1,1,94,0,0.690473," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, C\right)} a d x + {\left(24 \, C a \cos\left(d x + c\right)^{4} + 30 \, C a \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 4 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, A + 3 \, C\right)} a \cos\left(d x + c\right) + 16 \, {\left(5 \, A + 4 \, C\right)} a\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*A + 3*C)*a*d*x + (24*C*a*cos(d*x + c)^4 + 30*C*a*cos(d*x + c)^3 + 8*(5*A + 4*C)*a*cos(d*x + c)^2 + 15*(4*A + 3*C)*a*cos(d*x + c) + 16*(5*A + 4*C)*a)*sin(d*x + c))/d","A",0
2,1,76,0,0.441310," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A + 3 \, C\right)} a d x + {\left(6 \, C a \cos\left(d x + c\right)^{3} + 8 \, C a \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, A + 3 \, C\right)} a \cos\left(d x + c\right) + 8 \, {\left(3 \, A + 2 \, C\right)} a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*A + 3*C)*a*d*x + (6*C*a*cos(d*x + c)^3 + 8*C*a*cos(d*x + c)^2 + 3*(4*A + 3*C)*a*cos(d*x + c) + 8*(3*A + 2*C)*a)*sin(d*x + c))/d","A",0
3,1,56,0,0.438491," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + C\right)} a d x + {\left(2 \, C a \cos\left(d x + c\right)^{2} + 3 \, C a \cos\left(d x + c\right) + 2 \, {\left(3 \, A + 2 \, C\right)} a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*A + C)*a*d*x + (2*C*a*cos(d*x + c)^2 + 3*C*a*cos(d*x + c) + 2*(3*A + 2*C)*a)*sin(d*x + c))/d","A",0
4,1,63,0,0.896841," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{{\left(2 \, A + C\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) + {\left(C a \cos\left(d x + c\right) + 2 \, C a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*A + C)*a*d*x + A*a*log(sin(d*x + c) + 1) - A*a*log(-sin(d*x + c) + 1) + (C*a*cos(d*x + c) + 2*C*a)*sin(d*x + c))/d","A",0
5,1,86,0,1.149818," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, C a d x \cos\left(d x + c\right) + A a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - A a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a \cos\left(d x + c\right) + A a\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*C*a*d*x*cos(d*x + c) + A*a*cos(d*x + c)*log(sin(d*x + c) + 1) - A*a*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(C*a*cos(d*x + c) + A*a)*sin(d*x + c))/(d*cos(d*x + c))","B",0
6,1,101,0,0.551560," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, C a d x \cos\left(d x + c\right)^{2} + {\left(A + 2 \, C\right)} a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A + 2 \, C\right)} a \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A 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*(4*C*a*d*x*cos(d*x + c)^2 + (A + 2*C)*a*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A + 2*C)*a*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*a*cos(d*x + c) + A*a)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
7,1,107,0,0.709737," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(A + 2 \, C\right)} a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A + 2 \, C\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 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, A 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 + 2*C)*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(A + 2*C)*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(2*A + 3*C)*a*cos(d*x + c)^2 + 3*A*a*cos(d*x + c) + 2*A*a)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
8,1,129,0,0.598736," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 4 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, A + 4 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(2 \, A + 3 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 4 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, A 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*C)*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*A + 4*C)*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(2*A + 3*C)*a*cos(d*x + c)^3 + 3*(3*A + 4*C)*a*cos(d*x + c)^2 + 8*A*a*cos(d*x + c) + 6*A*a)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
9,1,126,0,1.112855," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(14 \, A + 11 \, C\right)} a^{2} d x + {\left(40 \, C a^{2} \cos\left(d x + c\right)^{5} + 96 \, C a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(6 \, A + 11 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 32 \, {\left(5 \, A + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(14 \, A + 11 \, C\right)} a^{2} \cos\left(d x + c\right) + 64 \, {\left(5 \, A + 4 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(14*A + 11*C)*a^2*d*x + (40*C*a^2*cos(d*x + c)^5 + 96*C*a^2*cos(d*x + c)^4 + 10*(6*A + 11*C)*a^2*cos(d*x + c)^3 + 32*(5*A + 4*C)*a^2*cos(d*x + c)^2 + 15*(14*A + 11*C)*a^2*cos(d*x + c) + 64*(5*A + 4*C)*a^2)*sin(d*x + c))/d","A",0
10,1,106,0,0.519300," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, C\right)} a^{2} d x + {\left(12 \, C a^{2} \cos\left(d x + c\right)^{4} + 30 \, C a^{2} \cos\left(d x + c\right)^{3} + 4 \, {\left(5 \, A + 9 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, A + 3 \, C\right)} a^{2} \cos\left(d x + c\right) + 4 \, {\left(25 \, A + 18 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(15*(4*A + 3*C)*a^2*d*x + (12*C*a^2*cos(d*x + c)^4 + 30*C*a^2*cos(d*x + c)^3 + 4*(5*A + 9*C)*a^2*cos(d*x + c)^2 + 15*(4*A + 3*C)*a^2*cos(d*x + c) + 4*(25*A + 18*C)*a^2)*sin(d*x + c))/d","A",0
11,1,86,0,0.543481," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(12 \, A + 7 \, C\right)} a^{2} d x + {\left(6 \, C a^{2} \cos\left(d x + c\right)^{3} + 16 \, C a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, A + 7 \, C\right)} a^{2} \cos\left(d x + c\right) + 16 \, {\left(3 \, A + 2 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(12*A + 7*C)*a^2*d*x + (6*C*a^2*cos(d*x + c)^3 + 16*C*a^2*cos(d*x + c)^2 + 3*(4*A + 7*C)*a^2*cos(d*x + c) + 16*(3*A + 2*C)*a^2)*sin(d*x + c))/d","A",0
12,1,95,0,0.682599," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{6 \, {\left(2 \, A + C\right)} a^{2} d x + 3 \, A a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, A a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{2} \cos\left(d x + c\right)^{2} + 3 \, C a^{2} \cos\left(d x + c\right) + {\left(3 \, A + 5 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(6*(2*A + C)*a^2*d*x + 3*A*a^2*log(sin(d*x + c) + 1) - 3*A*a^2*log(-sin(d*x + c) + 1) + 2*(C*a^2*cos(d*x + c)^2 + 3*C*a^2*cos(d*x + c) + (3*A + 5*C)*a^2)*sin(d*x + c))/d","A",0
13,1,116,0,0.680561," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, A + 3 \, C\right)} a^{2} d x \cos\left(d x + c\right) + 2 \, A a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, A a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(C a^{2} \cos\left(d x + c\right)^{2} + 4 \, C a^{2} \cos\left(d x + c\right) + 2 \, A a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((2*A + 3*C)*a^2*d*x*cos(d*x + c) + 2*A*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) - 2*A*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + (C*a^2*cos(d*x + c)^2 + 4*C*a^2*cos(d*x + c) + 2*A*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
14,1,129,0,0.777991," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{8 \, C a^{2} d x \cos\left(d x + c\right)^{2} + {\left(3 \, A + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, A + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{2} \cos\left(d x + c\right)^{2} + 4 \, A 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*(8*C*a^2*d*x*cos(d*x + c)^2 + (3*A + 2*C)*a^2*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (3*A + 2*C)*a^2*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*a^2*cos(d*x + c)^2 + 4*A*a^2*cos(d*x + c) + A*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
15,1,131,0,2.111912," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{6 \, C a^{2} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(A + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(5 \, A + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, A a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(6*C*a^2*d*x*cos(d*x + c)^3 + 3*(A + 2*C)*a^2*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(A + 2*C)*a^2*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*((5*A + 3*C)*a^2*cos(d*x + c)^2 + 3*A*a^2*cos(d*x + c) + A*a^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
16,1,141,0,0.625449," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A + 12 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(7 \, A + 12 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(2 \, A + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, A + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 16 \, A 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 + 12*C)*a^2*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(7*A + 12*C)*a^2*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(2*A + 3*C)*a^2*cos(d*x + c)^3 + 3*(7*A + 4*C)*a^2*cos(d*x + c)^2 + 16*A*a^2*cos(d*x + c) + 6*A*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
17,1,161,0,0.599696," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, A + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, A + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, {\left(18 \, A + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 15 \, {\left(3 \, A + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 4 \, {\left(9 \, A + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 30 \, A a^{2} \cos\left(d x + c\right) + 12 \, A a^{2}\right)} \sin\left(d x + c\right)}{120 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/120*(15*(3*A + 4*C)*a^2*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*A + 4*C)*a^2*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(4*(18*A + 25*C)*a^2*cos(d*x + c)^4 + 15*(3*A + 4*C)*a^2*cos(d*x + c)^3 + 4*(9*A + 5*C)*a^2*cos(d*x + c)^2 + 30*A*a^2*cos(d*x + c) + 12*A*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
18,1,146,0,0.617473," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(26 \, A + 21 \, C\right)} a^{3} d x + {\left(240 \, C a^{3} \cos\left(d x + c\right)^{6} + 840 \, C a^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(7 \, A + 27 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 210 \, {\left(6 \, A + 7 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(133 \, A + 108 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 105 \, {\left(26 \, A + 21 \, C\right)} a^{3} \cos\left(d x + c\right) + 32 \, {\left(133 \, A + 108 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(105*(26*A + 21*C)*a^3*d*x + (240*C*a^3*cos(d*x + c)^6 + 840*C*a^3*cos(d*x + c)^5 + 48*(7*A + 27*C)*a^3*cos(d*x + c)^4 + 210*(6*A + 7*C)*a^3*cos(d*x + c)^3 + 16*(133*A + 108*C)*a^3*cos(d*x + c)^2 + 105*(26*A + 21*C)*a^3*cos(d*x + c) + 32*(133*A + 108*C)*a^3)*sin(d*x + c))/d","A",0
19,1,126,0,1.061750," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(30 \, A + 23 \, C\right)} a^{3} d x + {\left(40 \, C a^{3} \cos\left(d x + c\right)^{5} + 144 \, C a^{3} \cos\left(d x + c\right)^{4} + 10 \, {\left(6 \, A + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(15 \, A + 17 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(30 \, A + 23 \, C\right)} a^{3} \cos\left(d x + c\right) + 16 \, {\left(45 \, A + 34 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(30*A + 23*C)*a^3*d*x + (40*C*a^3*cos(d*x + c)^5 + 144*C*a^3*cos(d*x + c)^4 + 10*(6*A + 23*C)*a^3*cos(d*x + c)^3 + 16*(15*A + 17*C)*a^3*cos(d*x + c)^2 + 15*(30*A + 23*C)*a^3*cos(d*x + c) + 16*(45*A + 34*C)*a^3)*sin(d*x + c))/d","A",0
20,1,106,0,0.636923," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(20 \, A + 13 \, C\right)} a^{3} d x + {\left(24 \, C a^{3} \cos\left(d x + c\right)^{4} + 90 \, C a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 19 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(12 \, A + 13 \, C\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(55 \, A + 38 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(20*A + 13*C)*a^3*d*x + (24*C*a^3*cos(d*x + c)^4 + 90*C*a^3*cos(d*x + c)^3 + 8*(5*A + 19*C)*a^3*cos(d*x + c)^2 + 15*(12*A + 13*C)*a^3*cos(d*x + c) + 8*(55*A + 38*C)*a^3)*sin(d*x + c))/d","A",0
21,1,112,0,2.477376," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{{\left(28 \, A + 15 \, C\right)} a^{3} d x + 4 \, A a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 4 \, A a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{3} \cos\left(d x + c\right)^{3} + 8 \, C a^{3} \cos\left(d x + c\right)^{2} + {\left(4 \, A + 15 \, C\right)} a^{3} \cos\left(d x + c\right) + 24 \, {\left(A + C\right)} a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*((28*A + 15*C)*a^3*d*x + 4*A*a^3*log(sin(d*x + c) + 1) - 4*A*a^3*log(-sin(d*x + c) + 1) + (2*C*a^3*cos(d*x + c)^3 + 8*C*a^3*cos(d*x + c)^2 + (4*A + 15*C)*a^3*cos(d*x + c) + 24*(A + C)*a^3)*sin(d*x + c))/d","A",0
22,1,138,0,0.527548," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(6 \, A + 5 \, C\right)} a^{3} d x \cos\left(d x + c\right) + 9 \, A a^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, A a^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{3} \cos\left(d x + c\right)^{3} + 9 \, C a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + 11 \, C\right)} a^{3} \cos\left(d x + c\right) + 6 \, A a^{3}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(3*(6*A + 5*C)*a^3*d*x*cos(d*x + c) + 9*A*a^3*cos(d*x + c)*log(sin(d*x + c) + 1) - 9*A*a^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*C*a^3*cos(d*x + c)^3 + 9*C*a^3*cos(d*x + c)^2 + 2*(3*A + 11*C)*a^3*cos(d*x + c) + 6*A*a^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
23,1,148,0,1.157823," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, A + 7 \, C\right)} a^{3} d x \cos\left(d x + c\right)^{2} + {\left(7 \, A + 2 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(7 \, A + 2 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{3} \cos\left(d x + c\right)^{3} + 6 \, C a^{3} \cos\left(d x + c\right)^{2} + 6 \, A 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*(2*(2*A + 7*C)*a^3*d*x*cos(d*x + c)^2 + (7*A + 2*C)*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (7*A + 2*C)*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(C*a^3*cos(d*x + c)^3 + 6*C*a^3*cos(d*x + c)^2 + 6*A*a^3*cos(d*x + c) + A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
24,1,151,0,0.674416," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{36 \, C a^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 6 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, A + 6 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, C a^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 9 \, A 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*(36*C*a^3*d*x*cos(d*x + c)^3 + 3*(5*A + 6*C)*a^3*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(5*A + 6*C)*a^3*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*C*a^3*cos(d*x + c)^3 + 2*(11*A + 3*C)*a^3*cos(d*x + c)^2 + 9*A*a^3*cos(d*x + c) + 2*A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
25,1,151,0,0.648285," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{16 \, C a^{3} d x \cos\left(d x + c\right)^{4} + {\left(15 \, A + 28 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(15 \, A + 28 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, {\left(A + C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(15 \, A + 4 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 8 \, A a^{3} \cos\left(d x + c\right) + 2 \, A a^{3}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*C*a^3*d*x*cos(d*x + c)^4 + (15*A + 28*C)*a^3*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (15*A + 28*C)*a^3*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*(A + C)*a^3*cos(d*x + c)^3 + (15*A + 4*C)*a^3*cos(d*x + c)^2 + 8*A*a^3*cos(d*x + c) + 2*A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
26,1,161,0,0.599519," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, A + 20 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(13 \, A + 20 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(38 \, A + 55 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 15 \, {\left(13 \, A + 12 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(19 \, A + 5 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 90 \, A 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 + 20*C)*a^3*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(13*A + 20*C)*a^3*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(38*A + 55*C)*a^3*cos(d*x + c)^4 + 15*(13*A + 12*C)*a^3*cos(d*x + c)^3 + 8*(19*A + 5*C)*a^3*cos(d*x + c)^2 + 90*A*a^3*cos(d*x + c) + 24*A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
27,1,181,0,0.714530," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left(23 \, A + 30 \, C\right)} a^{3} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(23 \, A + 30 \, C\right)} a^{3} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(34 \, A + 45 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} + 15 \, {\left(23 \, A + 30 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 16 \, {\left(17 \, A + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 10 \, {\left(23 \, A + 6 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 144 \, A a^{3} \cos\left(d x + c\right) + 40 \, A a^{3}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(23*A + 30*C)*a^3*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(23*A + 30*C)*a^3*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(34*A + 45*C)*a^3*cos(d*x + c)^5 + 15*(23*A + 30*C)*a^3*cos(d*x + c)^4 + 16*(17*A + 15*C)*a^3*cos(d*x + c)^3 + 10*(23*A + 6*C)*a^3*cos(d*x + c)^2 + 144*A*a^3*cos(d*x + c) + 40*A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
28,1,166,0,0.609414," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(392 \, A + 323 \, C\right)} a^{4} d x + {\left(1680 \, C a^{4} \cos\left(d x + c\right)^{7} + 7680 \, C a^{4} \cos\left(d x + c\right)^{6} + 280 \, {\left(8 \, A + 55 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 1536 \, {\left(7 \, A + 13 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(328 \, A + 323 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 512 \, {\left(63 \, A + 52 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(392 \, A + 323 \, C\right)} a^{4} \cos\left(d x + c\right) + 1024 \, {\left(63 \, A + 52 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{13440 \, d}"," ",0,"1/13440*(105*(392*A + 323*C)*a^4*d*x + (1680*C*a^4*cos(d*x + c)^7 + 7680*C*a^4*cos(d*x + c)^6 + 280*(8*A + 55*C)*a^4*cos(d*x + c)^5 + 1536*(7*A + 13*C)*a^4*cos(d*x + c)^4 + 70*(328*A + 323*C)*a^4*cos(d*x + c)^3 + 512*(63*A + 52*C)*a^4*cos(d*x + c)^2 + 105*(392*A + 323*C)*a^4*cos(d*x + c) + 1024*(63*A + 52*C)*a^4)*sin(d*x + c))/d","A",0
29,1,146,0,0.570594," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(14 \, A + 11 \, C\right)} a^{4} d x + {\left(60 \, C a^{4} \cos\left(d x + c\right)^{6} + 280 \, C a^{4} \cos\left(d x + c\right)^{5} + 12 \, {\left(7 \, A + 48 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(6 \, A + 11 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 4 \, {\left(238 \, A + 227 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(14 \, A + 11 \, C\right)} a^{4} \cos\left(d x + c\right) + 4 \, {\left(581 \, A + 454 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{420 \, d}"," ",0,"1/420*(105*(14*A + 11*C)*a^4*d*x + (60*C*a^4*cos(d*x + c)^6 + 280*C*a^4*cos(d*x + c)^5 + 12*(7*A + 48*C)*a^4*cos(d*x + c)^4 + 70*(6*A + 11*C)*a^4*cos(d*x + c)^3 + 4*(238*A + 227*C)*a^4*cos(d*x + c)^2 + 105*(14*A + 11*C)*a^4*cos(d*x + c) + 4*(581*A + 454*C)*a^4)*sin(d*x + c))/d","A",0
30,1,126,0,0.641445," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(10 \, A + 7 \, C\right)} a^{4} d x + {\left(40 \, C a^{4} \cos\left(d x + c\right)^{5} + 192 \, C a^{4} \cos\left(d x + c\right)^{4} + 10 \, {\left(6 \, A + 41 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 64 \, {\left(5 \, A + 9 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 15 \, {\left(54 \, A + 49 \, C\right)} a^{4} \cos\left(d x + c\right) + 64 \, {\left(25 \, A + 18 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(105*(10*A + 7*C)*a^4*d*x + (40*C*a^4*cos(d*x + c)^5 + 192*C*a^4*cos(d*x + c)^4 + 10*(6*A + 41*C)*a^4*cos(d*x + c)^3 + 64*(5*A + 9*C)*a^4*cos(d*x + c)^2 + 15*(54*A + 49*C)*a^4*cos(d*x + c) + 64*(25*A + 18*C)*a^4)*sin(d*x + c))/d","A",0
31,1,138,0,0.791224," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{15 \, {\left(12 \, A + 7 \, C\right)} a^{4} d x + 15 \, A a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, A a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, C a^{4} \cos\left(d x + c\right)^{4} + 30 \, C a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, A + 34 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, A + 7 \, C\right)} a^{4} \cos\left(d x + c\right) + 2 \, {\left(100 \, A + 83 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(15*(12*A + 7*C)*a^4*d*x + 15*A*a^4*log(sin(d*x + c) + 1) - 15*A*a^4*log(-sin(d*x + c) + 1) + (6*C*a^4*cos(d*x + c)^4 + 30*C*a^4*cos(d*x + c)^3 + 2*(5*A + 34*C)*a^4*cos(d*x + c)^2 + 15*(4*A + 7*C)*a^4*cos(d*x + c) + 2*(100*A + 83*C)*a^4)*sin(d*x + c))/d","A",0
32,1,158,0,0.689655," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(52 \, A + 35 \, C\right)} a^{4} d x \cos\left(d x + c\right) + 48 \, A a^{4} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 48 \, A a^{4} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, C a^{4} \cos\left(d x + c\right)^{4} + 32 \, C a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 27 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 32 \, {\left(3 \, A + 5 \, C\right)} a^{4} \cos\left(d x + c\right) + 24 \, A a^{4}\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}"," ",0,"1/24*(3*(52*A + 35*C)*a^4*d*x*cos(d*x + c) + 48*A*a^4*cos(d*x + c)*log(sin(d*x + c) + 1) - 48*A*a^4*cos(d*x + c)*log(-sin(d*x + c) + 1) + (6*C*a^4*cos(d*x + c)^4 + 32*C*a^4*cos(d*x + c)^3 + 3*(4*A + 27*C)*a^4*cos(d*x + c)^2 + 32*(3*A + 5*C)*a^4*cos(d*x + c) + 24*A*a^4)*sin(d*x + c))/(d*cos(d*x + c))","A",0
33,1,171,0,0.601909," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{24 \, {\left(2 \, A + 3 \, C\right)} a^{4} d x \cos\left(d x + c\right)^{2} + 3 \, {\left(13 \, A + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(13 \, A + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{4} \cos\left(d x + c\right)^{4} + 12 \, C a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A + 20 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 24 \, A a^{4} \cos\left(d x + c\right) + 3 \, A a^{4}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(24*(2*A + 3*C)*a^4*d*x*cos(d*x + c)^2 + 3*(13*A + 2*C)*a^4*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*(13*A + 2*C)*a^4*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*a^4*cos(d*x + c)^4 + 12*C*a^4*cos(d*x + c)^3 + 2*(3*A + 20*C)*a^4*cos(d*x + c)^2 + 24*A*a^4*cos(d*x + c) + 3*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
34,1,170,0,0.786826," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + 13 \, C\right)} a^{4} d x \cos\left(d x + c\right)^{3} + 6 \, {\left(3 \, A + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left(3 \, A + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(3 \, C a^{4} \cos\left(d x + c\right)^{4} + 24 \, C a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(20 \, A + 3 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 12 \, A a^{4} \cos\left(d x + c\right) + 2 \, A a^{4}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(3*(2*A + 13*C)*a^4*d*x*cos(d*x + c)^3 + 6*(3*A + 2*C)*a^4*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 6*(3*A + 2*C)*a^4*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + (3*C*a^4*cos(d*x + c)^4 + 24*C*a^4*cos(d*x + c)^3 + 2*(20*A + 3*C)*a^4*cos(d*x + c)^2 + 12*A*a^4*cos(d*x + c) + 2*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
35,1,171,0,0.641966," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{192 \, C a^{4} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(35 \, A + 52 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(35 \, A + 52 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, C a^{4} \cos\left(d x + c\right)^{4} + 32 \, {\left(5 \, A + 3 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(27 \, A + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 32 \, A 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*(192*C*a^4*d*x*cos(d*x + c)^4 + 3*(35*A + 52*C)*a^4*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(35*A + 52*C)*a^4*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*C*a^4*cos(d*x + c)^4 + 32*(5*A + 3*C)*a^4*cos(d*x + c)^3 + 3*(27*A + 4*C)*a^4*cos(d*x + c)^2 + 32*A*a^4*cos(d*x + c) + 6*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
36,1,177,0,0.602861," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{60 \, C a^{4} d x \cos\left(d x + c\right)^{5} + 15 \, {\left(7 \, A + 12 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(7 \, A + 12 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(83 \, A + 100 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 15 \, {\left(7 \, A + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(34 \, A + 5 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 30 \, A a^{4} \cos\left(d x + c\right) + 6 \, A a^{4}\right)} \sin\left(d x + c\right)}{60 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/60*(60*C*a^4*d*x*cos(d*x + c)^5 + 15*(7*A + 12*C)*a^4*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(7*A + 12*C)*a^4*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(2*(83*A + 100*C)*a^4*cos(d*x + c)^4 + 15*(7*A + 4*C)*a^4*cos(d*x + c)^3 + 2*(34*A + 5*C)*a^4*cos(d*x + c)^2 + 30*A*a^4*cos(d*x + c) + 6*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
37,1,181,0,0.840447," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{105 \, {\left(7 \, A + 10 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(7 \, A + 10 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(64 \, {\left(18 \, A + 25 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 15 \, {\left(49 \, A + 54 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 64 \, {\left(9 \, A + 5 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 10 \, {\left(41 \, A + 6 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 192 \, A 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 + 10*C)*a^4*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 105*(7*A + 10*C)*a^4*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(64*(18*A + 25*C)*a^4*cos(d*x + c)^5 + 15*(49*A + 54*C)*a^4*cos(d*x + c)^4 + 64*(9*A + 5*C)*a^4*cos(d*x + c)^3 + 10*(41*A + 6*C)*a^4*cos(d*x + c)^2 + 192*A*a^4*cos(d*x + c) + 40*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
38,1,201,0,0.731338," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^8,x, algorithm=""fricas"")","\frac{105 \, {\left(11 \, A + 14 \, C\right)} a^{4} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(11 \, A + 14 \, C\right)} a^{4} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, {\left(454 \, A + 581 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} + 105 \, {\left(11 \, A + 14 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 4 \, {\left(227 \, A + 238 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(11 \, A + 6 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 12 \, {\left(48 \, A + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 280 \, A a^{4} \cos\left(d x + c\right) + 60 \, A a^{4}\right)} \sin\left(d x + c\right)}{840 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/840*(105*(11*A + 14*C)*a^4*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(11*A + 14*C)*a^4*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 2*(4*(454*A + 581*C)*a^4*cos(d*x + c)^6 + 105*(11*A + 14*C)*a^4*cos(d*x + c)^5 + 4*(227*A + 238*C)*a^4*cos(d*x + c)^4 + 70*(11*A + 6*C)*a^4*cos(d*x + c)^3 + 12*(48*A + 7*C)*a^4*cos(d*x + c)^2 + 280*A*a^4*cos(d*x + c) + 60*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
39,1,113,0,2.426435," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left(4 \, A + 5 \, C\right)} d x \cos\left(d x + c\right) + 9 \, {\left(4 \, A + 5 \, C\right)} d x + {\left(6 \, C \cos\left(d x + c\right)^{4} - 2 \, C \cos\left(d x + c\right)^{3} + {\left(12 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(12 \, A + 19 \, C\right)} \cos\left(d x + c\right) - 48 \, A - 64 \, C\right)} \sin\left(d x + c\right)}{24 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/24*(9*(4*A + 5*C)*d*x*cos(d*x + c) + 9*(4*A + 5*C)*d*x + (6*C*cos(d*x + c)^4 - 2*C*cos(d*x + c)^3 + (12*A + 13*C)*cos(d*x + c)^2 - (12*A + 19*C)*cos(d*x + c) - 48*A - 64*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
40,1,97,0,0.505019," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(2 \, A + 3 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(2 \, A + 3 \, C\right)} d x - {\left(2 \, C \cos\left(d x + c\right)^{3} - C \cos\left(d x + c\right)^{2} + {\left(6 \, A + 7 \, C\right)} \cos\left(d x + c\right) + 12 \, A + 16 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/6*(3*(2*A + 3*C)*d*x*cos(d*x + c) + 3*(2*A + 3*C)*d*x - (2*C*cos(d*x + c)^3 - C*cos(d*x + c)^2 + (6*A + 7*C)*cos(d*x + c) + 12*A + 16*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
41,1,77,0,0.566297," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, A + 3 \, C\right)} d x \cos\left(d x + c\right) + {\left(2 \, A + 3 \, C\right)} d x + {\left(C \cos\left(d x + c\right)^{2} - C \cos\left(d x + c\right) - 2 \, A - 4 \, C\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*((2*A + 3*C)*d*x*cos(d*x + c) + (2*A + 3*C)*d*x + (C*cos(d*x + c)^2 - C*cos(d*x + c) - 2*A - 4*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
42,1,53,0,0.711761," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{C d x \cos\left(d x + c\right) + C d x - {\left(C \cos\left(d x + c\right) + A + 2 \, C\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"-(C*d*x*cos(d*x + c) + C*d*x - (C*cos(d*x + c) + A + 2*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
43,1,88,0,1.087346," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, C d x \cos\left(d x + c\right) + 2 \, C d x + {\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 + C\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*(2*C*d*x*cos(d*x + c) + 2*C*d*x + (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 + C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
44,1,109,0,0.730729," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(2 \, A + C\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*cos(d*x + c)^2 + A*cos(d*x + c))*log(sin(d*x + c) + 1) - (A*cos(d*x + c)^2 + A*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*((2*A + C)*cos(d*x + c) + A)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
45,1,152,0,0.625665," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(3 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(3 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(2 \, A + C\right)} \cos\left(d x + c\right)^{2} + A \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*C)*cos(d*x + c)^3 + (3*A + 2*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((3*A + 2*C)*cos(d*x + c)^3 + (3*A + 2*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(2*(2*A + C)*cos(d*x + c)^2 + A*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
46,1,172,0,0.612311," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(3 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(3 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, A + 2 \, C\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 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{2} - A \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*(3*((3*A + 2*C)*cos(d*x + c)^4 + (3*A + 2*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((3*A + 2*C)*cos(d*x + c)^4 + (3*A + 2*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(4*(4*A + 3*C)*cos(d*x + c)^3 + (7*A + 6*C)*cos(d*x + c)^2 - A*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
47,1,167,0,0.616091," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(28 \, A + 55 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(28 \, A + 55 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(28 \, A + 55 \, C\right)} d x + {\left(6 \, C \cos\left(d x + c\right)^{5} - 4 \, C \cos\left(d x + c\right)^{4} + {\left(12 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(4 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(172 \, A + 347 \, C\right)} \cos\left(d x + c\right) - 128 \, A - 256 \, C\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/24*(3*(28*A + 55*C)*d*x*cos(d*x + c)^2 + 6*(28*A + 55*C)*d*x*cos(d*x + c) + 3*(28*A + 55*C)*d*x + (6*C*cos(d*x + c)^5 - 4*C*cos(d*x + c)^4 + (12*A + 19*C)*cos(d*x + c)^3 - 6*(4*A + 9*C)*cos(d*x + c)^2 - (172*A + 347*C)*cos(d*x + c) - 128*A - 256*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
48,1,148,0,0.673095," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(2 \, A + 5 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(2 \, A + 5 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(2 \, A + 5 \, C\right)} d x - {\left(C \cos\left(d x + c\right)^{4} - C \cos\left(d x + c\right)^{3} + 3 \, {\left(A + 2 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(14 \, A + 33 \, C\right)} \cos\left(d x + c\right) + 10 \, A + 24 \, C\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/3*(3*(2*A + 5*C)*d*x*cos(d*x + c)^2 + 6*(2*A + 5*C)*d*x*cos(d*x + c) + 3*(2*A + 5*C)*d*x - (C*cos(d*x + c)^4 - C*cos(d*x + c)^3 + 3*(A + 2*C)*cos(d*x + c)^2 + (14*A + 33*C)*cos(d*x + c) + 10*A + 24*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
49,1,134,0,0.712288," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + 7 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(2 \, A + 7 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(2 \, A + 7 \, C\right)} d x + {\left(3 \, C \cos\left(d x + c\right)^{3} - 6 \, C \cos\left(d x + c\right)^{2} - {\left(10 \, A + 43 \, C\right)} \cos\left(d x + c\right) - 8 \, A - 32 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(2*A + 7*C)*d*x*cos(d*x + c)^2 + 6*(2*A + 7*C)*d*x*cos(d*x + c) + 3*(2*A + 7*C)*d*x + (3*C*cos(d*x + c)^3 - 6*C*cos(d*x + c)^2 - (10*A + 43*C)*cos(d*x + c) - 8*A - 32*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
50,1,102,0,1.121656," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, C d x \cos\left(d x + c\right)^{2} + 12 \, C d x \cos\left(d x + c\right) + 6 \, C d x - {\left(3 \, C \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 7 \, C\right)} \cos\left(d x + c\right) + A + 10 \, C\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/3*(6*C*d*x*cos(d*x + c)^2 + 12*C*d*x*cos(d*x + c) + 6*C*d*x - (3*C*cos(d*x + c)^2 + 2*(A + 7*C)*cos(d*x + c) + A + 10*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
51,1,91,0,1.670434," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, C d x \cos\left(d x + c\right)^{2} + 6 \, C d x \cos\left(d x + c\right) + 3 \, C d x + {\left({\left(A - 5 \, C\right)} \cos\left(d x + c\right) + 2 \, A - 4 \, C\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(3*C*d*x*cos(d*x + c)^2 + 6*C*d*x*cos(d*x + c) + 3*C*d*x + ((A - 5*C)*cos(d*x + c) + 2*A - 4*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
52,1,132,0,0.618826," ","integrate((A+C*cos(d*x+c)^2)*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(2 \, {\left(2 \, A - C\right)} \cos\left(d x + c\right) + 5 \, A - C\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(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*(2*(2*A - C)*cos(d*x + c) + 5*A - C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
53,1,167,0,0.546733," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(A \cos\left(d x + c\right)^{3} + 2 \, A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A \cos\left(d x + c\right)^{3} + 2 \, A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left({\left(10 \, A + C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A + C\right)} \cos\left(d x + c\right) + 3 \, A\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*(A*cos(d*x + c)^3 + 2*A*cos(d*x + c)^2 + A*cos(d*x + c))*log(sin(d*x + c) + 1) - 3*(A*cos(d*x + c)^3 + 2*A*cos(d*x + c)^2 + A*cos(d*x + c))*log(-sin(d*x + c) + 1) - ((10*A + C)*cos(d*x + c)^2 + 2*(7*A + C)*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))","A",0
54,1,222,0,0.474929," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(7 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(7 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(8 \, {\left(4 \, A + C\right)} \cos\left(d x + c\right)^{3} + {\left(43 \, A + 10 \, C\right)} \cos\left(d x + c\right)^{2} + 6 \, A \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 + 2*C)*cos(d*x + c)^4 + 2*(7*A + 2*C)*cos(d*x + c)^3 + (7*A + 2*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*((7*A + 2*C)*cos(d*x + c)^4 + 2*(7*A + 2*C)*cos(d*x + c)^3 + (7*A + 2*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(8*(4*A + C)*cos(d*x + c)^3 + (43*A + 10*C)*cos(d*x + c)^2 + 6*A*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
55,1,237,0,1.669394," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(5 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(5 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(5 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(5 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(12 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(33 \, A + 14 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A + C\right)} \cos\left(d x + c\right)^{2} - A \cos\left(d x + c\right) + A\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} + 2 \, a^{2} d \cos\left(d x + c\right)^{4} + a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/6*(3*((5*A + 2*C)*cos(d*x + c)^5 + 2*(5*A + 2*C)*cos(d*x + c)^4 + (5*A + 2*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((5*A + 2*C)*cos(d*x + c)^5 + 2*(5*A + 2*C)*cos(d*x + c)^4 + (5*A + 2*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(2*(12*A + 5*C)*cos(d*x + c)^4 + (33*A + 14*C)*cos(d*x + c)^3 + 3*(2*A + C)*cos(d*x + c)^2 - A*cos(d*x + c) + 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
56,1,201,0,0.716424," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(6 \, A + 23 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(6 \, A + 23 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(6 \, A + 23 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(6 \, A + 23 \, C\right)} d x - {\left(10 \, C \cos\left(d x + c\right)^{5} - 15 \, C \cos\left(d x + c\right)^{4} + 5 \, {\left(6 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(234 \, A + 869 \, C\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(38 \, A + 143 \, C\right)} \cos\left(d x + c\right) + 144 \, A + 544 \, C\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/30*(15*(6*A + 23*C)*d*x*cos(d*x + c)^3 + 45*(6*A + 23*C)*d*x*cos(d*x + c)^2 + 45*(6*A + 23*C)*d*x*cos(d*x + c) + 15*(6*A + 23*C)*d*x - (10*C*cos(d*x + c)^5 - 15*C*cos(d*x + c)^4 + 5*(6*A + 19*C)*cos(d*x + c)^3 + (234*A + 869*C)*cos(d*x + c)^2 + 9*(38*A + 143*C)*cos(d*x + c) + 144*A + 544*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
57,1,184,0,0.721068," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(2 \, A + 13 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(2 \, A + 13 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(2 \, A + 13 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(2 \, A + 13 \, C\right)} d x + {\left(15 \, C \cos\left(d x + c\right)^{4} - 45 \, C \cos\left(d x + c\right)^{3} - {\left(64 \, A + 479 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(34 \, A + 239 \, C\right)} \cos\left(d x + c\right) - 44 \, A - 304 \, C\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(15*(2*A + 13*C)*d*x*cos(d*x + c)^3 + 45*(2*A + 13*C)*d*x*cos(d*x + c)^2 + 45*(2*A + 13*C)*d*x*cos(d*x + c) + 15*(2*A + 13*C)*d*x + (15*C*cos(d*x + c)^4 - 45*C*cos(d*x + c)^3 - (64*A + 479*C)*cos(d*x + c)^2 - 3*(34*A + 239*C)*cos(d*x + c) - 44*A - 304*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
58,1,149,0,1.194214," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{45 \, C d x \cos\left(d x + c\right)^{3} + 135 \, C d x \cos\left(d x + c\right)^{2} + 135 \, C d x \cos\left(d x + c\right) + 45 \, C d x - {\left(15 \, C \cos\left(d x + c\right)^{3} + {\left(7 \, A + 117 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A + 57 \, C\right)} \cos\left(d x + c\right) + 2 \, A + 72 \, C\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/15*(45*C*d*x*cos(d*x + c)^3 + 135*C*d*x*cos(d*x + c)^2 + 135*C*d*x*cos(d*x + c) + 45*C*d*x - (15*C*cos(d*x + c)^3 + (7*A + 117*C)*cos(d*x + c)^2 + 3*(2*A + 57*C)*cos(d*x + c) + 2*A + 72*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
59,1,137,0,0.531519," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, C d x \cos\left(d x + c\right)^{3} + 45 \, C d x \cos\left(d x + c\right)^{2} + 45 \, C d x \cos\left(d x + c\right) + 15 \, C d x + {\left({\left(3 \, A - 32 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 17 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 22 \, C\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(15*C*d*x*cos(d*x + c)^3 + 45*C*d*x*cos(d*x + c)^2 + 45*C*d*x*cos(d*x + c) + 15*C*d*x + ((3*A - 32*C)*cos(d*x + c)^2 + 3*(3*A - 17*C)*cos(d*x + c) + 3*A - 22*C)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
60,1,89,0,1.434293," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(A + C\right)} \cos\left(d x + c\right) + 7 \, A + 2 \, C\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*((2*A + 7*C)*cos(d*x + c)^2 + 6*(A + C)*cos(d*x + c) + 7*A + 2*C)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
61,1,184,0,0.633396," ","integrate((A+C*cos(d*x+c)^2)*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({\left(22 \, A - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(17 \, A - 3 \, C\right)} \cos\left(d x + c\right) + 32 \, A - 3 \, C\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(15*(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*((22*A - 3*C)*cos(d*x + c)^2 + 3*(17*A - 3*C)*cos(d*x + c) + 32*A - 3*C)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
62,1,222,0,0.706818," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{45 \, {\left(A \cos\left(d x + c\right)^{4} + 3 \, A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 45 \, {\left(A \cos\left(d x + c\right)^{4} + 3 \, A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(36 \, A + C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(57 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(117 \, A + 7 \, C\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*(45*(A*cos(d*x + c)^4 + 3*A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 + A*cos(d*x + c))*log(sin(d*x + c) + 1) - 45*(A*cos(d*x + c)^4 + 3*A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 + A*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*(36*A + C)*cos(d*x + c)^3 + 3*(57*A + 2*C)*cos(d*x + c)^2 + (117*A + 7*C)*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
63,1,289,0,0.629783," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(13 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(13 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(13 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(13 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(13 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(13 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(76 \, A + 11 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(239 \, A + 34 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(479 \, A + 64 \, C\right)} \cos\left(d x + c\right)^{2} + 45 \, A \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 + 2*C)*cos(d*x + c)^5 + 3*(13*A + 2*C)*cos(d*x + c)^4 + 3*(13*A + 2*C)*cos(d*x + c)^3 + (13*A + 2*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 15*((13*A + 2*C)*cos(d*x + c)^5 + 3*(13*A + 2*C)*cos(d*x + c)^4 + 3*(13*A + 2*C)*cos(d*x + c)^3 + (13*A + 2*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(76*A + 11*C)*cos(d*x + c)^4 + 3*(239*A + 34*C)*cos(d*x + c)^3 + (479*A + 64*C)*cos(d*x + c)^2 + 45*A*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
64,1,306,0,1.036676," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(23 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(23 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(23 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(23 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(23 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(23 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(23 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(23 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(34 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{5} + 9 \, {\left(143 \, A + 38 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(869 \, A + 234 \, C\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(19 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{2} - 15 \, A \cos\left(d x + c\right) + 10 \, A\right)} \sin\left(d x + c\right)}{60 \, {\left(a^{3} d \cos\left(d x + c\right)^{6} + 3 \, a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + a^{3} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/60*(15*((23*A + 6*C)*cos(d*x + c)^6 + 3*(23*A + 6*C)*cos(d*x + c)^5 + 3*(23*A + 6*C)*cos(d*x + c)^4 + (23*A + 6*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 15*((23*A + 6*C)*cos(d*x + c)^6 + 3*(23*A + 6*C)*cos(d*x + c)^5 + 3*(23*A + 6*C)*cos(d*x + c)^4 + (23*A + 6*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(16*(34*A + 9*C)*cos(d*x + c)^5 + 9*(143*A + 38*C)*cos(d*x + c)^4 + (869*A + 234*C)*cos(d*x + c)^3 + 5*(19*A + 6*C)*cos(d*x + c)^2 - 15*A*cos(d*x + c) + 10*A)*sin(d*x + c))/(a^3*d*cos(d*x + c)^6 + 3*a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + a^3*d*cos(d*x + c)^3)","A",0
65,1,234,0,0.852274," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(2 \, A + 21 \, C\right)} d x \cos\left(d x + c\right)^{4} + 420 \, {\left(2 \, A + 21 \, C\right)} d x \cos\left(d x + c\right)^{3} + 630 \, {\left(2 \, A + 21 \, C\right)} d x \cos\left(d x + c\right)^{2} + 420 \, {\left(2 \, A + 21 \, C\right)} d x \cos\left(d x + c\right) + 105 \, {\left(2 \, A + 21 \, C\right)} d x + {\left(105 \, C \cos\left(d x + c\right)^{5} - 420 \, C \cos\left(d x + c\right)^{4} - 4 \, {\left(130 \, A + 1509 \, C\right)} \cos\left(d x + c\right)^{3} - 4 \, {\left(310 \, A + 3411 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(1070 \, A + 11619 \, C\right)} \cos\left(d x + c\right) - 320 \, A - 3456 \, C\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/210*(105*(2*A + 21*C)*d*x*cos(d*x + c)^4 + 420*(2*A + 21*C)*d*x*cos(d*x + c)^3 + 630*(2*A + 21*C)*d*x*cos(d*x + c)^2 + 420*(2*A + 21*C)*d*x*cos(d*x + c) + 105*(2*A + 21*C)*d*x + (105*C*cos(d*x + c)^5 - 420*C*cos(d*x + c)^4 - 4*(130*A + 1509*C)*cos(d*x + c)^3 - 4*(310*A + 3411*C)*cos(d*x + c)^2 - (1070*A + 11619*C)*cos(d*x + c) - 320*A - 3456*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
66,1,193,0,0.729640," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","-\frac{420 \, C d x \cos\left(d x + c\right)^{4} + 1680 \, C d x \cos\left(d x + c\right)^{3} + 2520 \, C d x \cos\left(d x + c\right)^{2} + 1680 \, C d x \cos\left(d x + c\right) + 420 \, C d x - {\left(105 \, C \cos\left(d x + c\right)^{4} + 4 \, {\left(9 \, A + 296 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A + 2636 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(6 \, A + 559 \, C\right)} \cos\left(d x + c\right) + 6 \, A + 664 \, C\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/105*(420*C*d*x*cos(d*x + c)^4 + 1680*C*d*x*cos(d*x + c)^3 + 2520*C*d*x*cos(d*x + c)^2 + 1680*C*d*x*cos(d*x + c) + 420*C*d*x - (105*C*cos(d*x + c)^4 + 4*(9*A + 296*C)*cos(d*x + c)^3 + (39*A + 2636*C)*cos(d*x + c)^2 + 4*(6*A + 559*C)*cos(d*x + c) + 6*A + 664*C)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
67,1,179,0,0.631366," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, C d x \cos\left(d x + c\right)^{4} + 420 \, C d x \cos\left(d x + c\right)^{3} + 630 \, C d x \cos\left(d x + c\right)^{2} + 420 \, C d x \cos\left(d x + c\right) + 105 \, C d x + {\left(13 \, {\left(A - 20 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(13 \, A - 155 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(32 \, A - 535 \, C\right)} \cos\left(d x + c\right) + 8 \, A - 160 \, C\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(105*C*d*x*cos(d*x + c)^4 + 420*C*d*x*cos(d*x + c)^3 + 630*C*d*x*cos(d*x + c)^2 + 420*C*d*x*cos(d*x + c) + 105*C*d*x + (13*(A - 20*C)*cos(d*x + c)^3 + 4*(13*A - 155*C)*cos(d*x + c)^2 + (32*A - 535*C)*cos(d*x + c) + 8*A - 160*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
68,1,124,0,2.267699," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(2 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(32 \, A + 39 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(13 \, A + 6 \, C\right)} \cos\left(d x + c\right) + 13 \, A + 6 \, C\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(4*(2*A + 9*C)*cos(d*x + c)^3 + (32*A + 39*C)*cos(d*x + c)^2 + 4*(13*A + 6*C)*cos(d*x + c) + 13*A + 6*C)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
69,1,123,0,0.433531," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(6 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(6 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(39 \, A + 32 \, C\right)} \cos\left(d x + c\right) + 36 \, A + 8 \, C\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*((6*A + 13*C)*cos(d*x + c)^3 + 4*(6*A + 13*C)*cos(d*x + c)^2 + (39*A + 32*C)*cos(d*x + c) + 36*A + 8*C)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
70,1,237,0,1.252551," ","integrate((A+C*cos(d*x+c)^2)*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(8 \, {\left(20 \, A - C\right)} \cos\left(d x + c\right)^{3} + {\left(535 \, A - 32 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(155 \, A - 13 \, C\right)} \cos\left(d x + c\right) + 260 \, A - 13 \, C\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/210*(105*(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*(8*(20*A - C)*cos(d*x + c)^3 + (535*A - 32*C)*cos(d*x + c)^2 + 4*(155*A - 13*C)*cos(d*x + c) + 260*A - 13*C)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
71,1,277,0,0.528255," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","-\frac{210 \, {\left(A \cos\left(d x + c\right)^{5} + 4 \, A \cos\left(d x + c\right)^{4} + 6 \, A \cos\left(d x + c\right)^{3} + 4 \, A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 210 \, {\left(A \cos\left(d x + c\right)^{5} + 4 \, A \cos\left(d x + c\right)^{4} + 6 \, A \cos\left(d x + c\right)^{3} + 4 \, A \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(2 \, {\left(332 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(559 \, A + 6 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2636 \, A + 39 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(296 \, A + 9 \, C\right)} \cos\left(d x + c\right) + 105 \, A\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} + 4 \, a^{4} d \cos\left(d x + c\right)^{4} + 6 \, a^{4} d \cos\left(d x + c\right)^{3} + 4 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/105*(210*(A*cos(d*x + c)^5 + 4*A*cos(d*x + c)^4 + 6*A*cos(d*x + c)^3 + 4*A*cos(d*x + c)^2 + A*cos(d*x + c))*log(sin(d*x + c) + 1) - 210*(A*cos(d*x + c)^5 + 4*A*cos(d*x + c)^4 + 6*A*cos(d*x + c)^3 + 4*A*cos(d*x + c)^2 + A*cos(d*x + c))*log(-sin(d*x + c) + 1) - (2*(332*A + 3*C)*cos(d*x + c)^4 + 4*(559*A + 6*C)*cos(d*x + c)^3 + (2636*A + 39*C)*cos(d*x + c)^2 + 4*(296*A + 9*C)*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))","A",0
72,1,354,0,1.275335," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left({\left(21 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(21 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(21 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(21 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(21 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(21 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(21 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(21 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(21 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(21 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(64 \, {\left(54 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(11619 \, A + 1070 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(3411 \, A + 310 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(1509 \, A + 130 \, C\right)} \cos\left(d x + c\right)^{2} + 420 \, A \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 + 2*C)*cos(d*x + c)^6 + 4*(21*A + 2*C)*cos(d*x + c)^5 + 6*(21*A + 2*C)*cos(d*x + c)^4 + 4*(21*A + 2*C)*cos(d*x + c)^3 + (21*A + 2*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 105*((21*A + 2*C)*cos(d*x + c)^6 + 4*(21*A + 2*C)*cos(d*x + c)^5 + 6*(21*A + 2*C)*cos(d*x + c)^4 + 4*(21*A + 2*C)*cos(d*x + c)^3 + (21*A + 2*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(64*(54*A + 5*C)*cos(d*x + c)^5 + (11619*A + 1070*C)*cos(d*x + c)^4 + 4*(3411*A + 310*C)*cos(d*x + c)^3 + 4*(1509*A + 130*C)*cos(d*x + c)^2 + 420*A*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
73,1,372,0,1.761605," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","-\frac{105 \, {\left({\left(11 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{7} + 4 \, {\left(11 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(11 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(11 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(11 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(11 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{7} + 4 \, {\left(11 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(11 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(11 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(11 \, A + 2 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(8 \, {\left(454 \, A + 83 \, C\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(6109 \, A + 1118 \, C\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(3592 \, A + 659 \, C\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(799 \, A + 148 \, C\right)} \cos\left(d x + c\right)^{3} + 35 \, {\left(14 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} - 70 \, A \cos\left(d x + c\right) + 35 \, A\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{7} + 4 \, a^{4} d \cos\left(d x + c\right)^{6} + 6 \, a^{4} d \cos\left(d x + c\right)^{5} + 4 \, a^{4} d \cos\left(d x + c\right)^{4} + a^{4} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/105*(105*((11*A + 2*C)*cos(d*x + c)^7 + 4*(11*A + 2*C)*cos(d*x + c)^6 + 6*(11*A + 2*C)*cos(d*x + c)^5 + 4*(11*A + 2*C)*cos(d*x + c)^4 + (11*A + 2*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 105*((11*A + 2*C)*cos(d*x + c)^7 + 4*(11*A + 2*C)*cos(d*x + c)^6 + 6*(11*A + 2*C)*cos(d*x + c)^5 + 4*(11*A + 2*C)*cos(d*x + c)^4 + (11*A + 2*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - (8*(454*A + 83*C)*cos(d*x + c)^6 + 2*(6109*A + 1118*C)*cos(d*x + c)^5 + 4*(3592*A + 659*C)*cos(d*x + c)^4 + 8*(799*A + 148*C)*cos(d*x + c)^3 + 35*(14*A + 3*C)*cos(d*x + c)^2 - 70*A*cos(d*x + c) + 35*A)*sin(d*x + c))/(a^4*d*cos(d*x + c)^7 + 4*a^4*d*cos(d*x + c)^6 + 6*a^4*d*cos(d*x + c)^5 + 4*a^4*d*cos(d*x + c)^4 + a^4*d*cos(d*x + c)^3)","A",0
