588301," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))/cos(d*x + c)^(7/2), x)","F",0
365,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,0,0,0,114.014922," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
367,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,0,0,0,2.562707," ","integrate(cos(d*x+c)^(5/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(B \cos\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral(B*cos(d*x + c)^(5/2), x)","F",0
384,0,0,0,1.126313," ","integrate(cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(B \cos\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(B*cos(d*x + c)^(3/2), x)","F",0
385,0,0,0,1.647520," ","integrate(cos(d*x+c)^(1/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(B \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral(B*sqrt(cos(d*x + c)), x)","F",0
386,0,0,0,1.259076," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral(B/sqrt(cos(d*x + c)), x)","F",0
387,0,0,0,2.571320," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(B/cos(d*x + c)^(3/2), x)","F",0
388,0,0,0,0.455001," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(B/cos(d*x + c)^(5/2), x)","F",0
389,0,0,0,97.865054," ","integrate(cos(d*x+c)^(5/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(B*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
390,0,0,0,94.556934," ","integrate(cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(B*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
391,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,0,0,0,3.760159," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(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)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
397,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,0,0,0,69.787942," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
399,0,0,0,1.029725," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
400,0,0,0,1.799229," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
401,0,0,0,1.025834," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
402,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,0,0,0,176.208535," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\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{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
404,0,0,0,7.271508," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\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{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
405,0,0,0,3.310248," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\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{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
406,0,0,0,2.510730," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\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{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
407,0,0,0,0.911916," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\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{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
408,0,0,0,0.888952," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\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{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
409,0,0,0,0.937006," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\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{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(11/2), x)","F",0
410,0,0,0,9.116678," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{4} + A a^{2} \cos\left(d x + c\right) + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^4 + A*a^2*cos(d*x + c) + (2*B*a*b + A*b^2)*cos(d*x + c)^3 + (B*a^2 + 2*A*a*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
411,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,0,0,0,106.740340," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
413,0,0,0,4.089723," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
414,0,0,0,2.228992," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
415,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,0,0,0,1.042177," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
417,0,0,0,0.533195," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(11/2), x)","F",0
418,0,0,0,0.498419," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{13}{2}}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(13/2), x)","F",0
419,0,0,0,39.857690," ","integrate((a+b*cos(d*x+c))^(5/2)*(3/2*b*B/a+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, B a b^{2} \cos\left(d x + c\right)^{3} + 3 \, B a^{2} b + {\left(4 \, B a^{2} b + 3 \, B b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{3} + 3 \, B a b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{2 \, a \cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(1/2*(2*B*a*b^2*cos(d*x + c)^3 + 3*B*a^2*b + (4*B*a^2*b + 3*B*b^3)*cos(d*x + c)^2 + 2*(B*a^3 + 3*B*a*b^2)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/(a*cos(d*x + c)^(5/2)), x)","F",0
420,0,0,0,2.606064," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
421,0,0,0,1.842404," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
422,0,0,0,1.370338," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)^2 + a*cos(d*x + c)), x)","F",0
423,0,0,0,0.729558," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)^3 + a*cos(d*x + c)^2), x)","F",0
424,0,0,0,0.782182," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)^4 + a*cos(d*x + c)^3), x)","F",0
425,0,0,0,0.523348," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b \cos\left(d x + c\right)^{5} + a \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)^5 + a*cos(d*x + c)^4), x)","F",0
426,0,0,0,99.979877," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
427,0,0,0,2.045802," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
428,0,0,0,0.575242," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \cos\left(d x + c\right)^{3} + 2 \, a b \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^3 + 2*a*b*cos(d*x + c)^2 + a^2*cos(d*x + c)), x)","F",0
429,0,0,0,1.013232," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \cos\left(d x + c\right)^{4} + 2 \, a b \cos\left(d x + c\right)^{3} + a^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^4 + 2*a*b*cos(d*x + c)^3 + a^2*cos(d*x + c)^2), x)","F",0
430,0,0,0,0.664813," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \cos\left(d x + c\right)^{5} + 2 \, a b \cos\left(d x + c\right)^{4} + a^{2} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^5 + 2*a*b*cos(d*x + c)^4 + a^2*cos(d*x + c)^3), x)","F",0
431,0,0,0,3.801264," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
432,0,0,0,1.369953," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
433,0,0,0,1.487793," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
434,0,0,0,0.719449," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \cos\left(d x + c\right)^{4} + 3 \, a b^{2} \cos\left(d x + c\right)^{3} + 3 \, a^{2} b \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^4 + 3*a*b^2*cos(d*x + c)^3 + 3*a^2*b*cos(d*x + c)^2 + a^3*cos(d*x + c)), x)","F",0
435,0,0,0,1.241191," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \cos\left(d x + c\right)^{5} + 3 \, a b^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} b \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^5 + 3*a*b^2*cos(d*x + c)^4 + 3*a^2*b*cos(d*x + c)^3 + a^3*cos(d*x + c)^2), x)","F",0
436,0,0,0,1.955203," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \cos\left(d x + c\right)^{6} + 3 \, a b^{2} \cos\left(d x + c\right)^{5} + 3 \, a^{2} b \cos\left(d x + c\right)^{4} + a^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^6 + 3*a*b^2*cos(d*x + c)^5 + 3*a^2*b*cos(d*x + c)^4 + a^3*cos(d*x + c)^3), x)","F",0
437,0,0,0,53.184093," ","integrate(cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(B*cos(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
438,0,0,0,1.518529," ","integrate(cos(d*x+c)^(1/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(B*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
439,0,0,0,0.820062," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} B \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*B*sqrt(cos(d*x + c))/(b*cos(d*x + c)^2 + a*cos(d*x + c)), x)","F",0
440,0,0,0,2.593418," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} B \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*B*sqrt(cos(d*x + c))/(b*cos(d*x + c)^3 + a*cos(d*x + c)^2), x)","F",0
441,0,0,0,0.871383," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(2+3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, \cos\left(d x + c\right) + 2} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{3 \, \cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(3*cos(d*x + c) + 2)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/(3*cos(d*x + c)^3 + 2*cos(d*x + c)^2), x)","F",0