74,1,110,0,1.186232," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, C \cos\left(d x + c\right)^{5} + 350 \, C \cos\left(d x + c\right)^{4} + 5 \, {\left(99 \, A + 80 \, C\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(99 \, A + 80 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(99 \, A + 80 \, C\right)} \cos\left(d x + c\right) + 1584 \, A + 1280 \, C\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*C*cos(d*x + c)^5 + 350*C*cos(d*x + c)^4 + 5*(99*A + 80*C)*cos(d*x + c)^3 + 6*(99*A + 80*C)*cos(d*x + c)^2 + 8*(99*A + 80*C)*cos(d*x + c) + 1584*A + 1280*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
75,1,93,0,0.610457," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, C \cos\left(d x + c\right)^{4} + 40 \, C \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 16 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(21 \, A + 16 \, C\right)} \cos\left(d x + c\right) + 168 \, A + 128 \, C\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*C*cos(d*x + c)^4 + 40*C*cos(d*x + c)^3 + 3*(21*A + 16*C)*cos(d*x + c)^2 + 4*(21*A + 16*C)*cos(d*x + c) + 168*A + 128*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
76,1,75,0,0.617231," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, C \cos\left(d x + c\right)^{3} + 18 \, C \cos\left(d x + c\right)^{2} + {\left(35 \, A + 24 \, C\right)} \cos\left(d x + c\right) + 70 \, A + 48 \, C\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*C*cos(d*x + c)^3 + 18*C*cos(d*x + c)^2 + (35*A + 24*C)*cos(d*x + c) + 70*A + 48*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
77,1,59,0,0.674073," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, C \cos\left(d x + c\right)^{2} + 4 \, C \cos\left(d x + c\right) + 15 \, A + 8 \, C\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*C*cos(d*x + c)^2 + 4*C*cos(d*x + c) + 15*A + 8*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
78,1,139,0,1.019728," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\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 \, {\left(C \cos\left(d x + c\right) + 2 \, C\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*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*(C*cos(d*x + c) + 2*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
79,1,155,0,1.500341," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(A \cos\left(d x + c\right)^{2} + 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 \, C \cos\left(d x + c\right) + 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*((A*cos(d*x + c)^2 + 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*C*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))","A",0
80,1,173,0,0.578151," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(3 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 \, A \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 + 8*C)*cos(d*x + c)^3 + (3*A + 8*C)*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*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
81,1,191,0,0.466081," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(5 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 8 \, C\right)} \cos\left(d x + c\right)^{2} + 10 \, A \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 + 8*C)*cos(d*x + c)^4 + (5*A + 8*C)*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 + 8*C)*cos(d*x + c)^2 + 10*A*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
82,1,208,0,0.499369," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^5*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(35 \, A + 48 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(35 \, A + 48 \, C\right)} \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(35 \, A + 48 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(35 \, A + 48 \, C\right)} \cos\left(d x + c\right)^{2} + 56 \, A \cos\left(d x + c\right) + 48 \, 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*((35*A + 48*C)*cos(d*x + c)^5 + (35*A + 48*C)*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*(35*A + 48*C)*cos(d*x + c)^3 + 2*(35*A + 48*C)*cos(d*x + c)^2 + 56*A*cos(d*x + c) + 48*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
83,1,119,0,0.399207," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, C a \cos\left(d x + c\right)^{5} + 245 \, C a \cos\left(d x + c\right)^{4} + 5 \, {\left(33 \, A + 56 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(143 \, A + 112 \, C\right)} a \cos\left(d x + c\right)^{2} + 4 \, {\left(143 \, A + 112 \, C\right)} a \cos\left(d x + c\right) + 8 \, {\left(143 \, A + 112 \, C\right)} a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{1155 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/1155*(105*C*a*cos(d*x + c)^5 + 245*C*a*cos(d*x + c)^4 + 5*(33*A + 56*C)*a*cos(d*x + c)^3 + 3*(143*A + 112*C)*a*cos(d*x + c)^2 + 4*(143*A + 112*C)*a*cos(d*x + c) + 8*(143*A + 112*C)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
84,1,100,0,0.408627," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, C a \cos\left(d x + c\right)^{4} + 85 \, C a \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 34 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(189 \, A + 136 \, C\right)} a \cos\left(d x + c\right) + 2 \, {\left(189 \, A + 136 \, C\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*C*a*cos(d*x + c)^4 + 85*C*a*cos(d*x + c)^3 + 3*(21*A + 34*C)*a*cos(d*x + c)^2 + (189*A + 136*C)*a*cos(d*x + c) + 2*(189*A + 136*C)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
85,1,81,0,0.465684," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, C a \cos\left(d x + c\right)^{3} + 39 \, C a \cos\left(d x + c\right)^{2} + {\left(35 \, A + 52 \, C\right)} a \cos\left(d x + c\right) + {\left(175 \, A + 104 \, C\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*C*a*cos(d*x + c)^3 + 39*C*a*cos(d*x + c)^2 + (35*A + 52*C)*a*cos(d*x + c) + (175*A + 104*C)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
86,1,161,0,0.478546," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{5 \, {\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(C a \cos\left(d x + c\right)^{2} + 3 \, C a \cos\left(d x + c\right) + {\left(5 \, A + 6 \, C\right)} a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{10 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/10*(5*(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*(C*a*cos(d*x + c)^2 + 3*C*a*cos(d*x + c) + (5*A + 6*C)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
87,1,174,0,0.476313," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{9 \, {\left(A a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{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 \, C a \cos\left(d x + c\right)^{2} + 10 \, C 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)}{12 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/12*(9*(A*a*cos(d*x + c)^2 + A*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*C*a*cos(d*x + c)^2 + 10*C*a*cos(d*x + c) + 3*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
88,1,189,0,0.615308," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(7 \, A + 8 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(7 \, A + 8 \, C\right)} a \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 \, C a \cos\left(d x + c\right)^{2} + 7 \, A 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 + 8*C)*a*cos(d*x + c)^3 + (7*A + 8*C)*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*(8*C*a*cos(d*x + c)^2 + 7*A*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
89,1,196,0,0.625844," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(11 \, A + 24 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(11 \, A + 24 \, C\right)} a \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 8 \, C\right)} a \cos\left(d x + c\right)^{2} + 22 \, A 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 + 24*C)*a*cos(d*x + c)^4 + (11*A + 24*C)*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 + 8*C)*a*cos(d*x + c)^2 + 22*A*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
90,1,212,0,0.513976," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{{\left({\left(75 \, A + 112 \, C\right)} a \cos\left(d x + c\right)^{5} + {\left(75 \, A + 112 \, C\right)} a \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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(75 \, A + 112 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(25 \, A + 16 \, C\right)} a \cos\left(d x + c\right)^{2} + 40 \, A a \cos\left(d x + c\right) + 16 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{256 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/256*(((75*A + 112*C)*a*cos(d*x + c)^5 + (75*A + 112*C)*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*((75*A + 112*C)*a*cos(d*x + c)^3 + 2*(25*A + 16*C)*a*cos(d*x + c)^2 + 40*A*a*cos(d*x + c) + 16*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
91,1,232,0,0.507204," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(133 \, A + 176 \, C\right)} a \cos\left(d x + c\right)^{6} + {\left(133 \, A + 176 \, C\right)} a \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(133 \, A + 176 \, C\right)} a \cos\left(d x + c\right)^{4} + 10 \, {\left(133 \, A + 176 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(133 \, A + 80 \, C\right)} a \cos\left(d x + c\right)^{2} + 912 \, A a \cos\left(d x + c\right) + 384 \, A a\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*((133*A + 176*C)*a*cos(d*x + c)^6 + (133*A + 176*C)*a*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*(133*A + 176*C)*a*cos(d*x + c)^4 + 10*(133*A + 176*C)*a*cos(d*x + c)^3 + 8*(133*A + 80*C)*a*cos(d*x + c)^2 + 912*A*a*cos(d*x + c) + 384*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)","A",0
92,1,151,0,0.402299," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, C a^{2} \cos\left(d x + c\right)^{6} + 11970 \, C a^{2} \cos\left(d x + c\right)^{5} + 35 \, {\left(143 \, A + 523 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(1859 \, A + 2092 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(10439 \, A + 8368 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 4 \, {\left(10439 \, A + 8368 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(10439 \, A + 8368 \, C\right)} 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) + d\right)}}"," ",0,"2/45045*(3465*C*a^2*cos(d*x + c)^6 + 11970*C*a^2*cos(d*x + c)^5 + 35*(143*A + 523*C)*a^2*cos(d*x + c)^4 + 10*(1859*A + 2092*C)*a^2*cos(d*x + c)^3 + 3*(10439*A + 8368*C)*a^2*cos(d*x + c)^2 + 4*(10439*A + 8368*C)*a^2*cos(d*x + c) + 8*(10439*A + 8368*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
93,1,129,0,0.402235," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, C a^{2} \cos\left(d x + c\right)^{5} + 224 \, C a^{2} \cos\left(d x + c\right)^{4} + {\left(99 \, A + 355 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 6 \, {\left(66 \, A + 71 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(759 \, A + 568 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(759 \, A + 568 \, C\right)} a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{693 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/693*(63*C*a^2*cos(d*x + c)^5 + 224*C*a^2*cos(d*x + c)^4 + (99*A + 355*C)*a^2*cos(d*x + c)^3 + 6*(66*A + 71*C)*a^2*cos(d*x + c)^2 + (759*A + 568*C)*a^2*cos(d*x + c) + 2*(759*A + 568*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
94,1,110,0,0.502834," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, C a^{2} \cos\left(d x + c\right)^{4} + 130 \, C a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 73 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(147 \, A + 146 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(903 \, A + 584 \, C\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*C*a^2*cos(d*x + c)^4 + 130*C*a^2*cos(d*x + c)^3 + 3*(21*A + 73*C)*a^2*cos(d*x + c)^2 + 2*(147*A + 146*C)*a^2*cos(d*x + c) + (903*A + 584*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
95,1,192,0,0.521958," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{21 \, {\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 \, C a^{2} \cos\left(d x + c\right)^{3} + 12 \, C a^{2} \cos\left(d x + c\right)^{2} + {\left(7 \, A + 23 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(28 \, A + 23 \, C\right)} a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{42 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/42*(21*(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*C*a^2*cos(d*x + c)^3 + 12*C*a^2*cos(d*x + c)^2 + (7*A + 23*C)*a^2*cos(d*x + c) + 2*(28*A + 23*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
96,1,204,0,0.442760," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{75 \, {\left(A a^{2} \cos\left(d x + c\right)^{2} + A 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(6 \, C a^{2} \cos\left(d x + c\right)^{3} + 28 \, C a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A + 43 \, C\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)}{60 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/60*(75*(A*a^2*cos(d*x + c)^2 + A*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*(6*C*a^2*cos(d*x + c)^3 + 28*C*a^2*cos(d*x + c)^2 + 2*(15*A + 43*C)*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)^2 + d*cos(d*x + c))","A",0
97,1,214,0,0.479053," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(19 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(19 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 \, C a^{2} \cos\left(d x + c\right)^{3} + 64 \, C a^{2} \cos\left(d x + c\right)^{2} + 33 \, A a^{2} \cos\left(d x + c\right) + 6 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/48*(3*((19*A + 8*C)*a^2*cos(d*x + c)^3 + (19*A + 8*C)*a^2*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*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*C*a^2*cos(d*x + c)^3 + 64*C*a^2*cos(d*x + c)^2 + 33*A*a^2*cos(d*x + c) + 6*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
98,1,220,0,0.650604," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(5 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(5 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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(48 \, C a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(25 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 34 \, A 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*(15*((5*A + 8*C)*a^2*cos(d*x + c)^4 + (5*A + 8*C)*a^2*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*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*(48*C*a^2*cos(d*x + c)^3 + 3*(25*A + 8*C)*a^2*cos(d*x + c)^2 + 34*A*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
99,1,226,0,0.512887," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(163 \, A + 304 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(163 \, A + 304 \, C\right)} a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 176 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(163 \, A + 48 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 184 \, A 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 + 304*C)*a^2*cos(d*x + c)^5 + (163*A + 304*C)*a^2*cos(d*x + c)^4)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*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 + 176*C)*a^2*cos(d*x + c)^3 + 2*(163*A + 48*C)*a^2*cos(d*x + c)^2 + 184*A*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
100,1,246,0,0.594894," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(283 \, A + 400 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(283 \, A + 400 \, C\right)} a^{2} \cos\left(d x + c\right)^{5}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 400 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(283 \, A + 272 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(283 \, A + 80 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 1392 \, A 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 + 400*C)*a^2*cos(d*x + c)^6 + (283*A + 400*C)*a^2*cos(d*x + c)^5)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*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 + 400*C)*a^2*cos(d*x + c)^4 + 10*(283*A + 272*C)*a^2*cos(d*x + c)^3 + 8*(283*A + 80*C)*a^2*cos(d*x + c)^2 + 1392*A*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
101,1,266,0,0.520076," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(1015 \, A + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{7} + {\left(1015 \, A + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{6}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 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(1015 \, A + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 2 \, {\left(1015 \, A + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(203 \, A + 184 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 48 \, {\left(29 \, A + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 896 \, A a^{2} \cos\left(d x + c\right) + 256 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{6144 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/6144*(3*((1015*A + 1304*C)*a^2*cos(d*x + c)^7 + (1015*A + 1304*C)*a^2*cos(d*x + c)^6)*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*(1015*A + 1304*C)*a^2*cos(d*x + c)^5 + 2*(1015*A + 1304*C)*a^2*cos(d*x + c)^4 + 8*(203*A + 184*C)*a^2*cos(d*x + c)^3 + 48*(29*A + 8*C)*a^2*cos(d*x + c)^2 + 896*A*a^2*cos(d*x + c) + 256*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)","A",0
102,1,191,0,0.435138," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(35 \, C \cos\left(d x + c\right)^{4} - 5 \, C \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(21 \, A + 29 \, C\right)} \cos\left(d x + c\right) + 273 \, A + 257 \, C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{315 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{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}}}{630 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/630*(4*(35*C*cos(d*x + c)^4 - 5*C*cos(d*x + c)^3 + 3*(21*A + 19*C)*cos(d*x + c)^2 - (21*A + 29*C)*cos(d*x + c) + 273*A + 257*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 315*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
103,1,173,0,0.463595," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(15 \, C \cos\left(d x + c\right)^{3} - 3 \, C \cos\left(d x + c\right)^{2} + {\left(35 \, A + 31 \, C\right)} \cos\left(d x + c\right) - 35 \, A - 43 \, C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{105 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{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*C*cos(d*x + c)^3 - 3*C*cos(d*x + c)^2 + (35*A + 31*C)*cos(d*x + c) - 35*A - 43*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 105*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
104,1,157,0,0.454564," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, C \cos\left(d x + c\right)^{2} - C \cos\left(d x + c\right) + 15 \, A + 13 \, C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{15 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{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*C*cos(d*x + c)^2 - C*cos(d*x + c) + 15*A + 13*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 15*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
105,1,142,0,0.414369," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(C \cos\left(d x + c\right) - C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{3 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{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*(C*cos(d*x + c) - C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 3*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
106,1,221,0,0.441968," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),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} C \sin\left(d x + c\right) + \frac{\sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\right)} a\right)} \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*((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)*C*sin(d*x + c) + sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
107,1,247,0,0.436442," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(A \cos\left(d x + c\right)^{2} + 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 \, \sqrt{a \cos\left(d x + c\right) + a} A \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A + C\right)} a \cos\left(d x + c\right)\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{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*cos(d*x + c)^2 + 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*sqrt(a*cos(d*x + c) + a)*A*sin(d*x + c) + 2*sqrt(2)*((A + C)*a*cos(d*x + c)^2 + (A + C)*a*cos(d*x + c))*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
108,1,276,0,0.505599," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(7 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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(A \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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{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 + 8*C)*cos(d*x + c)^3 + (7*A + 8*C)*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*cos(d*x + c) - 2*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 8*sqrt(2)*((A + C)*a*cos(d*x + c)^3 + (A + C)*a*cos(d*x + c)^2)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
109,1,295,0,0.519852," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(9 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(9 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 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(7 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + 8 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{48 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A + C\right)} a \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{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}}}{96 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/96*(3*((9*A + 8*C)*cos(d*x + c)^4 + (9*A + 8*C)*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*(7*A + 8*C)*cos(d*x + c)^2 - 2*A*cos(d*x + c) + 8*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 48*sqrt(2)*((A + C)*a*cos(d*x + c)^4 + (A + C)*a*cos(d*x + c)^3)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
110,1,312,0,0.551248," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(107 \, A + 112 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(107 \, A + 112 \, C\right)} \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(21 \, A + 16 \, C\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(43 \, A + 48 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, A \cos\left(d x + c\right) - 48 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{384 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{5} + {\left(A + C\right)} a \cos\left(d x + c\right)^{4}\right)} \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}}}{768 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/768*(3*((107*A + 112*C)*cos(d*x + c)^5 + (107*A + 112*C)*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*(21*A + 16*C)*cos(d*x + c)^3 - 2*(43*A + 48*C)*cos(d*x + c)^2 + 8*A*cos(d*x + c) - 48*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 384*sqrt(2)*((A + C)*a*cos(d*x + c)^5 + (A + C)*a*cos(d*x + c)^4)*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)^5 + a*d*cos(d*x + c)^4)","A",0
111,1,235,0,0.425657," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} {\left({\left(11 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A + 19 \, C\right)} \cos\left(d x + c\right) + 11 \, A + 19 \, C\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 \, C \cos\left(d x + c\right)^{4} - 36 \, C \cos\left(d x + c\right)^{3} + 28 \, {\left(5 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left(35 \, A + 67 \, C\right)} \cos\left(d x + c\right) - 665 \, A - 1201 \, C\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)*((11*A + 19*C)*cos(d*x + c)^2 + 2*(11*A + 19*C)*cos(d*x + c) + 11*A + 19*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)) + 4*(60*C*cos(d*x + c)^4 - 36*C*cos(d*x + c)^3 + 28*(5*A + 7*C)*cos(d*x + c)^2 - 12*(35*A + 67*C)*cos(d*x + c) - 665*A - 1201*C)*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
112,1,218,0,0.414888," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{5 \, \sqrt{2} {\left({\left(7 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A + 15 \, C\right)} \cos\left(d x + c\right) + 7 \, A + 15 \, C\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 \, C \cos\left(d x + c\right)^{3} - 4 \, C \cos\left(d x + c\right)^{2} + 4 \, {\left(5 \, A + 9 \, C\right)} \cos\left(d x + c\right) + 25 \, A + 49 \, C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{40 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/40*(5*sqrt(2)*((7*A + 15*C)*cos(d*x + c)^2 + 2*(7*A + 15*C)*cos(d*x + c) + 7*A + 15*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)) + 4*(4*C*cos(d*x + c)^3 - 4*C*cos(d*x + c)^2 + 4*(5*A + 9*C)*cos(d*x + c) + 25*A + 49*C)*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
113,1,201,0,0.440743," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(3 \, A + 11 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + 11 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 11 \, C\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 \, C \cos\left(d x + c\right)^{2} - 12 \, C \cos\left(d x + c\right) - 3 \, A - 19 \, C\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)*((3*A + 11*C)*cos(d*x + c)^2 + 2*(3*A + 11*C)*cos(d*x + c) + 3*A + 11*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)) + 4*(4*C*cos(d*x + c)^2 - 12*C*cos(d*x + c) - 3*A - 19*C)*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
114,1,181,0,0.428945," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(A - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 7 \, C\right)} \cos\left(d x + c\right) + A - 7 \, C\right)} \sqrt{a} \log\left(-\frac{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 \, C \cos\left(d x + c\right) + A + 5 \, C\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)*((A - 7*C)*cos(d*x + c)^2 + 2*(A - 7*C)*cos(d*x + c) + A - 7*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)) - 4*(4*C*cos(d*x + c) + A + 5*C)*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
115,1,279,0,0.566195," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(5 \, A - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - 3 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 3 \, C\right)} \sqrt{a} \log\left(-\frac{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 + C\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/8*(sqrt(2)*((5*A - 3*C)*cos(d*x + c)^2 + 2*(5*A - 3*C)*cos(d*x + c) + 5*A - 3*C)*sqrt(a)*log(-(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 + C)*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
116,1,313,0,0.460567," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(9 \, A + C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(9 \, A + C\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A + C\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \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) + 6 \, {\left(A \cos\left(d x + c\right)^{3} + 2 \, A \cos\left(d x + c\right)^{2} + 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({\left(3 \, A + C\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 + C)*cos(d*x + c)^3 + 2*(9*A + C)*cos(d*x + c)^2 + (9*A + C)*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)) + 6*(A*cos(d*x + c)^3 + 2*A*cos(d*x + c)^2 + 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*((3*A + C)*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
117,1,356,0,0.522825," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left({\left(13 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(13 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \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 + 8 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(19 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(19 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 2 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, A \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 + 5*C)*cos(d*x + c)^4 + 2*(13*A + 5*C)*cos(d*x + c)^3 + (13*A + 5*C)*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 + 8*C)*cos(d*x + c)^4 + 2*(19*A + 8*C)*cos(d*x + c)^3 + (19*A + 8*C)*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 + 2*C)*cos(d*x + c)^2 + 3*A*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
118,1,374,0,0.510915," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left({\left(17 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(17 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(17 \, A + 9 \, C\right)} \cos\left(d x + c\right)^{3}\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) + 3 \, {\left({\left(47 \, A + 24 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(47 \, A + 24 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(47 \, A + 24 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 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(9 \, {\left(7 \, A + 4 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(37 \, A + 24 \, C\right)} \cos\left(d x + c\right)^{2} - 6 \, A \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(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,"1/96*(12*sqrt(2)*((17*A + 9*C)*cos(d*x + c)^5 + 2*(17*A + 9*C)*cos(d*x + c)^4 + (17*A + 9*C)*cos(d*x + c)^3)*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)) + 3*((47*A + 24*C)*cos(d*x + c)^5 + 2*(47*A + 24*C)*cos(d*x + c)^4 + (47*A + 24*C)*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*(9*(7*A + 4*C)*cos(d*x + c)^3 + (37*A + 24*C)*cos(d*x + c)^2 - 6*A*cos(d*x + c) + 8*A)*sqrt(a*cos(d*x + c) + 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
119,1,266,0,0.450851," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(75 \, A + 283 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A + 283 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A + 283 \, C\right)} \cos\left(d x + c\right) + 75 \, A + 283 \, C\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 \, C \cos\left(d x + c\right)^{4} - 160 \, C \cos\left(d x + c\right)^{3} + 32 \, {\left(15 \, A + 49 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(255 \, A + 911 \, C\right)} \cos\left(d x + c\right) + 735 \, A + 2671 \, C\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)*((75*A + 283*C)*cos(d*x + c)^3 + 3*(75*A + 283*C)*cos(d*x + c)^2 + 3*(75*A + 283*C)*cos(d*x + c) + 75*A + 283*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)) + 4*(96*C*cos(d*x + c)^4 - 160*C*cos(d*x + c)^3 + 32*(15*A + 49*C)*cos(d*x + c)^2 + 5*(255*A + 911*C)*cos(d*x + c) + 735*A + 2671*C)*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
120,1,249,0,0.418539," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(19 \, A + 163 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 163 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 163 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 163 \, C\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 \, C \cos\left(d x + c\right)^{3} - 160 \, C \cos\left(d x + c\right)^{2} - {\left(39 \, A + 503 \, C\right)} \cos\left(d x + c\right) - 27 \, A - 299 \, C\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)*((19*A + 163*C)*cos(d*x + c)^3 + 3*(19*A + 163*C)*cos(d*x + c)^2 + 3*(19*A + 163*C)*cos(d*x + c) + 19*A + 163*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)) + 4*(32*C*cos(d*x + c)^3 - 160*C*cos(d*x + c)^2 - (39*A + 503*C)*cos(d*x + c) - 27*A - 299*C)*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
121,1,226,0,0.451740," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{5 \, \sqrt{2} {\left({\left(A - 15 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A - 15 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(A - 15 \, C\right)} \cos\left(d x + c\right) + A - 15 \, C\right)} \sqrt{a} \log\left(-\frac{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 \, C \cos\left(d x + c\right)^{2} + 5 \, {\left(A + 17 \, C\right)} \cos\left(d x + c\right) + A + 49 \, C\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*(5*sqrt(2)*((A - 15*C)*cos(d*x + c)^3 + 3*(A - 15*C)*cos(d*x + c)^2 + 3*(A - 15*C)*cos(d*x + c) + A - 15*C)*sqrt(a)*log(-(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*C*cos(d*x + c)^2 + 5*(A + 17*C)*cos(d*x + c) + A + 49*C)*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
122,1,225,0,0.436697," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(3 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 19 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 19 \, C\right)} \sqrt{a} \log\left(-\frac{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 - 13 \, C\right)} \cos\left(d x + c\right) + 7 \, A - 9 \, C\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 + 19*C)*cos(d*x + c)^3 + 3*(3*A + 19*C)*cos(d*x + c)^2 + 3*(3*A + 19*C)*cos(d*x + c) + 3*A + 19*C)*sqrt(a)*log(-(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 - 13*C)*cos(d*x + c) + 7*A - 9*C)*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
123,1,339,0,0.453599," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(43 \, A - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 5 \, C\right)} \cos\left(d x + c\right) + 43 \, A - 5 \, C\right)} \sqrt{a} \log\left(-\frac{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 - 5 \, C\right)} \cos\left(d x + c\right) + 15 \, A - C\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 - 5*C)*cos(d*x + c)^3 + 3*(43*A - 5*C)*cos(d*x + c)^2 + 3*(43*A - 5*C)*cos(d*x + c) + 43*A - 5*C)*sqrt(a)*log(-(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 - 5*C)*cos(d*x + c) + 15*A - C)*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
124,1,379,0,0.483140," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(115 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(115 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(115 \, A + 3 \, C\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \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) + 80 \, {\left(A \cos\left(d x + c\right)^{4} + 3 \, A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} + 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({\left(35 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(55 \, A + 7 \, C\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 + 3*C)*cos(d*x + c)^4 + 3*(115*A + 3*C)*cos(d*x + c)^3 + 3*(115*A + 3*C)*cos(d*x + c)^2 + (115*A + 3*C)*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)) + 80*(A*cos(d*x + c)^4 + 3*A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 + 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*((35*A + 3*C)*cos(d*x + c)^2 + (55*A + 7*C)*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
125,1,421,0,0.538386," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(219 \, A + 43 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(219 \, A + 43 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(219 \, A + 43 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(219 \, A + 43 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \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 + 8 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(39 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(39 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A + 8 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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(63 \, A + 11 \, C\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 20 \, A \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 + 43*C)*cos(d*x + c)^5 + 3*(219*A + 43*C)*cos(d*x + c)^4 + 3*(219*A + 43*C)*cos(d*x + c)^3 + (219*A + 43*C)*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 + 8*C)*cos(d*x + c)^5 + 3*(39*A + 8*C)*cos(d*x + c)^4 + 3*(39*A + 8*C)*cos(d*x + c)^3 + (39*A + 8*C)*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*((63*A + 11*C)*cos(d*x + c)^3 + 5*(19*A + 3*C)*cos(d*x + c)^2 + 20*A*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
126,0,0,0,0.433292," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{5} + C a \cos\left(d x + c\right)^{4} + A 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((C*a*cos(d*x + c)^5 + C*a*cos(d*x + c)^4 + A*a*cos(d*x + c)^3 + A*a*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
127,0,0,0,0.460198," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{4} + C a \cos\left(d x + c\right)^{3} + A 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((C*a*cos(d*x + c)^4 + C*a*cos(d*x + c)^3 + A*a*cos(d*x + c)^2 + A*a*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
128,0,0,0,0.462179," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)*sqrt(cos(d*x + c)), x)","F",0
129,0,0,0,0.619178," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)/sqrt(cos(d*x + c)), x)","F",0
130,0,0,0,0.504663," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)/cos(d*x + c)^(3/2), x)","F",0
131,0,0,0,0.525842," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)/cos(d*x + c)^(5/2), x)","F",0
132,0,0,0,0.408461," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)/cos(d*x + c)^(7/2), x)","F",0
133,0,0,0,0.586125," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)/cos(d*x + c)^(9/2), x)","F",0
134,0,0,0,0.476966," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{5} + 2 \, C a^{2} \cos\left(d x + c\right)^{4} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, A 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((C*a^2*cos(d*x + c)^5 + 2*C*a^2*cos(d*x + c)^4 + (A + C)*a^2*cos(d*x + c)^3 + 2*A*a^2*cos(d*x + c)^2 + A*a^2*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
135,0,0,0,0.707312," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)*sqrt(cos(d*x + c)), x)","F",0
136,0,0,0,0.426664," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)/sqrt(cos(d*x + c)), x)","F",0
137,0,0,0,0.424253," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)/cos(d*x + c)^(3/2), x)","F",0
138,0,0,0,0.423737," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)/cos(d*x + c)^(5/2), x)","F",0
139,0,0,0,0.431981," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)/cos(d*x + c)^(7/2), x)","F",0
140,0,0,0,0.415476," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)/cos(d*x + c)^(9/2), x)","F",0
141,0,0,0,0.424470," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)/cos(d*x + c)^(11/2), x)","F",0
142,0,0,0,0.440267," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{6} + 3 \, C a^{3} \cos\left(d x + c\right)^{5} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, A 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((C*a^3*cos(d*x + c)^6 + 3*C*a^3*cos(d*x + c)^5 + (A + 3*C)*a^3*cos(d*x + c)^4 + (3*A + C)*a^3*cos(d*x + c)^3 + 3*A*a^3*cos(d*x + c)^2 + A*a^3*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
143,0,0,0,0.443220," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)*sqrt(cos(d*x + c)), x)","F",0
144,0,0,0,0.429578," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)/sqrt(cos(d*x + c)), x)","F",0
145,0,0,0,0.466401," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(3/2), x)","F",0
146,0,0,0,0.523453," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(5/2), x)","F",0
147,0,0,0,0.504102," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(7/2), x)","F",0
148,0,0,0,0.575468," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(9/2), x)","F",0
149,0,0,0,0.427951," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(11/2), x)","F",0
150,0,0,0,0.432913," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}}{\cos\left(d x + c\right)^{\frac{13}{2}}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(13/2), x)","F",0
151,0,0,0,0.502190," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + A*cos(d*x + c)^2)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
152,0,0,0,0.457124," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + A*cos(d*x + c))*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
153,0,0,0,1.146298," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
154,0,0,0,0.475607," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)^2 + a*cos(d*x + c)), x)","F",0
155,0,0,0,0.449013," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)^3 + a*cos(d*x + c)^2), x)","F",0
156,0,0,0,0.458677," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)^4 + a*cos(d*x + c)^3), x)","F",0
157,0,0,0,0.495174," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{5} + a \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)^5 + a*cos(d*x + c)^4), x)","F",0
158,0,0,0,0.433490," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + 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
159,0,0,0,0.468419," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
160,0,0,0,0.419974," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
161,0,0,0,0.503465," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
162,0,0,0,0.470639," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
163,0,0,0,0.471475," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
164,0,0,0,0.517244," ","integrate(cos(d*x+c)^(7/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{5} + 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((C*cos(d*x + c)^5 + 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
165,0,0,0,0.535209," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + 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
166,0,0,0,0.432190," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
167,0,0,0,0.430323," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
168,0,0,0,0.437906," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
169,0,0,0,0.475372," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
170,0,0,0,0.537357," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
171,1,145,0,0.737326," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(48 \, C \cos\left(d x + c\right)^{3} + 56 \, C \cos\left(d x + c\right)^{2} + 2 \, {\left(48 \, A + 35 \, C\right)} \cos\left(d x + c\right) + 144 \, A + 105 \, C\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(48 \, A + 35 \, C\right)} \cos\left(d x + c\right) + 48 \, A + 35 \, C\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*C*cos(d*x + c)^3 + 56*C*cos(d*x + c)^2 + 2*(48*A + 35*C)*cos(d*x + c) + 144*A + 105*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((48*A + 35*C)*cos(d*x + c) + 48*A + 35*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) + d)","A",0
172,1,128,0,0.902557," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, C \cos\left(d x + c\right)^{2} + 10 \, C \cos\left(d x + c\right) + 24 \, A + 15 \, C\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(8 \, A + 5 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 5 \, C\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*C*cos(d*x + c)^2 + 10*C*cos(d*x + c) + 24*A + 15*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((8*A + 5*C)*cos(d*x + c) + 8*A + 5*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) + d)","A",0
173,1,114,0,0.794543," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, C \cos\left(d x + c\right) + 3 \, C\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(8 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 3 \, C\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*C*cos(d*x + c) + 3*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((8*A + 3*C)*cos(d*x + c) + 8*A + 3*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) + d)","A",0
174,1,119,0,0.516815," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(C \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left(C \cos\left(d x + c\right)^{2} + C \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\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,"((C*cos(d*x + c) + 2*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - (C*cos(d*x + c)^2 + C*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
175,1,123,0,0.449486," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(2 \, A \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(C \cos\left(d x + c\right)^{3} + C \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*((2*A*cos(d*x + c) + A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*(C*cos(d*x + c)^3 + C*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
176,1,80,0,0.406150," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(8 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, A \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*((8*A + 15*C)*cos(d*x + c)^2 + 4*A*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
177,1,97,0,0.469223," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(24 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(24 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 18 \, A \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*(2*(24*A + 35*C)*cos(d*x + c)^3 + (24*A + 35*C)*cos(d*x + c)^2 + 18*A*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
178,1,115,0,0.432006," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(16 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(16 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(16 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{2} + 40 \, A \cos\left(d x + c\right) + 35 \, 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*(16*A + 21*C)*cos(d*x + c)^4 + 4*(16*A + 21*C)*cos(d*x + c)^3 + 3*(16*A + 21*C)*cos(d*x + c)^2 + 40*A*cos(d*x + c) + 35*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
179,1,174,0,0.605785," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(384 \, C a \cos\left(d x + c\right)^{4} + 912 \, C a \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 10 \, {\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right) + 15 \, {\left(176 \, A + 133 \, 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) - 15 \, {\left({\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right) + {\left(176 \, A + 133 \, C\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)}{1920 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/1920*((384*C*a*cos(d*x + c)^4 + 912*C*a*cos(d*x + c)^3 + 8*(80*A + 133*C)*a*cos(d*x + c)^2 + 10*(176*A + 133*C)*a*cos(d*x + c) + 15*(176*A + 133*C)*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*((176*A + 133*C)*a*cos(d*x + c) + (176*A + 133*C)*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
180,1,155,0,0.570840," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(16 \, C a \cos\left(d x + c\right)^{3} + 40 \, C a \cos\left(d x + c\right)^{2} + 2 \, {\left(16 \, A + 25 \, C\right)} a \cos\left(d x + c\right) + {\left(112 \, A + 75 \, 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) - {\left({\left(112 \, A + 75 \, C\right)} a \cos\left(d x + c\right) + {\left(112 \, A + 75 \, C\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)}{64 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/64*((16*C*a*cos(d*x + c)^3 + 40*C*a*cos(d*x + c)^2 + 2*(16*A + 25*C)*a*cos(d*x + c) + (112*A + 75*C)*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((112*A + 75*C)*a*cos(d*x + c) + (112*A + 75*C)*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
181,1,138,0,0.537670," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, C a \cos\left(d x + c\right)^{2} + 22 \, C a \cos\left(d x + c\right) + 3 \, {\left(8 \, A + 11 \, 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({\left(24 \, A + 11 \, C\right)} a \cos\left(d x + c\right) + {\left(24 \, A + 11 \, C\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*C*a*cos(d*x + c)^2 + 22*C*a*cos(d*x + c) + 3*(8*A + 11*C)*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((24*A + 11*C)*a*cos(d*x + c) + (24*A + 11*C)*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
182,1,149,0,0.545300," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, C a \cos\left(d x + c\right)^{2} + 7 \, C a \cos\left(d x + c\right) + 8 \, 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(8 \, A + 7 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(8 \, A + 7 \, C\right)} a \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\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*C*a*cos(d*x + c)^2 + 7*C*a*cos(d*x + c) + 8*A*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((8*A + 7*C)*a*cos(d*x + c)^2 + (8*A + 7*C)*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
183,1,141,0,0.517749," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, C a \cos\left(d x + c\right)^{2} + 10 \, A 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) - 9 \, {\left(C a \cos\left(d x + c\right)^{3} + C 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)}{3 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/3*((3*C*a*cos(d*x + c)^2 + 10*A*a*cos(d*x + c) + 2*A*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 9*(C*a*cos(d*x + c)^3 + C*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
184,1,145,0,0.599901," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left({\left(6 \, A + 5 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, A 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) - 5 \, {\left(C a \cos\left(d x + c\right)^{4} + C a \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)}}{5 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/5*(((6*A + 5*C)*a*cos(d*x + c)^2 + 3*A*a*cos(d*x + c) + A*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 5*(C*a*cos(d*x + c)^4 + C*a*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
185,1,100,0,0.483816," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(104 \, A + 175 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(52 \, A + 35 \, C\right)} a \cos\left(d x + c\right)^{2} + 39 \, A 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*((104*A + 175*C)*a*cos(d*x + c)^3 + (52*A + 35*C)*a*cos(d*x + c)^2 + 39*A*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
186,1,119,0,0.485571," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(136 \, A + 189 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(136 \, A + 189 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(34 \, A + 21 \, C\right)} a \cos\left(d x + c\right)^{2} + 85 \, A 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*(2*(136*A + 189*C)*a*cos(d*x + c)^4 + (136*A + 189*C)*a*cos(d*x + c)^3 + 3*(34*A + 21*C)*a*cos(d*x + c)^2 + 85*A*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
187,1,138,0,0.509784," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(112 \, A + 143 \, C\right)} a \cos\left(d x + c\right)^{5} + 4 \, {\left(112 \, A + 143 \, C\right)} a \cos\left(d x + c\right)^{4} + 3 \, {\left(112 \, A + 143 \, C\right)} a \cos\left(d x + c\right)^{3} + 5 \, {\left(56 \, A + 33 \, C\right)} a \cos\left(d x + c\right)^{2} + 245 \, A a \cos\left(d x + c\right) + 105 \, 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)}{1155 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"2/1155*(8*(112*A + 143*C)*a*cos(d*x + c)^5 + 4*(112*A + 143*C)*a*cos(d*x + c)^4 + 3*(112*A + 143*C)*a*cos(d*x + c)^3 + 5*(56*A + 33*C)*a*cos(d*x + c)^2 + 245*A*a*cos(d*x + c) + 105*A*a)*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
188,1,208,0,0.587534," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(256 \, C a^{2} \cos\left(d x + c\right)^{5} + 896 \, C a^{2} \cos\left(d x + c\right)^{4} + 48 \, {\left(8 \, A + 29 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(184 \, A + 203 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right) + 3 \, {\left(1304 \, A + 1015 \, C\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(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(1304 \, A + 1015 \, C\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)}{1536 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/1536*((256*C*a^2*cos(d*x + c)^5 + 896*C*a^2*cos(d*x + c)^4 + 48*(8*A + 29*C)*a^2*cos(d*x + c)^3 + 8*(184*A + 203*C)*a^2*cos(d*x + c)^2 + 2*(1304*A + 1015*C)*a^2*cos(d*x + c) + 3*(1304*A + 1015*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((1304*A + 1015*C)*a^2*cos(d*x + c) + (1304*A + 1015*C)*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
189,1,188,0,0.575319," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(384 \, C a^{2} \cos\left(d x + c\right)^{4} + 1392 \, C a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 10 \, {\left(272 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, {\left(400 \, A + 283 \, C\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(400 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(400 \, A + 283 \, C\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*C*a^2*cos(d*x + c)^4 + 1392*C*a^2*cos(d*x + c)^3 + 8*(80*A + 283*C)*a^2*cos(d*x + c)^2 + 10*(272*A + 283*C)*a^2*cos(d*x + c) + 15*(400*A + 283*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*((400*A + 283*C)*a^2*cos(d*x + c) + (400*A + 283*C)*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
190,1,168,0,0.625998," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(48 \, C a^{2} \cos\left(d x + c\right)^{3} + 184 \, C a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(48 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right) + 3 \, {\left(176 \, A + 163 \, C\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(304 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(304 \, A + 163 \, C\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*C*a^2*cos(d*x + c)^3 + 184*C*a^2*cos(d*x + c)^2 + 2*(48*A + 163*C)*a^2*cos(d*x + c) + 3*(176*A + 163*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((304*A + 163*C)*a^2*cos(d*x + c) + (304*A + 163*C)*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