442,0,0,0,0.916881," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-2+3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, \cos\left(d x + c\right) - 2} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{3 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(3*cos(d*x + c) - 2)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/(3*cos(d*x + c)^3 - 2*cos(d*x + c)^2), x)","F",0
443,0,0,0,0.561494," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(2-3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-3 \, \cos\left(d x + c\right) + 2} \sqrt{\cos\left(d x + c\right)}}{3 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(-(cos(d*x + c) + 1)*sqrt(-3*cos(d*x + c) + 2)*sqrt(cos(d*x + c))/(3*cos(d*x + c)^3 - 2*cos(d*x + c)^2), x)","F",0
444,0,0,0,0.984064," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-2-3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-3 \, \cos\left(d x + c\right) - 2} \sqrt{\cos\left(d x + c\right)}}{3 \, \cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(-(cos(d*x + c) + 1)*sqrt(-3*cos(d*x + c) - 2)*sqrt(cos(d*x + c))/(3*cos(d*x + c)^3 + 2*cos(d*x + c)^2), x)","F",0
445,0,0,0,1.601816," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(3+2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, \cos\left(d x + c\right) + 3} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{2 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(2*cos(d*x + c) + 3)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/(2*cos(d*x + c)^3 + 3*cos(d*x + c)^2), x)","F",0
446,0,0,0,1.172253," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(3-2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-2 \, \cos\left(d x + c\right) + 3} \sqrt{\cos\left(d x + c\right)}}{2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(-(cos(d*x + c) + 1)*sqrt(-2*cos(d*x + c) + 3)*sqrt(cos(d*x + c))/(2*cos(d*x + c)^3 - 3*cos(d*x + c)^2), x)","F",0
447,0,0,0,0.952308," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-3+2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, \cos\left(d x + c\right) - 3} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(2*cos(d*x + c) - 3)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/(2*cos(d*x + c)^3 - 3*cos(d*x + c)^2), x)","F",0
448,0,0,0,1.489847," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-3-2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-2 \, \cos\left(d x + c\right) - 3} \sqrt{\cos\left(d x + c\right)}}{2 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(-(cos(d*x + c) + 1)*sqrt(-2*cos(d*x + c) - 3)*sqrt(cos(d*x + c))/(2*cos(d*x + c)^3 + 3*cos(d*x + c)^2), x)","F",0
449,0,0,0,1.768324," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^n*(A+B*cos(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{n} \left(c \cos\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^n*(c*cos(f*x + e))^m, x)","F",0
450,0,0,0,0.864175," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^4*(A+B*cos(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{4} \cos\left(f x + e\right)^{5} + A a^{4} + {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(f x + e\right)^{4} + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(f x + e\right)\right)} \left(c \cos\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*b^4*cos(f*x + e)^5 + A*a^4 + (4*B*a*b^3 + A*b^4)*cos(f*x + e)^4 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*cos(f*x + e)^3 + 2*(2*B*a^3*b + 3*A*a^2*b^2)*cos(f*x + e)^2 + (B*a^4 + 4*A*a^3*b)*cos(f*x + e))*(c*cos(f*x + e))^m, x)","F",0
451,0,0,0,0.977466," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^3*(A+B*cos(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \cos\left(f x + e\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(f x + e\right)\right)} \left(c \cos\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*b^3*cos(f*x + e)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(f*x + e)^3 + 3*(B*a^2*b + A*a*b^2)*cos(f*x + e)^2 + (B*a^3 + 3*A*a^2*b)*cos(f*x + e))*(c*cos(f*x + e))^m, x)","F",0
452,0,0,0,0.914237," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^2*(A+B*cos(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(f x + e\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(f x + e\right)\right)} \left(c \cos\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*b^2*cos(f*x + e)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(f*x + e)^2 + (B*a^2 + 2*A*a*b)*cos(f*x + e))*(c*cos(f*x + e))^m, x)","F",0
453,0,0,0,0.675232," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))*(A+B*cos(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(f x + e\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(f x + e\right)\right)} \left(c \cos\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*b*cos(f*x + e)^2 + A*a + (B*a + A*b)*cos(f*x + e))*(c*cos(f*x + e))^m, x)","F",0
454,0,0,0,0.895722," ","integrate((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(f x + e\right) + A\right)} \left(c \cos\left(f x + e\right)\right)^{m}}{b \cos\left(f x + e\right) + a}, x\right)"," ",0,"integral((B*cos(f*x + e) + A)*(c*cos(f*x + e))^m/(b*cos(f*x + e) + a), x)","F",0
455,0,0,0,1.977085," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^(3/2)*(A+B*cos(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(f x + e\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(f x + e\right)\right)} \sqrt{b \cos\left(f x + e\right) + a} \left(c \cos\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*b*cos(f*x + e)^2 + A*a + (B*a + A*b)*cos(f*x + e))*sqrt(b*cos(f*x + e) + a)*(c*cos(f*x + e))^m, x)","F",0
456,0,0,0,1.000674," ","integrate((c*cos(f*x+e))^m*(A+B*cos(f*x+e))*(a+b*cos(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(f x + e\right) + A\right)} \sqrt{b \cos\left(f x + e\right) + a} \left(c \cos\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*cos(f*x + e) + A)*sqrt(b*cos(f*x + e) + a)*(c*cos(f*x + e))^m, x)","F",0
457,0,0,0,1.026496," ","integrate((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(f x + e\right) + A\right)} \left(c \cos\left(f x + e\right)\right)^{m}}{\sqrt{b \cos\left(f x + e\right) + a}}, x\right)"," ",0,"integral((B*cos(f*x + e) + A)*(c*cos(f*x + e))^m/sqrt(b*cos(f*x + e) + a), x)","F",0
458,0,0,0,1.387558," ","integrate((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(f x + e\right) + A\right)} \sqrt{b \cos\left(f x + e\right) + a} \left(c \cos\left(f x + e\right)\right)^{m}}{b^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(f*x + e) + A)*sqrt(b*cos(f*x + e) + a)*(c*cos(f*x + e))^m/(b^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + a^2), x)","F",0
459,0,0,0,2.104614," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sec(d*x + c)^(7/2), x)","F",0
460,0,0,0,0.847234," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sec(d*x + c)^(5/2), x)","F",0
461,0,0,0,2.415432," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sec(d*x + c)^(3/2), x)","F",0
462,0,0,0,1.064707," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sqrt(sec(d*x + c)), x)","F",0
463,0,0,0,0.828387," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/sqrt(sec(d*x + c)), x)","F",0
464,0,0,0,1.129346," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a \cos\left(d x + c\right)^{2} + {\left(A + B\right)} a \cos\left(d x + c\right) + A a}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/sec(d*x + c)^(3/2), x)","F",0
465,0,0,0,1.892378," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)*sec(d*x + c)^(7/2), x)","F",0
466,0,0,0,0.971294," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)*sec(d*x + c)^(5/2), x)","F",0
467,0,0,0,1.287039," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)*sec(d*x + c)^(3/2), x)","F",0
468,0,0,0,1.098108," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)*sqrt(sec(d*x + c)), x)","F",0
469,0,0,0,0.811811," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + A a^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a^2*cos(d*x + c)^3 + (A + 2*B)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)/sqrt(sec(d*x + c)), x)","F",0
470,0,0,0,0.898998," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(9/2), x)","F",0
471,0,0,0,0.838155," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(7/2), x)","F",0
472,0,0,0,0.635532," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(5/2), x)","F",0
473,0,0,0,0.910110," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(3/2), x)","F",0
474,0,0,0,0.885654," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)*sqrt(sec(d*x + c)), x)","F",0
475,0,0,0,2.494870," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + A a^{3}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*a^3*cos(d*x + c)^4 + (A + 3*B)*a^3*cos(d*x + c)^3 + 3*(A + B)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)/sqrt(sec(d*x + c)), x)","F",0
476,0,0,0,1.437493," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
477,0,0,0,2.115495," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
478,0,0,0,0.449989," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