191,1,179,0,0.558995," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(8 \, C a^{2} \cos\left(d x + c\right)^{3} + 34 \, C a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 25 \, C\right)} a^{2} \cos\left(d x + c\right) + 48 \, 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({\left(8 \, A + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 5 \, C\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)}{24 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/24*((8*C*a^2*cos(d*x + c)^3 + 34*C*a^2*cos(d*x + c)^2 + 3*(8*A + 25*C)*a^2*cos(d*x + c) + 48*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*((8*A + 5*C)*a^2*cos(d*x + c)^2 + (8*A + 5*C)*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
192,1,177,0,0.550961," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(6 \, C a^{2} \cos\left(d x + c\right)^{3} + 33 \, C a^{2} \cos\left(d x + c\right)^{2} + 64 \, A 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) - 3 \, {\left({\left(8 \, A + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\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)}{12 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/12*((6*C*a^2*cos(d*x + c)^3 + 33*C*a^2*cos(d*x + c)^2 + 64*A*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) - 3*((8*A + 19*C)*a^2*cos(d*x + c)^3 + (8*A + 19*C)*a^2*cos(d*x + c)^2)*sqrt(a)*arctan(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
193,1,171,0,0.462559," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{{\left(15 \, C a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(43 \, A + 15 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 28 \, A a^{2} \cos\left(d x + c\right) + 6 \, 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) - 75 \, {\left(C a^{2} \cos\left(d x + c\right)^{4} + C 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)}{15 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/15*((15*C*a^2*cos(d*x + c)^3 + 2*(43*A + 15*C)*a^2*cos(d*x + c)^2 + 28*A*a^2*cos(d*x + c) + 6*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 75*(C*a^2*cos(d*x + c)^4 + C*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
194,1,176,0,0.474501," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(2 \, {\left(23 \, A + 28 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(23 \, A + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 12 \, A 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) - 21 \, {\left(C a^{2} \cos\left(d x + c\right)^{5} + C a^{2} \cos\left(d x + c\right)^{4}\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)}}{21 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"2/21*((2*(23*A + 28*C)*a^2*cos(d*x + c)^3 + (23*A + 7*C)*a^2*cos(d*x + c)^2 + 12*A*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) - 21*(C*a^2*cos(d*x + c)^5 + C*a^2*cos(d*x + c)^4)*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)^5 + d*cos(d*x + c)^4)","A",0
195,1,129,0,0.420660," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(584 \, A + 903 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 2 \, {\left(146 \, A + 147 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(73 \, A + 21 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 130 \, A 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*((584*A + 903*C)*a^2*cos(d*x + c)^4 + 2*(146*A + 147*C)*a^2*cos(d*x + c)^3 + 3*(73*A + 21*C)*a^2*cos(d*x + c)^2 + 130*A*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
196,1,148,0,0.481020," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(568 \, A + 759 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(568 \, A + 759 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 6 \, {\left(71 \, A + 66 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(355 \, A + 99 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 224 \, A a^{2} \cos\left(d x + c\right) + 63 \, 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)}{693 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"2/693*(2*(568*A + 759*C)*a^2*cos(d*x + c)^5 + (568*A + 759*C)*a^2*cos(d*x + c)^4 + 6*(71*A + 66*C)*a^2*cos(d*x + c)^3 + (355*A + 99*C)*a^2*cos(d*x + c)^2 + 224*A*a^2*cos(d*x + c) + 63*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
197,1,170,0,0.499990," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(8368 \, A + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + 4 \, {\left(8368 \, A + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 3 \, {\left(8368 \, A + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(2092 \, A + 1859 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 35 \, {\left(523 \, A + 143 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 11970 \, A a^{2} \cos\left(d x + c\right) + 3465 \, 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)}{45045 \, {\left(d \cos\left(d x + c\right)^{8} + d \cos\left(d x + c\right)^{7}\right)}}"," ",0,"2/45045*(8*(8368*A + 10439*C)*a^2*cos(d*x + c)^6 + 4*(8368*A + 10439*C)*a^2*cos(d*x + c)^5 + 3*(8368*A + 10439*C)*a^2*cos(d*x + c)^4 + 10*(2092*A + 1859*C)*a^2*cos(d*x + c)^3 + 35*(523*A + 143*C)*a^2*cos(d*x + c)^2 + 11970*A*a^2*cos(d*x + c) + 3465*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^8 + d*cos(d*x + c)^7)","A",0
198,1,192,0,3.828916," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, C \cos\left(d x + c\right)^{2} - 2 \, C \cos\left(d x + c\right) + 24 \, A + 21 \, C\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(8 \, A + 9 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 9 \, C\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{24 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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}}}{24 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/24*((8*C*cos(d*x + c)^2 - 2*C*cos(d*x + c) + 24*A + 21*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A + 9*C)*cos(d*x + c) + 8*A + 9*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 24*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
199,1,178,0,3.819878," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, C \cos\left(d x + c\right) - C\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(8 \, A + 7 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 7 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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*C*cos(d*x + c) - C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((8*A + 7*C)*cos(d*x + c) + 8*A + 7*C)*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 + C)*a*cos(d*x + c) + (A + C)*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
200,1,153,0,1.857249," ","integrate((A+C*cos(d*x+c)^2)/cos(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} C \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left(C \cos\left(d x + c\right) + C\right)} \sqrt{a} \arctan\left(\frac{\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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)*C*sqrt(cos(d*x + c))*sin(d*x + c) + (C*cos(d*x + c) + 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 + C)*a*cos(d*x + c) + (A + C)*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
201,1,179,0,1.869709," ","integrate((A+C*cos(d*x+c)^2)/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) - 2 \, {\left(C \cos\left(d x + c\right)^{2} + C \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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A + C\right)} a \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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)^{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) - 2*(C*cos(d*x + c)^2 + C*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 + C)*a*cos(d*x + c)^2 + (A + C)*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))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
202,1,155,0,0.498786," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A \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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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*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 + C)*a*cos(d*x + c)^3 + (A + C)*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
203,1,172,0,0.458498," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(13 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{2} - A \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 + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A + C\right)} a \cos\left(d x + c\right)^{3}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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 + 15*C)*cos(d*x + c)^2 - A*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 + C)*a*cos(d*x + c)^4 + (A + C)*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
204,1,189,0,0.475113," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(43 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(31 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, A \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) - \frac{105 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right)^{5} + {\left(A + C\right)} a \cos\left(d x + c\right)^{4}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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}}}{105 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"-1/105*(2*((43*A + 35*C)*cos(d*x + c)^3 - (31*A + 35*C)*cos(d*x + c)^2 + 3*A*cos(d*x + c) - 15*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 105*sqrt(2)*((A + C)*a*cos(d*x + c)^5 + (A + C)*a*cos(d*x + c)^4)*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)^5 + a*d*cos(d*x + c)^4)","A",0
205,1,247,0,9.809085," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(5 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A + 13 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 13 \, C\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) + {\left(2 \, C \cos\left(d x + c\right)^{2} - 3 \, C \cos\left(d x + c\right) - 2 \, A - 7 \, C\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(8 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A + 19 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 19 \, C\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 + 13*C)*cos(d*x + c)^2 + 2*(5*A + 13*C)*cos(d*x + c) + 5*A + 13*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*C*cos(d*x + c)^2 - 3*C*cos(d*x + c) - 2*A - 7*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((8*A + 19*C)*cos(d*x + c)^2 + 2*(8*A + 19*C)*cos(d*x + c) + 8*A + 19*C)*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
206,1,212,0,5.220767," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(A + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 9 \, C\right)} \cos\left(d x + c\right) + A + 9 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 \, C \cos\left(d x + c\right) + A + 3 \, C\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(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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 + 9*C)*cos(d*x + c)^2 + 2*(A + 9*C)*cos(d*x + c) + A + 9*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(2*C*cos(d*x + c) + A + 3*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 12*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*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
207,1,207,0,5.278938," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 5 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 + C\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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)*((3*A - 5*C)*cos(d*x + c)^2 + 2*(3*A - 5*C)*cos(d*x + c) + 3*A - 5*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*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 + C)*sqrt(cos(d*x + c))*sin(d*x + c) + 8*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*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
208,1,199,0,0.459681," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(7 \, A - C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(7 \, A - C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - C\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 + C\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 - C)*cos(d*x + c)^3 + 2*(7*A - C)*cos(d*x + c)^2 + (7*A - C)*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 + C)*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
209,1,217,0,0.501206," ","integrate((A+C*cos(d*x+c)^2)/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 + 3 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(11 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(11 \, A + 3 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 12 \, A \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 + 3*C)*cos(d*x + c)^4 + 2*(11*A + 3*C)*cos(d*x + c)^3 + (11*A + 3*C)*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 + 3*C)*cos(d*x + c)^2 + 12*A*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
210,1,234,0,0.520640," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{5 \, \sqrt{2} {\left({\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(15 \, A + 7 \, C\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{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 + 25 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(9 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} - 4 \, A \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)}{20 \, {\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,"-1/20*(5*sqrt(2)*((15*A + 7*C)*cos(d*x + c)^5 + 2*(15*A + 7*C)*cos(d*x + c)^4 + (15*A + 7*C)*cos(d*x + c)^3)*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 + 25*C)*cos(d*x + c)^3 + 4*(9*A + 5*C)*cos(d*x + c)^2 - 4*A*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)^5 + 2*a^2*d*cos(d*x + c)^4 + a^2*d*cos(d*x + c)^3)","A",0
211,1,278,0,10.780717," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 115 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 \, C \cos\left(d x + c\right)^{2} + {\left(7 \, A + 55 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 35 \, C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 160 \, {\left(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \sqrt{a} \arctan\left(\frac{\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 + 115*C)*cos(d*x + c)^3 + 3*(3*A + 115*C)*cos(d*x + c)^2 + 3*(3*A + 115*C)*cos(d*x + c) + 3*A + 115*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(16*C*cos(d*x + c)^2 + (7*A + 55*C)*cos(d*x + c) + 3*A + 35*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 160*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*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
212,1,265,0,11.112016," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 43 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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(A - 15 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 11 \, C\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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \sqrt{a} \arctan\left(\frac{\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)*((5*A - 43*C)*cos(d*x + c)^3 + 3*(5*A - 43*C)*cos(d*x + c)^2 + 3*(5*A - 43*C)*cos(d*x + c) + 5*A - 43*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*((A - 15*C)*cos(d*x + c) + 5*A - 11*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) + 64*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*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
213,1,217,0,0.580862," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 3 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 - 7 \, C\right)} \cos\left(d x + c\right) + 13 \, A - 3 \, C\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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 3*C)*cos(d*x + c)^2 + 3*(19*A + 3*C)*cos(d*x + c) + 19*A + 3*C)*sqrt(a)*arctan(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 - 7*C)*cos(d*x + c) + 13*A - 3*C)*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
214,1,246,0,0.584006," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{5 \, \sqrt{2} {\left({\left(15 \, A - C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right)^{2} + {\left(15 \, A - C\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 + C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(17 \, A + C\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*(5*sqrt(2)*((15*A - C)*cos(d*x + c)^4 + 3*(15*A - C)*cos(d*x + c)^3 + 3*(15*A - C)*cos(d*x + c)^2 + (15*A - C)*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 + C)*cos(d*x + c)^2 + 5*(17*A + C)*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
215,1,264,0,0.523772," ","integrate((A+C*cos(d*x+c)^2)/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 + 19 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(163 \, A + 19 \, C\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 + 27 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(503 \, A + 39 \, C\right)} \cos\left(d x + c\right)^{2} + 160 \, A \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 + 19*C)*cos(d*x + c)^5 + 3*(163*A + 19*C)*cos(d*x + c)^4 + 3*(163*A + 19*C)*cos(d*x + c)^3 + (163*A + 19*C)*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 + 27*C)*cos(d*x + c)^3 + (503*A + 39*C)*cos(d*x + c)^2 + 160*A*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
216,1,64,0,0.598261," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{45 \, B d x + {\left(24 \, C \cos\left(d x + c\right)^{4} + 30 \, B \cos\left(d x + c\right)^{3} + 32 \, C \cos\left(d x + c\right)^{2} + 45 \, B \cos\left(d x + c\right) + 64 \, C\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(45*B*d*x + (24*C*cos(d*x + c)^4 + 30*B*cos(d*x + c)^3 + 32*C*cos(d*x + c)^2 + 45*B*cos(d*x + c) + 64*C)*sin(d*x + c))/d","A",0
217,1,53,0,0.454507," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{9 \, C d x + {\left(6 \, C \cos\left(d x + c\right)^{3} + 8 \, B \cos\left(d x + c\right)^{2} + 9 \, C \cos\left(d x + c\right) + 16 \, B\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(9*C*d*x + (6*C*cos(d*x + c)^3 + 8*B*cos(d*x + c)^2 + 9*C*cos(d*x + c) + 16*B)*sin(d*x + c))/d","A",0
218,1,42,0,0.442054," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, B d x + {\left(2 \, C \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 4 \, C\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*B*d*x + (2*C*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 4*C)*sin(d*x + c))/d","A",0
219,1,29,0,0.458880," ","integrate(B*cos(d*x+c)+C*cos(d*x+c)^2,x, algorithm=""fricas"")","\frac{C d x + {\left(C \cos\left(d x + c\right) + 2 \, B\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(C*d*x + (C*cos(d*x + c) + 2*B)*sin(d*x + c))/d","A",0
220,1,17,0,0.514659," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{B d x + C \sin\left(d x + c\right)}{d}"," ",0,"(B*d*x + C*sin(d*x + c))/d","A",0
221,1,36,0,0.650648," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, C d x + B \log\left(\sin\left(d x + c\right) + 1\right) - B \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, d}"," ",0,"1/2*(2*C*d*x + B*log(sin(d*x + c) + 1) - B*log(-sin(d*x + c) + 1))/d","B",0
222,1,60,0,0.439615," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{C \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - C \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(C*cos(d*x + c)*log(sin(d*x + c) + 1) - C*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*B*sin(d*x + c))/(d*cos(d*x + c))","B",0
223,1,74,0,0.423538," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,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 \, {\left(2 \, C \cos\left(d x + c\right) + B\right)} \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*(2*C*cos(d*x + c) + B)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
224,1,88,0,0.431093," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, C \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, C \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, B \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + 2 \, B\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*C*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*C*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(4*B*cos(d*x + c)^2 + 3*C*cos(d*x + c) + 2*B)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
225,1,99,0,0.464061," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{9 \, B \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, B \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, C \cos\left(d x + c\right)^{3} + 9 \, B \cos\left(d x + c\right)^{2} + 8 \, C \cos\left(d x + c\right) + 6 \, B\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(9*B*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 9*B*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*C*cos(d*x + c)^3 + 9*B*cos(d*x + c)^2 + 8*C*cos(d*x + c) + 6*B)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
226,1,88,0,0.481040," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{45 \, {\left(B + C\right)} a d x + {\left(24 \, C a \cos\left(d x + c\right)^{4} + 30 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, B + 4 \, C\right)} a \cos\left(d x + c\right)^{2} + 45 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 16 \, {\left(5 \, B + 4 \, C\right)} a\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(45*(B + C)*a*d*x + (24*C*a*cos(d*x + c)^4 + 30*(B + C)*a*cos(d*x + c)^3 + 8*(5*B + 4*C)*a*cos(d*x + c)^2 + 45*(B + C)*a*cos(d*x + c) + 16*(5*B + 4*C)*a)*sin(d*x + c))/d","A",0
227,1,74,0,0.418719," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, B + 3 \, C\right)} a d x + {\left(6 \, C a \cos\left(d x + c\right)^{3} + 8 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, B + 3 \, C\right)} a \cos\left(d x + c\right) + 16 \, {\left(B + C\right)} a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*B + 3*C)*a*d*x + (6*C*a*cos(d*x + c)^3 + 8*(B + C)*a*cos(d*x + c)^2 + 3*(4*B + 3*C)*a*cos(d*x + c) + 16*(B + C)*a)*sin(d*x + c))/d","A",0
228,1,56,0,0.555591," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(B + C\right)} a d x + {\left(2 \, C a \cos\left(d x + c\right)^{2} + 3 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 2 \, {\left(3 \, B + 2 \, C\right)} a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(B + C)*a*d*x + (2*C*a*cos(d*x + c)^2 + 3*(B + C)*a*cos(d*x + c) + 2*(3*B + 2*C)*a)*sin(d*x + c))/d","A",0
229,1,38,0,0.454614," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{{\left(2 \, B + C\right)} a d x + {\left(C a \cos\left(d x + c\right) + 2 \, {\left(B + C\right)} a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*B + C)*a*d*x + (C*a*cos(d*x + c) + 2*(B + C)*a)*sin(d*x + c))/d","A",0
230,1,51,0,0.520781," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(B + C\right)} a d x + B a \log\left(\sin\left(d x + c\right) + 1\right) - B a \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, C a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(B + C)*a*d*x + B*a*log(sin(d*x + c) + 1) - B*a*log(-sin(d*x + c) + 1) + 2*C*a*sin(d*x + c))/d","A",0
231,1,79,0,0.443810," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, C a d x \cos\left(d x + c\right) + {\left(B + C\right)} a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B + C\right)} a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B a \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*C*a*d*x*cos(d*x + c) + (B + C)*a*cos(d*x + c)*log(sin(d*x + c) + 1) - (B + C)*a*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*B*a*sin(d*x + c))/(d*cos(d*x + c))","B",0
232,1,89,0,0.458823," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{{\left(B + 2 \, C\right)} a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B + 2 \, C\right)} a \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(B + C\right)} a \cos\left(d x + c\right) + B a\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((B + 2*C)*a*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (B + 2*C)*a*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*(B + C)*a*cos(d*x + c) + B*a)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
233,1,105,0,0.482240," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(2 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 2 \, B a\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(B + C)*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B + C)*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(2*B + 3*C)*a*cos(d*x + c)^2 + 3*(B + C)*a*cos(d*x + c) + 2*B*a)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
234,1,127,0,0.461857," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, B + 4 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, B + 4 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, B + 4 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 6 \, B a\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(3*B + 4*C)*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*B + 4*C)*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(B + C)*a*cos(d*x + c)^3 + 3*(3*B + 4*C)*a*cos(d*x + c)^2 + 8*(B + C)*a*cos(d*x + c) + 6*B*a)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
235,1,110,0,0.428577," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(7 \, B + 6 \, C\right)} a^{2} d x + {\left(24 \, C a^{2} \cos\left(d x + c\right)^{4} + 30 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(10 \, B + 9 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(7 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right) + 16 \, {\left(10 \, B + 9 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(7*B + 6*C)*a^2*d*x + (24*C*a^2*cos(d*x + c)^4 + 30*(B + 2*C)*a^2*cos(d*x + c)^3 + 8*(10*B + 9*C)*a^2*cos(d*x + c)^2 + 15*(7*B + 6*C)*a^2*cos(d*x + c) + 16*(10*B + 9*C)*a^2)*sin(d*x + c))/d","A",0
236,1,90,0,0.438342," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, B + 7 \, C\right)} a^{2} d x + {\left(6 \, C a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(5 \, B + 4 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(8*B + 7*C)*a^2*d*x + (6*C*a^2*cos(d*x + c)^3 + 8*(B + 2*C)*a^2*cos(d*x + c)^2 + 3*(8*B + 7*C)*a^2*cos(d*x + c) + 8*(5*B + 4*C)*a^2)*sin(d*x + c))/d","A",0
237,1,70,0,0.436009," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, B + 2 \, C\right)} a^{2} d x + {\left(2 \, C a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(6 \, B + 5 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(3*B + 2*C)*a^2*d*x + (2*C*a^2*cos(d*x + c)^2 + 3*(B + 2*C)*a^2*cos(d*x + c) + 2*(6*B + 5*C)*a^2)*sin(d*x + c))/d","A",0
238,1,79,0,0.504699," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(4 \, B + 3 \, C\right)} a^{2} d x + B a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - B a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(C a^{2} \cos\left(d x + c\right) + 2 \, {\left(B + 2 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((4*B + 3*C)*a^2*d*x + B*a^2*log(sin(d*x + c) + 1) - B*a^2*log(-sin(d*x + c) + 1) + (C*a^2*cos(d*x + c) + 2*(B + 2*C)*a^2)*sin(d*x + c))/d","A",0
239,1,108,0,0.440955," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(B + 2 \, C\right)} a^{2} d x \cos\left(d x + c\right) + {\left(2 \, B + C\right)} a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, B + C\right)} a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{2} \cos\left(d x + c\right) + B a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(B + 2*C)*a^2*d*x*cos(d*x + c) + (2*B + C)*a^2*cos(d*x + c)*log(sin(d*x + c) + 1) - (2*B + C)*a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(C*a^2*cos(d*x + c) + B*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
240,1,119,0,0.498487," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{4 \, C a^{2} d x \cos\left(d x + c\right)^{2} + {\left(3 \, B + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, B + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(2 \, B + C\right)} a^{2} \cos\left(d x + c\right) + B a^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*C*a^2*d*x*cos(d*x + c)^2 + (3*B + 4*C)*a^2*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (3*B + 4*C)*a^2*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*(2*B + C)*a^2*cos(d*x + c) + B*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
241,1,125,0,0.450700," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, B + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, B + 3 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(5 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B + C\right)} a^{2} \cos\left(d x + c\right) + 2 \, B a^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(2*B + 3*C)*a^2*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*B + 3*C)*a^2*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(5*B + 6*C)*a^2*cos(d*x + c)^2 + 3*(2*B + C)*a^2*cos(d*x + c) + 2*B*a^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
242,1,145,0,0.496838," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(7 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(4 \, B + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(2 \, B + C\right)} a^{2} \cos\left(d x + c\right) + 6 \, B a^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(7*B + 8*C)*a^2*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(7*B + 8*C)*a^2*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(4*B + 5*C)*a^2*cos(d*x + c)^3 + 3*(7*B + 8*C)*a^2*cos(d*x + c)^2 + 8*(2*B + C)*a^2*cos(d*x + c) + 6*B*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
243,1,165,0,0.455171," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(6 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(9 \, B + 10 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 15 \, {\left(6 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(9 \, B + 10 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 30 \, {\left(2 \, B + C\right)} a^{2} \cos\left(d x + c\right) + 24 \, B a^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(6*B + 7*C)*a^2*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(6*B + 7*C)*a^2*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(9*B + 10*C)*a^2*cos(d*x + c)^4 + 15*(6*B + 7*C)*a^2*cos(d*x + c)^3 + 8*(9*B + 10*C)*a^2*cos(d*x + c)^2 + 30*(2*B + C)*a^2*cos(d*x + c) + 24*B*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
244,1,130,0,0.458614," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(26 \, B + 23 \, C\right)} a^{3} d x + {\left(40 \, C a^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 10 \, {\left(18 \, B + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(19 \, B + 17 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(26 \, B + 23 \, C\right)} a^{3} \cos\left(d x + c\right) + 32 \, {\left(19 \, B + 17 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(26*B + 23*C)*a^3*d*x + (40*C*a^3*cos(d*x + c)^5 + 48*(B + 3*C)*a^3*cos(d*x + c)^4 + 10*(18*B + 23*C)*a^3*cos(d*x + c)^3 + 16*(19*B + 17*C)*a^3*cos(d*x + c)^2 + 15*(26*B + 23*C)*a^3*cos(d*x + c) + 32*(19*B + 17*C)*a^3)*sin(d*x + c))/d","A",0
245,1,110,0,0.443471," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(15 \, B + 13 \, C\right)} a^{3} d x + {\left(24 \, C a^{3} \cos\left(d x + c\right)^{4} + 30 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, B + 19 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(15 \, B + 13 \, C\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(45 \, B + 38 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(15*B + 13*C)*a^3*d*x + (24*C*a^3*cos(d*x + c)^4 + 30*(B + 3*C)*a^3*cos(d*x + c)^3 + 8*(15*B + 19*C)*a^3*cos(d*x + c)^2 + 15*(15*B + 13*C)*a^3*cos(d*x + c) + 8*(45*B + 38*C)*a^3)*sin(d*x + c))/d","A",0
246,1,90,0,0.427083," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, B + 3 \, C\right)} a^{3} d x + {\left(6 \, C a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 9 \, {\left(4 \, B + 5 \, C\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(11 \, B + 9 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(15*(4*B + 3*C)*a^3*d*x + (6*C*a^3*cos(d*x + c)^3 + 8*(B + 3*C)*a^3*cos(d*x + c)^2 + 9*(4*B + 5*C)*a^3*cos(d*x + c) + 8*(11*B + 9*C)*a^3)*sin(d*x + c))/d","A",0
247,1,102,0,0.428307," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, B + 5 \, C\right)} a^{3} d x + 3 \, B a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, B a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 2 \, {\left(9 \, B + 11 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(7*B + 5*C)*a^3*d*x + 3*B*a^3*log(sin(d*x + c) + 1) - 3*B*a^3*log(-sin(d*x + c) + 1) + (2*C*a^3*cos(d*x + c)^2 + 3*(B + 3*C)*a^3*cos(d*x + c) + 2*(9*B + 11*C)*a^3)*sin(d*x + c))/d","A",0
248,1,127,0,0.438118," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(6 \, B + 7 \, C\right)} a^{3} d x \cos\left(d x + c\right) + {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(C a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right) + 2 \, B a^{3}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((6*B + 7*C)*a^3*d*x*cos(d*x + c) + (3*B + C)*a^3*cos(d*x + c)*log(sin(d*x + c) + 1) - (3*B + C)*a^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + (C*a^3*cos(d*x + c)^2 + 2*(B + 3*C)*a^3*cos(d*x + c) + 2*B*a^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
249,1,137,0,0.428996," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{4 \, {\left(B + 3 \, C\right)} a^{3} d x \cos\left(d x + c\right)^{2} + {\left(7 \, B + 6 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(7 \, B + 6 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right) + B a^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*(B + 3*C)*a^3*d*x*cos(d*x + c)^2 + (7*B + 6*C)*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (7*B + 6*C)*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*a^3*cos(d*x + c)^2 + 2*(3*B + C)*a^3*cos(d*x + c) + B*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
250,1,141,0,0.478199," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{12 \, C a^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, B + 7 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, B + 7 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(11 \, B + 9 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right) + 2 \, B a^{3}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*C*a^3*d*x*cos(d*x + c)^3 + 3*(5*B + 7*C)*a^3*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(5*B + 7*C)*a^3*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(11*B + 9*C)*a^3*cos(d*x + c)^2 + 3*(3*B + C)*a^3*cos(d*x + c) + 2*B*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
251,1,145,0,0.466742," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B + 4 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, B + 4 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(9 \, B + 11 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 9 \, {\left(5 \, B + 4 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right) + 6 \, B a^{3}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(15*(3*B + 4*C)*a^3*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 15*(3*B + 4*C)*a^3*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(9*B + 11*C)*a^3*cos(d*x + c)^3 + 9*(5*B + 4*C)*a^3*cos(d*x + c)^2 + 8*(3*B + C)*a^3*cos(d*x + c) + 6*B*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
252,1,165,0,0.497730," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(13 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(38 \, B + 45 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 15 \, {\left(13 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(19 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 30 \, {\left(3 \, B + C\right)} a^{3} \cos\left(d x + c\right) + 24 \, B a^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(13*B + 15*C)*a^3*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(13*B + 15*C)*a^3*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(38*B + 45*C)*a^3*cos(d*x + c)^4 + 15*(13*B + 15*C)*a^3*cos(d*x + c)^3 + 8*(19*B + 15*C)*a^3*cos(d*x + c)^2 + 30*(3*B + C)*a^3*cos(d*x + c) + 24*B*a^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
253,1,98,0,0.442621," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left(B - C\right)} d x \cos\left(d x + c\right) + 9 \, {\left(B - C\right)} d x + {\left(2 \, C \cos\left(d x + c\right)^{3} + {\left(3 \, B - C\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, B - 7 \, C\right)} \cos\left(d x + c\right) - 12 \, B + 16 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/6*(9*(B - C)*d*x*cos(d*x + c) + 9*(B - C)*d*x + (2*C*cos(d*x + c)^3 + (3*B - C)*cos(d*x + c)^2 - (3*B - 7*C)*cos(d*x + c) - 12*B + 16*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
254,1,83,0,0.454982," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(2 \, B - 3 \, C\right)} d x \cos\left(d x + c\right) + {\left(2 \, B - 3 \, C\right)} d x - {\left(C \cos\left(d x + c\right)^{2} + {\left(2 \, B - C\right)} \cos\left(d x + c\right) + 4 \, B - 4 \, C\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/2*((2*B - 3*C)*d*x*cos(d*x + c) + (2*B - 3*C)*d*x - (C*cos(d*x + c)^2 + (2*B - C)*cos(d*x + c) + 4*B - 4*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
255,1,61,0,0.481005," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(B - C\right)} d x \cos\left(d x + c\right) + {\left(B - C\right)} d x + {\left(C \cos\left(d x + c\right) - B + 2 \, C\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"((B - C)*d*x*cos(d*x + c) + (B - C)*d*x + (C*cos(d*x + c) - B + 2*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
256,1,43,0,0.465436," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{C d x \cos\left(d x + c\right) + C d x + {\left(B - C\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"(C*d*x*cos(d*x + c) + C*d*x + (B - C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
257,1,74,0,0.425519," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(B \cos\left(d x + c\right) + B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B \cos\left(d x + c\right) + B\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B - C\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*((B*cos(d*x + c) + B)*log(sin(d*x + c) + 1) - (B*cos(d*x + c) + B)*log(-sin(d*x + c) + 1) - 2*(B - C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
258,1,127,0,0.718109," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left({\left(B - C\right)} \cos\left(d x + c\right)^{2} + {\left(B - C\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(B - C\right)} \cos\left(d x + c\right)^{2} + {\left(B - C\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(2 \, B - C\right)} \cos\left(d x + c\right) + B\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}"," ",0,"-1/2*(((B - C)*cos(d*x + c)^2 + (B - C)*cos(d*x + c))*log(sin(d*x + c) + 1) - ((B - C)*cos(d*x + c)^2 + (B - C)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*((2*B - C)*cos(d*x + c) + B)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
259,1,156,0,0.442315," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(B - C\right)} \cos\left(d x + c\right)^{2} + {\left(B - 2 \, C\right)} \cos\left(d x + c\right) - B\right)} \sin\left(d x + c\right)}{4 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/4*(((3*B - 2*C)*cos(d*x + c)^3 + (3*B - 2*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((3*B - 2*C)*cos(d*x + c)^3 + (3*B - 2*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(B - C)*cos(d*x + c)^2 + (B - 2*C)*cos(d*x + c) - B)*sin(d*x + c))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
260,1,168,0,0.434158," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{9 \, {\left({\left(B - C\right)} \cos\left(d x + c\right)^{4} + {\left(B - C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, {\left({\left(B - C\right)} \cos\left(d x + c\right)^{4} + {\left(B - C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(4 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(B - 3 \, C\right)} \cos\left(d x + c\right) + 2 \, B\right)} \sin\left(d x + c\right)}{12 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/12*(9*((B - C)*cos(d*x + c)^4 + (B - C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 9*((B - C)*cos(d*x + c)^4 + (B - C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(4*(4*B - 3*C)*cos(d*x + c)^3 + (7*B - 3*C)*cos(d*x + c)^2 - (B - 3*C)*cos(d*x + c) + 2*B)*sin(d*x + c))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
261,1,154,0,0.428130," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, B - 10 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(7 \, B - 10 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(7 \, B - 10 \, C\right)} d x + {\left(2 \, C \cos\left(d x + c\right)^{4} + {\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(B - 2 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(43 \, B - 66 \, C\right)} \cos\left(d x + c\right) - 32 \, B + 48 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(7*B - 10*C)*d*x*cos(d*x + c)^2 + 6*(7*B - 10*C)*d*x*cos(d*x + c) + 3*(7*B - 10*C)*d*x + (2*C*cos(d*x + c)^4 + (3*B - 2*C)*cos(d*x + c)^3 - 6*(B - 2*C)*cos(d*x + c)^2 - (43*B - 66*C)*cos(d*x + c) - 32*B + 48*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
262,1,138,0,0.429609," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(4 \, B - 7 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(4 \, B - 7 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(4 \, B - 7 \, C\right)} d x - {\left(3 \, C \cos\left(d x + c\right)^{3} + 6 \, {\left(B - C\right)} \cos\left(d x + c\right)^{2} + {\left(28 \, B - 43 \, C\right)} \cos\left(d x + c\right) + 20 \, B - 32 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/6*(3*(4*B - 7*C)*d*x*cos(d*x + c)^2 + 6*(4*B - 7*C)*d*x*cos(d*x + c) + 3*(4*B - 7*C)*d*x - (3*C*cos(d*x + c)^3 + 6*(B - C)*cos(d*x + c)^2 + (28*B - 43*C)*cos(d*x + c) + 20*B - 32*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
263,1,117,0,0.428843," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(B - 2 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(B - 2 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(B - 2 \, C\right)} d x + {\left(3 \, C \cos\left(d x + c\right)^{2} - {\left(5 \, B - 14 \, C\right)} \cos\left(d x + c\right) - 4 \, B + 10 \, C\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(3*(B - 2*C)*d*x*cos(d*x + c)^2 + 6*(B - 2*C)*d*x*cos(d*x + c) + 3*(B - 2*C)*d*x + (3*C*cos(d*x + c)^2 - (5*B - 14*C)*cos(d*x + c) - 4*B + 10*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
264,1,91,0,0.471344," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, C d x \cos\left(d x + c\right)^{2} + 6 \, C d x \cos\left(d x + c\right) + 3 \, C d x + {\left({\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right) + B - 4 \, C\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(3*C*d*x*cos(d*x + c)^2 + 6*C*d*x*cos(d*x + c) + 3*C*d*x + ((2*B - 5*C)*cos(d*x + c) + B - 4*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
265,1,58,0,0.454782," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left({\left(B + 2 \, C\right)} \cos\left(d x + c\right) + 2 \, B + C\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*((B + 2*C)*cos(d*x + c) + 2*B + C)*sin(d*x + c)/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
266,1,131,0,0.422334," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B \cos\left(d x + c\right)^{2} + 2 \, B \cos\left(d x + c\right) + B\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(4 \, B - C\right)} \cos\left(d x + c\right) + 5 \, B - 2 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + B)*log(sin(d*x + c) + 1) - 3*(B*cos(d*x + c)^2 + 2*B*cos(d*x + c) + B)*log(-sin(d*x + c) + 1) - 2*((4*B - C)*cos(d*x + c) + 5*B - 2*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
267,1,207,0,0.483539," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(2 \, B - C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, B - C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B - C\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(2 \, B - C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, B - C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B - C\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(5 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(14 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, B\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/6*(3*((2*B - C)*cos(d*x + c)^3 + 2*(2*B - C)*cos(d*x + c)^2 + (2*B - C)*cos(d*x + c))*log(sin(d*x + c) + 1) - 3*((2*B - C)*cos(d*x + c)^3 + 2*(2*B - C)*cos(d*x + c)^2 + (2*B - C)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*(5*B - 2*C)*cos(d*x + c)^2 + (14*B - 5*C)*cos(d*x + c) + 3*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))","B",0
268,1,228,0,0.485079," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(7 \, B - 4 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, B - 4 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, B - 4 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(7 \, B - 4 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, B - 4 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, B - 4 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(8 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(43 \, B - 28 \, C\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(B - C\right)} \cos\left(d x + c\right) - 3 \, B\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/12*(3*((7*B - 4*C)*cos(d*x + c)^4 + 2*(7*B - 4*C)*cos(d*x + c)^3 + (7*B - 4*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*((7*B - 4*C)*cos(d*x + c)^4 + 2*(7*B - 4*C)*cos(d*x + c)^3 + (7*B - 4*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(8*B - 5*C)*cos(d*x + c)^3 + (43*B - 28*C)*cos(d*x + c)^2 + 6*(B - C)*cos(d*x + c) - 3*B)*sin(d*x + c))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)","A",0
269,1,190,0,0.437319," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(6 \, B - 13 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(6 \, B - 13 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(6 \, B - 13 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(6 \, B - 13 \, C\right)} d x - {\left(15 \, C \cos\left(d x + c\right)^{4} + 15 \, {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(234 \, B - 479 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(114 \, B - 239 \, C\right)} \cos\left(d x + c\right) + 144 \, B - 304 \, C\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/30*(15*(6*B - 13*C)*d*x*cos(d*x + c)^3 + 45*(6*B - 13*C)*d*x*cos(d*x + c)^2 + 45*(6*B - 13*C)*d*x*cos(d*x + c) + 15*(6*B - 13*C)*d*x - (15*C*cos(d*x + c)^4 + 15*(2*B - 3*C)*cos(d*x + c)^3 + (234*B - 479*C)*cos(d*x + c)^2 + 3*(114*B - 239*C)*cos(d*x + c) + 144*B - 304*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
270,1,165,0,0.449406," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(B - 3 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(B - 3 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(B - 3 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(B - 3 \, C\right)} d x + {\left(15 \, C \cos\left(d x + c\right)^{3} - {\left(32 \, B - 117 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(17 \, B - 57 \, C\right)} \cos\left(d x + c\right) - 22 \, B + 72 \, C\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(15*(B - 3*C)*d*x*cos(d*x + c)^3 + 45*(B - 3*C)*d*x*cos(d*x + c)^2 + 45*(B - 3*C)*d*x*cos(d*x + c) + 15*(B - 3*C)*d*x + (15*C*cos(d*x + c)^3 - (32*B - 117*C)*cos(d*x + c)^2 - 3*(17*B - 57*C)*cos(d*x + c) - 22*B + 72*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
271,1,137,0,0.398480," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, C d x \cos\left(d x + c\right)^{3} + 45 \, C d x \cos\left(d x + c\right)^{2} + 45 \, C d x \cos\left(d x + c\right) + 15 \, C d x + {\left({\left(7 \, B - 32 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B - 17 \, C\right)} \cos\left(d x + c\right) + 2 \, B - 22 \, C\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(15*C*d*x*cos(d*x + c)^3 + 45*C*d*x*cos(d*x + c)^2 + 45*C*d*x*cos(d*x + c) + 15*C*d*x + ((7*B - 32*C)*cos(d*x + c)^2 + 3*(2*B - 17*C)*cos(d*x + c) + 2*B - 22*C)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
272,1,93,0,0.569593," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(3 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, B + 2 \, C\right)} \cos\left(d x + c\right) + 3 \, B + 2 \, C\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*((3*B + 7*C)*cos(d*x + c)^2 + 3*(3*B + 2*C)*cos(d*x + c) + 3*B + 2*C)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
273,1,93,0,0.469085," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 7 \, B + 3 \, C\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*((2*B + 3*C)*cos(d*x + c)^2 + 3*(2*B + 3*C)*cos(d*x + c) + 7*B + 3*C)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
274,1,185,0,0.416369," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(B \cos\left(d x + c\right)^{3} + 3 \, B \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(B \cos\left(d x + c\right)^{3} + 3 \, B \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + B\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(11 \, B - C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(17 \, B - 2 \, C\right)} \cos\left(d x + c\right) + 32 \, B - 7 \, C\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(15*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + B)*log(sin(d*x + c) + 1) - 15*(B*cos(d*x + c)^3 + 3*B*cos(d*x + c)^2 + 3*B*cos(d*x + c) + B)*log(-sin(d*x + c) + 1) - 2*(2*(11*B - C)*cos(d*x + c)^2 + 3*(17*B - 2*C)*cos(d*x + c) + 32*B - 7*C)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
275,1,272,0,0.468745," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(3 \, B - C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, B - C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, B - C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B - C\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(3 \, B - C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, B - C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, B - C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B - C\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(36 \, B - 11 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(57 \, B - 17 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(117 \, B - 32 \, C\right)} \cos\left(d x + c\right) + 15 \, B\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/30*(15*((3*B - C)*cos(d*x + c)^4 + 3*(3*B - C)*cos(d*x + c)^3 + 3*(3*B - C)*cos(d*x + c)^2 + (3*B - C)*cos(d*x + c))*log(sin(d*x + c) + 1) - 15*((3*B - C)*cos(d*x + c)^4 + 3*(3*B - C)*cos(d*x + c)^3 + 3*(3*B - C)*cos(d*x + c)^2 + (3*B - C)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*(36*B - 11*C)*cos(d*x + c)^3 + 3*(57*B - 17*C)*cos(d*x + c)^2 + (117*B - 32*C)*cos(d*x + c) + 15*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))","A",0
276,1,295,0,0.437082," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(13 \, B - 6 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(13 \, B - 6 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(13 \, B - 6 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, B - 6 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(13 \, B - 6 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(13 \, B - 6 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(13 \, B - 6 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, B - 6 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(19 \, B - 9 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(239 \, B - 114 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(479 \, B - 234 \, C\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right) - 15 \, B\right)} \sin\left(d x + c\right)}{60 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/60*(15*((13*B - 6*C)*cos(d*x + c)^5 + 3*(13*B - 6*C)*cos(d*x + c)^4 + 3*(13*B - 6*C)*cos(d*x + c)^3 + (13*B - 6*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 15*((13*B - 6*C)*cos(d*x + c)^5 + 3*(13*B - 6*C)*cos(d*x + c)^4 + 3*(13*B - 6*C)*cos(d*x + c)^3 + (13*B - 6*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(16*(19*B - 9*C)*cos(d*x + c)^4 + 3*(239*B - 114*C)*cos(d*x + c)^3 + (479*B - 234*C)*cos(d*x + c)^2 + 15*(3*B - 2*C)*cos(d*x + c) - 15*B)*sin(d*x + c))/(a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2)","A",0
277,1,64,0,0.403258," ","integrate((a+a*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, C \cos\left(d x + c\right)^{2} + {\left(5 \, B + 4 \, C\right)} \cos\left(d x + c\right) + 10 \, B + 8 \, C\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*C*cos(d*x + c)^2 + (5*B + 4*C)*cos(d*x + c) + 10*B + 8*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
278,1,88,0,0.409133," ","integrate((a+a*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, C a \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, B + 13 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(63 \, B + 52 \, C\right)} a \cos\left(d x + c\right) + 2 \, {\left(63 \, B + 52 \, C\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*C*a*cos(d*x + c)^3 + 3*(7*B + 13*C)*a*cos(d*x + c)^2 + (63*B + 52*C)*a*cos(d*x + c) + 2*(63*B + 52*C)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
279,1,116,0,0.465539," ","integrate((a+a*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, C a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(9 \, B + 26 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(60 \, B + 73 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(345 \, B + 292 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(345 \, B + 292 \, C\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*C*a^2*cos(d*x + c)^4 + 5*(9*B + 26*C)*a^2*cos(d*x + c)^3 + 3*(60*B + 73*C)*a^2*cos(d*x + c)^2 + (345*B + 292*C)*a^2*cos(d*x + c) + 2*(345*B + 292*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
280,1,149,0,0.467628," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(C \cos\left(d x + c\right) + 3 \, B - C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) - \frac{3 \, \sqrt{2} {\left({\left(B - C\right)} a \cos\left(d x + c\right) + {\left(B - C\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*(C*cos(d*x + c) + 3*B - C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) - 3*sqrt(2)*((B - C)*a*cos(d*x + c) + (B - C)*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
281,1,189,0,0.450752," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B - 7 \, C\right)} \cos\left(d x + c\right) + 3 \, B - 7 \, C\right)} \sqrt{a} \log\left(-\frac{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 \, C \cos\left(d x + c\right) - B + 5 \, C\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*B - 7*C)*cos(d*x + c)^2 + 2*(3*B - 7*C)*cos(d*x + c) + 3*B - 7*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)) - 4*(4*C*cos(d*x + c) - B + 5*C)*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