479,0,0,0,1.088979," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{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)}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
480,0,0,0,0.819005," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{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}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
481,0,0,0,2.452266," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{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}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
482,0,0,0,1.337993," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
483,0,0,0,1.325815," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
484,0,0,0,0.914190," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sqrt(sec(d*x + c))), x)","F",0
485,0,0,0,1.094744," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sec(d*x + c)^(3/2)), x)","F",0
486,0,0,0,2.048407," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sec(d*x + c)^(5/2)), x)","F",0
487,0,0,0,2.311681," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
488,0,0,0,0.853868," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
489,0,0,0,0.927403," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sqrt(sec(d*x + c))), x)","F",0
490,0,0,0,1.260591," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(3/2)), x)","F",0
491,0,0,0,0.508279," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(5/2)), x)","F",0
492,0,0,0,0.539704," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(7/2)), x)","F",0
493,1,121,0,0.674944," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(11/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, {\left(8 \, A + 9 \, B\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(8 \, A + 9 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(8 \, A + 9 \, B\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(8 \, A + 9 \, B\right)} \cos\left(d x + c\right) + 35 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/315*(16*(8*A + 9*B)*cos(d*x + c)^4 + 8*(8*A + 9*B)*cos(d*x + c)^3 + 6*(8*A + 9*B)*cos(d*x + c)^2 + 5*(8*A + 9*B)*cos(d*x + c) + 35*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^5 + d*cos(d*x + c)^4)*sqrt(cos(d*x + c)))","A",0
494,1,104,0,0.645707," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(6 \, A + 7 \, B\right)} \cos\left(d x + c\right) + 15 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/105*(8*(6*A + 7*B)*cos(d*x + c)^3 + 4*(6*A + 7*B)*cos(d*x + c)^2 + 3*(6*A + 7*B)*cos(d*x + c) + 15*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^4 + d*cos(d*x + c)^3)*sqrt(cos(d*x + c)))","A",0
495,1,86,0,0.631446," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(4 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 3 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/15*(2*(4*A + 5*B)*cos(d*x + c)^2 + (4*A + 5*B)*cos(d*x + c) + 3*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^3 + d*cos(d*x + c)^2)*sqrt(cos(d*x + c)))","A",0
496,1,65,0,0.657829," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(2 \, A + 3 \, B\right)} \cos\left(d x + c\right) + A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/3*((2*A + 3*B)*cos(d*x + c) + A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^2 + d*cos(d*x + c))*sqrt(cos(d*x + c)))","A",0
497,1,91,0,0.571435," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(B \cos\left(d x + c\right) + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{\sqrt{a \cos\left(d x + c\right) + a} A \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}\right)}}{d \cos\left(d x + c\right) + d}"," ",0,"-2*((B*cos(d*x + c) + B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - sqrt(a*cos(d*x + c) + a)*A*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
498,1,97,0,0.651011," ","integrate((A+B*cos(d*x+c))*(a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(2 \, A + B\right)} \cos\left(d x + c\right) + 2 \, A + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{d \cos\left(d x + c\right) + d}"," ",0,"(sqrt(a*cos(d*x + c) + a)*B*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*A + B)*cos(d*x + c) + 2*A + B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
499,1,127,0,0.579370," ","integrate((A+B*cos(d*x+c))*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 4 \, A + 3 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(2 \, B \cos\left(d x + c\right)^{2} + {\left(4 \, A + 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/4*(((4*A + 3*B)*cos(d*x + c) + 4*A + 3*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (2*B*cos(d*x + c)^2 + (4*A + 3*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
500,1,146,0,0.829439," ","integrate((A+B*cos(d*x+c))*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 6 \, A + 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(8 \, B \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(6 \, A + 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/24*(3*((6*A + 5*B)*cos(d*x + c) + 6*A + 5*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*B*cos(d*x + c)^3 + 2*(6*A + 5*B)*cos(d*x + c)^2 + 3*(6*A + 5*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
501,1,144,0,0.652095," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, {\left(168 \, A + 187 \, B\right)} a \cos\left(d x + c\right)^{5} + 8 \, {\left(168 \, A + 187 \, B\right)} a \cos\left(d x + c\right)^{4} + 6 \, {\left(168 \, A + 187 \, B\right)} a \cos\left(d x + c\right)^{3} + 5 \, {\left(168 \, A + 187 \, B\right)} a \cos\left(d x + c\right)^{2} + 35 \, {\left(21 \, A + 11 \, B\right)} a \cos\left(d x + c\right) + 315 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{3465 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/3465*(16*(168*A + 187*B)*a*cos(d*x + c)^5 + 8*(168*A + 187*B)*a*cos(d*x + c)^4 + 6*(168*A + 187*B)*a*cos(d*x + c)^3 + 5*(168*A + 187*B)*a*cos(d*x + c)^2 + 35*(21*A + 11*B)*a*cos(d*x + c) + 315*A*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^6 + d*cos(d*x + c)^5)*sqrt(cos(d*x + c)))","A",0
502,1,126,0,0.567966," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right)^{4} + 4 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(34 \, A + 39 \, B\right)} a \cos\left(d x + c\right)^{2} + 5 \, {\left(17 \, A + 9 \, B\right)} a \cos\left(d x + c\right) + 35 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/315*(8*(34*A + 39*B)*a*cos(d*x + c)^4 + 4*(34*A + 39*B)*a*cos(d*x + c)^3 + 3*(34*A + 39*B)*a*cos(d*x + c)^2 + 5*(17*A + 9*B)*a*cos(d*x + c) + 35*A*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^5 + d*cos(d*x + c)^4)*sqrt(cos(d*x + c)))","A",0
503,1,107,0,0.515053," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(52 \, A + 63 \, B\right)} a \cos\left(d x + c\right)^{3} + {\left(52 \, A + 63 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(13 \, A + 7 \, B\right)} a \cos\left(d x + c\right) + 15 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/105*(2*(52*A + 63*B)*a*cos(d*x + c)^3 + (52*A + 63*B)*a*cos(d*x + c)^2 + 3*(13*A + 7*B)*a*cos(d*x + c) + 15*A*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^4 + d*cos(d*x + c)^3)*sqrt(cos(d*x + c)))","A",0
504,1,88,0,0.796157," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(18 \, A + 25 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(9 \, A + 5 \, B\right)} a \cos\left(d x + c\right) + 3 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/15*((18*A + 25*B)*a*cos(d*x + c)^2 + (9*A + 5*B)*a*cos(d*x + c) + 3*A*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^3 + d*cos(d*x + c)^2)*sqrt(cos(d*x + c)))","A",0
505,1,130,0,0.613669," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, {\left(B a \cos\left(d x + c\right)^{2} + B a \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left({\left(5 \, A + 3 \, B\right)} a \cos\left(d x + c\right) + A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}\right)}}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"-2/3*(3*(B*a*cos(d*x + c)^2 + B*a*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - ((5*A + 3*B)*a*cos(d*x + c) + A*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
506,1,119,0,0.614605," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left({\left(2 \, A + 3 \, B\right)} a \cos\left(d x + c\right) + {\left(2 \, A + 3 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(B a \cos\left(d x + c\right) + 2 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{d \cos\left(d x + c\right) + d}"," ",0,"-(((2*A + 3*B)*a*cos(d*x + c) + (2*A + 3*B)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (B*a*cos(d*x + c) + 2*A*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
507,1,133,0,0.603850," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(12 \, A + 7 \, B\right)} a \cos\left(d x + c\right) + {\left(12 \, A + 7 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(2 \, B a \cos\left(d x + c\right)^{2} + {\left(4 \, A + 7 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/4*(((12*A + 7*B)*a*cos(d*x + c) + (12*A + 7*B)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (2*B*a*cos(d*x + c)^2 + (4*A + 7*B)*a*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