282,1,223,0,0.503605," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(5 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 5 \, B + 19 \, C\right)} \sqrt{a} \log\left(-\frac{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 \, B - 13 \, C\right)} \cos\left(d x + c\right) + B - 9 \, C\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*B + 19*C)*cos(d*x + c)^3 + 3*(5*B + 19*C)*cos(d*x + c)^2 + 3*(5*B + 19*C)*cos(d*x + c) + 5*B + 19*C)*sqrt(a)*log(-(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*B - 13*C)*cos(d*x + c) + B - 9*C)*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
283,0,0,0,0.448720," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} + B \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^3 + B*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
284,0,0,0,0.558907," ","integrate(cos(d*x+c)^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
285,0,0,0,0.633930," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) + B\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)*sqrt(cos(d*x + c)), x)","F",0
286,0,0,0,0.430528," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right) + B}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)/sqrt(cos(d*x + c)), x)","F",0
287,0,0,0,0.406169," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right) + B}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)/cos(d*x + c)^(3/2), x)","F",0
288,0,0,0,0.465182," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right) + B}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)/cos(d*x + c)^(5/2), x)","F",0
289,0,0,0,0.426286," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right) + B}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)/cos(d*x + c)^(7/2), x)","F",0
290,1,93,0,0.584242," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, A + 5 \, C\right)} d x + {\left(40 \, C \cos\left(d x + c\right)^{5} + 48 \, B \cos\left(d x + c\right)^{4} + 10 \, {\left(6 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{3} + 64 \, B \cos\left(d x + c\right)^{2} + 15 \, {\left(6 \, A + 5 \, C\right)} \cos\left(d x + c\right) + 128 \, B\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(6*A + 5*C)*d*x + (40*C*cos(d*x + c)^5 + 48*B*cos(d*x + c)^4 + 10*(6*A + 5*C)*cos(d*x + c)^3 + 64*B*cos(d*x + c)^2 + 15*(6*A + 5*C)*cos(d*x + c) + 128*B)*sin(d*x + c))/d","A",0
291,1,73,0,0.472061," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{45 \, B d x + {\left(24 \, C \cos\left(d x + c\right)^{4} + 30 \, B \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 4 \, C\right)} \cos\left(d x + c\right)^{2} + 45 \, B \cos\left(d x + c\right) + 80 \, A + 64 \, C\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(45*B*d*x + (24*C*cos(d*x + c)^4 + 30*B*cos(d*x + c)^3 + 8*(5*A + 4*C)*cos(d*x + c)^2 + 45*B*cos(d*x + c) + 80*A + 64*C)*sin(d*x + c))/d","A",0
292,1,65,0,0.441417," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A + 3 \, C\right)} d x + {\left(6 \, C \cos\left(d x + c\right)^{3} + 8 \, B \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 16 \, B\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*A + 3*C)*d*x + (6*C*cos(d*x + c)^3 + 8*B*cos(d*x + c)^2 + 3*(4*A + 3*C)*cos(d*x + c) + 16*B)*sin(d*x + c))/d","A",0
293,1,45,0,0.435926," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, B d x + {\left(2 \, C \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 6 \, A + 4 \, C\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*B*d*x + (2*C*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 6*A + 4*C)*sin(d*x + c))/d","A",0
294,1,33,0,0.459152," ","integrate(A+B*cos(d*x+c)+C*cos(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, A + C\right)} d x + {\left(C \cos\left(d x + c\right) + 2 \, B\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*A + C)*d*x + (C*cos(d*x + c) + 2*B)*sin(d*x + c))/d","A",0
295,1,45,0,0.416751," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{2 \, B d x + A \log\left(\sin\left(d x + c\right) + 1\right) - A \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, C \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*B*d*x + A*log(sin(d*x + c) + 1) - A*log(-sin(d*x + c) + 1) + 2*C*sin(d*x + c))/d","A",0
296,1,71,0,0.454181," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, C d x \cos\left(d x + c\right) + B \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - B \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, A \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*C*d*x*cos(d*x + c) + B*cos(d*x + c)*log(sin(d*x + c) + 1) - B*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*A*sin(d*x + c))/(d*cos(d*x + c))","B",0
297,1,82,0,0.442476," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(A + 2 \, C\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A + 2 \, C\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B \cos\left(d x + c\right) + A\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((A + 2*C)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A + 2*C)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*B*cos(d*x + c) + A)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
298,1,94,0,0.498433," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, B \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, B \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(2 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 2 \, A\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*B*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*B*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(2*A + 3*C)*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 2*A)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
299,1,117,0,0.427917," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 4 \, C\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, A + 4 \, C\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, B \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 4 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, B \cos\left(d x + c\right) + 6 \, A\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(3*A + 4*C)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*A + 4*C)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*B*cos(d*x + c)^3 + 3*(3*A + 4*C)*cos(d*x + c)^2 + 8*B*cos(d*x + c) + 6*A)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
300,1,122,0,0.448842," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{45 \, B \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 45 \, B \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(4 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{4} + 45 \, B \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 30 \, B \cos\left(d x + c\right) + 24 \, A\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(45*B*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 45*B*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(4*A + 5*C)*cos(d*x + c)^4 + 45*B*cos(d*x + c)^3 + 8*(4*A + 5*C)*cos(d*x + c)^2 + 30*B*cos(d*x + c) + 24*A)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
301,1,108,0,0.462444," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, B + 3 \, C\right)} a d x + {\left(24 \, C a \cos\left(d x + c\right)^{4} + 30 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 5 \, B + 4 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, A + 3 \, B + 3 \, C\right)} a \cos\left(d x + c\right) + 16 \, {\left(5 \, A + 5 \, B + 4 \, C\right)} a\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*A + 3*B + 3*C)*a*d*x + (24*C*a*cos(d*x + c)^4 + 30*(B + C)*a*cos(d*x + c)^3 + 8*(5*A + 5*B + 4*C)*a*cos(d*x + c)^2 + 15*(4*A + 3*B + 3*C)*a*cos(d*x + c) + 16*(5*A + 5*B + 4*C)*a)*sin(d*x + c))/d","A",0
302,1,87,0,0.445571," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A + 4 \, B + 3 \, C\right)} a d x + {\left(6 \, C a \cos\left(d x + c\right)^{3} + 8 \, {\left(B + C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, A + 4 \, B + 3 \, C\right)} a \cos\left(d x + c\right) + 8 \, {\left(3 \, A + 2 \, B + 2 \, C\right)} a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*A + 4*B + 3*C)*a*d*x + (6*C*a*cos(d*x + c)^3 + 8*(B + C)*a*cos(d*x + c)^2 + 3*(4*A + 4*B + 3*C)*a*cos(d*x + c) + 8*(3*A + 2*B + 2*C)*a)*sin(d*x + c))/d","A",0
303,1,62,0,0.417049," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + B + C\right)} a d x + {\left(2 \, C a \cos\left(d x + c\right)^{2} + 3 \, {\left(B + C\right)} a \cos\left(d x + c\right) + 2 \, {\left(3 \, A + 3 \, B + 2 \, C\right)} a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*A + B + C)*a*d*x + (2*C*a*cos(d*x + c)^2 + 3*(B + C)*a*cos(d*x + c) + 2*(3*A + 3*B + 2*C)*a)*sin(d*x + c))/d","A",0
304,1,68,0,0.427311," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{{\left(2 \, A + 2 \, B + C\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) + {\left(C a \cos\left(d x + c\right) + 2 \, {\left(B + C\right)} a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*A + 2*B + C)*a*d*x + A*a*log(sin(d*x + c) + 1) - A*a*log(-sin(d*x + c) + 1) + (C*a*cos(d*x + c) + 2*(B + C)*a)*sin(d*x + c))/d","A",0
305,1,92,0,0.432550," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(B + C\right)} 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 \, {\left(C a \cos\left(d x + c\right) + A a\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(B + C)*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*(C*a*cos(d*x + c) + A*a)*sin(d*x + c))/(d*cos(d*x + c))","A",0
306,1,109,0,0.442039," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, C a d x \cos\left(d x + c\right)^{2} + {\left(A + 2 \, B + 2 \, C\right)} a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A + 2 \, B + 2 \, C\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*(4*C*a*d*x*cos(d*x + c)^2 + (A + 2*B + 2*C)*a*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A + 2*B + 2*C)*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
307,1,114,0,0.449168," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(A + B + 2 \, C\right)} a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A + B + 2 \, C\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 + 3 \, C\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 + 2*C)*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(A + B + 2*C)*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(2*A + 3*B + 3*C)*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
308,1,143,0,0.438034," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 4 \, B + 4 \, C\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 + 4 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(2 \, A + 2 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 4 \, B + 4 \, C\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 + 4*C)*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*A + 4*B + 4*C)*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(2*A + 2*B + 3*C)*a*cos(d*x + c)^3 + 3*(3*A + 4*B + 4*C)*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
309,1,145,0,0.453516," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(14 \, A + 12 \, B + 11 \, C\right)} a^{2} d x + {\left(40 \, C a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(6 \, A + 12 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 16 \, {\left(10 \, A + 9 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(14 \, A + 12 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right) + 32 \, {\left(10 \, A + 9 \, B + 8 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(14*A + 12*B + 11*C)*a^2*d*x + (40*C*a^2*cos(d*x + c)^5 + 48*(B + 2*C)*a^2*cos(d*x + c)^4 + 10*(6*A + 12*B + 11*C)*a^2*cos(d*x + c)^3 + 16*(10*A + 9*B + 8*C)*a^2*cos(d*x + c)^2 + 15*(14*A + 12*B + 11*C)*a^2*cos(d*x + c) + 32*(10*A + 9*B + 8*C)*a^2)*sin(d*x + c))/d","A",0
310,1,122,0,0.455203," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, A + 7 \, B + 6 \, C\right)} a^{2} d x + {\left(24 \, C a^{2} \cos\left(d x + c\right)^{4} + 30 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 10 \, B + 9 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(8 \, A + 7 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(25 \, A + 20 \, B + 18 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(8*A + 7*B + 6*C)*a^2*d*x + (24*C*a^2*cos(d*x + c)^4 + 30*(B + 2*C)*a^2*cos(d*x + c)^3 + 8*(5*A + 10*B + 9*C)*a^2*cos(d*x + c)^2 + 15*(8*A + 7*B + 6*C)*a^2*cos(d*x + c) + 8*(25*A + 20*B + 18*C)*a^2)*sin(d*x + c))/d","A",0
311,1,99,0,0.600898," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(12 \, A + 8 \, B + 7 \, C\right)} a^{2} d x + {\left(6 \, C a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, A + 8 \, B + 7 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(6 \, A + 5 \, B + 4 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(12*A + 8*B + 7*C)*a^2*d*x + (6*C*a^2*cos(d*x + c)^3 + 8*(B + 2*C)*a^2*cos(d*x + c)^2 + 3*(4*A + 8*B + 7*C)*a^2*cos(d*x + c) + 8*(6*A + 5*B + 4*C)*a^2)*sin(d*x + c))/d","A",0
312,1,108,0,0.456382," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A + 3 \, B + 2 \, C\right)} a^{2} d x + 3 \, A a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, A a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(3 \, A + 6 \, B + 5 \, C\right)} a^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(4*A + 3*B + 2*C)*a^2*d*x + 3*A*a^2*log(sin(d*x + c) + 1) - 3*A*a^2*log(-sin(d*x + c) + 1) + (2*C*a^2*cos(d*x + c)^2 + 3*(B + 2*C)*a^2*cos(d*x + c) + 2*(3*A + 6*B + 5*C)*a^2)*sin(d*x + c))/d","A",0
313,1,130,0,0.447876," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, A + 4 \, B + 3 \, C\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) + {\left(C a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, A a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((2*A + 4*B + 3*C)*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) + (C*a^2*cos(d*x + c)^2 + 2*(B + 2*C)*a^2*cos(d*x + c) + 2*A*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
314,1,143,0,0.462281," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(B + 2 \, C\right)} a^{2} d x \cos\left(d x + c\right)^{2} + {\left(3 \, A + 4 \, B + 2 \, C\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 + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{2} \cos\left(d x + c\right)^{2} + 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 + 2*C)*a^2*d*x*cos(d*x + c)^2 + (3*A + 4*B + 2*C)*a^2*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (3*A + 4*B + 2*C)*a^2*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*a^2*cos(d*x + c)^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
315,1,150,0,0.552884," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{12 \, C a^{2} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, A + 3 \, B + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A + 3 \, B + 4 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(5 \, A + 6 \, B + 3 \, C\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*(12*C*a^2*d*x*cos(d*x + c)^3 + 3*(2*A + 3*B + 4*C)*a^2*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*A + 3*B + 4*C)*a^2*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(5*A + 6*B + 3*C)*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
316,1,157,0,0.510673," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(7 \, A + 8 \, B + 12 \, C\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 + 12 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(4 \, A + 5 \, B + 6 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, A + 8 \, B + 4 \, C\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 + 12*C)*a^2*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(7*A + 8*B + 12*C)*a^2*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(4*A + 5*B + 6*C)*a^2*cos(d*x + c)^3 + 3*(7*A + 8*B + 4*C)*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
317,1,180,0,0.458420," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, A + 7 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(6 \, A + 7 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(18 \, A + 20 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 15 \, {\left(6 \, A + 7 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(9 \, A + 10 \, B + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 30 \, {\left(2 \, A + B\right)} a^{2} \cos\left(d x + c\right) + 24 \, A a^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(6*A + 7*B + 8*C)*a^2*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(6*A + 7*B + 8*C)*a^2*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(18*A + 20*B + 25*C)*a^2*cos(d*x + c)^4 + 15*(6*A + 7*B + 8*C)*a^2*cos(d*x + c)^3 + 8*(9*A + 10*B + 5*C)*a^2*cos(d*x + c)^2 + 30*(2*A + B)*a^2*cos(d*x + c) + 24*A*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
318,1,168,0,0.447419," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(26 \, A + 23 \, B + 21 \, C\right)} a^{3} d x + {\left(240 \, C a^{3} \cos\left(d x + c\right)^{6} + 280 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(7 \, A + 21 \, B + 27 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 70 \, {\left(18 \, A + 23 \, B + 21 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(133 \, A + 119 \, B + 108 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 105 \, {\left(26 \, A + 23 \, B + 21 \, C\right)} a^{3} \cos\left(d x + c\right) + 32 \, {\left(133 \, A + 119 \, B + 108 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(105*(26*A + 23*B + 21*C)*a^3*d*x + (240*C*a^3*cos(d*x + c)^6 + 280*(B + 3*C)*a^3*cos(d*x + c)^5 + 48*(7*A + 21*B + 27*C)*a^3*cos(d*x + c)^4 + 70*(18*A + 23*B + 21*C)*a^3*cos(d*x + c)^3 + 16*(133*A + 119*B + 108*C)*a^3*cos(d*x + c)^2 + 105*(26*A + 23*B + 21*C)*a^3*cos(d*x + c) + 32*(133*A + 119*B + 108*C)*a^3)*sin(d*x + c))/d","A",0
319,1,145,0,0.446682," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(30 \, A + 26 \, B + 23 \, C\right)} a^{3} d x + {\left(40 \, C a^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 10 \, {\left(6 \, A + 18 \, B + 23 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 16 \, {\left(15 \, A + 19 \, B + 17 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(30 \, A + 26 \, B + 23 \, C\right)} a^{3} \cos\left(d x + c\right) + 16 \, {\left(45 \, A + 38 \, B + 34 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(30*A + 26*B + 23*C)*a^3*d*x + (40*C*a^3*cos(d*x + c)^5 + 48*(B + 3*C)*a^3*cos(d*x + c)^4 + 10*(6*A + 18*B + 23*C)*a^3*cos(d*x + c)^3 + 16*(15*A + 19*B + 17*C)*a^3*cos(d*x + c)^2 + 15*(30*A + 26*B + 23*C)*a^3*cos(d*x + c) + 16*(45*A + 38*B + 34*C)*a^3)*sin(d*x + c))/d","A",0
320,1,122,0,0.452596," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(20 \, A + 15 \, B + 13 \, C\right)} a^{3} d x + {\left(24 \, C a^{3} \cos\left(d x + c\right)^{4} + 30 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 15 \, B + 19 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 15 \, {\left(12 \, A + 15 \, B + 13 \, C\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(55 \, A + 45 \, B + 38 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(20*A + 15*B + 13*C)*a^3*d*x + (24*C*a^3*cos(d*x + c)^4 + 30*(B + 3*C)*a^3*cos(d*x + c)^3 + 8*(5*A + 15*B + 19*C)*a^3*cos(d*x + c)^2 + 15*(12*A + 15*B + 13*C)*a^3*cos(d*x + c) + 8*(55*A + 45*B + 38*C)*a^3)*sin(d*x + c))/d","A",0
321,1,131,0,0.479355," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left(28 \, A + 20 \, B + 15 \, C\right)} a^{3} d x + 12 \, A a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, A a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, C a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, A + 12 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(9 \, A + 11 \, B + 9 \, C\right)} a^{3}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(28*A + 20*B + 15*C)*a^3*d*x + 12*A*a^3*log(sin(d*x + c) + 1) - 12*A*a^3*log(-sin(d*x + c) + 1) + (6*C*a^3*cos(d*x + c)^3 + 8*(B + 3*C)*a^3*cos(d*x + c)^2 + 3*(4*A + 12*B + 15*C)*a^3*cos(d*x + c) + 8*(9*A + 11*B + 9*C)*a^3)*sin(d*x + c))/d","A",0
322,1,156,0,0.451334," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(6 \, A + 7 \, B + 5 \, C\right)} a^{3} d x \cos\left(d x + c\right) + 3 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + 9 \, B + 11 \, C\right)} a^{3} \cos\left(d x + c\right) + 6 \, A a^{3}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(3*(6*A + 7*B + 5*C)*a^3*d*x*cos(d*x + c) + 3*(3*A + B)*a^3*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*(3*A + B)*a^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*C*a^3*cos(d*x + c)^3 + 3*(B + 3*C)*a^3*cos(d*x + c)^2 + 2*(3*A + 9*B + 11*C)*a^3*cos(d*x + c) + 6*A*a^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
323,1,165,0,0.474055," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, A + 6 \, B + 7 \, C\right)} a^{3} d x \cos\left(d x + c\right)^{2} + {\left(7 \, A + 6 \, B + 2 \, C\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 + 2 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C a^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(B + 3 \, C\right)} 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*(2*(2*A + 6*B + 7*C)*a^3*d*x*cos(d*x + c)^2 + (7*A + 6*B + 2*C)*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (7*A + 6*B + 2*C)*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(C*a^3*cos(d*x + c)^3 + 2*(B + 3*C)*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
324,1,168,0,0.476686," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{12 \, {\left(B + 3 \, C\right)} a^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 7 \, B + 6 \, C\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 + 6 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, C a^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, A + 9 \, B + 3 \, C\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 + 3*C)*a^3*d*x*cos(d*x + c)^3 + 3*(5*A + 7*B + 6*C)*a^3*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(5*A + 7*B + 6*C)*a^3*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*C*a^3*cos(d*x + c)^3 + 2*(11*A + 9*B + 3*C)*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
325,1,173,0,0.498971," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{48 \, C a^{3} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(15 \, A + 20 \, B + 28 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(15 \, A + 20 \, B + 28 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(9 \, A + 11 \, B + 9 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(15 \, A + 12 \, B + 4 \, C\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*(48*C*a^3*d*x*cos(d*x + c)^4 + 3*(15*A + 20*B + 28*C)*a^3*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(15*A + 20*B + 28*C)*a^3*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(9*A + 11*B + 9*C)*a^3*cos(d*x + c)^3 + 3*(15*A + 12*B + 4*C)*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
326,1,180,0,0.439471," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(13 \, A + 15 \, B + 20 \, C\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 + 20 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(38 \, A + 45 \, B + 55 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 15 \, {\left(13 \, A + 15 \, B + 12 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 8 \, {\left(19 \, A + 15 \, B + 5 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 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 + 20*C)*a^3*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(13*A + 15*B + 20*C)*a^3*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(38*A + 45*B + 55*C)*a^3*cos(d*x + c)^4 + 15*(13*A + 15*B + 12*C)*a^3*cos(d*x + c)^3 + 8*(19*A + 15*B + 5*C)*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
327,1,203,0,0.461912," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left(23 \, A + 26 \, B + 30 \, C\right)} a^{3} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(23 \, A + 26 \, B + 30 \, C\right)} a^{3} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(34 \, A + 38 \, B + 45 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} + 15 \, {\left(23 \, A + 26 \, B + 30 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + 16 \, {\left(17 \, A + 19 \, B + 15 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + 10 \, {\left(23 \, A + 18 \, B + 6 \, C\right)} a^{3} \cos\left(d x + c\right)^{2} + 48 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right) + 40 \, A a^{3}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(23*A + 26*B + 30*C)*a^3*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(23*A + 26*B + 30*C)*a^3*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(34*A + 38*B + 45*C)*a^3*cos(d*x + c)^5 + 15*(23*A + 26*B + 30*C)*a^3*cos(d*x + c)^4 + 16*(17*A + 19*B + 15*C)*a^3*cos(d*x + c)^3 + 10*(23*A + 18*B + 6*C)*a^3*cos(d*x + c)^2 + 48*(3*A + B)*a^3*cos(d*x + c) + 40*A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
328,1,191,0,0.494484," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(392 \, A + 352 \, B + 323 \, C\right)} a^{4} d x + {\left(1680 \, C a^{4} \cos\left(d x + c\right)^{7} + 1920 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} + 280 \, {\left(8 \, A + 32 \, B + 55 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 1536 \, {\left(7 \, A + 12 \, B + 13 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(328 \, A + 352 \, B + 323 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 128 \, {\left(252 \, A + 227 \, B + 208 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(392 \, A + 352 \, B + 323 \, C\right)} a^{4} \cos\left(d x + c\right) + 256 \, {\left(252 \, A + 227 \, B + 208 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{13440 \, d}"," ",0,"1/13440*(105*(392*A + 352*B + 323*C)*a^4*d*x + (1680*C*a^4*cos(d*x + c)^7 + 1920*(B + 4*C)*a^4*cos(d*x + c)^6 + 280*(8*A + 32*B + 55*C)*a^4*cos(d*x + c)^5 + 1536*(7*A + 12*B + 13*C)*a^4*cos(d*x + c)^4 + 70*(328*A + 352*B + 323*C)*a^4*cos(d*x + c)^3 + 128*(252*A + 227*B + 208*C)*a^4*cos(d*x + c)^2 + 105*(392*A + 352*B + 323*C)*a^4*cos(d*x + c) + 256*(252*A + 227*B + 208*C)*a^4)*sin(d*x + c))/d","A",0
329,1,168,0,0.449689," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(56 \, A + 49 \, B + 44 \, C\right)} a^{4} d x + {\left(240 \, C a^{4} \cos\left(d x + c\right)^{6} + 280 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 48 \, {\left(7 \, A + 28 \, B + 48 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(24 \, A + 41 \, B + 44 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 16 \, {\left(238 \, A + 252 \, B + 227 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 105 \, {\left(56 \, A + 49 \, B + 44 \, C\right)} a^{4} \cos\left(d x + c\right) + 16 \, {\left(581 \, A + 504 \, B + 454 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(105*(56*A + 49*B + 44*C)*a^4*d*x + (240*C*a^4*cos(d*x + c)^6 + 280*(B + 4*C)*a^4*cos(d*x + c)^5 + 48*(7*A + 28*B + 48*C)*a^4*cos(d*x + c)^4 + 70*(24*A + 41*B + 44*C)*a^4*cos(d*x + c)^3 + 16*(238*A + 252*B + 227*C)*a^4*cos(d*x + c)^2 + 105*(56*A + 49*B + 44*C)*a^4*cos(d*x + c) + 16*(581*A + 504*B + 454*C)*a^4)*sin(d*x + c))/d","A",0
330,1,145,0,0.450636," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(10 \, A + 8 \, B + 7 \, C\right)} a^{4} d x + {\left(40 \, C a^{4} \cos\left(d x + c\right)^{5} + 48 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 10 \, {\left(6 \, A + 24 \, B + 41 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 32 \, {\left(10 \, A + 17 \, B + 18 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 15 \, {\left(54 \, A + 56 \, B + 49 \, C\right)} a^{4} \cos\left(d x + c\right) + 16 \, {\left(100 \, A + 83 \, B + 72 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(105*(10*A + 8*B + 7*C)*a^4*d*x + (40*C*a^4*cos(d*x + c)^5 + 48*(B + 4*C)*a^4*cos(d*x + c)^4 + 10*(6*A + 24*B + 41*C)*a^4*cos(d*x + c)^3 + 32*(10*A + 17*B + 18*C)*a^4*cos(d*x + c)^2 + 15*(54*A + 56*B + 49*C)*a^4*cos(d*x + c) + 16*(100*A + 83*B + 72*C)*a^4)*sin(d*x + c))/d","A",0
331,1,154,0,0.456517," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{15 \, {\left(48 \, A + 35 \, B + 28 \, C\right)} a^{4} d x + 60 \, A a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 60 \, A a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(24 \, C a^{4} \cos\left(d x + c\right)^{4} + 30 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 20 \, B + 34 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 15 \, {\left(16 \, A + 27 \, B + 28 \, C\right)} a^{4} \cos\left(d x + c\right) + 8 \, {\left(100 \, A + 100 \, B + 83 \, C\right)} a^{4}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(48*A + 35*B + 28*C)*a^4*d*x + 60*A*a^4*log(sin(d*x + c) + 1) - 60*A*a^4*log(-sin(d*x + c) + 1) + (24*C*a^4*cos(d*x + c)^4 + 30*(B + 4*C)*a^4*cos(d*x + c)^3 + 8*(5*A + 20*B + 34*C)*a^4*cos(d*x + c)^2 + 15*(16*A + 27*B + 28*C)*a^4*cos(d*x + c) + 8*(100*A + 100*B + 83*C)*a^4)*sin(d*x + c))/d","A",0
332,1,179,0,0.437529," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(52 \, A + 48 \, B + 35 \, C\right)} a^{4} d x \cos\left(d x + c\right) + 12 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, C a^{4} \cos\left(d x + c\right)^{4} + 8 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, A + 16 \, B + 27 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 32 \, {\left(3 \, A + 5 \, B + 5 \, C\right)} a^{4} \cos\left(d x + c\right) + 24 \, A a^{4}\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}"," ",0,"1/24*(3*(52*A + 48*B + 35*C)*a^4*d*x*cos(d*x + c) + 12*(4*A + B)*a^4*cos(d*x + c)*log(sin(d*x + c) + 1) - 12*(4*A + B)*a^4*cos(d*x + c)*log(-sin(d*x + c) + 1) + (6*C*a^4*cos(d*x + c)^4 + 8*(B + 4*C)*a^4*cos(d*x + c)^3 + 3*(4*A + 16*B + 27*C)*a^4*cos(d*x + c)^2 + 32*(3*A + 5*B + 5*C)*a^4*cos(d*x + c) + 24*A*a^4)*sin(d*x + c))/(d*cos(d*x + c))","A",0
333,1,191,0,0.450510," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{6 \, {\left(8 \, A + 13 \, B + 12 \, C\right)} a^{4} d x \cos\left(d x + c\right)^{2} + 3 \, {\left(13 \, A + 8 \, B + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(13 \, A + 8 \, B + 2 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C a^{4} \cos\left(d x + c\right)^{4} + 3 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(3 \, A + 12 \, B + 20 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 6 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) + 3 \, A a^{4}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(6*(8*A + 13*B + 12*C)*a^4*d*x*cos(d*x + c)^2 + 3*(13*A + 8*B + 2*C)*a^4*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*(13*A + 8*B + 2*C)*a^4*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*a^4*cos(d*x + c)^4 + 3*(B + 4*C)*a^4*cos(d*x + c)^3 + 2*(3*A + 12*B + 20*C)*a^4*cos(d*x + c)^2 + 6*(4*A + B)*a^4*cos(d*x + c) + 3*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
334,1,191,0,0.475330," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{6 \, {\left(2 \, A + 8 \, B + 13 \, C\right)} a^{4} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(12 \, A + 13 \, B + 8 \, C\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 + 8 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, C a^{4} \cos\left(d x + c\right)^{4} + 6 \, {\left(B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(20 \, A + 12 \, B + 3 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 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*(6*(2*A + 8*B + 13*C)*a^4*d*x*cos(d*x + c)^3 + 3*(12*A + 13*B + 8*C)*a^4*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(12*A + 13*B + 8*C)*a^4*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(3*C*a^4*cos(d*x + c)^4 + 6*(B + 4*C)*a^4*cos(d*x + c)^3 + 2*(20*A + 12*B + 3*C)*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
335,1,191,0,0.456129," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{48 \, {\left(B + 4 \, C\right)} a^{4} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(35 \, A + 48 \, B + 52 \, C\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 + 52 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, C a^{4} \cos\left(d x + c\right)^{4} + 32 \, {\left(5 \, A + 5 \, B + 3 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 3 \, {\left(27 \, A + 16 \, B + 4 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 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 + 4*C)*a^4*d*x*cos(d*x + c)^4 + 3*(35*A + 48*B + 52*C)*a^4*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(35*A + 48*B + 52*C)*a^4*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*C*a^4*cos(d*x + c)^4 + 32*(5*A + 5*B + 3*C)*a^4*cos(d*x + c)^3 + 3*(27*A + 16*B + 4*C)*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
336,1,196,0,0.613788," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{240 \, C a^{4} d x \cos\left(d x + c\right)^{5} + 15 \, {\left(28 \, A + 35 \, B + 48 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(28 \, A + 35 \, B + 48 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(83 \, A + 100 \, B + 100 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 15 \, {\left(28 \, A + 27 \, B + 16 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 8 \, {\left(34 \, A + 20 \, B + 5 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 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*(240*C*a^4*d*x*cos(d*x + c)^5 + 15*(28*A + 35*B + 48*C)*a^4*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(28*A + 35*B + 48*C)*a^4*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(83*A + 100*B + 100*C)*a^4*cos(d*x + c)^4 + 15*(28*A + 27*B + 16*C)*a^4*cos(d*x + c)^3 + 8*(34*A + 20*B + 5*C)*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
337,1,203,0,0.472768," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{105 \, {\left(7 \, A + 8 \, B + 10 \, C\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 + 10 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(72 \, A + 83 \, B + 100 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 15 \, {\left(49 \, A + 56 \, B + 54 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 32 \, {\left(18 \, A + 17 \, B + 10 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 10 \, {\left(41 \, A + 24 \, B + 6 \, C\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 + 10*C)*a^4*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 105*(7*A + 8*B + 10*C)*a^4*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(72*A + 83*B + 100*C)*a^4*cos(d*x + c)^5 + 15*(49*A + 56*B + 54*C)*a^4*cos(d*x + c)^4 + 32*(18*A + 17*B + 10*C)*a^4*cos(d*x + c)^3 + 10*(41*A + 24*B + 6*C)*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
338,1,226,0,0.491538," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^8,x, algorithm=""fricas"")","\frac{105 \, {\left(44 \, A + 49 \, B + 56 \, C\right)} a^{4} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(44 \, A + 49 \, B + 56 \, C\right)} a^{4} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(454 \, A + 504 \, B + 581 \, C\right)} a^{4} \cos\left(d x + c\right)^{6} + 105 \, {\left(44 \, A + 49 \, B + 56 \, C\right)} a^{4} \cos\left(d x + c\right)^{5} + 16 \, {\left(227 \, A + 252 \, B + 238 \, C\right)} a^{4} \cos\left(d x + c\right)^{4} + 70 \, {\left(44 \, A + 41 \, B + 24 \, C\right)} a^{4} \cos\left(d x + c\right)^{3} + 48 \, {\left(48 \, A + 28 \, B + 7 \, C\right)} a^{4} \cos\left(d x + c\right)^{2} + 280 \, {\left(4 \, A + B\right)} a^{4} \cos\left(d x + c\right) + 240 \, A a^{4}\right)} \sin\left(d x + c\right)}{3360 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/3360*(105*(44*A + 49*B + 56*C)*a^4*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(44*A + 49*B + 56*C)*a^4*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 2*(16*(454*A + 504*B + 581*C)*a^4*cos(d*x + c)^6 + 105*(44*A + 49*B + 56*C)*a^4*cos(d*x + c)^5 + 16*(227*A + 252*B + 238*C)*a^4*cos(d*x + c)^4 + 70*(44*A + 41*B + 24*C)*a^4*cos(d*x + c)^3 + 48*(48*A + 28*B + 7*C)*a^4*cos(d*x + c)^2 + 280*(4*A + B)*a^4*cos(d*x + c) + 240*A*a^4)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
339,1,134,0,0.424558," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left(4 \, A - 4 \, B + 5 \, C\right)} d x \cos\left(d x + c\right) + 9 \, {\left(4 \, A - 4 \, B + 5 \, C\right)} d x + {\left(6 \, C \cos\left(d x + c\right)^{4} + 2 \, {\left(4 \, B - C\right)} \cos\left(d x + c\right)^{3} + {\left(12 \, A - 4 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(12 \, A - 28 \, B + 19 \, C\right)} \cos\left(d x + c\right) - 48 \, A + 64 \, B - 64 \, C\right)} \sin\left(d x + c\right)}{24 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/24*(9*(4*A - 4*B + 5*C)*d*x*cos(d*x + c) + 9*(4*A - 4*B + 5*C)*d*x + (6*C*cos(d*x + c)^4 + 2*(4*B - C)*cos(d*x + c)^3 + (12*A - 4*B + 13*C)*cos(d*x + c)^2 - (12*A - 28*B + 19*C)*cos(d*x + c) - 48*A + 64*B - 64*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
340,1,114,0,0.420526," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(2 \, A - 3 \, B + 3 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(2 \, A - 3 \, B + 3 \, C\right)} d x - {\left(2 \, C \cos\left(d x + c\right)^{3} + {\left(3 \, B - C\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, A - 3 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 12 \, A - 12 \, B + 16 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/6*(3*(2*A - 3*B + 3*C)*d*x*cos(d*x + c) + 3*(2*A - 3*B + 3*C)*d*x - (2*C*cos(d*x + c)^3 + (3*B - C)*cos(d*x + c)^2 + (6*A - 3*B + 7*C)*cos(d*x + c) + 12*A - 12*B + 16*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
341,1,91,0,0.571891," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, A - 2 \, B + 3 \, C\right)} d x \cos\left(d x + c\right) + {\left(2 \, A - 2 \, B + 3 \, C\right)} d x + {\left(C \cos\left(d x + c\right)^{2} + {\left(2 \, B - C\right)} \cos\left(d x + c\right) - 2 \, A + 4 \, B - 4 \, C\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*((2*A - 2*B + 3*C)*d*x*cos(d*x + c) + (2*A - 2*B + 3*C)*d*x + (C*cos(d*x + c)^2 + (2*B - C)*cos(d*x + c) - 2*A + 4*B - 4*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
342,1,62,0,0.608501," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(B - C\right)} d x \cos\left(d x + c\right) + {\left(B - C\right)} d x + {\left(C \cos\left(d x + c\right) + A - B + 2 \, C\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"((B - C)*d*x*cos(d*x + c) + (B - C)*d*x + (C*cos(d*x + c) + A - B + 2*C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
343,1,91,0,0.894550," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, C d x \cos\left(d x + c\right) + 2 \, C d x + {\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 + C\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*(2*C*d*x*cos(d*x + c) + 2*C*d*x + (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 + C)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
344,1,128,0,0.431998," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""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 + C\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 + C)*cos(d*x + c) + A)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
345,1,171,0,0.428787," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(3 \, A - 2 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, A - 2 \, B + 2 \, C\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 + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, A - 2 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, {\left(2 \, A - 2 \, B + C\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 + 2*C)*cos(d*x + c)^3 + (3*A - 2*B + 2*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((3*A - 2*B + 2*C)*cos(d*x + c)^3 + (3*A - 2*B + 2*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(2*(2*A - 2*B + C)*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
346,1,194,0,0.475744," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(3 \, A - 3 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, A - 3 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(3 \, A - 3 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, A - 3 \, B + 2 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A - 3 \, B + 6 \, C\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*(3*((3*A - 3*B + 2*C)*cos(d*x + c)^4 + (3*A - 3*B + 2*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((3*A - 3*B + 2*C)*cos(d*x + c)^4 + (3*A - 3*B + 2*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(4*(4*A - 3*B + 3*C)*cos(d*x + c)^3 + (7*A - 3*B + 6*C)*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
347,1,172,0,0.419979," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(4 \, A - 7 \, B + 10 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(4 \, A - 7 \, B + 10 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(4 \, A - 7 \, B + 10 \, C\right)} d x - {\left(2 \, C \cos\left(d x + c\right)^{4} + {\left(3 \, B - 2 \, C\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(A - B + 2 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(28 \, A - 43 \, B + 66 \, C\right)} \cos\left(d x + c\right) + 20 \, A - 32 \, B + 48 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/6*(3*(4*A - 7*B + 10*C)*d*x*cos(d*x + c)^2 + 6*(4*A - 7*B + 10*C)*d*x*cos(d*x + c) + 3*(4*A - 7*B + 10*C)*d*x - (2*C*cos(d*x + c)^4 + (3*B - 2*C)*cos(d*x + c)^3 + 6*(A - B + 2*C)*cos(d*x + c)^2 + (28*A - 43*B + 66*C)*cos(d*x + c) + 20*A - 32*B + 48*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
348,1,153,0,0.427183," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A - 4 \, B + 7 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(2 \, A - 4 \, B + 7 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(2 \, A - 4 \, B + 7 \, C\right)} d x + {\left(3 \, C \cos\left(d x + c\right)^{3} + 6 \, {\left(B - C\right)} \cos\left(d x + c\right)^{2} - {\left(10 \, A - 28 \, B + 43 \, C\right)} \cos\left(d x + c\right) - 8 \, A + 20 \, B - 32 \, C\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(2*A - 4*B + 7*C)*d*x*cos(d*x + c)^2 + 6*(2*A - 4*B + 7*C)*d*x*cos(d*x + c) + 3*(2*A - 4*B + 7*C)*d*x + (3*C*cos(d*x + c)^3 + 6*(B - C)*cos(d*x + c)^2 - (10*A - 28*B + 43*C)*cos(d*x + c) - 8*A + 20*B - 32*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
349,1,120,0,0.534653," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(B - 2 \, C\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(B - 2 \, C\right)} d x \cos\left(d x + c\right) + 3 \, {\left(B - 2 \, C\right)} d x + {\left(3 \, C \cos\left(d x + c\right)^{2} + {\left(2 \, A - 5 \, B + 14 \, C\right)} \cos\left(d x + c\right) + A - 4 \, B + 10 \, C\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(3*(B - 2*C)*d*x*cos(d*x + c)^2 + 6*(B - 2*C)*d*x*cos(d*x + c) + 3*(B - 2*C)*d*x + (3*C*cos(d*x + c)^2 + (2*A - 5*B + 14*C)*cos(d*x + c) + A - 4*B + 10*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
350,1,95,0,0.504896," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, C d x \cos\left(d x + c\right)^{2} + 6 \, C d x \cos\left(d x + c\right) + 3 \, C d x + {\left({\left(A + 2 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 2 \, A + B - 4 \, C\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(3*C*d*x*cos(d*x + c)^2 + 6*C*d*x*cos(d*x + c) + 3*C*d*x + ((A + 2*B - 5*C)*cos(d*x + c) + 2*A + B - 4*C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
351,1,137,0,0.476055," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""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 - 2 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 2 \, B - C\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(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 - 2*C)*cos(d*x + c) + 5*A - 2*B - C)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
352,1,210,0,0.420107," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""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({\left(10 \, A - 4 \, B + C\right)} \cos\left(d x + c\right)^{2} + {\left(14 \, A - 5 \, B + 2 \, C\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*((10*A - 4*B + C)*cos(d*x + c)^2 + (14*A - 5*B + 2*C)*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))","A",0
353,1,252,0,0.419750," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(7 \, A - 4 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, A - 4 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A - 4 \, B + 2 \, C\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 + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(7 \, A - 4 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A - 4 \, B + 2 \, C\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 + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(43 \, A - 28 \, B + 10 \, C\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 + 2*C)*cos(d*x + c)^4 + 2*(7*A - 4*B + 2*C)*cos(d*x + c)^3 + (7*A - 4*B + 2*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*((7*A - 4*B + 2*C)*cos(d*x + c)^4 + 2*(7*A - 4*B + 2*C)*cos(d*x + c)^3 + (7*A - 4*B + 2*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(8*A - 5*B + 2*C)*cos(d*x + c)^3 + (43*A - 28*B + 10*C)*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
354,1,272,0,0.426708," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(10 \, A - 7 \, B + 4 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(10 \, A - 7 \, B + 4 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(10 \, A - 7 \, B + 4 \, C\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 + 4 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(10 \, A - 7 \, B + 4 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(10 \, A - 7 \, B + 4 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(12 \, A - 8 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(66 \, A - 43 \, B + 28 \, C\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(2 \, A - B + C\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 + 4*C)*cos(d*x + c)^5 + 2*(10*A - 7*B + 4*C)*cos(d*x + c)^4 + (10*A - 7*B + 4*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((10*A - 7*B + 4*C)*cos(d*x + c)^5 + 2*(10*A - 7*B + 4*C)*cos(d*x + c)^4 + (10*A - 7*B + 4*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(4*(12*A - 8*B + 5*C)*cos(d*x + c)^4 + (66*A - 43*B + 28*C)*cos(d*x + c)^3 + 6*(2*A - B + C)*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
355,1,229,0,0.421898," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(6 \, A - 13 \, B + 23 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(6 \, A - 13 \, B + 23 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(6 \, A - 13 \, B + 23 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(6 \, A - 13 \, B + 23 \, C\right)} d x - {\left(10 \, C \cos\left(d x + c\right)^{5} + 15 \, {\left(B - C\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(6 \, A - 9 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(234 \, A - 479 \, B + 869 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(114 \, A - 239 \, B + 429 \, C\right)} \cos\left(d x + c\right) + 144 \, A - 304 \, B + 544 \, C\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/30*(15*(6*A - 13*B + 23*C)*d*x*cos(d*x + c)^3 + 45*(6*A - 13*B + 23*C)*d*x*cos(d*x + c)^2 + 45*(6*A - 13*B + 23*C)*d*x*cos(d*x + c) + 15*(6*A - 13*B + 23*C)*d*x - (10*C*cos(d*x + c)^5 + 15*(B - C)*cos(d*x + c)^4 + 5*(6*A - 9*B + 19*C)*cos(d*x + c)^3 + (234*A - 479*B + 869*C)*cos(d*x + c)^2 + 3*(114*A - 239*B + 429*C)*cos(d*x + c) + 144*A - 304*B + 544*C)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
356,1,211,0,0.442392," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(2 \, A - 6 \, B + 13 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(2 \, A - 6 \, B + 13 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(2 \, A - 6 \, B + 13 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(2 \, A - 6 \, B + 13 \, C\right)} d x + {\left(15 \, C \cos\left(d x + c\right)^{4} + 15 \, {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(64 \, A - 234 \, B + 479 \, C\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(34 \, A - 114 \, B + 239 \, C\right)} \cos\left(d x + c\right) - 44 \, A + 144 \, B - 304 \, C\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(15*(2*A - 6*B + 13*C)*d*x*cos(d*x + c)^3 + 45*(2*A - 6*B + 13*C)*d*x*cos(d*x + c)^2 + 45*(2*A - 6*B + 13*C)*d*x*cos(d*x + c) + 15*(2*A - 6*B + 13*C)*d*x + (15*C*cos(d*x + c)^4 + 15*(2*B - 3*C)*cos(d*x + c)^3 - (64*A - 234*B + 479*C)*cos(d*x + c)^2 - 3*(34*A - 114*B + 239*C)*cos(d*x + c) - 44*A + 144*B - 304*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
357,1,173,0,0.408845," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(B - 3 \, C\right)} d x \cos\left(d x + c\right)^{3} + 45 \, {\left(B - 3 \, C\right)} d x \cos\left(d x + c\right)^{2} + 45 \, {\left(B - 3 \, C\right)} d x \cos\left(d x + c\right) + 15 \, {\left(B - 3 \, C\right)} d x + {\left(15 \, C \cos\left(d x + c\right)^{3} + {\left(7 \, A - 32 \, B + 117 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A - 17 \, B + 57 \, C\right)} \cos\left(d x + c\right) + 2 \, A - 22 \, B + 72 \, C\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(15*(B - 3*C)*d*x*cos(d*x + c)^3 + 45*(B - 3*C)*d*x*cos(d*x + c)^2 + 45*(B - 3*C)*d*x*cos(d*x + c) + 15*(B - 3*C)*d*x + (15*C*cos(d*x + c)^3 + (7*A - 32*B + 117*C)*cos(d*x + c)^2 + 3*(2*A - 17*B + 57*C)*cos(d*x + c) + 2*A - 22*B + 72*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
358,1,146,0,0.478521," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, C d x \cos\left(d x + c\right)^{3} + 45 \, C d x \cos\left(d x + c\right)^{2} + 45 \, C d x \cos\left(d x + c\right) + 15 \, C d x + {\left({\left(3 \, A + 7 \, B - 32 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 2 \, B - 17 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 2 \, B - 22 \, C\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(15*C*d*x*cos(d*x + c)^3 + 45*C*d*x*cos(d*x + c)^2 + 45*C*d*x*cos(d*x + c) + 15*C*d*x + ((3*A + 7*B - 32*C)*cos(d*x + c)^2 + 3*(3*A + 2*B - 17*C)*cos(d*x + c) + 3*A + 2*B - 22*C)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
359,1,102,0,0.436210," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, A + 3 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A + 3 \, B + 2 \, C\right)} \cos\left(d x + c\right) + 7 \, A + 3 \, B + 2 \, C\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*((2*A + 3*B + 7*C)*cos(d*x + c)^2 + 3*(2*A + 3*B + 2*C)*cos(d*x + c) + 7*A + 3*B + 2*C)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
360,1,193,0,0.459527," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""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({\left(22 \, A - 2 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(17 \, A - 2 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 32 \, A - 7 \, B - 3 \, C\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(15*(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*((22*A - 2*B - 3*C)*cos(d*x + c)^2 + 3*(17*A - 2*B - 3*C)*cos(d*x + c) + 32*A - 7*B - 3*C)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
361,1,279,0,0.519925," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""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 + C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(57 \, A - 17 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(117 \, A - 32 \, B + 7 \, C\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 + C)*cos(d*x + c)^3 + 3*(57*A - 17*B + 2*C)*cos(d*x + c)^2 + (117*A - 32*B + 7*C)*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
362,1,328,0,0.520317," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(13 \, A - 6 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(13 \, A - 6 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(13 \, A - 6 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, A - 6 \, B + 2 \, C\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 + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(13 \, A - 6 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(13 \, A - 6 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, A - 6 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, {\left(76 \, A - 36 \, B + 11 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(239 \, A - 114 \, B + 34 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(479 \, A - 234 \, B + 64 \, C\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 + 2*C)*cos(d*x + c)^5 + 3*(13*A - 6*B + 2*C)*cos(d*x + c)^4 + 3*(13*A - 6*B + 2*C)*cos(d*x + c)^3 + (13*A - 6*B + 2*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 15*((13*A - 6*B + 2*C)*cos(d*x + c)^5 + 3*(13*A - 6*B + 2*C)*cos(d*x + c)^4 + 3*(13*A - 6*B + 2*C)*cos(d*x + c)^3 + (13*A - 6*B + 2*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*(76*A - 36*B + 11*C)*cos(d*x + c)^4 + 3*(239*A - 114*B + 34*C)*cos(d*x + c)^3 + (479*A - 234*B + 64*C)*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
363,1,346,0,0.464255," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(23 \, A - 13 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(23 \, A - 13 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(23 \, A - 13 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(23 \, A - 13 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(23 \, A - 13 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(23 \, A - 13 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(23 \, A - 13 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(23 \, A - 13 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(34 \, A - 19 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(429 \, A - 239 \, B + 114 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(869 \, A - 479 \, B + 234 \, C\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(19 \, A - 9 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left(A - B\right)} \cos\left(d x + c\right) + 10 \, A\right)} \sin\left(d x + c\right)}{60 \, {\left(a^{3} d \cos\left(d x + c\right)^{6} + 3 \, a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + a^{3} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/60*(15*((23*A - 13*B + 6*C)*cos(d*x + c)^6 + 3*(23*A - 13*B + 6*C)*cos(d*x + c)^5 + 3*(23*A - 13*B + 6*C)*cos(d*x + c)^4 + (23*A - 13*B + 6*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 15*((23*A - 13*B + 6*C)*cos(d*x + c)^6 + 3*(23*A - 13*B + 6*C)*cos(d*x + c)^5 + 3*(23*A - 13*B + 6*C)*cos(d*x + c)^4 + (23*A - 13*B + 6*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(16*(34*A - 19*B + 9*C)*cos(d*x + c)^5 + 3*(429*A - 239*B + 114*C)*cos(d*x + c)^4 + (869*A - 479*B + 234*C)*cos(d*x + c)^3 + 5*(19*A - 9*B + 6*C)*cos(d*x + c)^2 - 15*(A - B)*cos(d*x + c) + 10*A)*sin(d*x + c))/(a^3*d*cos(d*x + c)^6 + 3*a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + a^3*d*cos(d*x + c)^3)","A",0
364,1,265,0,0.447487," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} d x \cos\left(d x + c\right)^{4} + 420 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} d x \cos\left(d x + c\right)^{3} + 630 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} d x \cos\left(d x + c\right)^{2} + 420 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} d x \cos\left(d x + c\right) + 105 \, {\left(2 \, A - 8 \, B + 21 \, C\right)} d x + {\left(105 \, C \cos\left(d x + c\right)^{5} + 210 \, {\left(B - 2 \, C\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(130 \, A - 592 \, B + 1509 \, C\right)} \cos\left(d x + c\right)^{3} - 4 \, {\left(310 \, A - 1318 \, B + 3411 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(1070 \, A - 4472 \, B + 11619 \, C\right)} \cos\left(d x + c\right) - 320 \, A + 1328 \, B - 3456 \, C\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/210*(105*(2*A - 8*B + 21*C)*d*x*cos(d*x + c)^4 + 420*(2*A - 8*B + 21*C)*d*x*cos(d*x + c)^3 + 630*(2*A - 8*B + 21*C)*d*x*cos(d*x + c)^2 + 420*(2*A - 8*B + 21*C)*d*x*cos(d*x + c) + 105*(2*A - 8*B + 21*C)*d*x + (105*C*cos(d*x + c)^5 + 210*(B - 2*C)*cos(d*x + c)^4 - 4*(130*A - 592*B + 1509*C)*cos(d*x + c)^3 - 4*(310*A - 1318*B + 3411*C)*cos(d*x + c)^2 - (1070*A - 4472*B + 11619*C)*cos(d*x + c) - 320*A + 1328*B - 3456*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
365,1,223,0,0.420756," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(B - 4 \, C\right)} d x \cos\left(d x + c\right)^{4} + 420 \, {\left(B - 4 \, C\right)} d x \cos\left(d x + c\right)^{3} + 630 \, {\left(B - 4 \, C\right)} d x \cos\left(d x + c\right)^{2} + 420 \, {\left(B - 4 \, C\right)} d x \cos\left(d x + c\right) + 105 \, {\left(B - 4 \, C\right)} d x + {\left(105 \, C \cos\left(d x + c\right)^{4} + 4 \, {\left(9 \, A - 65 \, B + 296 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A - 620 \, B + 2636 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(24 \, A - 535 \, B + 2236 \, C\right)} \cos\left(d x + c\right) + 6 \, A - 160 \, B + 664 \, C\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(105*(B - 4*C)*d*x*cos(d*x + c)^4 + 420*(B - 4*C)*d*x*cos(d*x + c)^3 + 630*(B - 4*C)*d*x*cos(d*x + c)^2 + 420*(B - 4*C)*d*x*cos(d*x + c) + 105*(B - 4*C)*d*x + (105*C*cos(d*x + c)^4 + 4*(9*A - 65*B + 296*C)*cos(d*x + c)^3 + (39*A - 620*B + 2636*C)*cos(d*x + c)^2 + (24*A - 535*B + 2236*C)*cos(d*x + c) + 6*A - 160*B + 664*C)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
366,1,191,0,0.424933," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, C d x \cos\left(d x + c\right)^{4} + 420 \, C d x \cos\left(d x + c\right)^{3} + 630 \, C d x \cos\left(d x + c\right)^{2} + 420 \, C d x \cos\left(d x + c\right) + 105 \, C d x + {\left({\left(13 \, A + 36 \, B - 260 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(52 \, A + 39 \, B - 620 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(32 \, A + 24 \, B - 535 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 6 \, B - 160 \, C\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(105*C*d*x*cos(d*x + c)^4 + 420*C*d*x*cos(d*x + c)^3 + 630*C*d*x*cos(d*x + c)^2 + 420*C*d*x*cos(d*x + c) + 105*C*d*x + ((13*A + 36*B - 260*C)*cos(d*x + c)^3 + (52*A + 39*B - 620*C)*cos(d*x + c)^2 + (32*A + 24*B - 535*C)*cos(d*x + c) + 8*A + 6*B - 160*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
367,1,135,0,0.422307," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(8 \, A + 13 \, B + 36 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(32 \, A + 52 \, B + 39 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(13 \, A + 8 \, B + 6 \, C\right)} \cos\left(d x + c\right) + 13 \, A + 8 \, B + 6 \, C\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*((8*A + 13*B + 36*C)*cos(d*x + c)^3 + (32*A + 52*B + 39*C)*cos(d*x + c)^2 + 4*(13*A + 8*B + 6*C)*cos(d*x + c) + 13*A + 8*B + 6*C)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
368,1,135,0,0.486233," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left({\left(6 \, A + 8 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(6 \, A + 8 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(39 \, A + 52 \, B + 32 \, C\right)} \cos\left(d x + c\right) + 36 \, A + 13 \, B + 8 \, C\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*((6*A + 8*B + 13*C)*cos(d*x + c)^3 + 4*(6*A + 8*B + 13*C)*cos(d*x + c)^2 + (39*A + 52*B + 32*C)*cos(d*x + c) + 36*A + 13*B + 8*C)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
369,1,248,0,0.473906," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""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 - 4 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(535 \, A - 24 \, B - 32 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(620 \, A - 39 \, B - 52 \, C\right)} \cos\left(d x + c\right) + 260 \, A - 36 \, B - 13 \, C\right)} \sin\left(d x + c\right)}{210 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/210*(105*(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 - 4*C)*cos(d*x + c)^3 + (535*A - 24*B - 32*C)*cos(d*x + c)^2 + (620*A - 39*B - 52*C)*cos(d*x + c) + 260*A - 36*B - 13*C)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
370,1,348,0,0.486995," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""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(2 \, {\left(332 \, A - 80 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(2236 \, A - 535 \, B + 24 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(2636 \, A - 620 \, B + 39 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(296 \, A - 65 \, B + 9 \, C\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*(2*(332*A - 80*B + 3*C)*cos(d*x + c)^4 + (2236*A - 535*B + 24*C)*cos(d*x + c)^3 + (2636*A - 620*B + 39*C)*cos(d*x + c)^2 + 4*(296*A - 65*B + 9*C)*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))","A",0
371,1,402,0,0.481566," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left({\left(21 \, A - 8 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(21 \, A - 8 \, B + 2 \, C\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 + 2 \, C\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{5} + 6 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(21 \, A - 8 \, B + 2 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(21 \, A - 8 \, B + 2 \, C\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 + 20 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(11619 \, A - 4472 \, B + 1070 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(3411 \, A - 1318 \, B + 310 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(1509 \, A - 592 \, B + 130 \, C\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 + 2*C)*cos(d*x + c)^6 + 4*(21*A - 8*B + 2*C)*cos(d*x + c)^5 + 6*(21*A - 8*B + 2*C)*cos(d*x + c)^4 + 4*(21*A - 8*B + 2*C)*cos(d*x + c)^3 + (21*A - 8*B + 2*C)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 105*((21*A - 8*B + 2*C)*cos(d*x + c)^6 + 4*(21*A - 8*B + 2*C)*cos(d*x + c)^5 + 6*(21*A - 8*B + 2*C)*cos(d*x + c)^4 + 4*(21*A - 8*B + 2*C)*cos(d*x + c)^3 + (21*A - 8*B + 2*C)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(16*(216*A - 83*B + 20*C)*cos(d*x + c)^5 + (11619*A - 4472*B + 1070*C)*cos(d*x + c)^4 + 4*(3411*A - 1318*B + 310*C)*cos(d*x + c)^3 + 4*(1509*A - 592*B + 130*C)*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
372,1,422,0,0.473023," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","-\frac{105 \, {\left({\left(44 \, A - 21 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{7} + 4 \, {\left(44 \, A - 21 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(44 \, A - 21 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(44 \, A - 21 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(44 \, A - 21 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(44 \, A - 21 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{7} + 4 \, {\left(44 \, A - 21 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(44 \, A - 21 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(44 \, A - 21 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(44 \, A - 21 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, {\left(454 \, A - 216 \, B + 83 \, C\right)} \cos\left(d x + c\right)^{6} + {\left(24436 \, A - 11619 \, B + 4472 \, C\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(7184 \, A - 3411 \, B + 1318 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(3196 \, A - 1509 \, B + 592 \, C\right)} \cos\left(d x + c\right)^{3} + 70 \, {\left(14 \, A - 6 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} - 35 \, {\left(4 \, A - 3 \, B\right)} \cos\left(d x + c\right) + 70 \, A\right)} \sin\left(d x + c\right)}{420 \, {\left(a^{4} d \cos\left(d x + c\right)^{7} + 4 \, a^{4} d \cos\left(d x + c\right)^{6} + 6 \, a^{4} d \cos\left(d x + c\right)^{5} + 4 \, a^{4} d \cos\left(d x + c\right)^{4} + a^{4} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/420*(105*((44*A - 21*B + 8*C)*cos(d*x + c)^7 + 4*(44*A - 21*B + 8*C)*cos(d*x + c)^6 + 6*(44*A - 21*B + 8*C)*cos(d*x + c)^5 + 4*(44*A - 21*B + 8*C)*cos(d*x + c)^4 + (44*A - 21*B + 8*C)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 105*((44*A - 21*B + 8*C)*cos(d*x + c)^7 + 4*(44*A - 21*B + 8*C)*cos(d*x + c)^6 + 6*(44*A - 21*B + 8*C)*cos(d*x + c)^5 + 4*(44*A - 21*B + 8*C)*cos(d*x + c)^4 + (44*A - 21*B + 8*C)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(16*(454*A - 216*B + 83*C)*cos(d*x + c)^6 + (24436*A - 11619*B + 4472*C)*cos(d*x + c)^5 + 4*(7184*A - 3411*B + 1318*C)*cos(d*x + c)^4 + 4*(3196*A - 1509*B + 592*C)*cos(d*x + c)^3 + 70*(14*A - 6*B + 3*C)*cos(d*x + c)^2 - 35*(4*A - 3*B)*cos(d*x + c) + 70*A)*sin(d*x + c))/(a^4*d*cos(d*x + c)^7 + 4*a^4*d*cos(d*x + c)^6 + 6*a^4*d*cos(d*x + c)^5 + 4*a^4*d*cos(d*x + c)^4 + a^4*d*cos(d*x + c)^3)","A",0
373,1,128,0,0.442503," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, C \cos\left(d x + c\right)^{5} + 35 \, {\left(11 \, B + 10 \, C\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(99 \, A + 88 \, B + 80 \, C\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(99 \, A + 88 \, B + 80 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(99 \, A + 88 \, B + 80 \, C\right)} \cos\left(d x + c\right) + 1584 \, A + 1408 \, B + 1280 \, C\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*C*cos(d*x + c)^5 + 35*(11*B + 10*C)*cos(d*x + c)^4 + 5*(99*A + 88*B + 80*C)*cos(d*x + c)^3 + 6*(99*A + 88*B + 80*C)*cos(d*x + c)^2 + 8*(99*A + 88*B + 80*C)*cos(d*x + c) + 1584*A + 1408*B + 1280*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
374,1,108,0,0.409913," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, C \cos\left(d x + c\right)^{4} + 5 \, {\left(9 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 18 \, B + 16 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(21 \, A + 18 \, B + 16 \, C\right)} \cos\left(d x + c\right) + 168 \, A + 144 \, B + 128 \, C\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*C*cos(d*x + c)^4 + 5*(9*B + 8*C)*cos(d*x + c)^3 + 3*(21*A + 18*B + 16*C)*cos(d*x + c)^2 + 4*(21*A + 18*B + 16*C)*cos(d*x + c) + 168*A + 144*B + 128*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
375,1,87,0,0.444175," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, C \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, B + 6 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(35 \, A + 28 \, B + 24 \, C\right)} \cos\left(d x + c\right) + 70 \, A + 56 \, B + 48 \, C\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*C*cos(d*x + c)^3 + 3*(7*B + 6*C)*cos(d*x + c)^2 + (35*A + 28*B + 24*C)*cos(d*x + c) + 70*A + 56*B + 48*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
376,1,67,0,0.425364," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, C \cos\left(d x + c\right)^{2} + {\left(5 \, B + 4 \, C\right)} \cos\left(d x + c\right) + 15 \, A + 10 \, B + 8 \, C\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*C*cos(d*x + c)^2 + (5*B + 4*C)*cos(d*x + c) + 15*A + 10*B + 8*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
377,1,142,0,0.960860," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\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 \, {\left(C \cos\left(d x + c\right) + 3 \, B + 2 \, C\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*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*(C*cos(d*x + c) + 3*B + 2*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
378,1,163,0,0.452332," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""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 \, {\left(2 \, C \cos\left(d x + c\right) + 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*(((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*(2*C*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))","A",0
379,1,184,0,0.573268," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(3 \, A + 4 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 4 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 8*C)*cos(d*x + c)^3 + (3*A + 4*B + 8*C)*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
380,1,206,0,0.572253," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(5 \, A + 6 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, A + 6 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 8 \, C\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 + 8*C)*cos(d*x + c)^4 + (5*A + 6*B + 8*C)*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 + 8*C)*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
381,1,226,0,0.714112," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(35 \, A + 40 \, B + 48 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(35 \, A + 40 \, B + 48 \, C\right)} \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(35 \, A + 40 \, B + 48 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(35 \, A + 40 \, B + 48 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(7 \, A + 8 \, B\right)} \cos\left(d x + c\right) + 48 \, 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*((35*A + 40*B + 48*C)*cos(d*x + c)^5 + (35*A + 40*B + 48*C)*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*(35*A + 40*B + 48*C)*cos(d*x + c)^3 + 2*(35*A + 40*B + 48*C)*cos(d*x + c)^2 + 8*(7*A + 8*B)*cos(d*x + c) + 48*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
382,1,137,0,0.413718," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, C a \cos\left(d x + c\right)^{5} + 35 \, {\left(11 \, B + 21 \, C\right)} a \cos\left(d x + c\right)^{4} + 5 \, {\left(99 \, A + 187 \, B + 168 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(429 \, A + 374 \, B + 336 \, C\right)} a \cos\left(d x + c\right)^{2} + 4 \, {\left(429 \, A + 374 \, B + 336 \, C\right)} a \cos\left(d x + c\right) + 8 \, {\left(429 \, A + 374 \, B + 336 \, C\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*C*a*cos(d*x + c)^5 + 35*(11*B + 21*C)*a*cos(d*x + c)^4 + 5*(99*A + 187*B + 168*C)*a*cos(d*x + c)^3 + 3*(429*A + 374*B + 336*C)*a*cos(d*x + c)^2 + 4*(429*A + 374*B + 336*C)*a*cos(d*x + c) + 8*(429*A + 374*B + 336*C)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
383,1,115,0,0.510669," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, C a \cos\left(d x + c\right)^{4} + 5 \, {\left(9 \, B + 17 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 39 \, B + 34 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(189 \, A + 156 \, B + 136 \, C\right)} a \cos\left(d x + c\right) + 2 \, {\left(189 \, A + 156 \, B + 136 \, C\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*C*a*cos(d*x + c)^4 + 5*(9*B + 17*C)*a*cos(d*x + c)^3 + 3*(21*A + 39*B + 34*C)*a*cos(d*x + c)^2 + (189*A + 156*B + 136*C)*a*cos(d*x + c) + 2*(189*A + 156*B + 136*C)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
384,1,93,0,0.446922," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, C a \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, B + 13 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(35 \, A + 63 \, B + 52 \, C\right)} a \cos\left(d x + c\right) + {\left(175 \, A + 126 \, B + 104 \, C\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*C*a*cos(d*x + c)^3 + 3*(7*B + 13*C)*a*cos(d*x + c)^2 + (35*A + 63*B + 52*C)*a*cos(d*x + c) + (175*A + 126*B + 104*C)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
385,1,170,0,0.477696," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{15 \, {\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(3 \, C a \cos\left(d x + c\right)^{2} + {\left(5 \, B + 9 \, C\right)} a \cos\left(d x + c\right) + {\left(15 \, A + 25 \, B + 18 \, C\right)} a\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*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*(3*C*a*cos(d*x + c)^2 + (5*B + 9*C)*a*cos(d*x + c) + (15*A + 25*B + 18*C)*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
386,1,192,0,0.500501," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(3 \, A + 2 \, B\right)} a \cos\left(d x + c\right)^{2} + {\left(3 \, A + 2 \, B\right)} a \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{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 \, C a \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, B + 5 \, C\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)}{12 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/12*(3*((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*C*a*cos(d*x + c)^2 + 2*(3*B + 5*C)*a*cos(d*x + c) + 3*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
387,1,200,0,0.594916," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(7 \, A + 12 \, B + 8 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(7 \, A + 12 \, B + 8 \, C\right)} a \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 \, C a \cos\left(d x + c\right)^{2} + {\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 + 8*C)*a*cos(d*x + c)^3 + (7*A + 12*B + 8*C)*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*(8*C*a*cos(d*x + c)^2 + (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
388,1,211,0,0.588852," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(11 \, A + 14 \, B + 24 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(11 \, A + 14 \, B + 24 \, C\right)} a \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 8 \, C\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 + 24*C)*a*cos(d*x + c)^4 + (11*A + 14*B + 24*C)*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 + 8*C)*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
389,1,232,0,0.718828," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(75 \, A + 88 \, B + 112 \, C\right)} a \cos\left(d x + c\right)^{5} + {\left(75 \, A + 88 \, B + 112 \, C\right)} a \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 112 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(75 \, A + 88 \, B + 48 \, C\right)} a \cos\left(d x + c\right)^{2} + 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 + 112*C)*a*cos(d*x + c)^5 + (75*A + 88*B + 112*C)*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 + 112*C)*a*cos(d*x + c)^3 + 2*(75*A + 88*B + 48*C)*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
390,1,253,0,1.157403," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(133 \, A + 150 \, B + 176 \, C\right)} a \cos\left(d x + c\right)^{6} + {\left(133 \, A + 150 \, B + 176 \, C\right)} a \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(133 \, A + 150 \, B + 176 \, C\right)} a \cos\left(d x + c\right)^{4} + 10 \, {\left(133 \, A + 150 \, B + 176 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(133 \, A + 150 \, B + 80 \, C\right)} a \cos\left(d x + c\right)^{2} + 48 \, {\left(19 \, A + 10 \, B\right)} a \cos\left(d x + c\right) + 384 \, A a\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*((133*A + 150*B + 176*C)*a*cos(d*x + c)^6 + (133*A + 150*B + 176*C)*a*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*(133*A + 150*B + 176*C)*a*cos(d*x + c)^4 + 10*(133*A + 150*B + 176*C)*a*cos(d*x + c)^3 + 8*(133*A + 150*B + 80*C)*a*cos(d*x + c)^2 + 48*(19*A + 10*B)*a*cos(d*x + c) + 384*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)","A",0
391,1,172,0,0.672699," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, C a^{2} \cos\left(d x + c\right)^{6} + 315 \, {\left(13 \, B + 38 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 35 \, {\left(143 \, A + 416 \, B + 523 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(3718 \, A + 4615 \, B + 4184 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(10439 \, A + 9230 \, B + 8368 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 4 \, {\left(10439 \, A + 9230 \, B + 8368 \, C\right)} a^{2} \cos\left(d x + c\right) + 8 \, {\left(10439 \, A + 9230 \, B + 8368 \, C\right)} 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) + d\right)}}"," ",0,"2/45045*(3465*C*a^2*cos(d*x + c)^6 + 315*(13*B + 38*C)*a^2*cos(d*x + c)^5 + 35*(143*A + 416*B + 523*C)*a^2*cos(d*x + c)^4 + 5*(3718*A + 4615*B + 4184*C)*a^2*cos(d*x + c)^3 + 3*(10439*A + 9230*B + 8368*C)*a^2*cos(d*x + c)^2 + 4*(10439*A + 9230*B + 8368*C)*a^2*cos(d*x + c) + 8*(10439*A + 9230*B + 8368*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
392,1,148,0,0.444827," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, C a^{2} \cos\left(d x + c\right)^{5} + 35 \, {\left(11 \, B + 32 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(99 \, A + 286 \, B + 355 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(660 \, A + 803 \, B + 710 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(3795 \, A + 3212 \, B + 2840 \, C\right)} a^{2} \cos\left(d x + c\right) + 2 \, {\left(3795 \, A + 3212 \, B + 2840 \, C\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*C*a^2*cos(d*x + c)^5 + 35*(11*B + 32*C)*a^2*cos(d*x + c)^4 + 5*(99*A + 286*B + 355*C)*a^2*cos(d*x + c)^3 + 3*(660*A + 803*B + 710*C)*a^2*cos(d*x + c)^2 + (3795*A + 3212*B + 2840*C)*a^2*cos(d*x + c) + 2*(3795*A + 3212*B + 2840*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
393,1,124,0,0.475619," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, C a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(9 \, B + 26 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A + 60 \, B + 73 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(294 \, A + 345 \, B + 292 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(903 \, A + 690 \, B + 584 \, C\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*C*a^2*cos(d*x + c)^4 + 5*(9*B + 26*C)*a^2*cos(d*x + c)^3 + 3*(21*A + 60*B + 73*C)*a^2*cos(d*x + c)^2 + (294*A + 345*B + 292*C)*a^2*cos(d*x + c) + (903*A + 690*B + 584*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
394,1,203,0,0.550508," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{105 \, {\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(15 \, C a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, B + 20 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(35 \, A + 98 \, B + 115 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(280 \, A + 301 \, B + 230 \, C\right)} a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{210 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/210*(105*(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*(15*C*a^2*cos(d*x + c)^3 + 3*(7*B + 20*C)*a^2*cos(d*x + c)^2 + (35*A + 98*B + 115*C)*a^2*cos(d*x + c) + (280*A + 301*B + 230*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
395,1,225,0,0.544610," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{15 \, {\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(6 \, C a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, B + 14 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, A + 40 \, B + 43 \, C\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)}{60 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/60*(15*((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*(6*C*a^2*cos(d*x + c)^3 + 2*(5*B + 14*C)*a^2*cos(d*x + c)^2 + 2*(15*A + 40*B + 43*C)*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)^2 + d*cos(d*x + c))","A",0
396,1,232,0,0.916361," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(19 \, A + 20 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(19 \, A + 20 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 \, C a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(3 \, B + 8 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(11 \, A + 4 \, B\right)} a^{2} \cos\left(d x + c\right) + 6 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/48*(3*((19*A + 20*B + 8*C)*a^2*cos(d*x + c)^3 + (19*A + 20*B + 8*C)*a^2*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*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*C*a^2*cos(d*x + c)^3 + 8*(3*B + 8*C)*a^2*cos(d*x + c)^2 + 3*(11*A + 4*B)*a^2*cos(d*x + c) + 6*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
397,1,235,0,0.850300," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(25 \, A + 38 \, B + 40 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(25 \, A + 38 \, B + 40 \, C\right)} a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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(48 \, C a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(25 \, A + 22 \, B + 8 \, C\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 + 40*C)*a^2*cos(d*x + c)^4 + (25*A + 38*B + 40*C)*a^2*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*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*(48*C*a^2*cos(d*x + c)^3 + 3*(25*A + 22*B + 8*C)*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
398,1,244,0,0.686088," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(163 \, A + 200 \, B + 304 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(163 \, A + 200 \, B + 304 \, C\right)} a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 176 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(163 \, A + 136 \, B + 48 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 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 + 304*C)*a^2*cos(d*x + c)^5 + (163*A + 200*B + 304*C)*a^2*cos(d*x + c)^4)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*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 + 176*C)*a^2*cos(d*x + c)^3 + 2*(163*A + 136*B + 48*C)*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
399,1,267,0,0.707674," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(283 \, A + 326 \, B + 400 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + {\left(283 \, A + 326 \, B + 400 \, C\right)} a^{2} \cos\left(d x + c\right)^{5}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 400 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(283 \, A + 326 \, B + 272 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(283 \, A + 230 \, B + 80 \, C\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 + 400*C)*a^2*cos(d*x + c)^6 + (283*A + 326*B + 400*C)*a^2*cos(d*x + c)^5)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*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 + 400*C)*a^2*cos(d*x + c)^4 + 10*(283*A + 326*B + 272*C)*a^2*cos(d*x + c)^3 + 8*(283*A + 230*B + 80*C)*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
400,1,290,0,0.838605," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(1015 \, A + 1132 \, B + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{7} + {\left(1015 \, A + 1132 \, B + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{6}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 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(1015 \, A + 1132 \, B + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 10 \, {\left(1015 \, A + 1132 \, B + 1304 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(1015 \, A + 1132 \, B + 920 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 48 \, {\left(145 \, A + 116 \, B + 40 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 128 \, {\left(35 \, A + 12 \, B\right)} a^{2} \cos\left(d x + c\right) + 1280 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{30720 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/30720*(15*((1015*A + 1132*B + 1304*C)*a^2*cos(d*x + c)^7 + (1015*A + 1132*B + 1304*C)*a^2*cos(d*x + c)^6)*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*(1015*A + 1132*B + 1304*C)*a^2*cos(d*x + c)^5 + 10*(1015*A + 1132*B + 1304*C)*a^2*cos(d*x + c)^4 + 8*(1015*A + 1132*B + 920*C)*a^2*cos(d*x + c)^3 + 48*(145*A + 116*B + 40*C)*a^2*cos(d*x + c)^2 + 128*(35*A + 12*B)*a^2*cos(d*x + c) + 1280*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)","A",0
401,1,212,0,0.502728," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(35 \, C \cos\left(d x + c\right)^{4} + 5 \, {\left(9 \, B - C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(21 \, A - 3 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(21 \, A - 93 \, B + 29 \, C\right)} \cos\left(d x + c\right) + 273 \, A - 129 \, B + 257 \, C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{315 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{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}}}{630 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/630*(4*(35*C*cos(d*x + c)^4 + 5*(9*B - C)*cos(d*x + c)^3 + 3*(21*A - 3*B + 19*C)*cos(d*x + c)^2 - (21*A - 93*B + 29*C)*cos(d*x + c) + 273*A - 129*B + 257*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 315*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
402,1,191,0,0.593065," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(15 \, C \cos\left(d x + c\right)^{3} + 3 \, {\left(7 \, B - C\right)} \cos\left(d x + c\right)^{2} + {\left(35 \, A - 7 \, B + 31 \, C\right)} \cos\left(d x + c\right) - 35 \, A + 91 \, B - 43 \, C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{105 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{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*C*cos(d*x + c)^3 + 3*(7*B - C)*cos(d*x + c)^2 + (35*A - 7*B + 31*C)*cos(d*x + c) - 35*A + 91*B - 43*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 105*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
403,1,171,0,0.439210," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, C \cos\left(d x + c\right)^{2} + {\left(5 \, B - C\right)} \cos\left(d x + c\right) + 15 \, A - 5 \, B + 13 \, C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{15 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{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*C*cos(d*x + c)^2 + (5*B - C)*cos(d*x + c) + 15*A - 5*B + 13*C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 15*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
404,1,151,0,0.489013," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(C \cos\left(d x + c\right) + 3 \, B - C\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{3 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\right)} a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{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*(C*cos(d*x + c) + 3*B - C)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 3*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
405,1,227,0,0.498680," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""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} C \sin\left(d x + c\right) + \frac{\sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\right)} a\right)} \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*((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)*C*sin(d*x + c) + sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
406,1,261,0,0.549707," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B + C\right)} a \cos\left(d x + c\right)\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{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 + C)*a*cos(d*x + c)^2 + (A - B + C)*a*cos(d*x + c))*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
407,1,292,0,0.597891," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(7 \, A - 4 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, A - 4 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{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 + 8*C)*cos(d*x + c)^3 + (7*A - 4*B + 8*C)*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 + C)*a*cos(d*x + c)^3 + (A - B + C)*a*cos(d*x + c)^2)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
408,1,314,0,0.642159," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(9 \, A - 14 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(9 \, A - 14 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 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(7 \, A - 2 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(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) + \frac{48 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{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}}}{96 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/96*(3*((9*A - 14*B + 8*C)*cos(d*x + c)^4 + (9*A - 14*B + 8*C)*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*(7*A - 2*B + 8*C)*cos(d*x + c)^2 - 2*(A - 6*B)*cos(d*x + c) + 8*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 48*sqrt(2)*((A - B + C)*a*cos(d*x + c)^4 + (A - B + C)*a*cos(d*x + c)^3)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
409,1,334,0,0.941761," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(107 \, A - 72 \, B + 112 \, C\right)} \cos\left(d x + c\right)^{5} + {\left(107 \, A - 72 \, B + 112 \, C\right)} \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(21 \, A - 56 \, B + 16 \, C\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(43 \, A - 8 \, B + 48 \, C\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(A - 8 \, B\right)} \cos\left(d x + c\right) - 48 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{384 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{5} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{4}\right)} \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}}}{768 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/768*(3*((107*A - 72*B + 112*C)*cos(d*x + c)^5 + (107*A - 72*B + 112*C)*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*(21*A - 56*B + 16*C)*cos(d*x + c)^3 - 2*(43*A - 8*B + 48*C)*cos(d*x + c)^2 + 8*(A - 8*B)*cos(d*x + c) - 48*A)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 384*sqrt(2)*((A - B + C)*a*cos(d*x + c)^5 + (A - B + C)*a*cos(d*x + c)^4)*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)^5 + a*d*cos(d*x + c)^4)","A",0
410,1,259,0,0.522989," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} {\left({\left(11 \, A - 15 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(11 \, A - 15 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 11 \, A - 15 \, B + 19 \, C\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 \, C \cos\left(d x + c\right)^{4} + 12 \, {\left(7 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{3} + 28 \, {\left(5 \, A - 3 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left(35 \, A - 63 \, B + 67 \, C\right)} \cos\left(d x + c\right) - 665 \, A + 1029 \, B - 1201 \, C\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)*((11*A - 15*B + 19*C)*cos(d*x + c)^2 + 2*(11*A - 15*B + 19*C)*cos(d*x + c) + 11*A - 15*B + 19*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)) + 4*(60*C*cos(d*x + c)^4 + 12*(7*B - 3*C)*cos(d*x + c)^3 + 28*(5*A - 3*B + 7*C)*cos(d*x + c)^2 - 12*(35*A - 63*B + 67*C)*cos(d*x + c) - 665*A + 1029*B - 1201*C)*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
411,1,239,0,0.517440," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(7 \, A - 11 \, B + 15 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 11 \, B + 15 \, C\right)} \cos\left(d x + c\right) + 7 \, A - 11 \, B + 15 \, C\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 \, C \cos\left(d x + c\right)^{3} + 4 \, {\left(5 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(5 \, A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right) + 75 \, A - 95 \, B + 147 \, C\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)*((7*A - 11*B + 15*C)*cos(d*x + c)^2 + 2*(7*A - 11*B + 15*C)*cos(d*x + c) + 7*A - 11*B + 15*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)) + 4*(12*C*cos(d*x + c)^3 + 4*(5*B - 3*C)*cos(d*x + c)^2 + 12*(5*A - 5*B + 9*C)*cos(d*x + c) + 75*A - 95*B + 147*C)*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
412,1,217,0,0.449153," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(3 \, A - 7 \, B + 11 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 7 \, B + 11 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 7 \, B + 11 \, C\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 \, C \cos\left(d x + c\right)^{2} + 12 \, {\left(B - C\right)} \cos\left(d x + c\right) - 3 \, A + 15 \, B - 19 \, C\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)*((3*A - 7*B + 11*C)*cos(d*x + c)^2 + 2*(3*A - 7*B + 11*C)*cos(d*x + c) + 3*A - 7*B + 11*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)) + 4*(4*C*cos(d*x + c)^2 + 12*(B - C)*cos(d*x + c) - 3*A + 15*B - 19*C)*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
413,1,193,0,0.420352," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(A + 3 \, B - 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 3 \, B - 7 \, C\right)} \cos\left(d x + c\right) + A + 3 \, B - 7 \, C\right)} \sqrt{a} \log\left(-\frac{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 \, C \cos\left(d x + c\right) + A - B + 5 \, C\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)*((A + 3*B - 7*C)*cos(d*x + c)^2 + 2*(A + 3*B - 7*C)*cos(d*x + c) + A + 3*B - 7*C)*sqrt(a)*log(-(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*C*cos(d*x + c) + A - B + 5*C)*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
414,1,291,0,0.448141," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(5 \, A - B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - B - 3 \, C\right)} \cos\left(d x + c\right) + 5 \, A - B - 3 \, C\right)} \sqrt{a} \log\left(-\frac{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 + C\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/8*(sqrt(2)*((5*A - B - 3*C)*cos(d*x + c)^2 + 2*(5*A - B - 3*C)*cos(d*x + c) + 5*A - B - 3*C)*sqrt(a)*log(-(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 + C)*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
415,1,343,0,0.505724," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(9 \, A - 5 \, B + C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(9 \, A - 5 \, B + C\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, A - 5 \, B + C\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \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 + C\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 + C)*cos(d*x + c)^3 + 2*(9*A - 5*B + C)*cos(d*x + c)^2 + (9*A - 5*B + C)*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 + C)*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
416,1,382,0,0.676573," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left({\left(13 \, A - 9 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(13 \, A - 9 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(13 \, A - 9 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \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 + 8 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(19 \, A - 12 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(19 \, A - 12 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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 + 2 \, C\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 + 5*C)*cos(d*x + c)^4 + 2*(13*A - 9*B + 5*C)*cos(d*x + c)^3 + (13*A - 9*B + 5*C)*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 + 8*C)*cos(d*x + c)^4 + 2*(19*A - 12*B + 8*C)*cos(d*x + c)^3 + (19*A - 12*B + 8*C)*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 + 2*C)*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
417,1,402,0,0.882563," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left({\left(17 \, A - 13 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(17 \, A - 13 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(17 \, A - 13 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{3}\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) + 3 \, {\left({\left(47 \, A - 38 \, B + 24 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(47 \, A - 38 \, B + 24 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(47 \, A - 38 \, B + 24 \, C\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 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(21 \, A - 14 \, B + 12 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(37 \, A - 18 \, B + 24 \, C\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left(A - 2 \, 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(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,"1/96*(12*sqrt(2)*((17*A - 13*B + 9*C)*cos(d*x + c)^5 + 2*(17*A - 13*B + 9*C)*cos(d*x + c)^4 + (17*A - 13*B + 9*C)*cos(d*x + c)^3)*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)) + 3*((47*A - 38*B + 24*C)*cos(d*x + c)^5 + 2*(47*A - 38*B + 24*C)*cos(d*x + c)^4 + (47*A - 38*B + 24*C)*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*(21*A - 14*B + 12*C)*cos(d*x + c)^3 + (37*A - 18*B + 24*C)*cos(d*x + c)^2 - 6*(A - 2*B)*cos(d*x + c) + 8*A)*sqrt(a*cos(d*x + c) + 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
418,1,291,0,0.463453," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(75 \, A - 163 \, B + 283 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 163 \, B + 283 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 163 \, B + 283 \, C\right)} \cos\left(d x + c\right) + 75 \, A - 163 \, B + 283 \, C\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 \, C \cos\left(d x + c\right)^{4} + 160 \, {\left(B - C\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(15 \, A - 25 \, B + 49 \, C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(255 \, A - 503 \, B + 911 \, C\right)} \cos\left(d x + c\right) + 735 \, A - 1495 \, B + 2671 \, C\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)*((75*A - 163*B + 283*C)*cos(d*x + c)^3 + 3*(75*A - 163*B + 283*C)*cos(d*x + c)^2 + 3*(75*A - 163*B + 283*C)*cos(d*x + c) + 75*A - 163*B + 283*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)) + 4*(96*C*cos(d*x + c)^4 + 160*(B - C)*cos(d*x + c)^3 + 32*(15*A - 25*B + 49*C)*cos(d*x + c)^2 + 5*(255*A - 503*B + 911*C)*cos(d*x + c) + 735*A - 1495*B + 2671*C)*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
419,1,273,0,0.430054," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(19 \, A - 75 \, B + 163 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A - 75 \, B + 163 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A - 75 \, B + 163 \, C\right)} \cos\left(d x + c\right) + 19 \, A - 75 \, B + 163 \, C\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 \, C \cos\left(d x + c\right)^{3} + 32 \, {\left(3 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(39 \, A - 255 \, B + 503 \, C\right)} \cos\left(d x + c\right) - 27 \, A + 147 \, B - 299 \, C\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)*((19*A - 75*B + 163*C)*cos(d*x + c)^3 + 3*(19*A - 75*B + 163*C)*cos(d*x + c)^2 + 3*(19*A - 75*B + 163*C)*cos(d*x + c) + 19*A - 75*B + 163*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)) + 4*(32*C*cos(d*x + c)^3 + 32*(3*B - 5*C)*cos(d*x + c)^2 - (39*A - 255*B + 503*C)*cos(d*x + c) - 27*A + 147*B - 299*C)*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
420,1,252,0,0.476959," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(5 \, A + 19 \, B - 75 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 19 \, B - 75 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 19 \, B - 75 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 19 \, B - 75 \, C\right)} \sqrt{a} \log\left(-\frac{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 \, C \cos\left(d x + c\right)^{2} + {\left(5 \, A - 13 \, B + 85 \, C\right)} \cos\left(d x + c\right) + A - 9 \, B + 49 \, C\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 - 75*C)*cos(d*x + c)^3 + 3*(5*A + 19*B - 75*C)*cos(d*x + c)^2 + 3*(5*A + 19*B - 75*C)*cos(d*x + c) + 5*A + 19*B - 75*C)*sqrt(a)*log(-(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*C*cos(d*x + c)^2 + (5*A - 13*B + 85*C)*cos(d*x + c) + A - 9*B + 49*C)*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
421,1,241,0,0.417308," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(3 \, A + 5 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 5 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 5 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 5 \, B + 19 \, C\right)} \sqrt{a} \log\left(-\frac{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 - 13 \, C\right)} \cos\left(d x + c\right) + 7 \, A + B - 9 \, C\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 + 19*C)*cos(d*x + c)^3 + 3*(3*A + 5*B + 19*C)*cos(d*x + c)^2 + 3*(3*A + 5*B + 19*C)*cos(d*x + c) + 3*A + 5*B + 19*C)*sqrt(a)*log(-(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 - 13*C)*cos(d*x + c) + 7*A + B - 9*C)*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
422,1,357,0,0.573425," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(43 \, A - 3 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A - 3 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A - 3 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 43 \, A - 3 \, B - 5 \, C\right)} \sqrt{a} \log\left(-\frac{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 - 5 \, C\right)} \cos\left(d x + c\right) + 15 \, A - 7 \, B - C\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 - 5*C)*cos(d*x + c)^3 + 3*(43*A - 3*B - 5*C)*cos(d*x + c)^2 + 3*(43*A - 3*B - 5*C)*cos(d*x + c) + 43*A - 3*B - 5*C)*sqrt(a)*log(-(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 - 5*C)*cos(d*x + c) + 15*A - 7*B - C)*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
423,1,421,0,0.584334," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(115 \, A - 43 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(115 \, A - 43 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(115 \, A - 43 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(115 \, A - 43 \, B + 3 \, C\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \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 + 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(55 \, A - 15 \, B + 7 \, C\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 + 3*C)*cos(d*x + c)^4 + 3*(115*A - 43*B + 3*C)*cos(d*x + c)^3 + 3*(115*A - 43*B + 3*C)*cos(d*x + c)^2 + (115*A - 43*B + 3*C)*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 + 3*C)*cos(d*x + c)^2 + (55*A - 15*B + 7*C)*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
424,1,457,0,0.775092," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(219 \, A - 115 \, B + 43 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(219 \, A - 115 \, B + 43 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(219 \, A - 115 \, B + 43 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(219 \, A - 115 \, B + 43 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \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 + 8 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(39 \, A - 20 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(39 \, A - 20 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(39 \, A - 20 \, B + 8 \, C\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 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(63 \, A - 35 \, B + 11 \, C\right)} \cos\left(d x + c\right)^{3} + 5 \, {\left(19 \, A - 11 \, B + 3 \, C\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 + 43*C)*cos(d*x + c)^5 + 3*(219*A - 115*B + 43*C)*cos(d*x + c)^4 + 3*(219*A - 115*B + 43*C)*cos(d*x + c)^3 + (219*A - 115*B + 43*C)*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 + 8*C)*cos(d*x + c)^5 + 3*(39*A - 20*B + 8*C)*cos(d*x + c)^4 + 3*(39*A - 20*B + 8*C)*cos(d*x + c)^3 + (39*A - 20*B + 8*C)*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*((63*A - 35*B + 11*C)*cos(d*x + c)^3 + 5*(19*A - 11*B + 3*C)*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
425,0,0,0,0.600762," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} + B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^3 + B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
426,0,0,0,0.462817," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c)), x)","F",0
427,0,0,0,0.414058," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sqrt(cos(d*x + c)), x)","F",0
428,0,0,0,0.417336," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/cos(d*x + c)^(3/2), x)","F",0
429,0,0,0,0.407634," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/cos(d*x + c)^(5/2), x)","F",0
430,0,0,0,0.432480," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/cos(d*x + c)^(7/2), x)","F",0
431,0,0,0,0.508165," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{5} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^5 + (B + C)*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
432,0,0,0,0.471936," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{4} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^4 + (B + C)*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
433,0,0,0,0.455640," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sqrt(cos(d*x + c)), x)","F",0
434,0,0,0,0.570848," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/sqrt(cos(d*x + c)), x)","F",0
435,0,0,0,0.557322," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/cos(d*x + c)^(3/2), x)","F",0
436,0,0,0,0.589904," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/cos(d*x + c)^(5/2), x)","F",0
437,0,0,0,0.444085," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/cos(d*x + c)^(7/2), x)","F",0
438,0,0,0,0.412106," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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{9}{2}}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/cos(d*x + c)^(9/2), x)","F",0
439,0,0,0,0.458327," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{5} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^5 + (B + 2*C)*a^2*cos(d*x + c)^4 + (A + 2*B + C)*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
440,0,0,0,0.590947," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
441,0,0,0,0.573362," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
442,0,0,0,0.468042," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
443,0,0,0,0.442412," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
444,0,0,0,0.461575," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
445,0,0,0,0.444648," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
446,0,0,0,0.504333," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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{11}{2}}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)/cos(d*x + c)^(11/2), x)","F",0
447,0,0,0,0.503502," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{6} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{5} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^6 + (B + 3*C)*a^3*cos(d*x + c)^5 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^4 + (3*A + 3*B + C)*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
448,0,0,0,0.471240," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
449,0,0,0,0.445691," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
450,0,0,0,0.482057," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
451,0,0,0,0.440410," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
452,0,0,0,0.561243," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
453,0,0,0,0.482800," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
454,0,0,0,0.483970," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
455,0,0,0,0.493015," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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{13}{2}}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)/cos(d*x + c)^(13/2), x)","F",0
456,0,0,0,0.465272," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + 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
457,0,0,0,0.470773," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
458,0,0,0,0.492686," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
459,0,0,0,0.486655," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
460,0,0,0,0.440525," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
461,0,0,0,0.543569," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
462,0,0,0,0.469207," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{5} + a \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c)^5 + a*cos(d*x + c)^4), x)","F",0
463,0,0,0,0.498912," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + 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
464,0,0,0,0.452533," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
465,0,0,0,0.497359," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
466,0,0,0,0.526308," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*cos(d*x + c)^2 + 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
467,0,0,0,0.474667," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*cos(d*x + c)^2 + 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
468,0,0,0,0.478036," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*cos(d*x + c)^2 + 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
469,0,0,0,0.533439," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{5} + 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((C*cos(d*x + c)^5 + 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
470,0,0,0,0.467163," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + 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
471,0,0,0,0.538656," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
472,0,0,0,0.441973," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*cos(d*x + c)^2 + 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
473,0,0,0,0.521307," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*cos(d*x + c)^2 + 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
474,0,0,0,0.463784," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*cos(d*x + c)^2 + 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
475,0,0,0,0.508919," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a^{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((C*cos(d*x + c)^2 + 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
476,1,163,0,0.970305," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(48 \, C \cos\left(d x + c\right)^{3} + 8 \, {\left(8 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right) + 144 \, A + 120 \, B + 105 \, C\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(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right) + 48 \, A + 40 \, B + 35 \, C\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*C*cos(d*x + c)^3 + 8*(8*B + 7*C)*cos(d*x + c)^2 + 2*(48*A + 40*B + 35*C)*cos(d*x + c) + 144*A + 120*B + 105*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((48*A + 40*B + 35*C)*cos(d*x + c) + 48*A + 40*B + 35*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) + d)","A",0