508,1,153,0,0.689924," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right) + {\left(14 \, A + 11 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(8 \, B a \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, A + 11 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(14 \, A + 11 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/24*(3*((14*A + 11*B)*a*cos(d*x + c) + (14*A + 11*B)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*B*a*cos(d*x + c)^3 + 2*(6*A + 11*B)*a*cos(d*x + c)^2 + 3*(14*A + 11*B)*a*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
509,1,171,0,0.691141," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right) + {\left(88 \, A + 75 \, B\right)} a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(48 \, B a \cos\left(d x + c\right)^{4} + 8 \, {\left(8 \, A + 15 \, B\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(88 \, A + 75 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/192*(3*((88*A + 75*B)*a*cos(d*x + c) + (88*A + 75*B)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (48*B*a*cos(d*x + c)^4 + 8*(8*A + 15*B)*a*cos(d*x + c)^3 + 2*(88*A + 75*B)*a*cos(d*x + c)^2 + 3*(88*A + 75*B)*a*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
510,1,176,0,0.566518," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(15/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, {\left(4184 \, A + 4615 \, B\right)} a^{2} \cos\left(d x + c\right)^{6} + 8 \, {\left(4184 \, A + 4615 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + 6 \, {\left(4184 \, A + 4615 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(4184 \, A + 4615 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 35 \, {\left(523 \, A + 416 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 315 \, {\left(38 \, A + 13 \, B\right)} a^{2} \cos\left(d x + c\right) + 3465 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{45045 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/45045*(16*(4184*A + 4615*B)*a^2*cos(d*x + c)^6 + 8*(4184*A + 4615*B)*a^2*cos(d*x + c)^5 + 6*(4184*A + 4615*B)*a^2*cos(d*x + c)^4 + 5*(4184*A + 4615*B)*a^2*cos(d*x + c)^3 + 35*(523*A + 416*B)*a^2*cos(d*x + c)^2 + 315*(38*A + 13*B)*a^2*cos(d*x + c) + 3465*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^7 + d*cos(d*x + c)^6)*sqrt(cos(d*x + c)))","A",0
511,1,156,0,0.691104," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} + 4 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(710 \, A + 803 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 5 \, {\left(355 \, A + 286 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 35 \, {\left(32 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right) + 315 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{3465 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/3465*(8*(710*A + 803*B)*a^2*cos(d*x + c)^5 + 4*(710*A + 803*B)*a^2*cos(d*x + c)^4 + 3*(710*A + 803*B)*a^2*cos(d*x + c)^3 + 5*(355*A + 286*B)*a^2*cos(d*x + c)^2 + 35*(32*A + 11*B)*a^2*cos(d*x + c) + 315*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^6 + d*cos(d*x + c)^5)*sqrt(cos(d*x + c)))","A",0
512,1,135,0,0.747948," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(292 \, A + 345 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(292 \, A + 345 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(73 \, A + 60 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 5 \, {\left(26 \, A + 9 \, B\right)} a^{2} \cos\left(d x + c\right) + 35 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/315*(2*(292*A + 345*B)*a^2*cos(d*x + c)^4 + (292*A + 345*B)*a^2*cos(d*x + c)^3 + 3*(73*A + 60*B)*a^2*cos(d*x + c)^2 + 5*(26*A + 9*B)*a^2*cos(d*x + c) + 35*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^5 + d*cos(d*x + c)^4)*sqrt(cos(d*x + c)))","A",0
513,1,114,0,0.571986," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(230 \, A + 301 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(115 \, A + 98 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, A + 7 \, B\right)} a^{2} \cos\left(d x + c\right) + 15 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/105*((230*A + 301*B)*a^2*cos(d*x + c)^3 + (115*A + 98*B)*a^2*cos(d*x + c)^2 + 3*(20*A + 7*B)*a^2*cos(d*x + c) + 15*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^4 + d*cos(d*x + c)^3)*sqrt(cos(d*x + c)))","A",0
514,1,162,0,0.645881," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, {\left(B a^{2} \cos\left(d x + c\right)^{3} + B a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left({\left(43 \, A + 40 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right) + 3 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}\right)}}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-2/15*(15*(B*a^2*cos(d*x + c)^3 + B*a^2*cos(d*x + c)^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - ((43*A + 40*B)*a^2*cos(d*x + c)^2 + (14*A + 5*B)*a^2*cos(d*x + c) + 3*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
515,1,166,0,0.584416," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(3 \, B a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A + 3 \, B\right)} a^{2} \cos\left(d x + c\right) + 2 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*((2*A + 5*B)*a^2*cos(d*x + c)^2 + (2*A + 5*B)*a^2*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (3*B*a^2*cos(d*x + c)^2 + 2*(8*A + 3*B)*a^2*cos(d*x + c) + 2*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
516,1,147,0,0.617085," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left({\left(20 \, A + 19 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(20 \, A + 19 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(2 \, B a^{2} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 11 \, B\right)} a^{2} \cos\left(d x + c\right) + 8 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/4*(((20*A + 19*B)*a^2*cos(d*x + c) + (20*A + 19*B)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (2*B*a^2*cos(d*x + c)^2 + (4*A + 11*B)*a^2*cos(d*x + c) + 8*A*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
517,1,163,0,0.801569," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(38 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(38 \, A + 25 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(8 \, B a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, A + 17 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(22 \, A + 25 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/24*(3*((38*A + 25*B)*a^2*cos(d*x + c) + (38*A + 25*B)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*B*a^2*cos(d*x + c)^3 + 2*(6*A + 17*B)*a^2*cos(d*x + c)^2 + 3*(22*A + 25*B)*a^2*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
518,1,183,0,0.926760," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(200 \, A + 163 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(48 \, B a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(8 \, A + 23 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(136 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(200 \, A + 163 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/192*(3*((200*A + 163*B)*a^2*cos(d*x + c) + (200*A + 163*B)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (48*B*a^2*cos(d*x + c)^4 + 8*(8*A + 23*B)*a^2*cos(d*x + c)^3 + 2*(136*A + 163*B)*a^2*cos(d*x + c)^2 + 3*(200*A + 163*B)*a^2*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
519,1,203,0,0.960208," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(326 \, A + 283 \, B\right)} a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(384 \, B a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(10 \, A + 29 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(230 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(326 \, A + 283 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{1920 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/1920*(15*((326*A + 283*B)*a^2*cos(d*x + c) + (326*A + 283*B)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (384*B*a^2*cos(d*x + c)^5 + 48*(10*A + 29*B)*a^2*cos(d*x + c)^4 + 8*(230*A + 283*B)*a^2*cos(d*x + c)^3 + 10*(326*A + 283*B)*a^2*cos(d*x + c)^2 + 15*(326*A + 283*B)*a^2*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
520,1,198,0,1.380102," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(11/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\frac{315 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{5} + {\left(A - B\right)} a \cos\left(d x + c\right)^{4}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \frac{2 \, {\left({\left(257 \, A - 129 \, B\right)} \cos\left(d x + c\right)^{4} - {\left(29 \, A - 93 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} - 5 \, {\left(A - 9 \, B\right)} \cos\left(d x + c\right) + 35 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{315 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/315*(315*sqrt(2)*((A - B)*a*cos(d*x + c)^5 + (A - B)*a*cos(d*x + c)^4)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*((257*A - 129*B)*cos(d*x + c)^4 - (29*A - 93*B)*cos(d*x + c)^3 + 3*(19*A - 3*B)*cos(d*x + c)^2 - 5*(A - 9*B)*cos(d*x + c) + 35*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)^5 + a*d*cos(d*x + c)^4)","A",0
521,1,181,0,0.739965," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\frac{105 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B\right)} a \cos\left(d x + c\right)^{3}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \frac{2 \, {\left({\left(43 \, A - 91 \, B\right)} \cos\left(d x + c\right)^{3} - {\left(31 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A - 7 \, B\right)} \cos\left(d x + c\right) - 15 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{105 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/105*(105*sqrt(2)*((A - B)*a*cos(d*x + c)^4 + (A - B)*a*cos(d*x + c)^3)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*((43*A - 91*B)*cos(d*x + c)^3 - (31*A - 7*B)*cos(d*x + c)^2 + 3*(A - 7*B)*cos(d*x + c) - 15*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
522,1,164,0,0.553471," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\frac{15 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B\right)} a \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \frac{2 \, {\left({\left(13 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(A - 5 \, B\right)} \cos\left(d x + c\right) + 3 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{15 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/15*(15*sqrt(2)*((A - B)*a*cos(d*x + c)^3 + (A - B)*a*cos(d*x + c)^2)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*((13*A - 5*B)*cos(d*x + c)^2 - (A - 5*B)*cos(d*x + c) + 3*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
523,1,143,0,1.825755," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\frac{3 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B\right)} a \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \frac{2 \, {\left({\left(A - 3 \, B\right)} \cos\left(d x + c\right) - A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{3 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*sqrt(2)*((A - B)*a*cos(d*x + c)^2 + (A - B)*a*cos(d*x + c))*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*((A - 3*B)*cos(d*x + c) - A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
524,1,110,0,0.766337," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} A \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{a d \cos\left(d x + c\right) + a d}"," ",0,"(sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*sqrt(a*cos(d*x + c) + a)*A*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d)","A",0
525,1,96,0,3.095034," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(A - B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, B \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{a d}"," ",0,"-(sqrt(2)*(A - B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*B*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a*d)","A",0
526,1,168,0,7.176071," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(2 \, A - B\right)} \cos\left(d x + c\right) + 2 \, A - B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{a d \cos\left(d x + c\right) + a d}"," ",0,"(sqrt(a*cos(d*x + c) + a)*B*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*A - B)*cos(d*x + c) + 2*A - B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
527,1,194,0,6.973150," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(4 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 4 \, A - 7 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{4 \, \sqrt{2} {\left({\left(A - B\right)} a \cos\left(d x + c\right) + {\left(A - B\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \frac{{\left(2 \, B \cos\left(d x + c\right)^{2} + {\left(4 \, A - B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/4*(((4*A - 7*B)*cos(d*x + c) + 4*A - 7*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 4*sqrt(2)*((A - B)*a*cos(d*x + c) + (A - B)*a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + (2*B*cos(d*x + c)^2 + (4*A - B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d)","A",0
528,1,208,0,33.098085," ","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=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} B b \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left(2 \, B a + {\left(2 \, A - B\right)} b + {\left(2 \, B a + {\left(2 \, A - B\right)} b\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{\sqrt{2} {\left({\left(A - B\right)} a^{2} - {\left(A - B\right)} a b + {\left({\left(A - B\right)} a^{2} - {\left(A - B\right)} a b\right)} \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{a d \cos\left(d x + c\right) + a d}"," ",0,"(sqrt(a*cos(d*x + c) + a)*B*b*sqrt(cos(d*x + c))*sin(d*x + c) - (2*B*a + (2*A - B)*b + (2*B*a + (2*A - B)*b)*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - sqrt(2)*((A - B)*a^2 - (A - B)*a*b + ((A - B)*a^2 - (A - B)*a*b)*cos(d*x + c))*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
529,1,237,0,0.693655," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{2} {\left({\left(19 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(19 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{4} + {\left(19 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(1201 \, A - 1029 \, B\right)} \cos\left(d x + c\right)^{4} + 12 \, {\left(67 \, A - 63 \, B\right)} \cos\left(d x + c\right)^{3} - 28 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(3 \, A - 7 \, B\right)} \cos\left(d x + c\right) - 60 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{420 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} + 2 \, a^{2} d \cos\left(d x + c\right)^{4} + a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/420*(105*sqrt(2)*((19*A - 15*B)*cos(d*x + c)^5 + 2*(19*A - 15*B)*cos(d*x + c)^4 + (19*A - 15*B)*cos(d*x + c)^3)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((1201*A - 1029*B)*cos(d*x + c)^4 + 12*(67*A - 63*B)*cos(d*x + c)^3 - 28*(7*A - 3*B)*cos(d*x + c)^2 + 12*(3*A - 7*B)*cos(d*x + c) - 60*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^5 + 2*a^2*d*cos(d*x + c)^4 + a^2*d*cos(d*x + c)^3)","A",0
530,1,220,0,2.016279," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(15 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(147 \, A - 95 \, B\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(9 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(3 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 12 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{60 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/60*(15*sqrt(2)*((15*A - 11*B)*cos(d*x + c)^4 + 2*(15*A - 11*B)*cos(d*x + c)^3 + (15*A - 11*B)*cos(d*x + c)^2)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((147*A - 95*B)*cos(d*x + c)^3 + 12*(9*A - 5*B)*cos(d*x + c)^2 - 4*(3*A - 5*B)*cos(d*x + c) + 12*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)","A",0
531,1,197,0,0.603665," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, A - 7 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(19 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(A - B\right)} \cos\left(d x + c\right) - 4 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/12*(3*sqrt(2)*((11*A - 7*B)*cos(d*x + c)^3 + 2*(11*A - 7*B)*cos(d*x + c)^2 + (11*A - 7*B)*cos(d*x + c))*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((19*A - 15*B)*cos(d*x + c)^2 + 12*(A - B)*cos(d*x + c) - 4*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))","A",0
532,1,163,0,0.755917," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 7 \, A - 3 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(5 \, A - B\right)} \cos\left(d x + c\right) + 4 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/4*(sqrt(2)*((7*A - 3*B)*cos(d*x + c)^2 + 2*(7*A - 3*B)*cos(d*x + c) + 7*A - 3*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((5*A - B)*cos(d*x + c) + 4*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
533,1,144,0,0.714492," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right) + 3 \, A + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(A - B\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/4*(sqrt(2)*((3*A + B)*cos(d*x + c)^2 + 2*(3*A + B)*cos(d*x + c) + 3*A + B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*(A - B)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
534,1,203,0,8.003442," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 5 \, B\right)} \cos\left(d x + c\right) + A - 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(A - B\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, {\left(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/4*(sqrt(2)*((A - 5*B)*cos(d*x + c)^2 + 2*(A - 5*B)*cos(d*x + c) + A - 5*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(A - B)*sqrt(cos(d*x + c))*sin(d*x + c) + 8*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