477,1,143,0,0.717448," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, C \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 24 \, A + 18 \, B + 15 \, C\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(8 \, A + 6 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 6 \, B + 5 \, C\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*C*cos(d*x + c)^2 + 2*(6*B + 5*C)*cos(d*x + c) + 24*A + 18*B + 15*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((8*A + 6*B + 5*C)*cos(d*x + c) + 8*A + 6*B + 5*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) + d)","A",0
478,1,123,0,0.705998," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, C \cos\left(d x + c\right) + 4 \, B + 3 \, C\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(8 \, A + 4 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 4 \, B + 3 \, C\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*C*cos(d*x + c) + 4*B + 3*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((8*A + 4*B + 3*C)*cos(d*x + c) + 8*A + 4*B + 3*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) + d)","A",0
479,1,127,0,0.504150," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(C \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(2 \, B + C\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, B + C\right)} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\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,"((C*cos(d*x + c) + 2*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*B + C)*cos(d*x + c)^2 + (2*B + C)*cos(d*x + c))*sqrt(a)*arctan(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
480,1,128,0,0.566042," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\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(C \cos\left(d x + c\right)^{3} + C \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*(((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*(C*cos(d*x + c)^3 + C*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
481,1,88,0,0.598784," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(8 \, A + 10 \, B + 15 \, C\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*((8*A + 10*B + 15*C)*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
482,1,109,0,0.577422," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(24 \, A + 28 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(24 \, A + 28 \, B + 35 \, C\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*(2*(24*A + 28*B + 35*C)*cos(d*x + c)^3 + (24*A + 28*B + 35*C)*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
483,1,130,0,0.552290," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(16 \, A + 18 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(16 \, A + 18 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(16 \, A + 18 \, B + 21 \, C\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} \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*(16*A + 18*B + 21*C)*cos(d*x + c)^4 + 4*(16*A + 18*B + 21*C)*cos(d*x + c)^3 + 3*(16*A + 18*B + 21*C)*cos(d*x + c)^2 + 5*(8*A + 9*B)*cos(d*x + c) + 35*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
484,1,195,0,0.982363," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(384 \, C a \cos\left(d x + c\right)^{4} + 48 \, {\left(10 \, B + 19 \, C\right)} a \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 10 \, {\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right) + 15 \, {\left(176 \, A + 150 \, B + 133 \, 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) - 15 \, {\left({\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right) + {\left(176 \, A + 150 \, B + 133 \, C\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)}{1920 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/1920*((384*C*a*cos(d*x + c)^4 + 48*(10*B + 19*C)*a*cos(d*x + c)^3 + 8*(80*A + 150*B + 133*C)*a*cos(d*x + c)^2 + 10*(176*A + 150*B + 133*C)*a*cos(d*x + c) + 15*(176*A + 150*B + 133*C)*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*((176*A + 150*B + 133*C)*a*cos(d*x + c) + (176*A + 150*B + 133*C)*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
485,1,174,0,1.160341," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(48 \, C a \cos\left(d x + c\right)^{3} + 8 \, {\left(8 \, B + 15 \, C\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(48 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right) + 3 \, {\left(112 \, A + 88 \, B + 75 \, 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({\left(112 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right) + {\left(112 \, A + 88 \, B + 75 \, C\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*C*a*cos(d*x + c)^3 + 8*(8*B + 15*C)*a*cos(d*x + c)^2 + 2*(48*A + 88*B + 75*C)*a*cos(d*x + c) + 3*(112*A + 88*B + 75*C)*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((112*A + 88*B + 75*C)*a*cos(d*x + c) + (112*A + 88*B + 75*C)*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
486,1,153,0,1.014221," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, C a \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B + 11 \, C\right)} a \cos\left(d x + c\right) + 3 \, {\left(8 \, A + 14 \, B + 11 \, 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({\left(24 \, A + 14 \, B + 11 \, C\right)} a \cos\left(d x + c\right) + {\left(24 \, A + 14 \, B + 11 \, C\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*C*a*cos(d*x + c)^2 + 2*(6*B + 11*C)*a*cos(d*x + c) + 3*(8*A + 14*B + 11*C)*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((24*A + 14*B + 11*C)*a*cos(d*x + c) + (24*A + 14*B + 11*C)*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
487,1,160,0,0.832492," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, C a \cos\left(d x + c\right)^{2} + {\left(4 \, B + 7 \, C\right)} a \cos\left(d x + c\right) + 8 \, 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(8 \, A + 12 \, B + 7 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(8 \, A + 12 \, B + 7 \, C\right)} a \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\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*C*a*cos(d*x + c)^2 + (4*B + 7*C)*a*cos(d*x + c) + 8*A*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((8*A + 12*B + 7*C)*a*cos(d*x + c)^2 + (8*A + 12*B + 7*C)*a*cos(d*x + c))*sqrt(a)*arctan(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
488,1,159,0,0.603925," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, C a \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A + 3 \, B\right)} 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) - 3 \, {\left({\left(2 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(2 \, B + 3 \, C\right)} 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)}{3 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/3*((3*C*a*cos(d*x + c)^2 + 2*(5*A + 3*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) - 3*((2*B + 3*C)*a*cos(d*x + c)^3 + (2*B + 3*C)*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
489,1,154,0,0.479740," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left({\left(18 \, A + 25 \, B + 15 \, C\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(C a \cos\left(d x + c\right)^{4} + C a \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*(((18*A + 25*B + 15*C)*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) - 15*(C*a*cos(d*x + c)^4 + C*a*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
490,1,112,0,0.477347," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(104 \, A + 126 \, B + 175 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(52 \, A + 63 \, B + 35 \, C\right)} a \cos\left(d x + c\right)^{2} + 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*((104*A + 126*B + 175*C)*a*cos(d*x + c)^3 + (52*A + 63*B + 35*C)*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
491,1,134,0,0.445718," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(136 \, A + 156 \, B + 189 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(136 \, A + 156 \, B + 189 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(34 \, A + 39 \, B + 21 \, C\right)} a \cos\left(d x + c\right)^{2} + 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*(2*(136*A + 156*B + 189*C)*a*cos(d*x + c)^4 + (136*A + 156*B + 189*C)*a*cos(d*x + c)^3 + 3*(34*A + 39*B + 21*C)*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
492,1,156,0,0.453097," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(336 \, A + 374 \, B + 429 \, C\right)} a \cos\left(d x + c\right)^{5} + 4 \, {\left(336 \, A + 374 \, B + 429 \, C\right)} a \cos\left(d x + c\right)^{4} + 3 \, {\left(336 \, A + 374 \, B + 429 \, C\right)} a \cos\left(d x + c\right)^{3} + 5 \, {\left(168 \, A + 187 \, B + 99 \, C\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} \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*(336*A + 374*B + 429*C)*a*cos(d*x + c)^5 + 4*(336*A + 374*B + 429*C)*a*cos(d*x + c)^4 + 3*(336*A + 374*B + 429*C)*a*cos(d*x + c)^3 + 5*(168*A + 187*B + 99*C)*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)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^7 + d*cos(d*x + c)^6)","A",0
493,1,232,0,1.069044," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(1280 \, C a^{2} \cos\left(d x + c\right)^{5} + 128 \, {\left(12 \, B + 35 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 48 \, {\left(40 \, A + 116 \, B + 145 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(920 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 10 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\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(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(1304 \, A + 1132 \, B + 1015 \, C\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)}{7680 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/7680*((1280*C*a^2*cos(d*x + c)^5 + 128*(12*B + 35*C)*a^2*cos(d*x + c)^4 + 48*(40*A + 116*B + 145*C)*a^2*cos(d*x + c)^3 + 8*(920*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^2 + 10*(1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c) + 15*(1304*A + 1132*B + 1015*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*((1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c) + (1304*A + 1132*B + 1015*C)*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
494,1,209,0,1.001157," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(384 \, C a^{2} \cos\left(d x + c\right)^{4} + 48 \, {\left(10 \, B + 29 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(80 \, A + 230 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 10 \, {\left(272 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right) + 15 \, {\left(400 \, A + 326 \, B + 283 \, C\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(400 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(400 \, A + 326 \, B + 283 \, C\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*C*a^2*cos(d*x + c)^4 + 48*(10*B + 29*C)*a^2*cos(d*x + c)^3 + 8*(80*A + 230*B + 283*C)*a^2*cos(d*x + c)^2 + 10*(272*A + 326*B + 283*C)*a^2*cos(d*x + c) + 15*(400*A + 326*B + 283*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*((400*A + 326*B + 283*C)*a^2*cos(d*x + c) + (400*A + 326*B + 283*C)*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
495,1,186,0,0.941206," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(48 \, C a^{2} \cos\left(d x + c\right)^{3} + 8 \, {\left(8 \, B + 23 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(48 \, A + 136 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right) + 3 \, {\left(176 \, A + 200 \, B + 163 \, C\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(304 \, A + 200 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(304 \, A + 200 \, B + 163 \, C\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*C*a^2*cos(d*x + c)^3 + 8*(8*B + 23*C)*a^2*cos(d*x + c)^2 + 2*(48*A + 136*B + 163*C)*a^2*cos(d*x + c) + 3*(176*A + 200*B + 163*C)*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((304*A + 200*B + 163*C)*a^2*cos(d*x + c) + (304*A + 200*B + 163*C)*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
496,1,194,0,0.797704," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(8 \, C a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, B + 17 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 22 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right) + 48 \, 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(40 \, A + 38 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(40 \, A + 38 \, B + 25 \, C\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)}{24 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/24*((8*C*a^2*cos(d*x + c)^3 + 2*(6*B + 17*C)*a^2*cos(d*x + c)^2 + 3*(8*A + 22*B + 25*C)*a^2*cos(d*x + c) + 48*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*((40*A + 38*B + 25*C)*a^2*cos(d*x + c)^2 + (40*A + 38*B + 25*C)*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
497,1,195,0,0.749360," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(6 \, C a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 3 \, 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) - 3 \, {\left({\left(8 \, A + 20 \, B + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(8 \, A + 20 \, B + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\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)}{12 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/12*((6*C*a^2*cos(d*x + c)^3 + 3*(4*B + 11*C)*a^2*cos(d*x + c)^2 + 8*(8*A + 3*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) - 3*((8*A + 20*B + 19*C)*a^2*cos(d*x + c)^3 + (8*A + 20*B + 19*C)*a^2*cos(d*x + c)^2)*sqrt(a)*arctan(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
498,1,192,0,0.577415," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{{\left(15 \, C a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(43 \, A + 40 \, B + 15 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right) + 6 \, 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({\left(2 \, B + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, B + 5 \, C\right)} 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)}{15 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/15*((15*C*a^2*cos(d*x + c)^3 + 2*(43*A + 40*B + 15*C)*a^2*cos(d*x + c)^2 + 2*(14*A + 5*B)*a^2*cos(d*x + c) + 6*A*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*((2*B + 5*C)*a^2*cos(d*x + c)^4 + (2*B + 5*C)*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
499,1,187,0,0.550339," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left({\left(230 \, A + 301 \, B + 280 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(115 \, A + 98 \, B + 35 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 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(C a^{2} \cos\left(d x + c\right)^{5} + C a^{2} \cos\left(d x + c\right)^{4}\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)}}{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 + 280*C)*a^2*cos(d*x + c)^3 + (115*A + 98*B + 35*C)*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) - 105*(C*a^2*cos(d*x + c)^5 + C*a^2*cos(d*x + c)^4)*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)^5 + d*cos(d*x + c)^4)","A",0
500,1,143,0,0.530854," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(584 \, A + 690 \, B + 903 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(292 \, A + 345 \, B + 294 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(73 \, A + 60 \, B + 21 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 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*((584*A + 690*B + 903*C)*a^2*cos(d*x + c)^4 + (292*A + 345*B + 294*C)*a^2*cos(d*x + c)^3 + 3*(73*A + 60*B + 21*C)*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
501,1,167,0,0.491776," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(2840 \, A + 3212 \, B + 3795 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(2840 \, A + 3212 \, B + 3795 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(710 \, A + 803 \, B + 660 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 5 \, {\left(355 \, A + 286 \, B + 99 \, C\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*(2*(2840*A + 3212*B + 3795*C)*a^2*cos(d*x + c)^5 + (2840*A + 3212*B + 3795*C)*a^2*cos(d*x + c)^4 + 3*(710*A + 803*B + 660*C)*a^2*cos(d*x + c)^3 + 5*(355*A + 286*B + 99*C)*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
502,1,191,0,0.594548," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + 4 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 3 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(4184 \, A + 4615 \, B + 3718 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 35 \, {\left(523 \, A + 416 \, B + 143 \, C\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} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{45045 \, {\left(d \cos\left(d x + c\right)^{8} + d \cos\left(d x + c\right)^{7}\right)}}"," ",0,"2/45045*(8*(8368*A + 9230*B + 10439*C)*a^2*cos(d*x + c)^6 + 4*(8368*A + 9230*B + 10439*C)*a^2*cos(d*x + c)^5 + 3*(8368*A + 9230*B + 10439*C)*a^2*cos(d*x + c)^4 + 5*(4184*A + 4615*B + 3718*C)*a^2*cos(d*x + c)^3 + 35*(523*A + 416*B + 143*C)*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)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^8 + d*cos(d*x + c)^7)","A",0
503,1,213,0,27.956142," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, C \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, B - C\right)} \cos\left(d x + c\right) + 24 \, A - 6 \, B + 21 \, C\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(8 \, A - 14 \, B + 9 \, C\right)} \cos\left(d x + c\right) + 8 \, A - 14 \, B + 9 \, C\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{24 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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}}}{24 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/24*((8*C*cos(d*x + c)^2 + 2*(6*B - C)*cos(d*x + c) + 24*A - 6*B + 21*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) + 3*((8*A - 14*B + 9*C)*cos(d*x + c) + 8*A - 14*B + 9*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 24*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
504,1,193,0,28.664923," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, C \cos\left(d x + c\right) + 4 \, B - C\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(8 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 8 \, A - 4 \, B + 7 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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*C*cos(d*x + c) + 4*B - C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((8*A - 4*B + 7*C)*cos(d*x + c) + 8*A - 4*B + 7*C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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
505,1,171,0,11.159215," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} C \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(2 \, B - C\right)} \cos\left(d x + c\right) + 2 \, B - C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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)*C*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*B - C)*cos(d*x + c) + 2*B - 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 + C)*a*cos(d*x + c) + (A - B + C)*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
506,1,185,0,8.191868," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""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) - 2 \, {\left(C \cos\left(d x + c\right)^{2} + C \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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B + C\right)} a \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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)^{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) - 2*(C*cos(d*x + c)^2 + C*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 + C)*a*cos(d*x + c)^2 + (A - B + C)*a*cos(d*x + c))*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
507,1,165,0,0.548749," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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 + C)*a*cos(d*x + c)^3 + (A - B + C)*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
508,1,185,0,0.540701," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(13 \, A - 5 \, B + 15 \, C\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 + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{3}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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 + 15*C)*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 + C)*a*cos(d*x + c)^4 + (A - B + C)*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
509,1,205,0,0.640342," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(43 \, A - 91 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(31 \, A - 7 \, B + 35 \, C\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} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{105 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{5} + {\left(A - B + C\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)} \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}}}{105 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"-1/105*(2*((43*A - 91*B + 35*C)*cos(d*x + c)^3 - (31*A - 7*B + 35*C)*cos(d*x + c)^2 + 3*(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) - 105*sqrt(2)*((A - B + C)*a*cos(d*x + c)^5 + (A - B + C)*a*cos(d*x + c)^4)*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)^5 + a*d*cos(d*x + c)^4)","A",0
510,1,245,0,25.888503," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, B b \cos\left(d x + c\right) + 4 \, B a + {\left(4 \, A - B\right)} 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(4 \, {\left(2 \, A - B\right)} a - {\left(4 \, A - 7 \, B\right)} b + {\left(4 \, {\left(2 \, A - B\right)} a - {\left(4 \, A - 7 \, 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{4 \, \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}}}{4 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/4*((2*B*b*cos(d*x + c) + 4*B*a + (4*A - B)*b)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - (4*(2*A - B)*a - (4*A - 7*B)*b + (4*(2*A - B)*a - (4*A - 7*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))) + 4*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
511,1,273,0,77.279669," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 9 \, B + 13 \, C\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) + {\left(2 \, C \cos\left(d x + c\right)^{2} + {\left(4 \, B - 3 \, C\right)} \cos\left(d x + c\right) - 2 \, A + 6 \, B - 7 \, C\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(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 8 \, A - 12 \, B + 19 \, C\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 + 13*C)*cos(d*x + c)^2 + 2*(5*A - 9*B + 13*C)*cos(d*x + c) + 5*A - 9*B + 13*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*C*cos(d*x + c)^2 + (4*B - 3*C)*cos(d*x + c) - 2*A + 6*B - 7*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - ((8*A - 12*B + 19*C)*cos(d*x + c)^2 + 2*(8*A - 12*B + 19*C)*cos(d*x + c) + 8*A - 12*B + 19*C)*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
512,1,241,0,37.980267," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right) + A - 5 \, B + 9 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 \, C \cos\left(d x + c\right) + A - B + 3 \, C\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 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 2 \, B - 3 \, C\right)} \sqrt{a} \arctan\left(\frac{\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 + 9*C)*cos(d*x + c)^2 + 2*(A - 5*B + 9*C)*cos(d*x + c) + A - 5*B + 9*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(2*C*cos(d*x + c) + A - B + 3*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) + 4*((2*B - 3*C)*cos(d*x + c)^2 + 2*(2*B - 3*C)*cos(d*x + c) + 2*B - 3*C)*sqrt(a)*arctan(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
513,1,213,0,29.635627," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A + B - 5 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 + C\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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)*((3*A + B - 5*C)*cos(d*x + c)^2 + 2*(3*A + B - 5*C)*cos(d*x + c) + 3*A + B - 5*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*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 + C)*sqrt(cos(d*x + c))*sin(d*x + c) + 8*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*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
514,1,211,0,0.671900," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(7 \, A - 3 \, B - C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(7 \, A - 3 \, B - C\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, A - 3 \, B - C\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 + C\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 - C)*cos(d*x + c)^3 + 2*(7*A - 3*B - C)*cos(d*x + c)^2 + (7*A - 3*B - C)*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 + C)*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
515,1,233,0,0.562496," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(11 \, A - 7 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(11 \, A - 7 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(11 \, A - 7 \, B + 3 \, C\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 + 3 \, C\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 + 3*C)*cos(d*x + c)^4 + 2*(11*A - 7*B + 3*C)*cos(d*x + c)^3 + (11*A - 7*B + 3*C)*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 + 3*C)*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
516,1,255,0,0.541201," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{2} {\left({\left(15 \, A - 11 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(15 \, A - 11 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(15 \, A - 11 \, B + 7 \, C\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{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(147 \, A - 95 \, B + 75 \, C\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(9 \, A - 5 \, B + 5 \, C\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} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{60 \, {\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,"-1/60*(15*sqrt(2)*((15*A - 11*B + 7*C)*cos(d*x + c)^5 + 2*(15*A - 11*B + 7*C)*cos(d*x + c)^4 + (15*A - 11*B + 7*C)*cos(d*x + c)^3)*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*((147*A - 95*B + 75*C)*cos(d*x + c)^3 + 12*(9*A - 5*B + 5*C)*cos(d*x + c)^2 - 4*(3*A - 5*B)*cos(d*x + c) + 12*A)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^5 + 2*a^2*d*cos(d*x + c)^4 + a^2*d*cos(d*x + c)^3)","A",0
517,1,319,0,122.477465," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 43 \, B + 115 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 \, C \cos\left(d x + c\right)^{2} + {\left(7 \, A - 15 \, B + 55 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 11 \, B + 35 \, C\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 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 2 \, B - 5 \, C\right)} \sqrt{a} \arctan\left(\frac{\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 + 115*C)*cos(d*x + c)^3 + 3*(3*A - 43*B + 115*C)*cos(d*x + c)^2 + 3*(3*A - 43*B + 115*C)*cos(d*x + c) + 3*A - 43*B + 115*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(16*C*cos(d*x + c)^2 + (7*A - 15*B + 55*C)*cos(d*x + c) + 3*A - 11*B + 35*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) + 32*((2*B - 5*C)*cos(d*x + c)^3 + 3*(2*B - 5*C)*cos(d*x + c)^2 + 3*(2*B - 5*C)*cos(d*x + c) + 2*B - 5*C)*sqrt(a)*arctan(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
518,1,283,0,96.580915," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B - 43 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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(A + 7 \, B - 15 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B - 11 \, C\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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \sqrt{a} \arctan\left(\frac{\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)*((5*A + 3*B - 43*C)*cos(d*x + c)^3 + 3*(5*A + 3*B - 43*C)*cos(d*x + c)^2 + 3*(5*A + 3*B - 43*C)*cos(d*x + c) + 5*A + 3*B - 43*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*((A + 7*B - 15*C)*cos(d*x + c) + 5*A + 3*B - 11*C)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) + 64*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*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
519,1,235,0,1.366716," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B + 3 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 - 7 \, C\right)} \cos\left(d x + c\right) + 13 \, A - 5 \, B - 3 \, C\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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 5*B + 3*C)*cos(d*x + c)^2 + 3*(19*A + 5*B + 3*C)*cos(d*x + c) + 19*A + 5*B + 3*C)*sqrt(a)*arctan(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 - 7*C)*cos(d*x + c) + 13*A - 5*B - 3*C)*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
520,1,264,0,0.959962," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(75 \, A - 19 \, B - 5 \, C\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 + C\right)} \cos\left(d x + c\right)^{2} + {\left(85 \, A - 13 \, B + 5 \, C\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 - 5*C)*cos(d*x + c)^4 + 3*(75*A - 19*B - 5*C)*cos(d*x + c)^3 + 3*(75*A - 19*B - 5*C)*cos(d*x + c)^2 + (75*A - 19*B - 5*C)*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 + C)*cos(d*x + c)^2 + (85*A - 13*B + 5*C)*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
521,1,288,0,2.013977," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(163 \, A - 75 \, B + 19 \, C\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 + 27 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(503 \, A - 255 \, B + 39 \, C\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 + 19*C)*cos(d*x + c)^5 + 3*(163*A - 75*B + 19*C)*cos(d*x + c)^4 + 3*(163*A - 75*B + 19*C)*cos(d*x + c)^3 + (163*A - 75*B + 19*C)*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 + 27*C)*cos(d*x + c)^3 + (503*A - 255*B + 39*C)*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
522,1,94,0,0.608124," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, C\right)} a d x + {\left(24 \, C b \cos\left(d x + c\right)^{4} + 30 \, C a \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, A + 4 \, C\right)} b \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, A + 3 \, C\right)} a \cos\left(d x + c\right) + 16 \, {\left(5 \, A + 4 \, C\right)} b\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*A + 3*C)*a*d*x + (24*C*b*cos(d*x + c)^4 + 30*C*a*cos(d*x + c)^3 + 8*(5*A + 4*C)*b*cos(d*x + c)^2 + 15*(4*A + 3*C)*a*cos(d*x + c) + 16*(5*A + 4*C)*b)*sin(d*x + c))/d","A",0
523,1,76,0,0.796505," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, A + 3 \, C\right)} b d x + {\left(6 \, C b \cos\left(d x + c\right)^{3} + 8 \, C a \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, A + 3 \, C\right)} b \cos\left(d x + c\right) + 8 \, {\left(3 \, A + 2 \, C\right)} a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*A + 3*C)*b*d*x + (6*C*b*cos(d*x + c)^3 + 8*C*a*cos(d*x + c)^2 + 3*(4*A + 3*C)*b*cos(d*x + c) + 8*(3*A + 2*C)*a)*sin(d*x + c))/d","A",0
524,1,56,0,0.785230," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, A + C\right)} a d x + {\left(2 \, C b \cos\left(d x + c\right)^{2} + 3 \, C a \cos\left(d x + c\right) + 2 \, {\left(3 \, A + 2 \, C\right)} b\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*A + C)*a*d*x + (2*C*b*cos(d*x + c)^2 + 3*C*a*cos(d*x + c) + 2*(3*A + 2*C)*b)*sin(d*x + c))/d","A",0
525,1,63,0,1.494218," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{{\left(2 \, A + C\right)} b 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) + {\left(C b \cos\left(d x + c\right) + 2 \, C a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*A + C)*b*d*x + A*a*log(sin(d*x + c) + 1) - A*a*log(-sin(d*x + c) + 1) + (C*b*cos(d*x + c) + 2*C*a)*sin(d*x + c))/d","A",0
526,1,86,0,1.436371," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, C a d x \cos\left(d x + c\right) + A b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - A b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C b \cos\left(d x + c\right) + A a\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*C*a*d*x*cos(d*x + c) + A*b*cos(d*x + c)*log(sin(d*x + c) + 1) - A*b*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(C*b*cos(d*x + c) + A*a)*sin(d*x + c))/(d*cos(d*x + c))","B",0
527,1,101,0,1.679372," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, C b d x \cos\left(d x + c\right)^{2} + {\left(A + 2 \, C\right)} a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A + 2 \, C\right)} a \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A b \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*(4*C*b*d*x*cos(d*x + c)^2 + (A + 2*C)*a*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A + 2*C)*a*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*A*b*cos(d*x + c) + A*a)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
528,1,107,0,0.863098," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(A + 2 \, C\right)} b \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A + 2 \, C\right)} b \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(2 \, A + 3 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, A b \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 + 2*C)*b*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(A + 2*C)*b*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(2*A + 3*C)*a*cos(d*x + c)^2 + 3*A*b*cos(d*x + c) + 2*A*a)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
529,1,129,0,0.864242," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, A + 4 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, A + 4 \, C\right)} a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(2 \, A + 3 \, C\right)} b \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 4 \, C\right)} a \cos\left(d x + c\right)^{2} + 8 \, A b \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*C)*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*A + 4*C)*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(2*A + 3*C)*b*cos(d*x + c)^3 + 3*(3*A + 4*C)*a*cos(d*x + c)^2 + 8*A*b*cos(d*x + c) + 6*A*a)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
530,1,147,0,0.917941," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, A + 4 \, C\right)} b \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, A + 4 \, C\right)} b \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(4 \, A + 5 \, C\right)} a \cos\left(d x + c\right)^{4} + 15 \, {\left(3 \, A + 4 \, C\right)} b \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, A + 5 \, C\right)} a \cos\left(d x + c\right)^{2} + 30 \, A b \cos\left(d x + c\right) + 24 \, A a\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(3*A + 4*C)*b*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*A + 4*C)*b*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(4*A + 5*C)*a*cos(d*x + c)^4 + 15*(3*A + 4*C)*b*cos(d*x + c)^3 + 8*(4*A + 5*C)*a*cos(d*x + c)^2 + 30*A*b*cos(d*x + c) + 24*A*a)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
531,1,159,0,0.783271," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(2 \, {\left(4 \, A + 3 \, C\right)} a^{2} + {\left(6 \, A + 5 \, C\right)} b^{2}\right)} d x + {\left(40 \, C b^{2} \cos\left(d x + c\right)^{5} + 96 \, C a b \cos\left(d x + c\right)^{4} + 32 \, {\left(5 \, A + 4 \, C\right)} a b \cos\left(d x + c\right)^{2} + 10 \, {\left(6 \, C a^{2} + {\left(6 \, A + 5 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{3} + 64 \, {\left(5 \, A + 4 \, C\right)} a b + 15 \, {\left(2 \, {\left(4 \, A + 3 \, C\right)} a^{2} + {\left(6 \, A + 5 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(2*(4*A + 3*C)*a^2 + (6*A + 5*C)*b^2)*d*x + (40*C*b^2*cos(d*x + c)^5 + 96*C*a*b*cos(d*x + c)^4 + 32*(5*A + 4*C)*a*b*cos(d*x + c)^2 + 10*(6*C*a^2 + (6*A + 5*C)*b^2)*cos(d*x + c)^3 + 64*(5*A + 4*C)*a*b + 15*(2*(4*A + 3*C)*a^2 + (6*A + 5*C)*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
532,1,123,0,1.226157," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, A + 3 \, C\right)} a b d x + {\left(12 \, C b^{2} \cos\left(d x + c\right)^{4} + 30 \, C a b \cos\left(d x + c\right)^{3} + 15 \, {\left(4 \, A + 3 \, C\right)} a b \cos\left(d x + c\right) + 20 \, {\left(3 \, A + 2 \, C\right)} a^{2} + 8 \, {\left(5 \, A + 4 \, C\right)} b^{2} + 4 \, {\left(5 \, C a^{2} + {\left(5 \, A + 4 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(15*(4*A + 3*C)*a*b*d*x + (12*C*b^2*cos(d*x + c)^4 + 30*C*a*b*cos(d*x + c)^3 + 15*(4*A + 3*C)*a*b*cos(d*x + c) + 20*(3*A + 2*C)*a^2 + 8*(5*A + 4*C)*b^2 + 4*(5*C*a^2 + (5*A + 4*C)*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
533,1,104,0,0.862262," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{2} + {\left(4 \, A + 3 \, C\right)} b^{2}\right)} d x + {\left(6 \, C b^{2} \cos\left(d x + c\right)^{3} + 16 \, C a b \cos\left(d x + c\right)^{2} + 16 \, {\left(3 \, A + 2 \, C\right)} a b + 3 \, {\left(4 \, C a^{2} + {\left(4 \, A + 3 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*(2*A + C)*a^2 + (4*A + 3*C)*b^2)*d*x + (6*C*b^2*cos(d*x + c)^3 + 16*C*a*b*cos(d*x + c)^2 + 16*(3*A + 2*C)*a*b + 3*(4*C*a^2 + (4*A + 3*C)*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
534,1,99,0,0.982234," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{6 \, {\left(2 \, A + C\right)} a b d x + 3 \, A a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, A a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C b^{2} \cos\left(d x + c\right)^{2} + 3 \, C a b \cos\left(d x + c\right) + 3 \, C a^{2} + {\left(3 \, A + 2 \, C\right)} b^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(6*(2*A + C)*a*b*d*x + 3*A*a^2*log(sin(d*x + c) + 1) - 3*A*a^2*log(-sin(d*x + c) + 1) + 2*(C*b^2*cos(d*x + c)^2 + 3*C*a*b*cos(d*x + c) + 3*C*a^2 + (3*A + 2*C)*b^2)*sin(d*x + c))/d","A",0
535,1,119,0,0.952718," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, A a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, A a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{2} + {\left(2 \, A + C\right)} b^{2}\right)} d x \cos\left(d x + c\right) + {\left(C b^{2} \cos\left(d x + c\right)^{2} + 4 \, C a b \cos\left(d x + c\right) + 2 \, A a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*A*a*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 2*A*a*b*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*C*a^2 + (2*A + C)*b^2)*d*x*cos(d*x + c) + (C*b^2*cos(d*x + c)^2 + 4*C*a*b*cos(d*x + c) + 2*A*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
536,1,139,0,0.936420," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{8 \, C a b d x \cos\left(d x + c\right)^{2} + {\left({\left(A + 2 \, C\right)} a^{2} + 2 \, A b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A + 2 \, C\right)} a^{2} + 2 \, A b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C b^{2} \cos\left(d x + c\right)^{2} + 4 \, A a b \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*(8*C*a*b*d*x*cos(d*x + c)^2 + ((A + 2*C)*a^2 + 2*A*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - ((A + 2*C)*a^2 + 2*A*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*b^2*cos(d*x + c)^2 + 4*A*a*b*cos(d*x + c) + A*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
537,1,136,0,0.958842," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{6 \, C b^{2} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(A + 2 \, C\right)} a b \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A + 2 \, C\right)} a b \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left({\left(2 \, A + 3 \, C\right)} a^{2} + 3 \, A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(6*C*b^2*d*x*cos(d*x + c)^3 + 3*(A + 2*C)*a*b*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(A + 2*C)*a*b*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(3*A*a*b*cos(d*x + c) + A*a^2 + ((2*A + 3*C)*a^2 + 3*A*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
538,1,171,0,0.927215," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{2} + 4 \, {\left(A + 2 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{2} + 4 \, {\left(A + 2 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(2 \, A + 3 \, C\right)} a b \cos\left(d x + c\right)^{3} + 16 \, A a b \cos\left(d x + c\right) + 6 \, A a^{2} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{2} + 4 \, A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*((3*A + 4*C)*a^2 + 4*(A + 2*C)*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*((3*A + 4*C)*a^2 + 4*(A + 2*C)*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(2*A + 3*C)*a*b*cos(d*x + c)^3 + 16*A*a*b*cos(d*x + c) + 6*A*a^2 + 3*((3*A + 4*C)*a^2 + 4*A*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
539,1,180,0,1.484823," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, A + 4 \, C\right)} a b \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, A + 4 \, C\right)} a b \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(15 \, {\left(3 \, A + 4 \, C\right)} a b \cos\left(d x + c\right)^{3} + 4 \, {\left(2 \, {\left(4 \, A + 5 \, C\right)} a^{2} + 5 \, {\left(2 \, A + 3 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} + 30 \, A a b \cos\left(d x + c\right) + 12 \, A a^{2} + 4 \, {\left({\left(4 \, A + 5 \, C\right)} a^{2} + 5 \, A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{120 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/120*(15*(3*A + 4*C)*a*b*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*A + 4*C)*a*b*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(15*(3*A + 4*C)*a*b*cos(d*x + c)^3 + 4*(2*(4*A + 5*C)*a^2 + 5*(2*A + 3*C)*b^2)*cos(d*x + c)^4 + 30*A*a*b*cos(d*x + c) + 12*A*a^2 + 4*((4*A + 5*C)*a^2 + 5*A*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
540,1,189,0,1.829227," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, {\left(4 \, A + 3 \, C\right)} a^{2} b + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} d x + {\left(40 \, C b^{3} \cos\left(d x + c\right)^{5} + 144 \, C a b^{2} \cos\left(d x + c\right)^{4} + 80 \, {\left(3 \, A + 2 \, C\right)} a^{3} + 96 \, {\left(5 \, A + 4 \, C\right)} a b^{2} + 10 \, {\left(18 \, C a^{2} b + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(5 \, C a^{3} + 3 \, {\left(5 \, A + 4 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(6 \, {\left(4 \, A + 3 \, C\right)} a^{2} b + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(6*(4*A + 3*C)*a^2*b + (6*A + 5*C)*b^3)*d*x + (40*C*b^3*cos(d*x + c)^5 + 144*C*a*b^2*cos(d*x + c)^4 + 80*(3*A + 2*C)*a^3 + 96*(5*A + 4*C)*a*b^2 + 10*(18*C*a^2*b + (6*A + 5*C)*b^3)*cos(d*x + c)^3 + 16*(5*C*a^3 + 3*(5*A + 4*C)*a*b^2)*cos(d*x + c)^2 + 15*(6*(4*A + 3*C)*a^2*b + (6*A + 5*C)*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
541,1,153,0,0.813503," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, {\left(2 \, A + C\right)} a^{3} + 3 \, {\left(4 \, A + 3 \, C\right)} a b^{2}\right)} d x + {\left(24 \, C b^{3} \cos\left(d x + c\right)^{4} + 90 \, C a b^{2} \cos\left(d x + c\right)^{3} + 120 \, {\left(3 \, A + 2 \, C\right)} a^{2} b + 16 \, {\left(5 \, A + 4 \, C\right)} b^{3} + 8 \, {\left(15 \, C a^{2} b + {\left(5 \, A + 4 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, C a^{3} + 3 \, {\left(4 \, A + 3 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*(2*A + C)*a^3 + 3*(4*A + 3*C)*a*b^2)*d*x + (24*C*b^3*cos(d*x + c)^4 + 90*C*a*b^2*cos(d*x + c)^3 + 120*(3*A + 2*C)*a^2*b + 16*(5*A + 4*C)*b^3 + 8*(15*C*a^2*b + (5*A + 4*C)*b^3)*cos(d*x + c)^2 + 15*(4*C*a^3 + 3*(4*A + 3*C)*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
542,1,146,0,0.965562," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{4 \, A a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 4 \, A a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(12 \, {\left(2 \, A + C\right)} a^{2} b + {\left(4 \, A + 3 \, C\right)} b^{3}\right)} d x + {\left(2 \, C b^{3} \cos\left(d x + c\right)^{3} + 8 \, C a b^{2} \cos\left(d x + c\right)^{2} + 8 \, C a^{3} + 8 \, {\left(3 \, A + 2 \, C\right)} a b^{2} + {\left(12 \, C a^{2} b + {\left(4 \, A + 3 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(4*A*a^3*log(sin(d*x + c) + 1) - 4*A*a^3*log(-sin(d*x + c) + 1) + (12*(2*A + C)*a^2*b + (4*A + 3*C)*b^3)*d*x + (2*C*b^3*cos(d*x + c)^3 + 8*C*a*b^2*cos(d*x + c)^2 + 8*C*a^3 + 8*(3*A + 2*C)*a*b^2 + (12*C*a^2*b + (4*A + 3*C)*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
543,1,158,0,1.055603," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{9 \, A a^{2} b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, A a^{2} b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, C a^{3} + 3 \, {\left(2 \, A + C\right)} a b^{2}\right)} d x \cos\left(d x + c\right) + {\left(2 \, C b^{3} \cos\left(d x + c\right)^{3} + 9 \, C a b^{2} \cos\left(d x + c\right)^{2} + 6 \, A a^{3} + 2 \, {\left(9 \, C a^{2} b + {\left(3 \, A + 2 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(9*A*a^2*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 9*A*a^2*b*cos(d*x + c)*log(-sin(d*x + c) + 1) + 3*(2*C*a^3 + 3*(2*A + C)*a*b^2)*d*x*cos(d*x + c) + (2*C*b^3*cos(d*x + c)^3 + 9*C*a*b^2*cos(d*x + c)^2 + 6*A*a^3 + 2*(9*C*a^2*b + (3*A + 2*C)*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
544,1,171,0,1.746303," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, C a^{2} b + {\left(2 \, A + C\right)} b^{3}\right)} d x \cos\left(d x + c\right)^{2} + {\left({\left(A + 2 \, C\right)} a^{3} + 6 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A + 2 \, C\right)} a^{3} + 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(C b^{3} \cos\left(d x + c\right)^{3} + 6 \, C a b^{2} \cos\left(d x + c\right)^{2} + 6 \, A a^{2} b \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*(2*(6*C*a^2*b + (2*A + C)*b^3)*d*x*cos(d*x + c)^2 + ((A + 2*C)*a^3 + 6*A*a*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - ((A + 2*C)*a^3 + 6*A*a*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(C*b^3*cos(d*x + c)^3 + 6*C*a*b^2*cos(d*x + c)^2 + 6*A*a^2*b*cos(d*x + c) + A*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
545,1,178,0,2.158043," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{36 \, C a b^{2} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, {\left(A + 2 \, C\right)} a^{2} b + 2 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, {\left(A + 2 \, C\right)} a^{2} b + 2 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, C b^{3} \cos\left(d x + c\right)^{3} + 9 \, A a^{2} b \cos\left(d x + c\right) + 2 \, A a^{3} + 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{3} + 9 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(36*C*a*b^2*d*x*cos(d*x + c)^3 + 3*(3*(A + 2*C)*a^2*b + 2*A*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(3*(A + 2*C)*a^2*b + 2*A*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*C*b^3*cos(d*x + c)^3 + 9*A*a^2*b*cos(d*x + c) + 2*A*a^3 + 2*((2*A + 3*C)*a^3 + 9*A*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
546,1,199,0,0.829602," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{16 \, C b^{3} d x \cos\left(d x + c\right)^{4} + {\left({\left(3 \, A + 4 \, C\right)} a^{3} + 12 \, {\left(A + 2 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(3 \, A + 4 \, C\right)} a^{3} + 12 \, {\left(A + 2 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, A a^{2} b \cos\left(d x + c\right) + 2 \, A a^{3} + 8 \, {\left({\left(2 \, A + 3 \, C\right)} a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(3 \, A + 4 \, C\right)} a^{3} + 12 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*C*b^3*d*x*cos(d*x + c)^4 + ((3*A + 4*C)*a^3 + 12*(A + 2*C)*a*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - ((3*A + 4*C)*a^3 + 12*(A + 2*C)*a*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*A*a^2*b*cos(d*x + c) + 2*A*a^3 + 8*((2*A + 3*C)*a^2*b + A*b^3)*cos(d*x + c)^3 + ((3*A + 4*C)*a^3 + 12*A*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
547,1,225,0,0.818460," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, {\left(3 \, A + 4 \, C\right)} a^{2} b + 4 \, {\left(A + 2 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, {\left(3 \, A + 4 \, C\right)} a^{2} b + 4 \, {\left(A + 2 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(90 \, A a^{2} b \cos\left(d x + c\right) + 8 \, {\left(2 \, {\left(4 \, A + 5 \, C\right)} a^{3} + 15 \, {\left(2 \, A + 3 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{4} + 24 \, A a^{3} + 15 \, {\left(3 \, {\left(3 \, A + 4 \, C\right)} a^{2} b + 4 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left({\left(4 \, A + 5 \, C\right)} a^{3} + 15 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(3*(3*A + 4*C)*a^2*b + 4*(A + 2*C)*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*(3*A + 4*C)*a^2*b + 4*(A + 2*C)*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(90*A*a^2*b*cos(d*x + c) + 8*(2*(4*A + 5*C)*a^3 + 15*(2*A + 3*C)*a*b^2)*cos(d*x + c)^4 + 24*A*a^3 + 15*(3*(3*A + 4*C)*a^2*b + 4*A*b^3)*cos(d*x + c)^3 + 8*((4*A + 5*C)*a^3 + 15*A*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
548,1,262,0,0.958033," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 6 \, {\left(3 \, A + 4 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 6 \, {\left(3 \, A + 4 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(6 \, {\left(4 \, A + 5 \, C\right)} a^{2} b + 5 \, {\left(2 \, A + 3 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{5} + 144 \, A a^{2} b \cos\left(d x + c\right) + 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 6 \, {\left(3 \, A + 4 \, C\right)} a b^{2}\right)} \cos\left(d x + c\right)^{4} + 40 \, A a^{3} + 16 \, {\left(3 \, {\left(4 \, A + 5 \, C\right)} a^{2} b + 5 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 18 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*((5*A + 6*C)*a^3 + 6*(3*A + 4*C)*a*b^2)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*((5*A + 6*C)*a^3 + 6*(3*A + 4*C)*a*b^2)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(6*(4*A + 5*C)*a^2*b + 5*(2*A + 3*C)*b^3)*cos(d*x + c)^5 + 144*A*a^2*b*cos(d*x + c) + 15*((5*A + 6*C)*a^3 + 6*(3*A + 4*C)*a*b^2)*cos(d*x + c)^4 + 40*A*a^3 + 16*(3*(4*A + 5*C)*a^2*b + 5*A*b^3)*cos(d*x + c)^3 + 10*((5*A + 6*C)*a^3 + 18*A*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
549,1,251,0,1.114028," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(2 \, {\left(4 \, A + 3 \, C\right)} a^{3} b + {\left(6 \, A + 5 \, C\right)} a b^{3}\right)} d x + {\left(60 \, C b^{4} \cos\left(d x + c\right)^{6} + 280 \, C a b^{3} \cos\left(d x + c\right)^{5} + 140 \, {\left(3 \, A + 2 \, C\right)} a^{4} + 336 \, {\left(5 \, A + 4 \, C\right)} a^{2} b^{2} + 32 \, {\left(7 \, A + 6 \, C\right)} b^{4} + 12 \, {\left(42 \, C a^{2} b^{2} + {\left(7 \, A + 6 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left(6 \, C a^{3} b + {\left(6 \, A + 5 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(35 \, C a^{4} + 42 \, {\left(5 \, A + 4 \, C\right)} a^{2} b^{2} + 4 \, {\left(7 \, A + 6 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 105 \, {\left(2 \, {\left(4 \, A + 3 \, C\right)} a^{3} b + {\left(6 \, A + 5 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{420 \, d}"," ",0,"1/420*(105*(2*(4*A + 3*C)*a^3*b + (6*A + 5*C)*a*b^3)*d*x + (60*C*b^4*cos(d*x + c)^6 + 280*C*a*b^3*cos(d*x + c)^5 + 140*(3*A + 2*C)*a^4 + 336*(5*A + 4*C)*a^2*b^2 + 32*(7*A + 6*C)*b^4 + 12*(42*C*a^2*b^2 + (7*A + 6*C)*b^4)*cos(d*x + c)^4 + 70*(6*C*a^3*b + (6*A + 5*C)*a*b^3)*cos(d*x + c)^3 + 4*(35*C*a^4 + 42*(5*A + 4*C)*a^2*b^2 + 4*(7*A + 6*C)*b^4)*cos(d*x + c)^2 + 105*(2*(4*A + 3*C)*a^3*b + (6*A + 5*C)*a*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
550,1,212,0,0.980414," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, {\left(2 \, A + C\right)} a^{4} + 12 \, {\left(4 \, A + 3 \, C\right)} a^{2} b^{2} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} d x + {\left(40 \, C b^{4} \cos\left(d x + c\right)^{5} + 192 \, C a b^{3} \cos\left(d x + c\right)^{4} + 320 \, {\left(3 \, A + 2 \, C\right)} a^{3} b + 128 \, {\left(5 \, A + 4 \, C\right)} a b^{3} + 10 \, {\left(36 \, C a^{2} b^{2} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{3} + 64 \, {\left(5 \, C a^{3} b + {\left(5 \, A + 4 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(8 \, C a^{4} + 12 \, {\left(4 \, A + 3 \, C\right)} a^{2} b^{2} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(8*(2*A + C)*a^4 + 12*(4*A + 3*C)*a^2*b^2 + (6*A + 5*C)*b^4)*d*x + (40*C*b^4*cos(d*x + c)^5 + 192*C*a*b^3*cos(d*x + c)^4 + 320*(3*A + 2*C)*a^3*b + 128*(5*A + 4*C)*a*b^3 + 10*(36*C*a^2*b^2 + (6*A + 5*C)*b^4)*cos(d*x + c)^3 + 64*(5*C*a^3*b + (5*A + 4*C)*a*b^3)*cos(d*x + c)^2 + 15*(8*C*a^4 + 12*(4*A + 3*C)*a^2*b^2 + (6*A + 5*C)*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
551,1,195,0,1.173314," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{15 \, A a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, A a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 15 \, {\left(4 \, {\left(2 \, A + C\right)} a^{3} b + {\left(4 \, A + 3 \, C\right)} a b^{3}\right)} d x + {\left(6 \, C b^{4} \cos\left(d x + c\right)^{4} + 30 \, C a b^{3} \cos\left(d x + c\right)^{3} + 30 \, C a^{4} + 60 \, {\left(3 \, A + 2 \, C\right)} a^{2} b^{2} + 4 \, {\left(5 \, A + 4 \, C\right)} b^{4} + 2 \, {\left(30 \, C a^{2} b^{2} + {\left(5 \, A + 4 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, C a^{3} b + {\left(4 \, A + 3 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(15*A*a^4*log(sin(d*x + c) + 1) - 15*A*a^4*log(-sin(d*x + c) + 1) + 15*(4*(2*A + C)*a^3*b + (4*A + 3*C)*a*b^3)*d*x + (6*C*b^4*cos(d*x + c)^4 + 30*C*a*b^3*cos(d*x + c)^3 + 30*C*a^4 + 60*(3*A + 2*C)*a^2*b^2 + 4*(5*A + 4*C)*b^4 + 2*(30*C*a^2*b^2 + (5*A + 4*C)*b^4)*cos(d*x + c)^2 + 15*(4*C*a^3*b + (4*A + 3*C)*a*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
552,1,203,0,2.257596," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{48 \, A a^{3} b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 48 \, A a^{3} b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(8 \, C a^{4} + 24 \, {\left(2 \, A + C\right)} a^{2} b^{2} + {\left(4 \, A + 3 \, C\right)} b^{4}\right)} d x \cos\left(d x + c\right) + {\left(6 \, C b^{4} \cos\left(d x + c\right)^{4} + 32 \, C a b^{3} \cos\left(d x + c\right)^{3} + 24 \, A a^{4} + 3 \, {\left(24 \, C a^{2} b^{2} + {\left(4 \, A + 3 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 32 \, {\left(3 \, C a^{3} b + {\left(3 \, A + 2 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}"," ",0,"1/24*(48*A*a^3*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 48*A*a^3*b*cos(d*x + c)*log(-sin(d*x + c) + 1) + 3*(8*C*a^4 + 24*(2*A + C)*a^2*b^2 + (4*A + 3*C)*b^4)*d*x*cos(d*x + c) + (6*C*b^4*cos(d*x + c)^4 + 32*C*a*b^3*cos(d*x + c)^3 + 24*A*a^4 + 3*(24*C*a^2*b^2 + (4*A + 3*C)*b^4)*cos(d*x + c)^2 + 32*(3*C*a^3*b + (3*A + 2*C)*a*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
553,1,210,0,1.451774," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{24 \, {\left(2 \, C a^{3} b + {\left(2 \, A + C\right)} a b^{3}\right)} d x \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(A + 2 \, C\right)} a^{4} + 12 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(A + 2 \, C\right)} a^{4} + 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(2 \, C b^{4} \cos\left(d x + c\right)^{4} + 12 \, C a b^{3} \cos\left(d x + c\right)^{3} + 24 \, A a^{3} b \cos\left(d x + c\right) + 3 \, A a^{4} + 2 \, {\left(18 \, C a^{2} b^{2} + {\left(3 \, A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/12*(24*(2*C*a^3*b + (2*A + C)*a*b^3)*d*x*cos(d*x + c)^2 + 3*((A + 2*C)*a^4 + 12*A*a^2*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*((A + 2*C)*a^4 + 12*A*a^2*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*b^4*cos(d*x + c)^4 + 12*C*a*b^3*cos(d*x + c)^3 + 24*A*a^3*b*cos(d*x + c) + 3*A*a^4 + 2*(18*C*a^2*b^2 + (3*A + 2*C)*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
554,1,208,0,1.805155," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(12 \, C a^{2} b^{2} + {\left(2 \, A + C\right)} b^{4}\right)} d x \cos\left(d x + c\right)^{3} + 6 \, {\left({\left(A + 2 \, C\right)} a^{3} b + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left({\left(A + 2 \, C\right)} a^{3} b + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(3 \, C b^{4} \cos\left(d x + c\right)^{4} + 24 \, C a b^{3} \cos\left(d x + c\right)^{3} + 12 \, A a^{3} b \cos\left(d x + c\right) + 2 \, A a^{4} + 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{4} + 18 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(3*(12*C*a^2*b^2 + (2*A + C)*b^4)*d*x*cos(d*x + c)^3 + 6*((A + 2*C)*a^3*b + 2*A*a*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 6*((A + 2*C)*a^3*b + 2*A*a*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + (3*C*b^4*cos(d*x + c)^4 + 24*C*a*b^3*cos(d*x + c)^3 + 12*A*a^3*b*cos(d*x + c) + 2*A*a^4 + 2*((2*A + 3*C)*a^4 + 18*A*a^2*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
555,1,236,0,0.807636," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{192 \, C a b^{3} d x \cos\left(d x + c\right)^{4} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{4} + 24 \, {\left(A + 2 \, C\right)} a^{2} b^{2} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{4} + 24 \, {\left(A + 2 \, C\right)} a^{2} b^{2} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, C b^{4} \cos\left(d x + c\right)^{4} + 32 \, A a^{3} b \cos\left(d x + c\right) + 6 \, A a^{4} + 32 \, {\left({\left(2 \, A + 3 \, C\right)} a^{3} b + 3 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{4} + 24 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(192*C*a*b^3*d*x*cos(d*x + c)^4 + 3*((3*A + 4*C)*a^4 + 24*(A + 2*C)*a^2*b^2 + 8*A*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*((3*A + 4*C)*a^4 + 24*(A + 2*C)*a^2*b^2 + 8*A*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*C*b^4*cos(d*x + c)^4 + 32*A*a^3*b*cos(d*x + c) + 6*A*a^4 + 32*((2*A + 3*C)*a^3*b + 3*A*a*b^3)*cos(d*x + c)^3 + 3*((3*A + 4*C)*a^4 + 24*A*a^2*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
556,1,251,0,1.653276," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{60 \, C b^{4} d x \cos\left(d x + c\right)^{5} + 15 \, {\left({\left(3 \, A + 4 \, C\right)} a^{3} b + 4 \, {\left(A + 2 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(3 \, A + 4 \, C\right)} a^{3} b + 4 \, {\left(A + 2 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(30 \, A a^{3} b \cos\left(d x + c\right) + 6 \, A a^{4} + 2 \, {\left(2 \, {\left(4 \, A + 5 \, C\right)} a^{4} + 30 \, {\left(2 \, A + 3 \, C\right)} a^{2} b^{2} + 15 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left({\left(3 \, A + 4 \, C\right)} a^{3} b + 4 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left({\left(4 \, A + 5 \, C\right)} a^{4} + 30 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/60*(60*C*b^4*d*x*cos(d*x + c)^5 + 15*((3*A + 4*C)*a^3*b + 4*(A + 2*C)*a*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*((3*A + 4*C)*a^3*b + 4*(A + 2*C)*a*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(30*A*a^3*b*cos(d*x + c) + 6*A*a^4 + 2*(2*(4*A + 5*C)*a^4 + 30*(2*A + 3*C)*a^2*b^2 + 15*A*b^4)*cos(d*x + c)^4 + 15*((3*A + 4*C)*a^3*b + 4*A*a*b^3)*cos(d*x + c)^3 + 2*((4*A + 5*C)*a^4 + 30*A*a^2*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
557,1,297,0,0.927262," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 12 \, {\left(3 \, A + 4 \, C\right)} a^{2} b^{2} + 8 \, {\left(A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 12 \, {\left(3 \, A + 4 \, C\right)} a^{2} b^{2} + 8 \, {\left(A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(192 \, A a^{3} b \cos\left(d x + c\right) + 64 \, {\left(2 \, {\left(4 \, A + 5 \, C\right)} a^{3} b + 5 \, {\left(2 \, A + 3 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{5} + 40 \, A a^{4} + 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 12 \, {\left(3 \, A + 4 \, C\right)} a^{2} b^{2} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} + 64 \, {\left({\left(4 \, A + 5 \, C\right)} a^{3} b + 5 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 36 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*((5*A + 6*C)*a^4 + 12*(3*A + 4*C)*a^2*b^2 + 8*(A + 2*C)*b^4)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*((5*A + 6*C)*a^4 + 12*(3*A + 4*C)*a^2*b^2 + 8*(A + 2*C)*b^4)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(192*A*a^3*b*cos(d*x + c) + 64*(2*(4*A + 5*C)*a^3*b + 5*(2*A + 3*C)*a*b^3)*cos(d*x + c)^5 + 40*A*a^4 + 15*((5*A + 6*C)*a^4 + 12*(3*A + 4*C)*a^2*b^2 + 8*A*b^4)*cos(d*x + c)^4 + 64*((4*A + 5*C)*a^3*b + 5*A*a*b^3)*cos(d*x + c)^3 + 10*((5*A + 6*C)*a^4 + 36*A*a^2*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
558,1,325,0,0.948844," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^8,x, algorithm=""fricas"")","\frac{105 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} b + 2 \, {\left(3 \, A + 4 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} b + 2 \, {\left(3 \, A + 4 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, {\left(8 \, {\left(6 \, A + 7 \, C\right)} a^{4} + 84 \, {\left(4 \, A + 5 \, C\right)} a^{2} b^{2} + 35 \, {\left(2 \, A + 3 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{6} + 280 \, A a^{3} b \cos\left(d x + c\right) + 105 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} b + 2 \, {\left(3 \, A + 4 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)^{5} + 60 \, A a^{4} + 4 \, {\left(4 \, {\left(6 \, A + 7 \, C\right)} a^{4} + 42 \, {\left(4 \, A + 5 \, C\right)} a^{2} b^{2} + 35 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} b + 6 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left({\left(6 \, A + 7 \, C\right)} a^{4} + 42 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{840 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/840*(105*((5*A + 6*C)*a^3*b + 2*(3*A + 4*C)*a*b^3)*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*((5*A + 6*C)*a^3*b + 2*(3*A + 4*C)*a*b^3)*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 2*(4*(8*(6*A + 7*C)*a^4 + 84*(4*A + 5*C)*a^2*b^2 + 35*(2*A + 3*C)*b^4)*cos(d*x + c)^6 + 280*A*a^3*b*cos(d*x + c) + 105*((5*A + 6*C)*a^3*b + 2*(3*A + 4*C)*a*b^3)*cos(d*x + c)^5 + 60*A*a^4 + 4*(4*(6*A + 7*C)*a^4 + 42*(4*A + 5*C)*a^2*b^2 + 35*A*b^4)*cos(d*x + c)^4 + 70*((5*A + 6*C)*a^3*b + 6*A*a*b^3)*cos(d*x + c)^3 + 12*((6*A + 7*C)*a^4 + 42*A*a^2*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
559,1,132,0,0.804383," ","integrate((a+b*cos(d*x+c))^3*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, a^{5} + 8 \, a^{3} b^{2} - 9 \, a b^{4}\right)} d x - {\left(24 \, b^{5} \cos\left(d x + c\right)^{4} + 90 \, a b^{4} \cos\left(d x + c\right)^{3} - 360 \, a^{4} b + 160 \, a^{2} b^{3} + 64 \, b^{5} + 16 \, {\left(5 \, a^{2} b^{3} + 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left(8 \, a^{3} b^{2} - 9 \, 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^5 + 8*a^3*b^2 - 9*a*b^4)*d*x - (24*b^5*cos(d*x + c)^4 + 90*a*b^4*cos(d*x + c)^3 - 360*a^4*b + 160*a^2*b^3 + 64*b^5 + 16*(5*a^2*b^3 + 2*b^5)*cos(d*x + c)^2 - 15*(8*a^3*b^2 - 9*a*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
560,1,80,0,1.183999," ","integrate((a+b*cos(d*x+c))^2*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, a^{4} - 3 \, b^{4}\right)} d x - {\left(6 \, b^{4} \cos\left(d x + c\right)^{3} + 16 \, a b^{3} \cos\left(d x + c\right)^{2} + 9 \, b^{4} \cos\left(d x + c\right) - 48 \, a^{3} b + 32 \, a b^{3}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(8*a^4 - 3*b^4)*d*x - (6*b^4*cos(d*x + c)^3 + 16*a*b^3*cos(d*x + c)^2 + 9*b^4*cos(d*x + c) - 48*a^3*b + 32*a*b^3)*sin(d*x + c))/d","A",0
561,1,67,0,1.053036," ","integrate((a+b*cos(d*x+c))*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, a^{3} - a b^{2}\right)} d x - {\left(2 \, b^{3} \cos\left(d x + c\right)^{2} + 3 \, a b^{2} \cos\left(d x + c\right) - 6 \, a^{2} b + 4 \, b^{3}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*a^3 - a*b^2)*d*x - (2*b^3*cos(d*x + c)^2 + 3*a*b^2*cos(d*x + c) - 6*a^2*b + 4*b^3)*sin(d*x + c))/d","A",0
562,1,609,0,4.016692," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, C a^{6} + 4 \, {\left(2 \, A - C\right)} a^{4} b^{2} - {\left(4 \, A + C\right)} a^{2} b^{4} - {\left(4 \, A + 3 \, C\right)} b^{6}\right)} d x - 12 \, {\left(C a^{5} + A a^{3} b^{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(24 \, C a^{5} b + 8 \, {\left(3 \, A - C\right)} a^{3} b^{3} - 8 \, {\left(3 \, A + 2 \, C\right)} a b^{5} - 6 \, {\left(C a^{2} b^{4} - C b^{6}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(C a^{3} b^{3} - C a b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(4 \, C a^{4} b^{2} + {\left(4 \, A - C\right)} a^{2} b^{4} - {\left(4 \, A + 3 \, C\right)} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{2} b^{5} - b^{7}\right)} d}, \frac{3 \, {\left(8 \, C a^{6} + 4 \, {\left(2 \, A - C\right)} a^{4} b^{2} - {\left(4 \, A + C\right)} a^{2} b^{4} - {\left(4 \, A + 3 \, C\right)} b^{6}\right)} d x - 24 \, {\left(C a^{5} + A a^{3} 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) - {\left(24 \, C a^{5} b + 8 \, {\left(3 \, A - C\right)} a^{3} b^{3} - 8 \, {\left(3 \, A + 2 \, C\right)} a b^{5} - 6 \, {\left(C a^{2} b^{4} - C b^{6}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(C a^{3} b^{3} - C a b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(4 \, C a^{4} b^{2} + {\left(4 \, A - C\right)} a^{2} b^{4} - {\left(4 \, A + 3 \, C\right)} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{2} b^{5} - b^{7}\right)} d}\right]"," ",0,"[1/24*(3*(8*C*a^6 + 4*(2*A - C)*a^4*b^2 - (4*A + C)*a^2*b^4 - (4*A + 3*C)*b^6)*d*x - 12*(C*a^5 + A*a^3*b^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)) - (24*C*a^5*b + 8*(3*A - C)*a^3*b^3 - 8*(3*A + 2*C)*a*b^5 - 6*(C*a^2*b^4 - C*b^6)*cos(d*x + c)^3 + 8*(C*a^3*b^3 - C*a*b^5)*cos(d*x + c)^2 - 3*(4*C*a^4*b^2 + (4*A - C)*a^2*b^4 - (4*A + 3*C)*b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^5 - b^7)*d), 1/24*(3*(8*C*a^6 + 4*(2*A - C)*a^4*b^2 - (4*A + C)*a^2*b^4 - (4*A + 3*C)*b^6)*d*x - 24*(C*a^5 + A*a^3*b^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (24*C*a^5*b + 8*(3*A - C)*a^3*b^3 - 8*(3*A + 2*C)*a*b^5 - 6*(C*a^2*b^4 - C*b^6)*cos(d*x + c)^3 + 8*(C*a^3*b^3 - C*a*b^5)*cos(d*x + c)^2 - 3*(4*C*a^4*b^2 + (4*A - C)*a^2*b^4 - (4*A + 3*C)*b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^5 - b^7)*d)]","A",0
563,1,485,0,2.161476," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, C a^{5} + {\left(2 \, A - C\right)} a^{3} b^{2} - {\left(2 \, A + C\right)} a b^{4}\right)} d x + 3 \, {\left(C a^{4} + A a^{2} b^{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(6 \, C a^{4} b + 2 \, {\left(3 \, A - C\right)} a^{2} b^{3} - 2 \, {\left(3 \, A + 2 \, C\right)} b^{5} + 2 \, {\left(C a^{2} b^{3} - C b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - C a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} - b^{6}\right)} d}, -\frac{3 \, {\left(2 \, C a^{5} + {\left(2 \, A - C\right)} a^{3} b^{2} - {\left(2 \, A + C\right)} a b^{4}\right)} d x - 6 \, {\left(C a^{4} + A a^{2} 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) - {\left(6 \, C a^{4} b + 2 \, {\left(3 \, A - C\right)} a^{2} b^{3} - 2 \, {\left(3 \, A + 2 \, C\right)} b^{5} + 2 \, {\left(C a^{2} b^{3} - C b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - C a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} - b^{6}\right)} d}\right]"," ",0,"[-1/6*(3*(2*C*a^5 + (2*A - C)*a^3*b^2 - (2*A + C)*a*b^4)*d*x + 3*(C*a^4 + A*a^2*b^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)) - (6*C*a^4*b + 2*(3*A - C)*a^2*b^3 - 2*(3*A + 2*C)*b^5 + 2*(C*a^2*b^3 - C*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - C*a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d), -1/6*(3*(2*C*a^5 + (2*A - C)*a^3*b^2 - (2*A + C)*a*b^4)*d*x - 6*(C*a^4 + A*a^2*b^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*C*a^4*b + 2*(3*A - C)*a^2*b^3 - 2*(3*A + 2*C)*b^5 + 2*(C*a^2*b^3 - C*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - C*a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d)]","A",0
564,1,385,0,0.862237," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, C a^{4} + {\left(2 \, A - C\right)} a^{2} b^{2} - {\left(2 \, A + C\right)} b^{4}\right)} d x - {\left(C a^{3} + A a b^{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(2 \, C a^{3} b - 2 \, C a b^{3} - {\left(C a^{2} b^{2} - C 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 \, C a^{4} + {\left(2 \, A - C\right)} a^{2} b^{2} - {\left(2 \, A + C\right)} b^{4}\right)} d x - 2 \, {\left(C a^{3} + A 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) - {\left(2 \, C a^{3} b - 2 \, C a b^{3} - {\left(C a^{2} b^{2} - C 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*C*a^4 + (2*A - C)*a^2*b^2 - (2*A + C)*b^4)*d*x - (C*a^3 + A*a*b^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)) - (2*C*a^3*b - 2*C*a*b^3 - (C*a^2*b^2 - C*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d), 1/2*((2*C*a^4 + (2*A - C)*a^2*b^2 - (2*A + C)*b^4)*d*x - 2*(C*a^3 + A*a*b^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*C*a^3*b - 2*C*a*b^3 - (C*a^2*b^2 - C*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d)]","A",0
565,1,297,0,1.387545," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(C a^{3} - C a b^{2}\right)} d x + {\left(C a^{2} + A b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(C a^{2} b - C b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d}, -\frac{{\left(C a^{3} - C a b^{2}\right)} d x - {\left(C a^{2} + 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) - {\left(C a^{2} b - C b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d}\right]"," ",0,"[-1/2*(2*(C*a^3 - C*a*b^2)*d*x + (C*a^2 + A*b^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)) - 2*(C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d), -((C*a^3 - C*a*b^2)*d*x - (C*a^2 + A*b^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d)]","A",0
566,1,353,0,3.592058," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{3} - C a b^{2}\right)} d x - {\left(C a^{2} + A b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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} b - A b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{2} b - A b^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} b - a b^{3}\right)} d}, \frac{2 \, {\left(C a^{3} - C a b^{2}\right)} d x - 2 \, {\left(C a^{2} + 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) + {\left(A a^{2} b - A b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{2} b - A b^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} b - a b^{3}\right)} d}\right]"," ",0,"[1/2*(2*(C*a^3 - C*a*b^2)*d*x - (C*a^2 + A*b^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^2*b - A*b^3)*log(sin(d*x + c) + 1) - (A*a^2*b - A*b^3)*log(-sin(d*x + c) + 1))/((a^3*b - a*b^3)*d), 1/2*(2*(C*a^3 - C*a*b^2)*d*x - 2*(C*a^2 + A*b^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (A*a^2*b - A*b^3)*log(sin(d*x + c) + 1) - (A*a^2*b - A*b^3)*log(-sin(d*x + c) + 1))/((a^3*b - a*b^3)*d)]","A",0
567,1,412,0,2.186046," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{{\left(C a^{2} + A b^{2}\right)} \sqrt{-a^{2} + b^{2}} \cos\left(d x + c\right) \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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} b - A b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{2} b - 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(C a^{2} + 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(A a^{2} b - A b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(A a^{2} b - 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*((C*a^2 + 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)) + (A*a^2*b - A*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) - (A*a^2*b - 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*(C*a^2 + 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) - (A*a^2*b - A*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) + (A*a^2*b - 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))]","A",0
568,1,535,0,7.397911," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(C a^{2} b + 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({\left(A + 2 \, C\right)} a^{4} + {\left(A - 2 \, C\right)} a^{2} b^{2} - 2 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(A + 2 \, C\right)} a^{4} + {\left(A - 2 \, C\right)} a^{2} b^{2} - 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(A a^{3} b - 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(C a^{2} b + 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({\left(A + 2 \, C\right)} a^{4} + {\left(A - 2 \, C\right)} a^{2} b^{2} - 2 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(A + 2 \, C\right)} a^{4} + {\left(A - 2 \, C\right)} a^{2} b^{2} - 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(A a^{3} b - 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*(C*a^2*b + 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 + 2*C)*a^4 + (A - 2*C)*a^2*b^2 - 2*A*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + ((A + 2*C)*a^4 + (A - 2*C)*a^2*b^2 - 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*(A*a^3*b - 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*(C*a^2*b + 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 + 2*C)*a^4 + (A - 2*C)*a^2*b^2 - 2*A*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + ((A + 2*C)*a^4 + (A - 2*C)*a^2*b^2 - 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*(A*a^3*b - A*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
569,1,633,0,6.374761," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(C a^{2} b^{2} + 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({\left(A + 2 \, C\right)} a^{4} b + {\left(A - 2 \, C\right)} a^{2} b^{3} - 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(A + 2 \, C\right)} a^{4} b + {\left(A - 2 \, C\right)} a^{2} b^{3} - 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({\left(2 \, A + 3 \, C\right)} a^{5} + {\left(A - 3 \, C\right)} a^{3} b^{2} - 3 \, A a b^{4}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(A a^{4} b - A a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(d x + c\right)^{3}}, \frac{12 \, {\left(C a^{2} b^{2} + 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({\left(A + 2 \, C\right)} a^{4} b + {\left(A - 2 \, C\right)} a^{2} b^{3} - 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(A + 2 \, C\right)} a^{4} b + {\left(A - 2 \, C\right)} a^{2} b^{3} - 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({\left(2 \, A + 3 \, C\right)} a^{5} + {\left(A - 3 \, C\right)} a^{3} b^{2} - 3 \, A a b^{4}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(A a^{4} b - A a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[-1/12*(6*(C*a^2*b^2 + 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*((A + 2*C)*a^4*b + (A - 2*C)*a^2*b^3 - 2*A*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*((A + 2*C)*a^4*b + (A - 2*C)*a^2*b^3 - 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 + 3*C)*a^5 + (A - 3*C)*a^3*b^2 - 3*A*a*b^4)*cos(d*x + c)^2 - 3*(A*a^4*b - A*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d*cos(d*x + c)^3), 1/12*(12*(C*a^2*b^2 + 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*((A + 2*C)*a^4*b + (A - 2*C)*a^2*b^3 - 2*A*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*((A + 2*C)*a^4*b + (A - 2*C)*a^2*b^3 - 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 + 3*C)*a^5 + (A - 3*C)*a^3*b^2 - 3*A*a*b^4)*cos(d*x + c)^2 - 3*(A*a^4*b - A*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d*cos(d*x + c)^3)]","A",0
570,1,985,0,1.448042," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(4 \, C a^{7} b + {\left(2 \, A - 7 \, C\right)} a^{5} b^{3} - 2 \, {\left(2 \, A - C\right)} a^{3} b^{5} + {\left(2 \, A + C\right)} a b^{7}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(4 \, C a^{8} + {\left(2 \, A - 7 \, C\right)} a^{6} b^{2} - 2 \, {\left(2 \, A - C\right)} a^{4} b^{4} + {\left(2 \, A + C\right)} a^{2} b^{6}\right)} d x + 3 \, {\left(4 \, C a^{7} + {\left(2 \, A - 5 \, C\right)} a^{5} b^{2} - 3 \, A a^{3} b^{4} + {\left(4 \, C a^{6} b + {\left(2 \, A - 5 \, C\right)} a^{4} b^{3} - 3 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{7} b + {\left(6 \, A - 19 \, C\right)} a^{5} b^{3} - {\left(9 \, A - 5 \, C\right)} a^{3} b^{5} + {\left(3 \, A + 2 \, C\right)} a b^{7} + {\left(C a^{4} b^{4} - 2 \, C a^{2} b^{6} + C b^{8}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(C a^{5} b^{3} - 2 \, C a^{3} b^{5} + C a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{6} b^{2} + {\left(3 \, A - 10 \, C\right)} a^{4} b^{4} - 2 \, {\left(3 \, A - C\right)} a^{2} b^{6} + {\left(3 \, A + 2 \, C\right)} b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d\right)}}, -\frac{3 \, {\left(4 \, C a^{7} b + {\left(2 \, A - 7 \, C\right)} a^{5} b^{3} - 2 \, {\left(2 \, A - C\right)} a^{3} b^{5} + {\left(2 \, A + C\right)} a b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(4 \, C a^{8} + {\left(2 \, A - 7 \, C\right)} a^{6} b^{2} - 2 \, {\left(2 \, A - C\right)} a^{4} b^{4} + {\left(2 \, A + C\right)} a^{2} b^{6}\right)} d x - 3 \, {\left(4 \, C a^{7} + {\left(2 \, A - 5 \, C\right)} a^{5} b^{2} - 3 \, A a^{3} b^{4} + {\left(4 \, C a^{6} b + {\left(2 \, A - 5 \, C\right)} a^{4} b^{3} - 3 \, A a^{2} b^{5}\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 \, C a^{7} b + {\left(6 \, A - 19 \, C\right)} a^{5} b^{3} - {\left(9 \, A - 5 \, C\right)} a^{3} b^{5} + {\left(3 \, A + 2 \, C\right)} a b^{7} + {\left(C a^{4} b^{4} - 2 \, C a^{2} b^{6} + C b^{8}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(C a^{5} b^{3} - 2 \, C a^{3} b^{5} + C a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{6} b^{2} + {\left(3 \, A - 10 \, C\right)} a^{4} b^{4} - 2 \, {\left(3 \, A - C\right)} a^{2} b^{6} + {\left(3 \, A + 2 \, C\right)} b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d\right)}}\right]"," ",0,"[-1/6*(6*(4*C*a^7*b + (2*A - 7*C)*a^5*b^3 - 2*(2*A - C)*a^3*b^5 + (2*A + C)*a*b^7)*d*x*cos(d*x + c) + 6*(4*C*a^8 + (2*A - 7*C)*a^6*b^2 - 2*(2*A - C)*a^4*b^4 + (2*A + C)*a^2*b^6)*d*x + 3*(4*C*a^7 + (2*A - 5*C)*a^5*b^2 - 3*A*a^3*b^4 + (4*C*a^6*b + (2*A - 5*C)*a^4*b^3 - 3*A*a^2*b^5)*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*C*a^7*b + (6*A - 19*C)*a^5*b^3 - (9*A - 5*C)*a^3*b^5 + (3*A + 2*C)*a*b^7 + (C*a^4*b^4 - 2*C*a^2*b^6 + C*b^8)*cos(d*x + c)^3 - 2*(C*a^5*b^3 - 2*C*a^3*b^5 + C*a*b^7)*cos(d*x + c)^2 + (6*C*a^6*b^2 + (3*A - 10*C)*a^4*b^4 - 2*(3*A - C)*a^2*b^6 + (3*A + 2*C)*b^8)*cos(d*x + c))*sin(d*x + c))/((a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c) + (a^5*b^5 - 2*a^3*b^7 + a*b^9)*d), -1/3*(3*(4*C*a^7*b + (2*A - 7*C)*a^5*b^3 - 2*(2*A - C)*a^3*b^5 + (2*A + C)*a*b^7)*d*x*cos(d*x + c) + 3*(4*C*a^8 + (2*A - 7*C)*a^6*b^2 - 2*(2*A - C)*a^4*b^4 + (2*A + C)*a^2*b^6)*d*x - 3*(4*C*a^7 + (2*A - 5*C)*a^5*b^2 - 3*A*a^3*b^4 + (4*C*a^6*b + (2*A - 5*C)*a^4*b^3 - 3*A*a^2*b^5)*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*C*a^7*b + (6*A - 19*C)*a^5*b^3 - (9*A - 5*C)*a^3*b^5 + (3*A + 2*C)*a*b^7 + (C*a^4*b^4 - 2*C*a^2*b^6 + C*b^8)*cos(d*x + c)^3 - 2*(C*a^5*b^3 - 2*C*a^3*b^5 + C*a*b^7)*cos(d*x + c)^2 + (6*C*a^6*b^2 + (3*A - 10*C)*a^4*b^4 - 2*(3*A - C)*a^2*b^6 + (3*A + 2*C)*b^8)*cos(d*x + c))*sin(d*x + c))/((a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c) + (a^5*b^5 - 2*a^3*b^7 + a*b^9)*d)]","A",0
571,1,809,0,0.808832," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(6 \, C a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{2} b^{5} + {\left(2 \, A + C\right)} b^{7}\right)} d x \cos\left(d x + c\right) + {\left(6 \, C a^{7} + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} - 4 \, {\left(A - C\right)} a^{3} b^{4} + {\left(2 \, A + C\right)} a b^{6}\right)} d x - {\left(3 \, C a^{6} + {\left(A - 4 \, C\right)} a^{4} b^{2} - 2 \, A a^{2} b^{4} + {\left(3 \, C a^{5} b + {\left(A - 4 \, C\right)} a^{3} b^{3} - 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\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 \, C a^{6} b + 2 \, {\left(A - 5 \, C\right)} a^{4} b^{3} - 2 \, {\left(A - 2 \, C\right)} a^{2} b^{5} - {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{5} b^{2} - 2 \, C a^{3} b^{4} + C a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{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 \, C a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{2} b^{5} + {\left(2 \, A + C\right)} b^{7}\right)} d x \cos\left(d x + c\right) + {\left(6 \, C a^{7} + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} - 4 \, {\left(A - C\right)} a^{3} b^{4} + {\left(2 \, A + C\right)} a b^{6}\right)} d x - 2 \, {\left(3 \, C a^{6} + {\left(A - 4 \, C\right)} a^{4} b^{2} - 2 \, A a^{2} b^{4} + {\left(3 \, C a^{5} b + {\left(A - 4 \, C\right)} a^{3} b^{3} - 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\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 \, C a^{6} b + 2 \, {\left(A - 5 \, C\right)} a^{4} b^{3} - 2 \, {\left(A - 2 \, C\right)} a^{2} b^{5} - {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{5} b^{2} - 2 \, C a^{3} b^{4} + C a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{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*C*a^6*b + (2*A - 11*C)*a^4*b^3 - 4*(A - C)*a^2*b^5 + (2*A + C)*b^7)*d*x*cos(d*x + c) + (6*C*a^7 + (2*A - 11*C)*a^5*b^2 - 4*(A - C)*a^3*b^4 + (2*A + C)*a*b^6)*d*x - (3*C*a^6 + (A - 4*C)*a^4*b^2 - 2*A*a^2*b^4 + (3*C*a^5*b + (A - 4*C)*a^3*b^3 - 2*A*a*b^5)*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*C*a^6*b + 2*(A - 5*C)*a^4*b^3 - 2*(A - 2*C)*a^2*b^5 - (C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7)*cos(d*x + c)^2 + 3*(C*a^5*b^2 - 2*C*a^3*b^4 + C*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^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*C*a^6*b + (2*A - 11*C)*a^4*b^3 - 4*(A - C)*a^2*b^5 + (2*A + C)*b^7)*d*x*cos(d*x + c) + (6*C*a^7 + (2*A - 11*C)*a^5*b^2 - 4*(A - C)*a^3*b^4 + (2*A + C)*a*b^6)*d*x - 2*(3*C*a^6 + (A - 4*C)*a^4*b^2 - 2*A*a^2*b^4 + (3*C*a^5*b + (A - 4*C)*a^3*b^3 - 2*A*a*b^5)*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*C*a^6*b + 2*(A - 5*C)*a^4*b^3 - 2*(A - 2*C)*a^2*b^5 - (C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7)*cos(d*x + c)^2 + 3*(C*a^5*b^2 - 2*C*a^3*b^4 + C*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^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
572,1,632,0,1.088572," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(C a^{5} b - 2 \, C a^{3} b^{3} + C a b^{5}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(C a^{6} - 2 \, C a^{4} b^{2} + C a^{2} b^{4}\right)} d x + {\left(2 \, C a^{5} - 3 \, C a^{3} b^{2} - A a b^{4} + {\left(2 \, C a^{4} b - 3 \, C a^{2} b^{3} - A b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{5} b + {\left(A - 3 \, C\right)} a^{3} b^{3} - {\left(A - C\right)} a b^{5} + {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C 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{2 \, {\left(C a^{5} b - 2 \, C a^{3} b^{3} + C a b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{6} - 2 \, C a^{4} b^{2} + C a^{2} b^{4}\right)} d x - {\left(2 \, C a^{5} - 3 \, C a^{3} b^{2} - A a b^{4} + {\left(2 \, C a^{4} b - 3 \, C a^{2} b^{3} - A b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, C a^{5} b + {\left(A - 3 \, C\right)} a^{3} b^{3} - {\left(A - C\right)} a b^{5} + {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C 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*(4*(C*a^5*b - 2*C*a^3*b^3 + C*a*b^5)*d*x*cos(d*x + c) + 4*(C*a^6 - 2*C*a^4*b^2 + C*a^2*b^4)*d*x + (2*C*a^5 - 3*C*a^3*b^2 - A*a*b^4 + (2*C*a^4*b - 3*C*a^2*b^3 - A*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*C*a^5*b + (A - 3*C)*a^3*b^3 - (A - C)*a*b^5 + (C*a^4*b^2 - 2*C*a^2*b^4 + C*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*(C*a^5*b - 2*C*a^3*b^3 + C*a*b^5)*d*x*cos(d*x + c) + 2*(C*a^6 - 2*C*a^4*b^2 + C*a^2*b^4)*d*x - (2*C*a^5 - 3*C*a^3*b^2 - A*a*b^4 + (2*C*a^4*b - 3*C*a^2*b^3 - A*b^5)*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*C*a^5*b + (A - 3*C)*a^3*b^3 - (A - C)*a*b^5 + (C*a^4*b^2 - 2*C*a^2*b^4 + C*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
573,1,534,0,0.914346," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} d x - {\left(C a^{4} - {\left(A + 2 \, C\right)} a^{2} b^{2} + {\left(C a^{3} b - {\left(A + 2 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(C a^{4} b + {\left(A - C\right)} a^{2} b^{3} - A b^{5}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5}\right)} d x \cos\left(d x + c\right) + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} d x - {\left(C a^{4} - {\left(A + 2 \, C\right)} a^{2} b^{2} + {\left(C a^{3} b - {\left(A + 2 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(C a^{4} b + {\left(A - C\right)} a^{2} b^{3} - A b^{5}\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*(C*a^4*b - 2*C*a^2*b^3 + C*b^5)*d*x*cos(d*x + c) + 2*(C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*d*x - (C*a^4 - (A + 2*C)*a^2*b^2 + (C*a^3*b - (A + 2*C)*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*(C*a^4*b + (A - C)*a^2*b^3 - A*b^5)*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), ((C*a^4*b - 2*C*a^2*b^3 + C*b^5)*d*x*cos(d*x + c) + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*d*x - (C*a^4 - (A + 2*C)*a^2*b^2 + (C*a^3*b - (A + 2*C)*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))) - (C*a^4*b + (A - C)*a^2*b^3 - A*b^5)*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)]","A",0
574,1,666,0,5.505530," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, A + C\right)} a^{3} b - A a b^{3} + {\left({\left(2 \, A + C\right)} 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(C a^{5} + {\left(A - C\right)} a^{3} b^{2} - A a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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({\left(2 \, A + C\right)} a^{3} b - A a b^{3} + {\left({\left(2 \, A + C\right)} 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(C a^{5} + {\left(A - C\right)} a^{3} b^{2} - A a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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*(((2*A + C)*a^3*b - A*a*b^3 + ((2*A + C)*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*(C*a^5 + (A - C)*a^3*b^2 - 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*((2*A + C)*a^3*b - A*a*b^3 + ((2*A + C)*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*(C*a^5 + (A - C)*a^3*b^2 - 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
575,1,842,0,9.090133," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(C a^{4} b + 3 \, A a^{2} b^{3} - 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{5} + 3 \, A a^{3} b^{2} - 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(A a^{4} b^{2} - 2 \, A a^{2} b^{4} + A b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{5} b - 2 \, A a^{3} b^{3} + A a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(A a^{4} b^{2} - 2 \, A a^{2} b^{4} + A b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{5} b - 2 \, A a^{3} b^{3} + 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({\left(A - C\right)} a^{5} b - {\left(3 \, A - C\right)} a^{3} b^{3} + 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{{\left({\left(C a^{4} b + 3 \, A a^{2} b^{3} - 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{5} + 3 \, A a^{3} b^{2} - 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left({\left(A a^{4} b^{2} - 2 \, A a^{2} b^{4} + A b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{5} b - 2 \, A a^{3} b^{3} + A a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(A a^{4} b^{2} - 2 \, A a^{2} b^{4} + A b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{5} b - 2 \, A a^{3} b^{3} + A a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(A a^{6} - 2 \, A a^{4} b^{2} + A a^{2} b^{4} + {\left({\left(A - C\right)} a^{5} b - {\left(3 \, A - C\right)} a^{3} b^{3} + 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\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]"," ",0,"[1/2*(((C*a^4*b + 3*A*a^2*b^3 - 2*A*b^5)*cos(d*x + c)^2 + (C*a^5 + 3*A*a^3*b^2 - 2*A*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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^4*b^2 - 2*A*a^2*b^4 + A*b^6)*cos(d*x + c)^2 + (A*a^5*b - 2*A*a^3*b^3 + A*a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + 2*((A*a^4*b^2 - 2*A*a^2*b^4 + A*b^6)*cos(d*x + c)^2 + (A*a^5*b - 2*A*a^3*b^3 + 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 - C)*a^5*b - (3*A - C)*a^3*b^3 + 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)), (((C*a^4*b + 3*A*a^2*b^3 - 2*A*b^5)*cos(d*x + c)^2 + (C*a^5 + 3*A*a^3*b^2 - 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))) - ((A*a^4*b^2 - 2*A*a^2*b^4 + A*b^6)*cos(d*x + c)^2 + (A*a^5*b - 2*A*a^3*b^3 + A*a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((A*a^4*b^2 - 2*A*a^2*b^4 + A*b^6)*cos(d*x + c)^2 + (A*a^5*b - 2*A*a^3*b^3 + A*a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (A*a^6 - 2*A*a^4*b^2 + A*a^2*b^4 + ((A - C)*a^5*b - (3*A - C)*a^3*b^3 + 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
576,1,1149,0,27.618752," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left({\left(2 \, C a^{4} b^{2} + {\left(4 \, A - C\right)} a^{2} b^{4} - 3 \, A b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, C a^{5} b + {\left(4 \, A - C\right)} a^{3} b^{3} - 3 \, A a b^{5}\right)} \cos\left(d x + c\right)^{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({\left(A + 2 \, C\right)} a^{6} b + 4 \, {\left(A - C\right)} a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{7} + 4 \, {\left(A - C\right)} a^{5} b^{2} - {\left(11 \, A - 2 \, C\right)} a^{3} b^{4} + 6 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left({\left(A + 2 \, C\right)} a^{6} b + 4 \, {\left(A - C\right)} a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{7} + 4 \, {\left(A - C\right)} a^{5} b^{2} - {\left(11 \, A - 2 \, C\right)} a^{3} b^{4} + 6 \, A a b^{6}\right)} \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({\left(2 \, A - C\right)} a^{5} b^{2} - {\left(5 \, A - C\right)} a^{3} b^{4} + 3 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(A a^{6} b - 2 \, A a^{4} b^{3} + A a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{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(2 \, C a^{4} b^{2} + {\left(4 \, A - C\right)} a^{2} b^{4} - 3 \, A b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, C a^{5} b + {\left(4 \, A - C\right)} a^{3} b^{3} - 3 \, A a b^{5}\right)} \cos\left(d x + c\right)^{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({\left(A + 2 \, C\right)} a^{6} b + 4 \, {\left(A - C\right)} a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{7} + 4 \, {\left(A - C\right)} a^{5} b^{2} - {\left(11 \, A - 2 \, C\right)} a^{3} b^{4} + 6 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left({\left(A + 2 \, C\right)} a^{6} b + 4 \, {\left(A - C\right)} a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{7} + 4 \, {\left(A - C\right)} a^{5} b^{2} - {\left(11 \, A - 2 \, C\right)} a^{3} b^{4} + 6 \, A a b^{6}\right)} \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({\left(2 \, A - C\right)} a^{5} b^{2} - {\left(5 \, A - C\right)} a^{3} b^{4} + 3 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(A a^{6} b - 2 \, A a^{4} b^{3} + A a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{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*((2*C*a^4*b^2 + (4*A - C)*a^2*b^4 - 3*A*b^6)*cos(d*x + c)^3 + (2*C*a^5*b + (4*A - C)*a^3*b^3 - 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 + 2*C)*a^6*b + 4*(A - C)*a^4*b^3 - (11*A - 2*C)*a^2*b^5 + 6*A*b^7)*cos(d*x + c)^3 + ((A + 2*C)*a^7 + 4*(A - C)*a^5*b^2 - (11*A - 2*C)*a^3*b^4 + 6*A*a*b^6)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + (((A + 2*C)*a^6*b + 4*(A - C)*a^4*b^3 - (11*A - 2*C)*a^2*b^5 + 6*A*b^7)*cos(d*x + c)^3 + ((A + 2*C)*a^7 + 4*(A - C)*a^5*b^2 - (11*A - 2*C)*a^3*b^4 + 6*A*a*b^6)*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*((2*A - C)*a^5*b^2 - (5*A - C)*a^3*b^4 + 3*A*a*b^6)*cos(d*x + c)^2 - 3*(A*a^6*b - 2*A*a^4*b^3 + A*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^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*((2*C*a^4*b^2 + (4*A - C)*a^2*b^4 - 3*A*b^6)*cos(d*x + c)^3 + (2*C*a^5*b + (4*A - C)*a^3*b^3 - 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 + 2*C)*a^6*b + 4*(A - C)*a^4*b^3 - (11*A - 2*C)*a^2*b^5 + 6*A*b^7)*cos(d*x + c)^3 + ((A + 2*C)*a^7 + 4*(A - C)*a^5*b^2 - (11*A - 2*C)*a^3*b^4 + 6*A*a*b^6)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + (((A + 2*C)*a^6*b + 4*(A - C)*a^4*b^3 - (11*A - 2*C)*a^2*b^5 + 6*A*b^7)*cos(d*x + c)^3 + ((A + 2*C)*a^7 + 4*(A - C)*a^5*b^2 - (11*A - 2*C)*a^3*b^4 + 6*A*a*b^6)*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*((2*A - C)*a^5*b^2 - (5*A - C)*a^3*b^4 + 3*A*a*b^6)*cos(d*x + c)^2 - 3*(A*a^6*b - 2*A*a^4*b^3 + A*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^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
577,1,1305,0,18.534348," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(3 \, C a^{4} b^{3} + {\left(5 \, A - 2 \, C\right)} a^{2} b^{5} - 4 \, A b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, C a^{5} b^{2} + {\left(5 \, A - 2 \, C\right)} a^{3} b^{4} - 4 \, A a b^{6}\right)} \cos\left(d x + c\right)^{3}\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) + 3 \, {\left({\left({\left(A + 2 \, C\right)} a^{6} b^{2} + 2 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 4 \, A b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left({\left(A + 2 \, C\right)} a^{7} b + 2 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - {\left(7 \, A - 2 \, C\right)} a^{3} b^{5} + 4 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left({\left(A + 2 \, C\right)} a^{6} b^{2} + 2 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 4 \, A b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left({\left(A + 2 \, C\right)} a^{7} b + 2 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - {\left(7 \, A - 2 \, C\right)} a^{3} b^{5} + 4 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A a^{8} - 2 \, A a^{6} b^{2} + A a^{4} b^{4} + {\left({\left(2 \, A + 3 \, C\right)} a^{7} b + {\left(5 \, A - 9 \, C\right)} a^{5} b^{3} - {\left(19 \, A - 6 \, C\right)} a^{3} b^{5} + 12 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(2 \, A + 3 \, C\right)} a^{8} + 2 \, {\left(A - 3 \, C\right)} a^{6} b^{2} - {\left(10 \, A - 3 \, C\right)} a^{4} b^{4} + 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(A a^{7} b - 2 \, A a^{5} b^{3} + A a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{3}\right)}}, \frac{6 \, {\left({\left(3 \, C a^{4} b^{3} + {\left(5 \, A - 2 \, C\right)} a^{2} b^{5} - 4 \, A b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, C a^{5} b^{2} + {\left(5 \, A - 2 \, C\right)} a^{3} b^{4} - 4 \, A a b^{6}\right)} \cos\left(d x + c\right)^{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) - 3 \, {\left({\left({\left(A + 2 \, C\right)} a^{6} b^{2} + 2 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 4 \, A b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left({\left(A + 2 \, C\right)} a^{7} b + 2 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - {\left(7 \, A - 2 \, C\right)} a^{3} b^{5} + 4 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left({\left(A + 2 \, C\right)} a^{6} b^{2} + 2 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 4 \, A b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left({\left(A + 2 \, C\right)} a^{7} b + 2 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - {\left(7 \, A - 2 \, C\right)} a^{3} b^{5} + 4 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{8} - 2 \, A a^{6} b^{2} + A a^{4} b^{4} + {\left({\left(2 \, A + 3 \, C\right)} a^{7} b + {\left(5 \, A - 9 \, C\right)} a^{5} b^{3} - {\left(19 \, A - 6 \, C\right)} a^{3} b^{5} + 12 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(2 \, A + 3 \, C\right)} a^{8} + 2 \, {\left(A - 3 \, C\right)} a^{6} b^{2} - {\left(10 \, A - 3 \, C\right)} a^{4} b^{4} + 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(A a^{7} b - 2 \, A a^{5} b^{3} + A a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[-1/6*(3*((3*C*a^4*b^3 + (5*A - 2*C)*a^2*b^5 - 4*A*b^7)*cos(d*x + c)^4 + (3*C*a^5*b^2 + (5*A - 2*C)*a^3*b^4 - 4*A*a*b^6)*cos(d*x + c)^3)*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)) + 3*(((A + 2*C)*a^6*b^2 + 2*(A - 2*C)*a^4*b^4 - (7*A - 2*C)*a^2*b^6 + 4*A*b^8)*cos(d*x + c)^4 + ((A + 2*C)*a^7*b + 2*(A - 2*C)*a^5*b^3 - (7*A - 2*C)*a^3*b^5 + 4*A*a*b^7)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*(((A + 2*C)*a^6*b^2 + 2*(A - 2*C)*a^4*b^4 - (7*A - 2*C)*a^2*b^6 + 4*A*b^8)*cos(d*x + c)^4 + ((A + 2*C)*a^7*b + 2*(A - 2*C)*a^5*b^3 - (7*A - 2*C)*a^3*b^5 + 4*A*a*b^7)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(A*a^8 - 2*A*a^6*b^2 + A*a^4*b^4 + ((2*A + 3*C)*a^7*b + (5*A - 9*C)*a^5*b^3 - (19*A - 6*C)*a^3*b^5 + 12*A*a*b^7)*cos(d*x + c)^3 + ((2*A + 3*C)*a^8 + 2*(A - 3*C)*a^6*b^2 - (10*A - 3*C)*a^4*b^4 + 6*A*a^2*b^6)*cos(d*x + c)^2 - 2*(A*a^7*b - 2*A*a^5*b^3 + A*a^3*b^5)*cos(d*x + c))*sin(d*x + c))/((a^9*b - 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^4 + (a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c)^3), 1/6*(6*((3*C*a^4*b^3 + (5*A - 2*C)*a^2*b^5 - 4*A*b^7)*cos(d*x + c)^4 + (3*C*a^5*b^2 + (5*A - 2*C)*a^3*b^4 - 4*A*a*b^6)*cos(d*x + c)^3)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*(((A + 2*C)*a^6*b^2 + 2*(A - 2*C)*a^4*b^4 - (7*A - 2*C)*a^2*b^6 + 4*A*b^8)*cos(d*x + c)^4 + ((A + 2*C)*a^7*b + 2*(A - 2*C)*a^5*b^3 - (7*A - 2*C)*a^3*b^5 + 4*A*a*b^7)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) + 3*(((A + 2*C)*a^6*b^2 + 2*(A - 2*C)*a^4*b^4 - (7*A - 2*C)*a^2*b^6 + 4*A*b^8)*cos(d*x + c)^4 + ((A + 2*C)*a^7*b + 2*(A - 2*C)*a^5*b^3 - (7*A - 2*C)*a^3*b^5 + 4*A*a*b^7)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) + 2*(A*a^8 - 2*A*a^6*b^2 + A*a^4*b^4 + ((2*A + 3*C)*a^7*b + (5*A - 9*C)*a^5*b^3 - (19*A - 6*C)*a^3*b^5 + 12*A*a*b^7)*cos(d*x + c)^3 + ((2*A + 3*C)*a^8 + 2*(A - 3*C)*a^6*b^2 - (10*A - 3*C)*a^4*b^4 + 6*A*a^2*b^6)*cos(d*x + c)^2 - 2*(A*a^7*b - 2*A*a^5*b^3 + A*a^3*b^5)*cos(d*x + c))*sin(d*x + c))/((a^9*b - 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^4 + (a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c)^3)]","A",0
578,1,1535,0,1.005137," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(12 \, C a^{8} b^{2} + {\left(2 \, A - 35 \, C\right)} a^{6} b^{4} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{4} b^{6} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{2} b^{8} - {\left(2 \, A + C\right)} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(12 \, C a^{9} b + {\left(2 \, A - 35 \, C\right)} a^{7} b^{3} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{5} b^{5} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{3} b^{7} - {\left(2 \, A + C\right)} a b^{9}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(12 \, C a^{10} + {\left(2 \, A - 35 \, C\right)} a^{8} b^{2} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{6} b^{4} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{4} b^{6} - {\left(2 \, A + C\right)} a^{2} b^{8}\right)} d x - {\left(12 \, C a^{9} + {\left(2 \, A - 29 \, C\right)} a^{7} b^{2} - 5 \, {\left(A - 4 \, C\right)} a^{5} b^{4} + 6 \, A a^{3} b^{6} + {\left(12 \, C a^{7} b^{2} + {\left(2 \, A - 29 \, C\right)} a^{5} b^{4} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} + 6 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, C a^{8} b + {\left(2 \, A - 29 \, C\right)} a^{6} b^{3} - 5 \, {\left(A - 4 \, C\right)} a^{4} b^{5} + 6 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\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 \, C a^{9} b + {\left(2 \, A - 33 \, C\right)} a^{7} b^{3} - {\left(7 \, A - 27 \, C\right)} a^{5} b^{5} + {\left(5 \, A - 6 \, C\right)} a^{3} b^{7} - {\left(C a^{6} b^{4} - 3 \, C a^{4} b^{6} + 3 \, C a^{2} b^{8} - C b^{10}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(C a^{7} b^{3} - 3 \, C a^{5} b^{5} + 3 \, C a^{3} b^{7} - C a b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, C a^{8} b^{2} + {\left(3 \, A - 50 \, C\right)} a^{6} b^{4} - {\left(9 \, A - 43 \, C\right)} a^{4} b^{6} + {\left(6 \, A - 11 \, C\right)} a^{2} b^{8}\right)} \cos\left(d x + c\right)\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 \, C a^{8} b^{2} + {\left(2 \, A - 35 \, C\right)} a^{6} b^{4} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{4} b^{6} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{2} b^{8} - {\left(2 \, A + C\right)} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, C a^{9} b + {\left(2 \, A - 35 \, C\right)} a^{7} b^{3} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{5} b^{5} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{3} b^{7} - {\left(2 \, A + C\right)} a b^{9}\right)} d x \cos\left(d x + c\right) + {\left(12 \, C a^{10} + {\left(2 \, A - 35 \, C\right)} a^{8} b^{2} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{6} b^{4} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{4} b^{6} - {\left(2 \, A + C\right)} a^{2} b^{8}\right)} d x - {\left(12 \, C a^{9} + {\left(2 \, A - 29 \, C\right)} a^{7} b^{2} - 5 \, {\left(A - 4 \, C\right)} a^{5} b^{4} + 6 \, A a^{3} b^{6} + {\left(12 \, C a^{7} b^{2} + {\left(2 \, A - 29 \, C\right)} a^{5} b^{4} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} + 6 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, C a^{8} b + {\left(2 \, A - 29 \, C\right)} a^{6} b^{3} - 5 \, {\left(A - 4 \, C\right)} a^{4} b^{5} + 6 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\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 \, C a^{9} b + {\left(2 \, A - 33 \, C\right)} a^{7} b^{3} - {\left(7 \, A - 27 \, C\right)} a^{5} b^{5} + {\left(5 \, A - 6 \, C\right)} a^{3} b^{7} - {\left(C a^{6} b^{4} - 3 \, C a^{4} b^{6} + 3 \, C a^{2} b^{8} - C b^{10}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(C a^{7} b^{3} - 3 \, C a^{5} b^{5} + 3 \, C a^{3} b^{7} - C a b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, C a^{8} b^{2} + {\left(3 \, A - 50 \, C\right)} a^{6} b^{4} - {\left(9 \, A - 43 \, C\right)} a^{4} b^{6} + {\left(6 \, A - 11 \, C\right)} a^{2} b^{8}\right)} \cos\left(d x + c\right)\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*C*a^8*b^2 + (2*A - 35*C)*a^6*b^4 - 3*(2*A - 11*C)*a^4*b^6 + 3*(2*A - 3*C)*a^2*b^8 - (2*A + C)*b^10)*d*x*cos(d*x + c)^2 + 4*(12*C*a^9*b + (2*A - 35*C)*a^7*b^3 - 3*(2*A - 11*C)*a^5*b^5 + 3*(2*A - 3*C)*a^3*b^7 - (2*A + C)*a*b^9)*d*x*cos(d*x + c) + 2*(12*C*a^10 + (2*A - 35*C)*a^8*b^2 - 3*(2*A - 11*C)*a^6*b^4 + 3*(2*A - 3*C)*a^4*b^6 - (2*A + C)*a^2*b^8)*d*x - (12*C*a^9 + (2*A - 29*C)*a^7*b^2 - 5*(A - 4*C)*a^5*b^4 + 6*A*a^3*b^6 + (12*C*a^7*b^2 + (2*A - 29*C)*a^5*b^4 - 5*(A - 4*C)*a^3*b^6 + 6*A*a*b^8)*cos(d*x + c)^2 + 2*(12*C*a^8*b + (2*A - 29*C)*a^6*b^3 - 5*(A - 4*C)*a^4*b^5 + 6*A*a^2*b^7)*cos(d*x + c))*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*C*a^9*b + (2*A - 33*C)*a^7*b^3 - (7*A - 27*C)*a^5*b^5 + (5*A - 6*C)*a^3*b^7 - (C*a^6*b^4 - 3*C*a^4*b^6 + 3*C*a^2*b^8 - C*b^10)*cos(d*x + c)^3 + 4*(C*a^7*b^3 - 3*C*a^5*b^5 + 3*C*a^3*b^7 - C*a*b^9)*cos(d*x + c)^2 + (18*C*a^8*b^2 + (3*A - 50*C)*a^6*b^4 - (9*A - 43*C)*a^4*b^6 + (6*A - 11*C)*a^2*b^8)*cos(d*x + c))*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*C*a^8*b^2 + (2*A - 35*C)*a^6*b^4 - 3*(2*A - 11*C)*a^4*b^6 + 3*(2*A - 3*C)*a^2*b^8 - (2*A + C)*b^10)*d*x*cos(d*x + c)^2 + 2*(12*C*a^9*b + (2*A - 35*C)*a^7*b^3 - 3*(2*A - 11*C)*a^5*b^5 + 3*(2*A - 3*C)*a^3*b^7 - (2*A + C)*a*b^9)*d*x*cos(d*x + c) + (12*C*a^10 + (2*A - 35*C)*a^8*b^2 - 3*(2*A - 11*C)*a^6*b^4 + 3*(2*A - 3*C)*a^4*b^6 - (2*A + C)*a^2*b^8)*d*x - (12*C*a^9 + (2*A - 29*C)*a^7*b^2 - 5*(A - 4*C)*a^5*b^4 + 6*A*a^3*b^6 + (12*C*a^7*b^2 + (2*A - 29*C)*a^5*b^4 - 5*(A - 4*C)*a^3*b^6 + 6*A*a*b^8)*cos(d*x + c)^2 + 2*(12*C*a^8*b + (2*A - 29*C)*a^6*b^3 - 5*(A - 4*C)*a^4*b^5 + 6*A*a^2*b^7)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (12*C*a^9*b + (2*A - 33*C)*a^7*b^3 - (7*A - 27*C)*a^5*b^5 + (5*A - 6*C)*a^3*b^7 - (C*a^6*b^4 - 3*C*a^4*b^6 + 3*C*a^2*b^8 - C*b^10)*cos(d*x + c)^3 + 4*(C*a^7*b^3 - 3*C*a^5*b^5 + 3*C*a^3*b^7 - C*a*b^9)*cos(d*x + c)^2 + (18*C*a^8*b^2 + (3*A - 50*C)*a^6*b^4 - (9*A - 43*C)*a^4*b^6 + (6*A - 11*C)*a^2*b^8)*cos(d*x + c))*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
579,1,1202,0,3.451389," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(C a^{7} b^{2} - 3 \, C a^{5} b^{4} + 3 \, C a^{3} b^{6} - C a b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 24 \, {\left(C a^{8} b - 3 \, C a^{6} b^{3} + 3 \, C a^{4} b^{5} - C a^{2} b^{7}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(C a^{9} - 3 \, C a^{7} b^{2} + 3 \, C a^{5} b^{4} - C a^{3} b^{6}\right)} d x + {\left(6 \, C a^{8} - 15 \, C a^{6} b^{2} + {\left(A + 12 \, C\right)} a^{4} b^{4} + 2 \, A a^{2} b^{6} + {\left(6 \, C a^{6} b^{2} - 15 \, C a^{4} b^{4} + {\left(A + 12 \, C\right)} a^{2} b^{6} + 2 \, A b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, C a^{7} b - 15 \, C a^{5} b^{3} + {\left(A + 12 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7}\right)} \cos\left(d x + c\right)\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 \, C a^{8} b - 17 \, C a^{6} b^{3} - {\left(3 \, A - 13 \, C\right)} a^{4} b^{5} + {\left(3 \, A - 2 \, C\right)} a^{2} b^{7} + 2 \, {\left(C a^{6} b^{3} - 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} - C b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} + {\left(A - 25 \, C\right)} a^{5} b^{4} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} + 4 \, {\left(A - C\right)} a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{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{6 \, {\left(C a^{7} b^{2} - 3 \, C a^{5} b^{4} + 3 \, C a^{3} b^{6} - C a b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 12 \, {\left(C a^{8} b - 3 \, C a^{6} b^{3} + 3 \, C a^{4} b^{5} - C a^{2} b^{7}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(C a^{9} - 3 \, C a^{7} b^{2} + 3 \, C a^{5} b^{4} - C a^{3} b^{6}\right)} d x - {\left(6 \, C a^{8} - 15 \, C a^{6} b^{2} + {\left(A + 12 \, C\right)} a^{4} b^{4} + 2 \, A a^{2} b^{6} + {\left(6 \, C a^{6} b^{2} - 15 \, C a^{4} b^{4} + {\left(A + 12 \, C\right)} a^{2} b^{6} + 2 \, A b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, C a^{7} b - 15 \, C a^{5} b^{3} + {\left(A + 12 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7}\right)} \cos\left(d x + c\right)\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 \, C a^{8} b - 17 \, C a^{6} b^{3} - {\left(3 \, A - 13 \, C\right)} a^{4} b^{5} + {\left(3 \, A - 2 \, C\right)} a^{2} b^{7} + 2 \, {\left(C a^{6} b^{3} - 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} - C b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} + {\left(A - 25 \, C\right)} a^{5} b^{4} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} + 4 \, {\left(A - C\right)} a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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*(12*(C*a^7*b^2 - 3*C*a^5*b^4 + 3*C*a^3*b^6 - C*a*b^8)*d*x*cos(d*x + c)^2 + 24*(C*a^8*b - 3*C*a^6*b^3 + 3*C*a^4*b^5 - C*a^2*b^7)*d*x*cos(d*x + c) + 12*(C*a^9 - 3*C*a^7*b^2 + 3*C*a^5*b^4 - C*a^3*b^6)*d*x + (6*C*a^8 - 15*C*a^6*b^2 + (A + 12*C)*a^4*b^4 + 2*A*a^2*b^6 + (6*C*a^6*b^2 - 15*C*a^4*b^4 + (A + 12*C)*a^2*b^6 + 2*A*b^8)*cos(d*x + c)^2 + 2*(6*C*a^7*b - 15*C*a^5*b^3 + (A + 12*C)*a^3*b^5 + 2*A*a*b^7)*cos(d*x + c))*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*C*a^8*b - 17*C*a^6*b^3 - (3*A - 13*C)*a^4*b^5 + (3*A - 2*C)*a^2*b^7 + 2*(C*a^6*b^3 - 3*C*a^4*b^5 + 3*C*a^2*b^7 - C*b^9)*cos(d*x + c)^2 + (9*C*a^7*b^2 + (A - 25*C)*a^5*b^4 - 5*(A - 4*C)*a^3*b^6 + 4*(A - C)*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^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*(6*(C*a^7*b^2 - 3*C*a^5*b^4 + 3*C*a^3*b^6 - C*a*b^8)*d*x*cos(d*x + c)^2 + 12*(C*a^8*b - 3*C*a^6*b^3 + 3*C*a^4*b^5 - C*a^2*b^7)*d*x*cos(d*x + c) + 6*(C*a^9 - 3*C*a^7*b^2 + 3*C*a^5*b^4 - C*a^3*b^6)*d*x - (6*C*a^8 - 15*C*a^6*b^2 + (A + 12*C)*a^4*b^4 + 2*A*a^2*b^6 + (6*C*a^6*b^2 - 15*C*a^4*b^4 + (A + 12*C)*a^2*b^6 + 2*A*b^8)*cos(d*x + c)^2 + 2*(6*C*a^7*b - 15*C*a^5*b^3 + (A + 12*C)*a^3*b^5 + 2*A*a*b^7)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*C*a^8*b - 17*C*a^6*b^3 - (3*A - 13*C)*a^4*b^5 + (3*A - 2*C)*a^2*b^7 + 2*(C*a^6*b^3 - 3*C*a^4*b^5 + 3*C*a^2*b^7 - C*b^9)*cos(d*x + c)^2 + (9*C*a^7*b^2 + (A - 25*C)*a^5*b^4 - 5*(A - 4*C)*a^3*b^6 + 4*(A - C)*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^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