535,1,246,0,10.958223," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - 9 \, B\right)} \cos\left(d x + c\right) + 5 \, A - 9 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 4 \, {\left({\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 3 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(2 \, B \cos\left(d x + c\right)^{2} - {\left(A - 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/4*(sqrt(2)*((5*A - 9*B)*cos(d*x + c)^2 + 2*(5*A - 9*B)*cos(d*x + c) + 5*A - 9*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 4*((2*A - 3*B)*cos(d*x + c)^2 + 2*(2*A - 3*B)*cos(d*x + c) + 2*A - 3*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(2*B*cos(d*x + c)^2 - (A - 3*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
536,1,266,0,0.606785," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(283 \, A - 163 \, B\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(2671 \, A - 1495 \, B\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(911 \, A - 503 \, B\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(49 \, A - 25 \, B\right)} \cos\left(d x + c\right)^{2} - 160 \, {\left(A - B\right)} \cos\left(d x + c\right) + 96 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{480 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/480*(15*sqrt(2)*((283*A - 163*B)*cos(d*x + c)^5 + 3*(283*A - 163*B)*cos(d*x + c)^4 + 3*(283*A - 163*B)*cos(d*x + c)^3 + (283*A - 163*B)*cos(d*x + c)^2)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((2671*A - 1495*B)*cos(d*x + c)^4 + 5*(911*A - 503*B)*cos(d*x + c)^3 + 32*(49*A - 25*B)*cos(d*x + c)^2 - 160*(A - B)*cos(d*x + c) + 96*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2)","A",0
537,1,246,0,0.873418," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(163 \, A - 75 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(299 \, A - 147 \, B\right)} \cos\left(d x + c\right)^{3} + {\left(503 \, A - 255 \, B\right)} \cos\left(d x + c\right)^{2} + 32 \, {\left(5 \, A - 3 \, B\right)} \cos\left(d x + c\right) - 32 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{96 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/96*(3*sqrt(2)*((163*A - 75*B)*cos(d*x + c)^4 + 3*(163*A - 75*B)*cos(d*x + c)^3 + 3*(163*A - 75*B)*cos(d*x + c)^2 + (163*A - 75*B)*cos(d*x + c))*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((299*A - 147*B)*cos(d*x + c)^3 + (503*A - 255*B)*cos(d*x + c)^2 + 32*(5*A - 3*B)*cos(d*x + c) - 32*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))","A",0
538,1,210,0,0.742896," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 19 \, B\right)} \cos\left(d x + c\right) + 75 \, A - 19 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(49 \, A - 9 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(85 \, A - 13 \, B\right)} \cos\left(d x + c\right) + 32 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(sqrt(2)*((75*A - 19*B)*cos(d*x + c)^3 + 3*(75*A - 19*B)*cos(d*x + c)^2 + 3*(75*A - 19*B)*cos(d*x + c) + 75*A - 19*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((49*A - 9*B)*cos(d*x + c)^2 + (85*A - 13*B)*cos(d*x + c) + 32*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
539,1,207,0,0.715680," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(9 \, A - B\right)} \cos\left(d x + c\right)^{2} + {\left(13 \, A - 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/32*(sqrt(2)*((19*A + 5*B)*cos(d*x + c)^3 + 3*(19*A + 5*B)*cos(d*x + c)^2 + 3*(19*A + 5*B)*cos(d*x + c) + 19*A + 5*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((9*A - B)*cos(d*x + c)^2 + (13*A - 5*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
540,1,205,0,0.568171," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left({\left(A + 7 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A + 3 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/32*(sqrt(2)*((5*A + 3*B)*cos(d*x + c)^3 + 3*(5*A + 3*B)*cos(d*x + c)^2 + 3*(5*A + 3*B)*cos(d*x + c) + 5*A + 3*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*((A + 7*B)*cos(d*x + c)^2 + (5*A + 3*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
541,1,277,0,16.161728," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 43 \, B\right)} \cos\left(d x + c\right) + 3 \, A - 43 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + 64 \, {\left(B \cos\left(d x + c\right)^{3} + 3 \, B \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left({\left(7 \, A - 15 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/32*(sqrt(2)*((3*A - 43*B)*cos(d*x + c)^3 + 3*(3*A - 43*B)*cos(d*x + c)^2 + 3*(3*A - 43*B)*cos(d*x + c) + 3*A - 43*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 64*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*((7*A - 15*B)*cos(d*x + c)^2 + (3*A - 11*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
542,1,313,0,29.034729," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 115 \, B\right)} \cos\left(d x + c\right) + 43 \, A - 115 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 32 \, {\left({\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(16 \, B \cos\left(d x + c\right)^{3} - 5 \, {\left(3 \, A - 11 \, B\right)} \cos\left(d x + c\right)^{2} - {\left(11 \, A - 35 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(sqrt(2)*((43*A - 115*B)*cos(d*x + c)^3 + 3*(43*A - 115*B)*cos(d*x + c)^2 + 3*(43*A - 115*B)*cos(d*x + c) + 43*A - 115*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 32*((2*A - 5*B)*cos(d*x + c)^3 + 3*(2*A - 5*B)*cos(d*x + c)^2 + 3*(2*A - 5*B)*cos(d*x + c) + 2*A - 5*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(16*B*cos(d*x + c)^3 - 5*(3*A - 11*B)*cos(d*x + c)^2 - (11*A - 35*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
543,1,295,0,0.835998," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(1015 \, A - 363 \, B\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(1015 \, A - 363 \, B\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(1015 \, A - 363 \, B\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(1015 \, A - 363 \, B\right)} \cos\left(d x + c\right)^{2} + {\left(1015 \, A - 363 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(1887 \, A - 691 \, B\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2541 \, A - 937 \, B\right)} \cos\left(d x + c\right)^{3} + 39 \, {\left(109 \, A - 41 \, B\right)} \cos\left(d x + c\right)^{2} + 128 \, {\left(7 \, A - 3 \, B\right)} \cos\left(d x + c\right) - 128 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} + 4 \, a^{4} d \cos\left(d x + c\right)^{4} + 6 \, a^{4} d \cos\left(d x + c\right)^{3} + 4 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/384*(3*sqrt(2)*((1015*A - 363*B)*cos(d*x + c)^5 + 4*(1015*A - 363*B)*cos(d*x + c)^4 + 6*(1015*A - 363*B)*cos(d*x + c)^3 + 4*(1015*A - 363*B)*cos(d*x + c)^2 + (1015*A - 363*B)*cos(d*x + c))*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((1887*A - 691*B)*cos(d*x + c)^4 + 2*(2541*A - 937*B)*cos(d*x + c)^3 + 39*(109*A - 41*B)*cos(d*x + c)^2 + 128*(7*A - 3*B)*cos(d*x + c) - 128*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^5 + 4*a^4*d*cos(d*x + c)^4 + 6*a^4*d*cos(d*x + c)^3 + 4*a^4*d*cos(d*x + c)^2 + a^4*d*cos(d*x + c))","A",0
544,1,260,0,1.336997," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{9 \, \sqrt{2} {\left({\left(121 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(121 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(121 \, A - 21 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(121 \, A - 21 \, B\right)} \cos\left(d x + c\right) + 121 \, A - 21 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(691 \, A - 103 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(937 \, A - 133 \, B\right)} \cos\left(d x + c\right)^{2} + 39 \, {\left(41 \, A - 5 \, B\right)} \cos\left(d x + c\right) + 384 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(9*sqrt(2)*((121*A - 21*B)*cos(d*x + c)^4 + 4*(121*A - 21*B)*cos(d*x + c)^3 + 6*(121*A - 21*B)*cos(d*x + c)^2 + 4*(121*A - 21*B)*cos(d*x + c) + 121*A - 21*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((691*A - 103*B)*cos(d*x + c)^3 + 2*(937*A - 133*B)*cos(d*x + c)^2 + 39*(41*A - 5*B)*cos(d*x + c) + 384*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
545,1,257,0,0.774584," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(63 \, A + 13 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(63 \, A + 13 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(63 \, A + 13 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(63 \, A + 13 \, B\right)} \cos\left(d x + c\right) + 63 \, A + 13 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(103 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(133 \, A - B\right)} \cos\left(d x + c\right)^{2} + 39 \, {\left(5 \, A - B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(3*sqrt(2)*((63*A + 13*B)*cos(d*x + c)^4 + 4*(63*A + 13*B)*cos(d*x + c)^3 + 6*(63*A + 13*B)*cos(d*x + c)^2 + 4*(63*A + 13*B)*cos(d*x + c) + 63*A + 13*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((103*A + 5*B)*cos(d*x + c)^3 + 2*(133*A - B)*cos(d*x + c)^2 + 39*(5*A - B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
546,1,255,0,2.387797," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(13 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(13 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(13 \, A + 7 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(13 \, A + 7 \, B\right)} \cos\left(d x + c\right) + 13 \, A + 7 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left({\left(5 \, A - 17 \, B\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(A + 35 \, B\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(13 \, A + 7 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(3*sqrt(2)*((13*A + 7*B)*cos(d*x + c)^4 + 4*(13*A + 7*B)*cos(d*x + c)^3 + 6*(13*A + 7*B)*cos(d*x + c)^2 + 4*(13*A + 7*B)*cos(d*x + c) + 13*A + 7*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((5*A - 17*B)*cos(d*x + c)^3 - 2*(A + 35*B)*cos(d*x + c)^2 - 3*(13*A + 7*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
547,1,257,0,1.508661," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right) + 7 \, A + 5 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left({\left(17 \, A + 67 \, B\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(7 \, A + 5 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(3*sqrt(2)*((7*A + 5*B)*cos(d*x + c)^4 + 4*(7*A + 5*B)*cos(d*x + c)^3 + 6*(7*A + 5*B)*cos(d*x + c)^2 + 4*(7*A + 5*B)*cos(d*x + c) + 7*A + 5*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*((17*A + 67*B)*cos(d*x + c)^3 + 10*(7*A + 5*B)*cos(d*x + c)^2 + 3*(7*A + 5*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
548,1,338,0,27.169171," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(5 \, A - 177 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(5 \, A - 177 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(5 \, A - 177 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(5 \, A - 177 \, B\right)} \cos\left(d x + c\right) + 5 \, A - 177 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + 768 \, {\left(B \cos\left(d x + c\right)^{4} + 4 \, B \cos\left(d x + c\right)^{3} + 6 \, B \cos\left(d x + c\right)^{2} + 4 \, B \cos\left(d x + c\right) + B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left({\left(67 \, A - 247 \, B\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(25 \, A - 181 \, B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A - 49 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(3*sqrt(2)*((5*A - 177*B)*cos(d*x + c)^4 + 4*(5*A - 177*B)*cos(d*x + c)^3 + 6*(5*A - 177*B)*cos(d*x + c)^2 + 4*(5*A - 177*B)*cos(d*x + c) + 5*A - 177*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 768*(B*cos(d*x + c)^4 + 4*B*cos(d*x + c)^3 + 6*B*cos(d*x + c)^2 + 4*B*cos(d*x + c) + B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*((67*A - 247*B)*cos(d*x + c)^3 + 2*(25*A - 181*B)*cos(d*x + c)^2 + 3*(5*A - 49*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
549,1,379,0,52.359732," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(177 \, A - 637 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(177 \, A - 637 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(177 \, A - 637 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(177 \, A - 637 \, B\right)} \cos\left(d x + c\right) + 177 \, A - 637 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 384 \, {\left({\left(2 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(2 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(2 \, A - 7 \, B\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(2 \, A - 7 \, B\right)} \cos\left(d x + c\right) + 2 \, A - 7 \, B\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(192 \, B \cos\left(d x + c\right)^{4} - {\left(247 \, A - 1099 \, B\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(181 \, A - 721 \, B\right)} \cos\left(d x + c\right)^{2} - 21 \, {\left(7 \, A - 27 \, B\right)} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(3*sqrt(2)*((177*A - 637*B)*cos(d*x + c)^4 + 4*(177*A - 637*B)*cos(d*x + c)^3 + 6*(177*A - 637*B)*cos(d*x + c)^2 + 4*(177*A - 637*B)*cos(d*x + c) + 177*A - 637*B)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 384*((2*A - 7*B)*cos(d*x + c)^4 + 4*(2*A - 7*B)*cos(d*x + c)^3 + 6*(2*A - 7*B)*cos(d*x + c)^2 + 4*(2*A - 7*B)*cos(d*x + c) + 2*A - 7*B)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(192*B*cos(d*x + c)^4 - (247*A - 1099*B)*cos(d*x + c)^3 - 2*(181*A - 721*B)*cos(d*x + c)^2 - 21*(7*A - 27*B)*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
550,0,0,0,0.590386," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\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)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sec(d*x + c)^(7/2), x)","F",0
551,0,0,0,4.579857," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\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)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sec(d*x + c)^(5/2), x)","F",0
552,0,0,0,1.097445," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\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)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sec(d*x + c)^(3/2), x)","F",0
553,0,0,0,1.825984," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\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)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
554,0,0,0,1.726611," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
555,0,0,0,0.736626," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))/sec(d*x + c)^(3/2), x)","F",0
556,0,0,0,0.906954," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sec(d*x + c)^(7/2), x)","F",0
557,0,0,0,2.987279," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sec(d*x + c)^(5/2), x)","F",0
558,0,0,0,1.406195," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sec(d*x + c)^(3/2), x)","F",0
559,0,0,0,1.808598," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
560,0,0,0,0.786084," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
561,0,0,0,1.027568," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sec(d*x + c)^(9/2), x)","F",0
562,0,0,0,1.015018," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sec(d*x + c)^(7/2), x)","F",0
563,0,0,0,1.027191," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sec(d*x + c)^(5/2), x)","F",0
564,0,0,0,0.839126," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sec(d*x + c)^(3/2), x)","F",0
565,0,0,0,1.440116," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
566,0,0,0,0.957943," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B b^{3} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*b^3*cos(d*x + c)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + 3*(B*a^2*b + A*a*b^2)*cos(d*x + c)^2 + (B*a^3 + 3*A*a^2*b)*cos(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
567,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
568,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
569,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
570,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,0,0,0,160.198786," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{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}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
572,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
577,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,0,0,0,1.074779," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(B \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral(B*sec(d*x + c)^(5/2), x)","F",0
585,0,0,0,0.980669," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(B \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(B*sec(d*x + c)^(3/2), x)","F",0
586,0,0,0,1.436843," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(B \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral(B*sqrt(sec(d*x + c)), x)","F",0
587,0,0,0,0.647331," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral(B/sqrt(sec(d*x + c)), x)","F",0
588,0,0,0,0.884723," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(B/sec(d*x + c)^(3/2), x)","F",0
589,0,0,0,1.367003," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(B/sec(d*x + c)^(5/2), x)","F",0
590,0,0,0,1.636179," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(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{9}{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
591,0,0,0,0.562708," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(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}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
592,0,0,0,0.688674," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(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{5}{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
593,0,0,0,1.172617," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(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}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
594,0,0,0,1.473145," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(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)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
595,0,0,0,2.272401," ","integrate((A+B*cos(d*x+c))*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
596,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,0,0,0,2.835151," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\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{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(11/2), x)","F",0
598,0,0,0,1.057567," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\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{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
599,0,0,0,0.580722," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\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{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
600,0,0,0,1.136110," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\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{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
601,0,0,0,1.709242," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\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{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
602,0,0,0,72.047310," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\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{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
603,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,0,0,0,1.062648," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{13}{2}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(13/2), x)","F",0
606,0,0,0,1.167426," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(11/2), x)","F",0
607,0,0,0,1.014795," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
608,0,0,0,27.550318," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
609,0,0,0,65.794383," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
610,0,0,0,2.095125," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
611,0,0,0,94.330016," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
612,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,0,0,0,5.785820," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(d*x + c)^2 + (B*a^2 + 2*A*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
614,0,0,0,0.703362," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
615,0,0,0,0.861381," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
616,0,0,0,0.442619," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
617,0,0,0,1.050127," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
618,0,0,0,1.267226," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
619,0,0,0,1.835281," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{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}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
620,0,0,0,0.558092," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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{5}{2}}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
621,0,0,0,0.485211," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
622,0,0,0,0.541205," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
623,0,0,0,0.866026," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(sec(d*x + c))), x)","F",0
624,0,0,0,53.904229," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sec(d*x + c)^(3/2)), x)","F",0
625,0,0,0,0.612495," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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{5}{2}}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
626,0,0,0,0.581379," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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}}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
627,0,0,0,0.640976," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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)}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
628,0,0,0,0.744607," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sqrt(sec(d*x + c))), x)","F",0
629,0,0,0,25.692228," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sec(d*x + c)^(3/2)), x)","F",0
630,0,0,0,1.601613," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sec(d*x + c)^(5/2)), x)","F",0
631,0,0,0,0.526842," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(B*sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
632,0,0,0,0.643560," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(B*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
633,0,0,0,0.712605," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral(B/(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
634,0,0,0,25.389607," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B}{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(B/(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
635,0,0,0,0.475677," ","integrate((a+b*cos(f*x+e))^n*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{n} \left(c \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^n*(c*sec(f*x + e))^m, x)","F",0
636,0,0,0,0.680964," ","integrate((a+b*cos(f*x+e))^4*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{4} \cos\left(f x + e\right)^{5} + A a^{4} + {\left(4 \, B a b^{3} + A b^{4}\right)} \cos\left(f x + e\right)^{4} + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(f x + e\right)\right)} \left(c \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*b^4*cos(f*x + e)^5 + A*a^4 + (4*B*a*b^3 + A*b^4)*cos(f*x + e)^4 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*cos(f*x + e)^3 + 2*(2*B*a^3*b + 3*A*a^2*b^2)*cos(f*x + e)^2 + (B*a^4 + 4*A*a^3*b)*cos(f*x + e))*(c*sec(f*x + e))^m, x)","F",0
637,0,0,0,0.435487," ","integrate((a+b*cos(f*x+e))^3*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{3} \cos\left(f x + e\right)^{4} + A a^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(f x + e\right)\right)} \left(c \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*b^3*cos(f*x + e)^4 + A*a^3 + (3*B*a*b^2 + A*b^3)*cos(f*x + e)^3 + 3*(B*a^2*b + A*a*b^2)*cos(f*x + e)^2 + (B*a^3 + 3*A*a^2*b)*cos(f*x + e))*(c*sec(f*x + e))^m, x)","F",0
638,0,0,0,0.478066," ","integrate((a+b*cos(f*x+e))^2*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(f x + e\right)^{3} + A a^{2} + {\left(2 \, B a b + A b^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B a^{2} + 2 \, A a b\right)} \cos\left(f x + e\right)\right)} \left(c \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*b^2*cos(f*x + e)^3 + A*a^2 + (2*B*a*b + A*b^2)*cos(f*x + e)^2 + (B*a^2 + 2*A*a*b)*cos(f*x + e))*(c*sec(f*x + e))^m, x)","F",0
639,0,0,0,0.461799," ","integrate((a+b*cos(f*x+e))*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(f x + e\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(f x + e\right)\right)} \left(c \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*b*cos(f*x + e)^2 + A*a + (B*a + A*b)*cos(f*x + e))*(c*sec(f*x + e))^m, x)","F",0
640,0,0,0,0.460863," ","integrate((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(f x + e\right) + A\right)} \left(c \sec\left(f x + e\right)\right)^{m}}{b \cos\left(f x + e\right) + a}, x\right)"," ",0,"integral((B*cos(f*x + e) + A)*(c*sec(f*x + e))^m/(b*cos(f*x + e) + a), x)","F",0
641,0,0,0,0.494514," ","integrate((a+b*cos(f*x+e))^(3/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(f x + e\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(f x + e\right)\right)} \sqrt{b \cos\left(f x + e\right) + a} \left(c \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*b*cos(f*x + e)^2 + A*a + (B*a + A*b)*cos(f*x + e))*sqrt(b*cos(f*x + e) + a)*(c*sec(f*x + e))^m, x)","F",0
642,0,0,0,0.462645," ","integrate((a+b*cos(f*x+e))^(1/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(f x + e\right) + A\right)} \sqrt{b \cos\left(f x + e\right) + a} \left(c \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((B*cos(f*x + e) + A)*sqrt(b*cos(f*x + e) + a)*(c*sec(f*x + e))^m, x)","F",0
643,0,0,0,0.484940," ","integrate((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(f x + e\right) + A\right)} \left(c \sec\left(f x + e\right)\right)^{m}}{\sqrt{b \cos\left(f x + e\right) + a}}, x\right)"," ",0,"integral((B*cos(f*x + e) + A)*(c*sec(f*x + e))^m/sqrt(b*cos(f*x + e) + a), x)","F",0
644,0,0,0,0.462073," ","integrate((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(f x + e\right) + A\right)} \sqrt{b \cos\left(f x + e\right) + a} \left(c \sec\left(f x + e\right)\right)^{m}}{b^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((B*cos(f*x + e) + A)*sqrt(b*cos(f*x + e) + a)*(c*sec(f*x + e))^m/(b^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + a^2), x)","F",0