580,1,1051,0,1.245215," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} d x - {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} + 3 \, {\left(A + 2 \, C\right)} a^{3} b^{4} + {\left(2 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} + 3 \, {\left(A + 2 \, C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} + 3 \, {\left(A + 2 \, C\right)} a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{7} b - {\left(2 \, A + 7 \, C\right)} a^{5} b^{3} + {\left(A + 5 \, C\right)} a^{3} b^{5} + A a b^{7} + {\left(3 \, C a^{6} b^{2} - {\left(A + 9 \, C\right)} a^{4} b^{4} - {\left(A - 6 \, C\right)} a^{2} b^{6} + 2 \, A b^{8}\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(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} d x - {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} + 3 \, {\left(A + 2 \, C\right)} a^{3} b^{4} + {\left(2 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} + 3 \, {\left(A + 2 \, C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} + 3 \, {\left(A + 2 \, C\right)} a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, C a^{7} b - {\left(2 \, A + 7 \, C\right)} a^{5} b^{3} + {\left(A + 5 \, C\right)} a^{3} b^{5} + A a b^{7} + {\left(3 \, C a^{6} b^{2} - {\left(A + 9 \, C\right)} a^{4} b^{4} - {\left(A - 6 \, C\right)} a^{2} b^{6} + 2 \, A b^{8}\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*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8)*d*x*cos(d*x + c)^2 + 8*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*d*x*cos(d*x + c) + 4*(C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*d*x - (2*C*a^7 - 5*C*a^5*b^2 + 3*(A + 2*C)*a^3*b^4 + (2*C*a^5*b^2 - 5*C*a^3*b^4 + 3*(A + 2*C)*a*b^6)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 + 3*(A + 2*C)*a^2*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*C*a^7*b - (2*A + 7*C)*a^5*b^3 + (A + 5*C)*a^3*b^5 + A*a*b^7 + (3*C*a^6*b^2 - (A + 9*C)*a^4*b^4 - (A - 6*C)*a^2*b^6 + 2*A*b^8)*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*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8)*d*x*cos(d*x + c)^2 + 4*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*d*x*cos(d*x + c) + 2*(C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*d*x - (2*C*a^7 - 5*C*a^5*b^2 + 3*(A + 2*C)*a^3*b^4 + (2*C*a^5*b^2 - 5*C*a^3*b^4 + 3*(A + 2*C)*a*b^6)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 + 3*(A + 2*C)*a^2*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*C*a^7*b - (2*A + 7*C)*a^5*b^3 + (A + 5*C)*a^3*b^5 + A*a*b^7 + (3*C*a^6*b^2 - (A + 9*C)*a^4*b^4 - (A - 6*C)*a^2*b^6 + 2*A*b^8)*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
581,1,709,0,1.168661," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, A + C\right)} a^{4} + {\left(A + 2 \, C\right)} a^{2} b^{2} + {\left({\left(2 \, A + C\right)} a^{2} b^{2} + {\left(A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, A + C\right)} a^{3} b + {\left(A + 2 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(4 \, A + 3 \, C\right)} a^{4} b - {\left(5 \, A + 3 \, C\right)} a^{2} b^{3} + A b^{5} - {\left(C a^{5} - {\left(3 \, A + 5 \, C\right)} a^{3} b^{2} + {\left(3 \, A + 4 \, C\right)} a b^{4}\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({\left(2 \, A + C\right)} a^{4} + {\left(A + 2 \, C\right)} a^{2} b^{2} + {\left({\left(2 \, A + C\right)} a^{2} b^{2} + {\left(A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, A + C\right)} a^{3} b + {\left(A + 2 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left({\left(4 \, A + 3 \, C\right)} a^{4} b - {\left(5 \, A + 3 \, C\right)} a^{2} b^{3} + A b^{5} - {\left(C a^{5} - {\left(3 \, A + 5 \, C\right)} a^{3} b^{2} + {\left(3 \, A + 4 \, C\right)} a b^{4}\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 + C)*a^4 + (A + 2*C)*a^2*b^2 + ((2*A + C)*a^2*b^2 + (A + 2*C)*b^4)*cos(d*x + c)^2 + 2*((2*A + C)*a^3*b + (A + 2*C)*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*A + 3*C)*a^4*b - (5*A + 3*C)*a^2*b^3 + A*b^5 - (C*a^5 - (3*A + 5*C)*a^3*b^2 + (3*A + 4*C)*a*b^4)*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 + C)*a^4 + (A + 2*C)*a^2*b^2 + ((2*A + C)*a^2*b^2 + (A + 2*C)*b^4)*cos(d*x + c)^2 + 2*((2*A + C)*a^3*b + (A + 2*C)*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - ((4*A + 3*C)*a^4*b - (5*A + 3*C)*a^2*b^3 + A*b^5 - (C*a^5 - (3*A + 5*C)*a^3*b^2 + (3*A + 4*C)*a*b^4)*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)]","A",0
582,1,1308,0,18.909052," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, {\left(2 \, A + C\right)} a^{6} b - 5 \, A a^{4} b^{3} + 2 \, A a^{2} b^{5} + {\left(3 \, {\left(2 \, A + C\right)} a^{4} b^{3} - 5 \, A a^{2} b^{5} + 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, A + C\right)} a^{5} b^{2} - 5 \, A a^{3} b^{4} + 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(2 \, C a^{8} + {\left(6 \, A - C\right)} a^{6} b^{2} - {\left(9 \, A + C\right)} a^{4} b^{4} + 3 \, A a^{2} b^{6} + {\left(C a^{7} b + {\left(5 \, A + C\right)} a^{5} b^{3} - {\left(7 \, A + 2 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7}\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(3 \, {\left(2 \, A + C\right)} a^{6} b - 5 \, A a^{4} b^{3} + 2 \, A a^{2} b^{5} + {\left(3 \, {\left(2 \, A + C\right)} a^{4} b^{3} - 5 \, A a^{2} b^{5} + 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, A + C\right)} a^{5} b^{2} - 5 \, A a^{3} b^{4} + 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{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(2 \, C a^{8} + {\left(6 \, A - C\right)} a^{6} b^{2} - {\left(9 \, A + C\right)} a^{4} b^{4} + 3 \, A a^{2} b^{6} + {\left(C a^{7} b + {\left(5 \, A + C\right)} a^{5} b^{3} - {\left(7 \, A + 2 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7}\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*((3*(2*A + C)*a^6*b - 5*A*a^4*b^3 + 2*A*a^2*b^5 + (3*(2*A + C)*a^4*b^3 - 5*A*a^2*b^5 + 2*A*b^7)*cos(d*x + c)^2 + 2*(3*(2*A + C)*a^5*b^2 - 5*A*a^3*b^4 + 2*A*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*(2*C*a^8 + (6*A - C)*a^6*b^2 - (9*A + C)*a^4*b^4 + 3*A*a^2*b^6 + (C*a^7*b + (5*A + C)*a^5*b^3 - (7*A + 2*C)*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*((3*(2*A + C)*a^6*b - 5*A*a^4*b^3 + 2*A*a^2*b^5 + (3*(2*A + C)*a^4*b^3 - 5*A*a^2*b^5 + 2*A*b^7)*cos(d*x + c)^2 + 2*(3*(2*A + C)*a^5*b^2 - 5*A*a^3*b^4 + 2*A*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(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) - (2*C*a^8 + (6*A - C)*a^6*b^2 - (9*A + C)*a^4*b^4 + 3*A*a^2*b^6 + (C*a^7*b + (5*A + C)*a^5*b^3 - (7*A + 2*C)*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
583,1,1548,0,29.737701," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, C a^{6} b^{2} + {\left(12 \, A + C\right)} a^{4} b^{4} - 15 \, A a^{2} b^{6} + 6 \, A b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, C a^{7} b + {\left(12 \, A + C\right)} a^{5} b^{3} - 15 \, A a^{3} b^{5} + 6 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{8} + {\left(12 \, A + C\right)} a^{6} b^{2} - 15 \, A a^{4} b^{4} + 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\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({\left(A a^{6} b^{3} - 3 \, A a^{4} b^{5} + 3 \, A a^{2} b^{7} - A b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(A a^{7} b^{2} - 3 \, A a^{5} b^{4} + 3 \, A a^{3} b^{6} - A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{8} b - 3 \, A a^{6} b^{3} + 3 \, A a^{4} b^{5} - A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left({\left(A a^{6} b^{3} - 3 \, A a^{4} b^{5} + 3 \, A a^{2} b^{7} - A b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(A a^{7} b^{2} - 3 \, A a^{5} b^{4} + 3 \, A a^{3} b^{6} - A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{8} b - 3 \, A a^{6} b^{3} + 3 \, A a^{4} b^{5} - 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({\left(2 \, A - 3 \, C\right)} a^{7} b^{2} - {\left(13 \, A - 3 \, C\right)} a^{5} b^{4} + 17 \, A a^{3} b^{6} - 6 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, {\left(A - C\right)} a^{8} b - 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} + {\left(25 \, A - C\right)} a^{4} b^{5} - 9 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{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(2 \, C a^{6} b^{2} + {\left(12 \, A + C\right)} a^{4} b^{4} - 15 \, A a^{2} b^{6} + 6 \, A b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, C a^{7} b + {\left(12 \, A + C\right)} a^{5} b^{3} - 15 \, A a^{3} b^{5} + 6 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{8} + {\left(12 \, A + C\right)} a^{6} b^{2} - 15 \, A a^{4} b^{4} + 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\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({\left(A a^{6} b^{3} - 3 \, A a^{4} b^{5} + 3 \, A a^{2} b^{7} - A b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(A a^{7} b^{2} - 3 \, A a^{5} b^{4} + 3 \, A a^{3} b^{6} - A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{8} b - 3 \, A a^{6} b^{3} + 3 \, A a^{4} b^{5} - A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(A a^{6} b^{3} - 3 \, A a^{4} b^{5} + 3 \, A a^{2} b^{7} - A b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(A a^{7} b^{2} - 3 \, A a^{5} b^{4} + 3 \, A a^{3} b^{6} - A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{8} b - 3 \, A a^{6} b^{3} + 3 \, A a^{4} b^{5} - 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({\left(2 \, A - 3 \, C\right)} a^{7} b^{2} - {\left(13 \, A - 3 \, C\right)} a^{5} b^{4} + 17 \, A a^{3} b^{6} - 6 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, {\left(A - C\right)} a^{8} b - 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} + {\left(25 \, A - C\right)} a^{4} b^{5} - 9 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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*(((2*C*a^6*b^2 + (12*A + C)*a^4*b^4 - 15*A*a^2*b^6 + 6*A*b^8)*cos(d*x + c)^3 + 2*(2*C*a^7*b + (12*A + C)*a^5*b^3 - 15*A*a^3*b^5 + 6*A*a*b^7)*cos(d*x + c)^2 + (2*C*a^8 + (12*A + C)*a^6*b^2 - 15*A*a^4*b^4 + 6*A*a^2*b^6)*cos(d*x + c))*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^6*b^3 - 3*A*a^4*b^5 + 3*A*a^2*b^7 - A*b^9)*cos(d*x + c)^3 + 2*(A*a^7*b^2 - 3*A*a^5*b^4 + 3*A*a^3*b^6 - A*a*b^8)*cos(d*x + c)^2 + (A*a^8*b - 3*A*a^6*b^3 + 3*A*a^4*b^5 - A*a^2*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) - 6*((A*a^6*b^3 - 3*A*a^4*b^5 + 3*A*a^2*b^7 - A*b^9)*cos(d*x + c)^3 + 2*(A*a^7*b^2 - 3*A*a^5*b^4 + 3*A*a^3*b^6 - A*a*b^8)*cos(d*x + c)^2 + (A*a^8*b - 3*A*a^6*b^3 + 3*A*a^4*b^5 - 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 - 3*C)*a^7*b^2 - (13*A - 3*C)*a^5*b^4 + 17*A*a^3*b^6 - 6*A*a*b^8)*cos(d*x + c)^2 + (4*(A - C)*a^8*b - 5*(4*A - C)*a^6*b^3 + (25*A - C)*a^4*b^5 - 9*A*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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*(((2*C*a^6*b^2 + (12*A + C)*a^4*b^4 - 15*A*a^2*b^6 + 6*A*b^8)*cos(d*x + c)^3 + 2*(2*C*a^7*b + (12*A + C)*a^5*b^3 - 15*A*a^3*b^5 + 6*A*a*b^7)*cos(d*x + c)^2 + (2*C*a^8 + (12*A + C)*a^6*b^2 - 15*A*a^4*b^4 + 6*A*a^2*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*((A*a^6*b^3 - 3*A*a^4*b^5 + 3*A*a^2*b^7 - A*b^9)*cos(d*x + c)^3 + 2*(A*a^7*b^2 - 3*A*a^5*b^4 + 3*A*a^3*b^6 - A*a*b^8)*cos(d*x + c)^2 + (A*a^8*b - 3*A*a^6*b^3 + 3*A*a^4*b^5 - A*a^2*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + 3*((A*a^6*b^3 - 3*A*a^4*b^5 + 3*A*a^2*b^7 - A*b^9)*cos(d*x + c)^3 + 2*(A*a^7*b^2 - 3*A*a^5*b^4 + 3*A*a^3*b^6 - A*a*b^8)*cos(d*x + c)^2 + (A*a^8*b - 3*A*a^6*b^3 + 3*A*a^4*b^5 - 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 - 3*C)*a^7*b^2 - (13*A - 3*C)*a^5*b^4 + 17*A*a^3*b^6 - 6*A*a*b^8)*cos(d*x + c)^2 + (4*(A - C)*a^8*b - 5*(4*A - C)*a^6*b^3 + (25*A - C)*a^4*b^5 - 9*A*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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
584,1,2078,0,43.309294," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(6 \, C a^{6} b^{3} + 5 \, {\left(4 \, A - C\right)} a^{4} b^{5} - {\left(29 \, A - 2 \, C\right)} a^{2} b^{7} + 12 \, A b^{9}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(6 \, C a^{7} b^{2} + 5 \, {\left(4 \, A - C\right)} a^{5} b^{4} - {\left(29 \, A - 2 \, C\right)} a^{3} b^{6} + 12 \, A a b^{8}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{8} b + 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} - {\left(29 \, A - 2 \, C\right)} a^{4} b^{5} + 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2}\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({\left(A + 2 \, C\right)} a^{8} b^{2} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{6} b^{4} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{4} b^{6} + {\left(35 \, A - 2 \, C\right)} a^{2} b^{8} - 12 \, A b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left({\left(A + 2 \, C\right)} a^{9} b + 3 \, {\left(3 \, A - 2 \, C\right)} a^{7} b^{3} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{5} b^{5} + {\left(35 \, A - 2 \, C\right)} a^{3} b^{7} - 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{10} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{8} b^{2} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{6} b^{4} + {\left(35 \, A - 2 \, C\right)} a^{4} b^{6} - 12 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left({\left(A + 2 \, C\right)} a^{8} b^{2} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{6} b^{4} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{4} b^{6} + {\left(35 \, A - 2 \, C\right)} a^{2} b^{8} - 12 \, A b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left({\left(A + 2 \, C\right)} a^{9} b + 3 \, {\left(3 \, A - 2 \, C\right)} a^{7} b^{3} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{5} b^{5} + {\left(35 \, A - 2 \, C\right)} a^{3} b^{7} - 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{10} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{8} b^{2} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{6} b^{4} + {\left(35 \, A - 2 \, C\right)} a^{4} b^{6} - 12 \, A a^{2} b^{8}\right)} \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({\left(6 \, A - 5 \, C\right)} a^{7} b^{3} - {\left(27 \, A - 7 \, C\right)} a^{5} b^{5} + {\left(33 \, A - 2 \, C\right)} a^{3} b^{7} - 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} - {\left({\left(11 \, A - 6 \, C\right)} a^{8} b^{2} - {\left(43 \, A - 9 \, C\right)} a^{6} b^{4} + {\left(50 \, A - 3 \, C\right)} a^{4} b^{6} - 18 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(A a^{9} b - 3 \, A a^{7} b^{3} + 3 \, A a^{5} b^{5} - A a^{3} b^{7}\right)} \cos\left(d x + c\right)\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(6 \, C a^{6} b^{3} + 5 \, {\left(4 \, A - C\right)} a^{4} b^{5} - {\left(29 \, A - 2 \, C\right)} a^{2} b^{7} + 12 \, A b^{9}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(6 \, C a^{7} b^{2} + 5 \, {\left(4 \, A - C\right)} a^{5} b^{4} - {\left(29 \, A - 2 \, C\right)} a^{3} b^{6} + 12 \, A a b^{8}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, C a^{8} b + 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} - {\left(29 \, A - 2 \, C\right)} a^{4} b^{5} + 12 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2}\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({\left(A + 2 \, C\right)} a^{8} b^{2} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{6} b^{4} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{4} b^{6} + {\left(35 \, A - 2 \, C\right)} a^{2} b^{8} - 12 \, A b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left({\left(A + 2 \, C\right)} a^{9} b + 3 \, {\left(3 \, A - 2 \, C\right)} a^{7} b^{3} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{5} b^{5} + {\left(35 \, A - 2 \, C\right)} a^{3} b^{7} - 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{10} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{8} b^{2} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{6} b^{4} + {\left(35 \, A - 2 \, C\right)} a^{4} b^{6} - 12 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left({\left(A + 2 \, C\right)} a^{8} b^{2} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{6} b^{4} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{4} b^{6} + {\left(35 \, A - 2 \, C\right)} a^{2} b^{8} - 12 \, A b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left({\left(A + 2 \, C\right)} a^{9} b + 3 \, {\left(3 \, A - 2 \, C\right)} a^{7} b^{3} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{5} b^{5} + {\left(35 \, A - 2 \, C\right)} a^{3} b^{7} - 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{10} + 3 \, {\left(3 \, A - 2 \, C\right)} a^{8} b^{2} - 3 \, {\left(11 \, A - 2 \, C\right)} a^{6} b^{4} + {\left(35 \, A - 2 \, C\right)} a^{4} b^{6} - 12 \, A a^{2} b^{8}\right)} \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({\left(6 \, A - 5 \, C\right)} a^{7} b^{3} - {\left(27 \, A - 7 \, C\right)} a^{5} b^{5} + {\left(33 \, A - 2 \, C\right)} a^{3} b^{7} - 12 \, A a b^{9}\right)} \cos\left(d x + c\right)^{3} - {\left({\left(11 \, A - 6 \, C\right)} a^{8} b^{2} - {\left(43 \, A - 9 \, C\right)} a^{6} b^{4} + {\left(50 \, A - 3 \, C\right)} a^{4} b^{6} - 18 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(A a^{9} b - 3 \, A a^{7} b^{3} + 3 \, A a^{5} b^{5} - A a^{3} b^{7}\right)} \cos\left(d x + c\right)\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*(((6*C*a^6*b^3 + 5*(4*A - C)*a^4*b^5 - (29*A - 2*C)*a^2*b^7 + 12*A*b^9)*cos(d*x + c)^4 + 2*(6*C*a^7*b^2 + 5*(4*A - C)*a^5*b^4 - (29*A - 2*C)*a^3*b^6 + 12*A*a*b^8)*cos(d*x + c)^3 + (6*C*a^8*b + 5*(4*A - C)*a^6*b^3 - (29*A - 2*C)*a^4*b^5 + 12*A*a^2*b^7)*cos(d*x + c)^2)*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*C)*a^8*b^2 + 3*(3*A - 2*C)*a^6*b^4 - 3*(11*A - 2*C)*a^4*b^6 + (35*A - 2*C)*a^2*b^8 - 12*A*b^10)*cos(d*x + c)^4 + 2*((A + 2*C)*a^9*b + 3*(3*A - 2*C)*a^7*b^3 - 3*(11*A - 2*C)*a^5*b^5 + (35*A - 2*C)*a^3*b^7 - 12*A*a*b^9)*cos(d*x + c)^3 + ((A + 2*C)*a^10 + 3*(3*A - 2*C)*a^8*b^2 - 3*(11*A - 2*C)*a^6*b^4 + (35*A - 2*C)*a^4*b^6 - 12*A*a^2*b^8)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + (((A + 2*C)*a^8*b^2 + 3*(3*A - 2*C)*a^6*b^4 - 3*(11*A - 2*C)*a^4*b^6 + (35*A - 2*C)*a^2*b^8 - 12*A*b^10)*cos(d*x + c)^4 + 2*((A + 2*C)*a^9*b + 3*(3*A - 2*C)*a^7*b^3 - 3*(11*A - 2*C)*a^5*b^5 + (35*A - 2*C)*a^3*b^7 - 12*A*a*b^9)*cos(d*x + c)^3 + ((A + 2*C)*a^10 + 3*(3*A - 2*C)*a^8*b^2 - 3*(11*A - 2*C)*a^6*b^4 + (35*A - 2*C)*a^4*b^6 - 12*A*a^2*b^8)*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 - ((6*A - 5*C)*a^7*b^3 - (27*A - 7*C)*a^5*b^5 + (33*A - 2*C)*a^3*b^7 - 12*A*a*b^9)*cos(d*x + c)^3 - ((11*A - 6*C)*a^8*b^2 - (43*A - 9*C)*a^6*b^4 + (50*A - 3*C)*a^4*b^6 - 18*A*a^2*b^8)*cos(d*x + c)^2 - 4*(A*a^9*b - 3*A*a^7*b^3 + 3*A*a^5*b^5 - A*a^3*b^7)*cos(d*x + c))*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*((6*C*a^6*b^3 + 5*(4*A - C)*a^4*b^5 - (29*A - 2*C)*a^2*b^7 + 12*A*b^9)*cos(d*x + c)^4 + 2*(6*C*a^7*b^2 + 5*(4*A - C)*a^5*b^4 - (29*A - 2*C)*a^3*b^6 + 12*A*a*b^8)*cos(d*x + c)^3 + (6*C*a^8*b + 5*(4*A - C)*a^6*b^3 - (29*A - 2*C)*a^4*b^5 + 12*A*a^2*b^7)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (((A + 2*C)*a^8*b^2 + 3*(3*A - 2*C)*a^6*b^4 - 3*(11*A - 2*C)*a^4*b^6 + (35*A - 2*C)*a^2*b^8 - 12*A*b^10)*cos(d*x + c)^4 + 2*((A + 2*C)*a^9*b + 3*(3*A - 2*C)*a^7*b^3 - 3*(11*A - 2*C)*a^5*b^5 + (35*A - 2*C)*a^3*b^7 - 12*A*a*b^9)*cos(d*x + c)^3 + ((A + 2*C)*a^10 + 3*(3*A - 2*C)*a^8*b^2 - 3*(11*A - 2*C)*a^6*b^4 + (35*A - 2*C)*a^4*b^6 - 12*A*a^2*b^8)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + (((A + 2*C)*a^8*b^2 + 3*(3*A - 2*C)*a^6*b^4 - 3*(11*A - 2*C)*a^4*b^6 + (35*A - 2*C)*a^2*b^8 - 12*A*b^10)*cos(d*x + c)^4 + 2*((A + 2*C)*a^9*b + 3*(3*A - 2*C)*a^7*b^3 - 3*(11*A - 2*C)*a^5*b^5 + (35*A - 2*C)*a^3*b^7 - 12*A*a*b^9)*cos(d*x + c)^3 + ((A + 2*C)*a^10 + 3*(3*A - 2*C)*a^8*b^2 - 3*(11*A - 2*C)*a^6*b^4 + (35*A - 2*C)*a^4*b^6 - 12*A*a^2*b^8)*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 - ((6*A - 5*C)*a^7*b^3 - (27*A - 7*C)*a^5*b^5 + (33*A - 2*C)*a^3*b^7 - 12*A*a*b^9)*cos(d*x + c)^3 - ((11*A - 6*C)*a^8*b^2 - (43*A - 9*C)*a^6*b^4 + (50*A - 3*C)*a^4*b^6 - 18*A*a^2*b^8)*cos(d*x + c)^2 - 4*(A*a^9*b - 3*A*a^7*b^3 + 3*A*a^5*b^5 - A*a^3*b^7)*cos(d*x + c))*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
585,1,2395,0,0.856939," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(20 \, C a^{10} b^{3} + {\left(2 \, A - 79 \, C\right)} a^{8} b^{5} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{6} b^{7} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{4} b^{9} - 8 \, {\left(A - 2 \, C\right)} a^{2} b^{11} + {\left(2 \, A + C\right)} b^{13}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(20 \, C a^{11} b^{2} + {\left(2 \, A - 79 \, C\right)} a^{9} b^{4} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{7} b^{6} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{5} b^{8} - 8 \, {\left(A - 2 \, C\right)} a^{3} b^{10} + {\left(2 \, A + C\right)} a b^{12}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(20 \, C a^{12} b + {\left(2 \, A - 79 \, C\right)} a^{10} b^{3} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{8} b^{5} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{6} b^{7} - 8 \, {\left(A - 2 \, C\right)} a^{4} b^{9} + {\left(2 \, A + C\right)} a^{2} b^{11}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(20 \, C a^{13} + {\left(2 \, A - 79 \, C\right)} a^{11} b^{2} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{9} b^{4} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{7} b^{6} - 8 \, {\left(A - 2 \, C\right)} a^{5} b^{8} + {\left(2 \, A + C\right)} a^{3} b^{10}\right)} d x - 3 \, {\left(20 \, C a^{12} + {\left(2 \, A - 69 \, C\right)} a^{10} b^{2} - 7 \, {\left(A - 12 \, C\right)} a^{8} b^{4} + 8 \, {\left(A - 5 \, C\right)} a^{6} b^{6} - 8 \, A a^{4} b^{8} + {\left(20 \, C a^{9} b^{3} + {\left(2 \, A - 69 \, C\right)} a^{7} b^{5} - 7 \, {\left(A - 12 \, C\right)} a^{5} b^{7} + 8 \, {\left(A - 5 \, C\right)} a^{3} b^{9} - 8 \, A a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, C a^{10} b^{2} + {\left(2 \, A - 69 \, C\right)} a^{8} b^{4} - 7 \, {\left(A - 12 \, C\right)} a^{6} b^{6} + 8 \, {\left(A - 5 \, C\right)} a^{4} b^{8} - 8 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, C a^{11} b + {\left(2 \, A - 69 \, C\right)} a^{9} b^{3} - 7 \, {\left(A - 12 \, C\right)} a^{7} b^{5} + 8 \, {\left(A - 5 \, C\right)} a^{5} b^{7} - 8 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(60 \, C a^{12} b + {\left(6 \, A - 227 \, C\right)} a^{10} b^{3} - {\left(23 \, A - 313 \, C\right)} a^{8} b^{5} + {\left(43 \, A - 170 \, C\right)} a^{6} b^{7} - 2 \, {\left(13 \, A - 12 \, C\right)} a^{4} b^{9} - 3 \, {\left(C a^{8} b^{5} - 4 \, C a^{6} b^{7} + 6 \, C a^{4} b^{9} - 4 \, C a^{2} b^{11} + C b^{13}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(C a^{9} b^{4} - 4 \, C a^{7} b^{6} + 6 \, C a^{5} b^{8} - 4 \, C a^{3} b^{10} + C a b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(110 \, C a^{10} b^{3} + {\left(11 \, A - 421 \, C\right)} a^{8} b^{5} - {\left(43 \, A - 590 \, C\right)} a^{6} b^{7} + 2 \, {\left(34 \, A - 171 \, C\right)} a^{4} b^{9} - 9 \, {\left(4 \, A - 7 \, C\right)} a^{2} b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(50 \, C a^{11} b^{2} + 5 \, {\left(A - 38 \, C\right)} a^{9} b^{4} - {\left(20 \, A - 263 \, C\right)} a^{7} b^{6} + {\left(35 \, A - 146 \, C\right)} a^{5} b^{8} - {\left(20 \, A - 23 \, C\right)} a^{3} b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{9} - 4 \, a^{6} b^{11} + 6 \, a^{4} b^{13} - 4 \, a^{2} b^{15} + b^{17}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{8} - 4 \, a^{7} b^{10} + 6 \, a^{5} b^{12} - 4 \, a^{3} b^{14} + a b^{16}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{7} - 4 \, a^{8} b^{9} + 6 \, a^{6} b^{11} - 4 \, a^{4} b^{13} + a^{2} b^{15}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{6} - 4 \, a^{9} b^{8} + 6 \, a^{7} b^{10} - 4 \, a^{5} b^{12} + a^{3} b^{14}\right)} d\right)}}, \frac{3 \, {\left(20 \, C a^{10} b^{3} + {\left(2 \, A - 79 \, C\right)} a^{8} b^{5} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{6} b^{7} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{4} b^{9} - 8 \, {\left(A - 2 \, C\right)} a^{2} b^{11} + {\left(2 \, A + C\right)} b^{13}\right)} d x \cos\left(d x + c\right)^{3} + 9 \, {\left(20 \, C a^{11} b^{2} + {\left(2 \, A - 79 \, C\right)} a^{9} b^{4} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{7} b^{6} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{5} b^{8} - 8 \, {\left(A - 2 \, C\right)} a^{3} b^{10} + {\left(2 \, A + C\right)} a b^{12}\right)} d x \cos\left(d x + c\right)^{2} + 9 \, {\left(20 \, C a^{12} b + {\left(2 \, A - 79 \, C\right)} a^{10} b^{3} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{8} b^{5} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{6} b^{7} - 8 \, {\left(A - 2 \, C\right)} a^{4} b^{9} + {\left(2 \, A + C\right)} a^{2} b^{11}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(20 \, C a^{13} + {\left(2 \, A - 79 \, C\right)} a^{11} b^{2} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{9} b^{4} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{7} b^{6} - 8 \, {\left(A - 2 \, C\right)} a^{5} b^{8} + {\left(2 \, A + C\right)} a^{3} b^{10}\right)} d x - 3 \, {\left(20 \, C a^{12} + {\left(2 \, A - 69 \, C\right)} a^{10} b^{2} - 7 \, {\left(A - 12 \, C\right)} a^{8} b^{4} + 8 \, {\left(A - 5 \, C\right)} a^{6} b^{6} - 8 \, A a^{4} b^{8} + {\left(20 \, C a^{9} b^{3} + {\left(2 \, A - 69 \, C\right)} a^{7} b^{5} - 7 \, {\left(A - 12 \, C\right)} a^{5} b^{7} + 8 \, {\left(A - 5 \, C\right)} a^{3} b^{9} - 8 \, A a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, C a^{10} b^{2} + {\left(2 \, A - 69 \, C\right)} a^{8} b^{4} - 7 \, {\left(A - 12 \, C\right)} a^{6} b^{6} + 8 \, {\left(A - 5 \, C\right)} a^{4} b^{8} - 8 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, C a^{11} b + {\left(2 \, A - 69 \, C\right)} a^{9} b^{3} - 7 \, {\left(A - 12 \, C\right)} a^{7} b^{5} + 8 \, {\left(A - 5 \, C\right)} a^{5} b^{7} - 8 \, A a^{3} b^{9}\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(60 \, C a^{12} b + {\left(6 \, A - 227 \, C\right)} a^{10} b^{3} - {\left(23 \, A - 313 \, C\right)} a^{8} b^{5} + {\left(43 \, A - 170 \, C\right)} a^{6} b^{7} - 2 \, {\left(13 \, A - 12 \, C\right)} a^{4} b^{9} - 3 \, {\left(C a^{8} b^{5} - 4 \, C a^{6} b^{7} + 6 \, C a^{4} b^{9} - 4 \, C a^{2} b^{11} + C b^{13}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(C a^{9} b^{4} - 4 \, C a^{7} b^{6} + 6 \, C a^{5} b^{8} - 4 \, C a^{3} b^{10} + C a b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(110 \, C a^{10} b^{3} + {\left(11 \, A - 421 \, C\right)} a^{8} b^{5} - {\left(43 \, A - 590 \, C\right)} a^{6} b^{7} + 2 \, {\left(34 \, A - 171 \, C\right)} a^{4} b^{9} - 9 \, {\left(4 \, A - 7 \, C\right)} a^{2} b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(50 \, C a^{11} b^{2} + 5 \, {\left(A - 38 \, C\right)} a^{9} b^{4} - {\left(20 \, A - 263 \, C\right)} a^{7} b^{6} + {\left(35 \, A - 146 \, C\right)} a^{5} b^{8} - {\left(20 \, A - 23 \, C\right)} a^{3} b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{9} - 4 \, a^{6} b^{11} + 6 \, a^{4} b^{13} - 4 \, a^{2} b^{15} + b^{17}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{8} - 4 \, a^{7} b^{10} + 6 \, a^{5} b^{12} - 4 \, a^{3} b^{14} + a b^{16}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{7} - 4 \, a^{8} b^{9} + 6 \, a^{6} b^{11} - 4 \, a^{4} b^{13} + a^{2} b^{15}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{6} - 4 \, a^{9} b^{8} + 6 \, a^{7} b^{10} - 4 \, a^{5} b^{12} + a^{3} b^{14}\right)} d\right)}}\right]"," ",0,"[1/12*(6*(20*C*a^10*b^3 + (2*A - 79*C)*a^8*b^5 - 4*(2*A - 29*C)*a^6*b^7 + 2*(6*A - 37*C)*a^4*b^9 - 8*(A - 2*C)*a^2*b^11 + (2*A + C)*b^13)*d*x*cos(d*x + c)^3 + 18*(20*C*a^11*b^2 + (2*A - 79*C)*a^9*b^4 - 4*(2*A - 29*C)*a^7*b^6 + 2*(6*A - 37*C)*a^5*b^8 - 8*(A - 2*C)*a^3*b^10 + (2*A + C)*a*b^12)*d*x*cos(d*x + c)^2 + 18*(20*C*a^12*b + (2*A - 79*C)*a^10*b^3 - 4*(2*A - 29*C)*a^8*b^5 + 2*(6*A - 37*C)*a^6*b^7 - 8*(A - 2*C)*a^4*b^9 + (2*A + C)*a^2*b^11)*d*x*cos(d*x + c) + 6*(20*C*a^13 + (2*A - 79*C)*a^11*b^2 - 4*(2*A - 29*C)*a^9*b^4 + 2*(6*A - 37*C)*a^7*b^6 - 8*(A - 2*C)*a^5*b^8 + (2*A + C)*a^3*b^10)*d*x - 3*(20*C*a^12 + (2*A - 69*C)*a^10*b^2 - 7*(A - 12*C)*a^8*b^4 + 8*(A - 5*C)*a^6*b^6 - 8*A*a^4*b^8 + (20*C*a^9*b^3 + (2*A - 69*C)*a^7*b^5 - 7*(A - 12*C)*a^5*b^7 + 8*(A - 5*C)*a^3*b^9 - 8*A*a*b^11)*cos(d*x + c)^3 + 3*(20*C*a^10*b^2 + (2*A - 69*C)*a^8*b^4 - 7*(A - 12*C)*a^6*b^6 + 8*(A - 5*C)*a^4*b^8 - 8*A*a^2*b^10)*cos(d*x + c)^2 + 3*(20*C*a^11*b + (2*A - 69*C)*a^9*b^3 - 7*(A - 12*C)*a^7*b^5 + 8*(A - 5*C)*a^5*b^7 - 8*A*a^3*b^9)*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*(60*C*a^12*b + (6*A - 227*C)*a^10*b^3 - (23*A - 313*C)*a^8*b^5 + (43*A - 170*C)*a^6*b^7 - 2*(13*A - 12*C)*a^4*b^9 - 3*(C*a^8*b^5 - 4*C*a^6*b^7 + 6*C*a^4*b^9 - 4*C*a^2*b^11 + C*b^13)*cos(d*x + c)^4 + 15*(C*a^9*b^4 - 4*C*a^7*b^6 + 6*C*a^5*b^8 - 4*C*a^3*b^10 + C*a*b^12)*cos(d*x + c)^3 + (110*C*a^10*b^3 + (11*A - 421*C)*a^8*b^5 - (43*A - 590*C)*a^6*b^7 + 2*(34*A - 171*C)*a^4*b^9 - 9*(4*A - 7*C)*a^2*b^11)*cos(d*x + c)^2 + 3*(50*C*a^11*b^2 + 5*(A - 38*C)*a^9*b^4 - (20*A - 263*C)*a^7*b^6 + (35*A - 146*C)*a^5*b^8 - (20*A - 23*C)*a^3*b^10)*cos(d*x + c))*sin(d*x + c))/((a^8*b^9 - 4*a^6*b^11 + 6*a^4*b^13 - 4*a^2*b^15 + b^17)*d*cos(d*x + c)^3 + 3*(a^9*b^8 - 4*a^7*b^10 + 6*a^5*b^12 - 4*a^3*b^14 + a*b^16)*d*cos(d*x + c)^2 + 3*(a^10*b^7 - 4*a^8*b^9 + 6*a^6*b^11 - 4*a^4*b^13 + a^2*b^15)*d*cos(d*x + c) + (a^11*b^6 - 4*a^9*b^8 + 6*a^7*b^10 - 4*a^5*b^12 + a^3*b^14)*d), 1/6*(3*(20*C*a^10*b^3 + (2*A - 79*C)*a^8*b^5 - 4*(2*A - 29*C)*a^6*b^7 + 2*(6*A - 37*C)*a^4*b^9 - 8*(A - 2*C)*a^2*b^11 + (2*A + C)*b^13)*d*x*cos(d*x + c)^3 + 9*(20*C*a^11*b^2 + (2*A - 79*C)*a^9*b^4 - 4*(2*A - 29*C)*a^7*b^6 + 2*(6*A - 37*C)*a^5*b^8 - 8*(A - 2*C)*a^3*b^10 + (2*A + C)*a*b^12)*d*x*cos(d*x + c)^2 + 9*(20*C*a^12*b + (2*A - 79*C)*a^10*b^3 - 4*(2*A - 29*C)*a^8*b^5 + 2*(6*A - 37*C)*a^6*b^7 - 8*(A - 2*C)*a^4*b^9 + (2*A + C)*a^2*b^11)*d*x*cos(d*x + c) + 3*(20*C*a^13 + (2*A - 79*C)*a^11*b^2 - 4*(2*A - 29*C)*a^9*b^4 + 2*(6*A - 37*C)*a^7*b^6 - 8*(A - 2*C)*a^5*b^8 + (2*A + C)*a^3*b^10)*d*x - 3*(20*C*a^12 + (2*A - 69*C)*a^10*b^2 - 7*(A - 12*C)*a^8*b^4 + 8*(A - 5*C)*a^6*b^6 - 8*A*a^4*b^8 + (20*C*a^9*b^3 + (2*A - 69*C)*a^7*b^5 - 7*(A - 12*C)*a^5*b^7 + 8*(A - 5*C)*a^3*b^9 - 8*A*a*b^11)*cos(d*x + c)^3 + 3*(20*C*a^10*b^2 + (2*A - 69*C)*a^8*b^4 - 7*(A - 12*C)*a^6*b^6 + 8*(A - 5*C)*a^4*b^8 - 8*A*a^2*b^10)*cos(d*x + c)^2 + 3*(20*C*a^11*b + (2*A - 69*C)*a^9*b^3 - 7*(A - 12*C)*a^7*b^5 + 8*(A - 5*C)*a^5*b^7 - 8*A*a^3*b^9)*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))) - (60*C*a^12*b + (6*A - 227*C)*a^10*b^3 - (23*A - 313*C)*a^8*b^5 + (43*A - 170*C)*a^6*b^7 - 2*(13*A - 12*C)*a^4*b^9 - 3*(C*a^8*b^5 - 4*C*a^6*b^7 + 6*C*a^4*b^9 - 4*C*a^2*b^11 + C*b^13)*cos(d*x + c)^4 + 15*(C*a^9*b^4 - 4*C*a^7*b^6 + 6*C*a^5*b^8 - 4*C*a^3*b^10 + C*a*b^12)*cos(d*x + c)^3 + (110*C*a^10*b^3 + (11*A - 421*C)*a^8*b^5 - (43*A - 590*C)*a^6*b^7 + 2*(34*A - 171*C)*a^4*b^9 - 9*(4*A - 7*C)*a^2*b^11)*cos(d*x + c)^2 + 3*(50*C*a^11*b^2 + 5*(A - 38*C)*a^9*b^4 - (20*A - 263*C)*a^7*b^6 + (35*A - 146*C)*a^5*b^8 - (20*A - 23*C)*a^3*b^10)*cos(d*x + c))*sin(d*x + c))/((a^8*b^9 - 4*a^6*b^11 + 6*a^4*b^13 - 4*a^2*b^15 + b^17)*d*cos(d*x + c)^3 + 3*(a^9*b^8 - 4*a^7*b^10 + 6*a^5*b^12 - 4*a^3*b^14 + a*b^16)*d*cos(d*x + c)^2 + 3*(a^10*b^7 - 4*a^8*b^9 + 6*a^6*b^11 - 4*a^4*b^13 + a^2*b^15)*d*cos(d*x + c) + (a^11*b^6 - 4*a^9*b^8 + 6*a^7*b^10 - 4*a^5*b^12 + a^3*b^14)*d)]","B",0
586,1,1919,0,0.764702," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{48 \, {\left(C a^{9} b^{3} - 4 \, C a^{7} b^{5} + 6 \, C a^{5} b^{7} - 4 \, C a^{3} b^{9} + C a b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 144 \, {\left(C a^{10} b^{2} - 4 \, C a^{8} b^{4} + 6 \, C a^{6} b^{6} - 4 \, C a^{4} b^{8} + C a^{2} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 144 \, {\left(C a^{11} b - 4 \, C a^{9} b^{3} + 6 \, C a^{7} b^{5} - 4 \, C a^{5} b^{7} + C a^{3} b^{9}\right)} d x \cos\left(d x + c\right) + 48 \, {\left(C a^{12} - 4 \, C a^{10} b^{2} + 6 \, C a^{8} b^{4} - 4 \, C a^{6} b^{6} + C a^{4} b^{8}\right)} d x + 3 \, {\left(8 \, C a^{11} - 28 \, C a^{9} b^{2} + 35 \, C a^{7} b^{4} - {\left(3 \, A + 20 \, C\right)} a^{5} b^{6} - 2 \, A a^{3} b^{8} + {\left(8 \, C a^{8} b^{3} - 28 \, C a^{6} b^{5} + 35 \, C a^{4} b^{7} - {\left(3 \, A + 20 \, C\right)} a^{2} b^{9} - 2 \, A b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, C a^{9} b^{2} - 28 \, C a^{7} b^{4} + 35 \, C a^{5} b^{6} - {\left(3 \, A + 20 \, C\right)} a^{3} b^{8} - 2 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, C a^{10} b - 28 \, C a^{8} b^{3} + 35 \, C a^{6} b^{5} - {\left(3 \, A + 20 \, C\right)} a^{4} b^{7} - 2 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\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 \, C a^{11} b - 92 \, C a^{9} b^{3} + {\left(4 \, A + 133 \, C\right)} a^{7} b^{5} + {\left(7 \, A - 71 \, C\right)} a^{5} b^{7} - {\left(11 \, A - 6 \, C\right)} a^{3} b^{9} + 6 \, {\left(C a^{8} b^{4} - 4 \, C a^{6} b^{6} + 6 \, C a^{4} b^{8} - 4 \, C a^{2} b^{10} + C b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(44 \, C a^{9} b^{3} + {\left(2 \, A - 169 \, C\right)} a^{7} b^{5} - {\left(7 \, A - 239 \, C\right)} a^{5} b^{7} + {\left(23 \, A - 132 \, C\right)} a^{3} b^{9} - 18 \, {\left(A - C\right)} a b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, C a^{10} b^{2} - 77 \, C a^{8} b^{4} + {\left(A + 110 \, C\right)} a^{6} b^{6} + {\left(8 \, A - 59 \, C\right)} a^{4} b^{8} - 3 \, {\left(3 \, A - 2 \, C\right)} a^{2} b^{10}\right)} \cos\left(d x + c\right)\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{24 \, {\left(C a^{9} b^{3} - 4 \, C a^{7} b^{5} + 6 \, C a^{5} b^{7} - 4 \, C a^{3} b^{9} + C a b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 72 \, {\left(C a^{10} b^{2} - 4 \, C a^{8} b^{4} + 6 \, C a^{6} b^{6} - 4 \, C a^{4} b^{8} + C a^{2} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 72 \, {\left(C a^{11} b - 4 \, C a^{9} b^{3} + 6 \, C a^{7} b^{5} - 4 \, C a^{5} b^{7} + C a^{3} b^{9}\right)} d x \cos\left(d x + c\right) + 24 \, {\left(C a^{12} - 4 \, C a^{10} b^{2} + 6 \, C a^{8} b^{4} - 4 \, C a^{6} b^{6} + C a^{4} b^{8}\right)} d x - 3 \, {\left(8 \, C a^{11} - 28 \, C a^{9} b^{2} + 35 \, C a^{7} b^{4} - {\left(3 \, A + 20 \, C\right)} a^{5} b^{6} - 2 \, A a^{3} b^{8} + {\left(8 \, C a^{8} b^{3} - 28 \, C a^{6} b^{5} + 35 \, C a^{4} b^{7} - {\left(3 \, A + 20 \, C\right)} a^{2} b^{9} - 2 \, A b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, C a^{9} b^{2} - 28 \, C a^{7} b^{4} + 35 \, C a^{5} b^{6} - {\left(3 \, A + 20 \, C\right)} a^{3} b^{8} - 2 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, C a^{10} b - 28 \, C a^{8} b^{3} + 35 \, C a^{6} b^{5} - {\left(3 \, A + 20 \, C\right)} a^{4} b^{7} - 2 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\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 \, C a^{11} b - 92 \, C a^{9} b^{3} + {\left(4 \, A + 133 \, C\right)} a^{7} b^{5} + {\left(7 \, A - 71 \, C\right)} a^{5} b^{7} - {\left(11 \, A - 6 \, C\right)} a^{3} b^{9} + 6 \, {\left(C a^{8} b^{4} - 4 \, C a^{6} b^{6} + 6 \, C a^{4} b^{8} - 4 \, C a^{2} b^{10} + C b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(44 \, C a^{9} b^{3} + {\left(2 \, A - 169 \, C\right)} a^{7} b^{5} - {\left(7 \, A - 239 \, C\right)} a^{5} b^{7} + {\left(23 \, A - 132 \, C\right)} a^{3} b^{9} - 18 \, {\left(A - C\right)} a b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, C a^{10} b^{2} - 77 \, C a^{8} b^{4} + {\left(A + 110 \, C\right)} a^{6} b^{6} + {\left(8 \, A - 59 \, C\right)} a^{4} b^{8} - 3 \, {\left(3 \, A - 2 \, C\right)} a^{2} b^{10}\right)} \cos\left(d x + c\right)\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*(48*(C*a^9*b^3 - 4*C*a^7*b^5 + 6*C*a^5*b^7 - 4*C*a^3*b^9 + C*a*b^11)*d*x*cos(d*x + c)^3 + 144*(C*a^10*b^2 - 4*C*a^8*b^4 + 6*C*a^6*b^6 - 4*C*a^4*b^8 + C*a^2*b^10)*d*x*cos(d*x + c)^2 + 144*(C*a^11*b - 4*C*a^9*b^3 + 6*C*a^7*b^5 - 4*C*a^5*b^7 + C*a^3*b^9)*d*x*cos(d*x + c) + 48*(C*a^12 - 4*C*a^10*b^2 + 6*C*a^8*b^4 - 4*C*a^6*b^6 + C*a^4*b^8)*d*x + 3*(8*C*a^11 - 28*C*a^9*b^2 + 35*C*a^7*b^4 - (3*A + 20*C)*a^5*b^6 - 2*A*a^3*b^8 + (8*C*a^8*b^3 - 28*C*a^6*b^5 + 35*C*a^4*b^7 - (3*A + 20*C)*a^2*b^9 - 2*A*b^11)*cos(d*x + c)^3 + 3*(8*C*a^9*b^2 - 28*C*a^7*b^4 + 35*C*a^5*b^6 - (3*A + 20*C)*a^3*b^8 - 2*A*a*b^10)*cos(d*x + c)^2 + 3*(8*C*a^10*b - 28*C*a^8*b^3 + 35*C*a^6*b^5 - (3*A + 20*C)*a^4*b^7 - 2*A*a^2*b^9)*cos(d*x + c))*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*C*a^11*b - 92*C*a^9*b^3 + (4*A + 133*C)*a^7*b^5 + (7*A - 71*C)*a^5*b^7 - (11*A - 6*C)*a^3*b^9 + 6*(C*a^8*b^4 - 4*C*a^6*b^6 + 6*C*a^4*b^8 - 4*C*a^2*b^10 + C*b^12)*cos(d*x + c)^3 + (44*C*a^9*b^3 + (2*A - 169*C)*a^7*b^5 - (7*A - 239*C)*a^5*b^7 + (23*A - 132*C)*a^3*b^9 - 18*(A - C)*a*b^11)*cos(d*x + c)^2 + 3*(20*C*a^10*b^2 - 77*C*a^8*b^4 + (A + 110*C)*a^6*b^6 + (8*A - 59*C)*a^4*b^8 - 3*(3*A - 2*C)*a^2*b^10)*cos(d*x + c))*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*(24*(C*a^9*b^3 - 4*C*a^7*b^5 + 6*C*a^5*b^7 - 4*C*a^3*b^9 + C*a*b^11)*d*x*cos(d*x + c)^3 + 72*(C*a^10*b^2 - 4*C*a^8*b^4 + 6*C*a^6*b^6 - 4*C*a^4*b^8 + C*a^2*b^10)*d*x*cos(d*x + c)^2 + 72*(C*a^11*b - 4*C*a^9*b^3 + 6*C*a^7*b^5 - 4*C*a^5*b^7 + C*a^3*b^9)*d*x*cos(d*x + c) + 24*(C*a^12 - 4*C*a^10*b^2 + 6*C*a^8*b^4 - 4*C*a^6*b^6 + C*a^4*b^8)*d*x - 3*(8*C*a^11 - 28*C*a^9*b^2 + 35*C*a^7*b^4 - (3*A + 20*C)*a^5*b^6 - 2*A*a^3*b^8 + (8*C*a^8*b^3 - 28*C*a^6*b^5 + 35*C*a^4*b^7 - (3*A + 20*C)*a^2*b^9 - 2*A*b^11)*cos(d*x + c)^3 + 3*(8*C*a^9*b^2 - 28*C*a^7*b^4 + 35*C*a^5*b^6 - (3*A + 20*C)*a^3*b^8 - 2*A*a*b^10)*cos(d*x + c)^2 + 3*(8*C*a^10*b - 28*C*a^8*b^3 + 35*C*a^6*b^5 - (3*A + 20*C)*a^4*b^7 - 2*A*a^2*b^9)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (24*C*a^11*b - 92*C*a^9*b^3 + (4*A + 133*C)*a^7*b^5 + (7*A - 71*C)*a^5*b^7 - (11*A - 6*C)*a^3*b^9 + 6*(C*a^8*b^4 - 4*C*a^6*b^6 + 6*C*a^4*b^8 - 4*C*a^2*b^10 + C*b^12)*cos(d*x + c)^3 + (44*C*a^9*b^3 + (2*A - 169*C)*a^7*b^5 - (7*A - 239*C)*a^5*b^7 + (23*A - 132*C)*a^3*b^9 - 18*(A - C)*a*b^11)*cos(d*x + c)^2 + 3*(20*C*a^10*b^2 - 77*C*a^8*b^4 + (A + 110*C)*a^6*b^6 + (8*A - 59*C)*a^4*b^8 - 3*(3*A - 2*C)*a^2*b^10)*cos(d*x + c))*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
587,1,1735,0,0.672462," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 36 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 36 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} d x - 3 \, {\left(2 \, C a^{10} - 7 \, C a^{8} b^{2} - {\left(A - 8 \, C\right)} a^{6} b^{4} - 4 \, {\left(A + 2 \, C\right)} a^{4} b^{6} + {\left(2 \, C a^{7} b^{3} - 7 \, C a^{5} b^{5} - {\left(A - 8 \, C\right)} a^{3} b^{7} - 4 \, {\left(A + 2 \, C\right)} a b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{8} b^{2} - 7 \, C a^{6} b^{4} - {\left(A - 8 \, C\right)} a^{4} b^{6} - 4 \, {\left(A + 2 \, C\right)} a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{9} b - 7 \, C a^{7} b^{3} - {\left(A - 8 \, C\right)} a^{5} b^{5} - 4 \, {\left(A + 2 \, C\right)} a^{3} b^{7}\right)} \cos\left(d x + c\right)\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 \, C a^{10} b - 23 \, C a^{8} b^{3} + {\left(13 \, A + 43 \, C\right)} a^{6} b^{5} - {\left(11 \, A + 26 \, C\right)} a^{4} b^{7} - 2 \, A a^{2} b^{9} + {\left(11 \, C a^{8} b^{3} - {\left(A + 43 \, C\right)} a^{6} b^{5} + {\left(11 \, A + 68 \, C\right)} a^{4} b^{7} - 4 \, {\left(A + 9 \, C\right)} a^{2} b^{9} - 6 \, A b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, C a^{9} b^{2} - {\left(A + 20 \, C\right)} a^{7} b^{4} + 5 \, {\left(2 \, A + 7 \, C\right)} a^{5} b^{6} - {\left(7 \, A + 20 \, C\right)} a^{3} b^{8} - 2 \, A a b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{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(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} d x - 3 \, {\left(2 \, C a^{10} - 7 \, C a^{8} b^{2} - {\left(A - 8 \, C\right)} a^{6} b^{4} - 4 \, {\left(A + 2 \, C\right)} a^{4} b^{6} + {\left(2 \, C a^{7} b^{3} - 7 \, C a^{5} b^{5} - {\left(A - 8 \, C\right)} a^{3} b^{7} - 4 \, {\left(A + 2 \, C\right)} a b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{8} b^{2} - 7 \, C a^{6} b^{4} - {\left(A - 8 \, C\right)} a^{4} b^{6} - 4 \, {\left(A + 2 \, C\right)} a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{9} b - 7 \, C a^{7} b^{3} - {\left(A - 8 \, C\right)} a^{5} b^{5} - 4 \, {\left(A + 2 \, C\right)} a^{3} b^{7}\right)} \cos\left(d x + c\right)\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 \, C a^{10} b - 23 \, C a^{8} b^{3} + {\left(13 \, A + 43 \, C\right)} a^{6} b^{5} - {\left(11 \, A + 26 \, C\right)} a^{4} b^{7} - 2 \, A a^{2} b^{9} + {\left(11 \, C a^{8} b^{3} - {\left(A + 43 \, C\right)} a^{6} b^{5} + {\left(11 \, A + 68 \, C\right)} a^{4} b^{7} - 4 \, {\left(A + 9 \, C\right)} a^{2} b^{9} - 6 \, A b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, C a^{9} b^{2} - {\left(A + 20 \, C\right)} a^{7} b^{4} + 5 \, {\left(2 \, A + 7 \, C\right)} a^{5} b^{6} - {\left(7 \, A + 20 \, C\right)} a^{3} b^{8} - 2 \, A a b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{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*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11)*d*x*cos(d*x + c)^3 + 36*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*d*x*cos(d*x + c)^2 + 36*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*d*x*cos(d*x + c) + 12*(C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*d*x - 3*(2*C*a^10 - 7*C*a^8*b^2 - (A - 8*C)*a^6*b^4 - 4*(A + 2*C)*a^4*b^6 + (2*C*a^7*b^3 - 7*C*a^5*b^5 - (A - 8*C)*a^3*b^7 - 4*(A + 2*C)*a*b^9)*cos(d*x + c)^3 + 3*(2*C*a^8*b^2 - 7*C*a^6*b^4 - (A - 8*C)*a^4*b^6 - 4*(A + 2*C)*a^2*b^8)*cos(d*x + c)^2 + 3*(2*C*a^9*b - 7*C*a^7*b^3 - (A - 8*C)*a^5*b^5 - 4*(A + 2*C)*a^3*b^7)*cos(d*x + c))*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*C*a^10*b - 23*C*a^8*b^3 + (13*A + 43*C)*a^6*b^5 - (11*A + 26*C)*a^4*b^7 - 2*A*a^2*b^9 + (11*C*a^8*b^3 - (A + 43*C)*a^6*b^5 + (11*A + 68*C)*a^4*b^7 - 4*(A + 9*C)*a^2*b^9 - 6*A*b^11)*cos(d*x + c)^2 + 3*(5*C*a^9*b^2 - (A + 20*C)*a^7*b^4 + 5*(2*A + 7*C)*a^5*b^6 - (7*A + 20*C)*a^3*b^8 - 2*A*a*b^10)*cos(d*x + c))*sin(d*x + c))/((a^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*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11)*d*x*cos(d*x + c)^3 + 18*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*d*x*cos(d*x + c)^2 + 18*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*d*x*cos(d*x + c) + 6*(C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*d*x - 3*(2*C*a^10 - 7*C*a^8*b^2 - (A - 8*C)*a^6*b^4 - 4*(A + 2*C)*a^4*b^6 + (2*C*a^7*b^3 - 7*C*a^5*b^5 - (A - 8*C)*a^3*b^7 - 4*(A + 2*C)*a*b^9)*cos(d*x + c)^3 + 3*(2*C*a^8*b^2 - 7*C*a^6*b^4 - (A - 8*C)*a^4*b^6 - 4*(A + 2*C)*a^2*b^8)*cos(d*x + c)^2 + 3*(2*C*a^9*b - 7*C*a^7*b^3 - (A - 8*C)*a^5*b^5 - 4*(A + 2*C)*a^3*b^7)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*C*a^10*b - 23*C*a^8*b^3 + (13*A + 43*C)*a^6*b^5 - (11*A + 26*C)*a^4*b^7 - 2*A*a^2*b^9 + (11*C*a^8*b^3 - (A + 43*C)*a^6*b^5 + (11*A + 68*C)*a^4*b^7 - 4*(A + 9*C)*a^2*b^9 - 6*A*b^11)*cos(d*x + c)^2 + 3*(5*C*a^9*b^2 - (A + 20*C)*a^7*b^4 + 5*(2*A + 7*C)*a^5*b^6 - (7*A + 20*C)*a^3*b^8 - 2*A*a*b^10)*cos(d*x + c))*sin(d*x + c))/((a^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
588,1,1103,0,0.626459," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(4 \, A + 3 \, C\right)} a^{5} b + {\left(A + 2 \, C\right)} a^{3} b^{3} + {\left({\left(4 \, A + 3 \, C\right)} a^{2} b^{4} + {\left(A + 2 \, C\right)} b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(4 \, A + 3 \, C\right)} a^{3} b^{3} + {\left(A + 2 \, C\right)} a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(4 \, A + 3 \, C\right)} a^{4} b^{2} + {\left(A + 2 \, C\right)} a^{2} b^{4}\right)} \cos\left(d x + c\right)\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 \, {\left(3 \, A + 2 \, C\right)} a^{7} + {\left(4 \, A + 7 \, C\right)} a^{5} b^{2} - 11 \, {\left(A + C\right)} a^{3} b^{4} + A a b^{6} + {\left(2 \, C a^{7} + {\left(2 \, A - 7 \, C\right)} a^{5} b^{2} + {\left(11 \, A + 23 \, C\right)} a^{3} b^{4} - {\left(13 \, A + 18 \, C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{6} b + {\left(7 \, A + 8 \, C\right)} a^{4} b^{3} - {\left(10 \, A + 9 \, C\right)} a^{2} b^{5} + A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{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({\left(4 \, A + 3 \, C\right)} a^{5} b + {\left(A + 2 \, C\right)} a^{3} b^{3} + {\left({\left(4 \, A + 3 \, C\right)} a^{2} b^{4} + {\left(A + 2 \, C\right)} b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(4 \, A + 3 \, C\right)} a^{3} b^{3} + {\left(A + 2 \, C\right)} a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(4 \, A + 3 \, C\right)} a^{4} b^{2} + {\left(A + 2 \, C\right)} a^{2} b^{4}\right)} \cos\left(d x + c\right)\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 \, {\left(3 \, A + 2 \, C\right)} a^{7} + {\left(4 \, A + 7 \, C\right)} a^{5} b^{2} - 11 \, {\left(A + C\right)} a^{3} b^{4} + A a b^{6} + {\left(2 \, C a^{7} + {\left(2 \, A - 7 \, C\right)} a^{5} b^{2} + {\left(11 \, A + 23 \, C\right)} a^{3} b^{4} - {\left(13 \, A + 18 \, C\right)} a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{6} b + {\left(7 \, A + 8 \, C\right)} a^{4} b^{3} - {\left(10 \, A + 9 \, C\right)} a^{2} b^{5} + A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{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*((4*A + 3*C)*a^5*b + (A + 2*C)*a^3*b^3 + ((4*A + 3*C)*a^2*b^4 + (A + 2*C)*b^6)*cos(d*x + c)^3 + 3*((4*A + 3*C)*a^3*b^3 + (A + 2*C)*a*b^5)*cos(d*x + c)^2 + 3*((4*A + 3*C)*a^4*b^2 + (A + 2*C)*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*(2*(3*A + 2*C)*a^7 + (4*A + 7*C)*a^5*b^2 - 11*(A + C)*a^3*b^4 + A*a*b^6 + (2*C*a^7 + (2*A - 7*C)*a^5*b^2 + (11*A + 23*C)*a^3*b^4 - (13*A + 18*C)*a*b^6)*cos(d*x + c)^2 + 3*((2*A + C)*a^6*b + (7*A + 8*C)*a^4*b^3 - (10*A + 9*C)*a^2*b^5 + A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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*((4*A + 3*C)*a^5*b + (A + 2*C)*a^3*b^3 + ((4*A + 3*C)*a^2*b^4 + (A + 2*C)*b^6)*cos(d*x + c)^3 + 3*((4*A + 3*C)*a^3*b^3 + (A + 2*C)*a*b^5)*cos(d*x + c)^2 + 3*((4*A + 3*C)*a^4*b^2 + (A + 2*C)*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))) - (2*(3*A + 2*C)*a^7 + (4*A + 7*C)*a^5*b^2 - 11*(A + C)*a^3*b^4 + A*a*b^6 + (2*C*a^7 + (2*A - 7*C)*a^5*b^2 + (11*A + 23*C)*a^3*b^4 - (13*A + 18*C)*a*b^6)*cos(d*x + c)^2 + 3*((2*A + C)*a^6*b + (7*A + 8*C)*a^4*b^3 - (10*A + 9*C)*a^2*b^5 + A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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
589,1,1105,0,0.608643," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(2 \, A + C\right)} a^{6} + {\left(3 \, A + 4 \, C\right)} a^{4} b^{2} + {\left({\left(2 \, A + C\right)} a^{3} b^{3} + {\left(3 \, A + 4 \, C\right)} a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(2 \, A + C\right)} a^{4} b^{2} + {\left(3 \, A + 4 \, C\right)} a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{5} b + {\left(3 \, A + 4 \, C\right)} a^{3} b^{3}\right)} \cos\left(d x + c\right)\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(18 \, A + 13 \, C\right)} a^{6} b - {\left(23 \, A + 11 \, C\right)} a^{4} b^{3} + {\left(7 \, A - 2 \, C\right)} a^{2} b^{5} - 2 \, A b^{7} - {\left(C a^{6} b - 11 \, {\left(A + C\right)} a^{4} b^{3} + {\left(7 \, A + 4 \, C\right)} a^{2} b^{5} + 2 \, {\left(2 \, A + 3 \, C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{7} - {\left(9 \, A + 10 \, C\right)} a^{5} b^{2} + {\left(8 \, A + 7 \, C\right)} a^{3} b^{4} + {\left(A + 2 \, C\right)} a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{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({\left(2 \, A + C\right)} a^{6} + {\left(3 \, A + 4 \, C\right)} a^{4} b^{2} + {\left({\left(2 \, A + C\right)} a^{3} b^{3} + {\left(3 \, A + 4 \, C\right)} a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(2 \, A + C\right)} a^{4} b^{2} + {\left(3 \, A + 4 \, C\right)} a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{5} b + {\left(3 \, A + 4 \, C\right)} a^{3} b^{3}\right)} \cos\left(d x + c\right)\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(18 \, A + 13 \, C\right)} a^{6} b - {\left(23 \, A + 11 \, C\right)} a^{4} b^{3} + {\left(7 \, A - 2 \, C\right)} a^{2} b^{5} - 2 \, A b^{7} - {\left(C a^{6} b - 11 \, {\left(A + C\right)} a^{4} b^{3} + {\left(7 \, A + 4 \, C\right)} a^{2} b^{5} + 2 \, {\left(2 \, A + 3 \, C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{7} - {\left(9 \, A + 10 \, C\right)} a^{5} b^{2} + {\left(8 \, A + 7 \, C\right)} a^{3} b^{4} + {\left(A + 2 \, C\right)} a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{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 + C)*a^6 + (3*A + 4*C)*a^4*b^2 + ((2*A + C)*a^3*b^3 + (3*A + 4*C)*a*b^5)*cos(d*x + c)^3 + 3*((2*A + C)*a^4*b^2 + (3*A + 4*C)*a^2*b^4)*cos(d*x + c)^2 + 3*((2*A + C)*a^5*b + (3*A + 4*C)*a^3*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*((18*A + 13*C)*a^6*b - (23*A + 11*C)*a^4*b^3 + (7*A - 2*C)*a^2*b^5 - 2*A*b^7 - (C*a^6*b - 11*(A + C)*a^4*b^3 + (7*A + 4*C)*a^2*b^5 + 2*(2*A + 3*C)*b^7)*cos(d*x + c)^2 - 3*(C*a^7 - (9*A + 10*C)*a^5*b^2 + (8*A + 7*C)*a^3*b^4 + (A + 2*C)*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^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 + C)*a^6 + (3*A + 4*C)*a^4*b^2 + ((2*A + C)*a^3*b^3 + (3*A + 4*C)*a*b^5)*cos(d*x + c)^3 + 3*((2*A + C)*a^4*b^2 + (3*A + 4*C)*a^2*b^4)*cos(d*x + c)^2 + 3*((2*A + C)*a^5*b + (3*A + 4*C)*a^3*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))) - ((18*A + 13*C)*a^6*b - (23*A + 11*C)*a^4*b^3 + (7*A - 2*C)*a^2*b^5 - 2*A*b^7 - (C*a^6*b - 11*(A + C)*a^4*b^3 + (7*A + 4*C)*a^2*b^5 + 2*(2*A + 3*C)*b^7)*cos(d*x + c)^2 - 3*(C*a^7 - (9*A + 10*C)*a^5*b^2 + (8*A + 7*C)*a^3*b^4 + (A + 2*C)*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^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
590,1,2159,0,25.238363," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{9} b - {\left(8 \, A - C\right)} a^{7} b^{3} + 7 \, A a^{5} b^{5} - 2 \, A a^{3} b^{7} + {\left(4 \, {\left(2 \, A + C\right)} a^{6} b^{4} - {\left(8 \, A - C\right)} a^{4} b^{6} + 7 \, A a^{2} b^{8} - 2 \, A b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{7} b^{3} - {\left(8 \, A - C\right)} a^{5} b^{5} + 7 \, A a^{3} b^{7} - 2 \, A a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{8} b^{2} - {\left(8 \, A - C\right)} a^{6} b^{4} + 7 \, A a^{4} b^{6} - 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)\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(6 \, C a^{11} + 4 \, {\left(9 \, A + C\right)} a^{9} b^{2} - {\left(68 \, A + 11 \, C\right)} a^{7} b^{4} + {\left(43 \, A + C\right)} a^{5} b^{6} - 11 \, A a^{3} b^{8} + {\left(2 \, C a^{9} b^{2} + {\left(26 \, A + 11 \, C\right)} a^{7} b^{4} - {\left(43 \, A + 13 \, C\right)} a^{5} b^{6} + 23 \, A a^{3} b^{8} - 6 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{10} b + {\left(20 \, A + 7 \, C\right)} a^{8} b^{3} - 5 \, {\left(7 \, A + 2 \, C\right)} a^{6} b^{5} + {\left(20 \, A + C\right)} a^{4} b^{7} - 5 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{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(4 \, {\left(2 \, A + C\right)} a^{9} b - {\left(8 \, A - C\right)} a^{7} b^{3} + 7 \, A a^{5} b^{5} - 2 \, A a^{3} b^{7} + {\left(4 \, {\left(2 \, A + C\right)} a^{6} b^{4} - {\left(8 \, A - C\right)} a^{4} b^{6} + 7 \, A a^{2} b^{8} - 2 \, A b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{7} b^{3} - {\left(8 \, A - C\right)} a^{5} b^{5} + 7 \, A a^{3} b^{7} - 2 \, A a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{8} b^{2} - {\left(8 \, A - C\right)} a^{6} b^{4} + 7 \, A a^{4} b^{6} - 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)\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(6 \, C a^{11} + 4 \, {\left(9 \, A + C\right)} a^{9} b^{2} - {\left(68 \, A + 11 \, C\right)} a^{7} b^{4} + {\left(43 \, A + C\right)} a^{5} b^{6} - 11 \, A a^{3} b^{8} + {\left(2 \, C a^{9} b^{2} + {\left(26 \, A + 11 \, C\right)} a^{7} b^{4} - {\left(43 \, A + 13 \, C\right)} a^{5} b^{6} + 23 \, A a^{3} b^{8} - 6 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{10} b + {\left(20 \, A + 7 \, C\right)} a^{8} b^{3} - 5 \, {\left(7 \, A + 2 \, C\right)} a^{6} b^{5} + {\left(20 \, A + C\right)} a^{4} b^{7} - 5 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{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*(4*(2*A + C)*a^9*b - (8*A - C)*a^7*b^3 + 7*A*a^5*b^5 - 2*A*a^3*b^7 + (4*(2*A + C)*a^6*b^4 - (8*A - C)*a^4*b^6 + 7*A*a^2*b^8 - 2*A*b^10)*cos(d*x + c)^3 + 3*(4*(2*A + C)*a^7*b^3 - (8*A - C)*a^5*b^5 + 7*A*a^3*b^7 - 2*A*a*b^9)*cos(d*x + c)^2 + 3*(4*(2*A + C)*a^8*b^2 - (8*A - C)*a^6*b^4 + 7*A*a^4*b^6 - 2*A*a^2*b^8)*cos(d*x + c))*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*(6*C*a^11 + 4*(9*A + C)*a^9*b^2 - (68*A + 11*C)*a^7*b^4 + (43*A + C)*a^5*b^6 - 11*A*a^3*b^8 + (2*C*a^9*b^2 + (26*A + 11*C)*a^7*b^4 - (43*A + 13*C)*a^5*b^6 + 23*A*a^3*b^8 - 6*A*a*b^10)*cos(d*x + c)^2 + 3*(2*C*a^10*b + (20*A + 7*C)*a^8*b^3 - 5*(7*A + 2*C)*a^6*b^5 + (20*A + C)*a^4*b^7 - 5*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^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*(4*(2*A + C)*a^9*b - (8*A - C)*a^7*b^3 + 7*A*a^5*b^5 - 2*A*a^3*b^7 + (4*(2*A + C)*a^6*b^4 - (8*A - C)*a^4*b^6 + 7*A*a^2*b^8 - 2*A*b^10)*cos(d*x + c)^3 + 3*(4*(2*A + C)*a^7*b^3 - (8*A - C)*a^5*b^5 + 7*A*a^3*b^7 - 2*A*a*b^9)*cos(d*x + c)^2 + 3*(4*(2*A + C)*a^8*b^2 - (8*A - C)*a^6*b^4 + 7*A*a^4*b^6 - 2*A*a^2*b^8)*cos(d*x + c))*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) - (6*C*a^11 + 4*(9*A + C)*a^9*b^2 - (68*A + 11*C)*a^7*b^4 + (43*A + C)*a^5*b^6 - 11*A*a^3*b^8 + (2*C*a^9*b^2 + (26*A + 11*C)*a^7*b^4 - (43*A + 13*C)*a^5*b^6 + 23*A*a^3*b^8 - 6*A*a*b^10)*cos(d*x + c)^2 + 3*(2*C*a^10*b + (20*A + 7*C)*a^8*b^3 - 5*(7*A + 2*C)*a^6*b^5 + (20*A + C)*a^4*b^7 - 5*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^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
591,1,2410,0,35.616573," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, C a^{8} b^{3} + {\left(20 \, A + 3 \, C\right)} a^{6} b^{5} - 35 \, A a^{4} b^{7} + 28 \, A a^{2} b^{9} - 8 \, A b^{11}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, C a^{9} b^{2} + {\left(20 \, A + 3 \, C\right)} a^{7} b^{4} - 35 \, A a^{5} b^{6} + 28 \, A a^{3} b^{8} - 8 \, A a b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{10} b + {\left(20 \, A + 3 \, C\right)} a^{8} b^{3} - 35 \, A a^{6} b^{5} + 28 \, A a^{4} b^{7} - 8 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{11} + {\left(20 \, A + 3 \, C\right)} a^{9} b^{2} - 35 \, A a^{7} b^{4} + 28 \, A a^{5} b^{6} - 8 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)\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) + 24 \, {\left({\left(A a^{8} b^{4} - 4 \, A a^{6} b^{6} + 6 \, A a^{4} b^{8} - 4 \, A a^{2} b^{10} + A b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(A a^{9} b^{3} - 4 \, A a^{7} b^{5} + 6 \, A a^{5} b^{7} - 4 \, A a^{3} b^{9} + A a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{10} b^{2} - 4 \, A a^{8} b^{4} + 6 \, A a^{6} b^{6} - 4 \, A a^{4} b^{8} + A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{11} b - 4 \, A a^{9} b^{3} + 6 \, A a^{7} b^{5} - 4 \, A a^{5} b^{7} + A a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 24 \, {\left({\left(A a^{8} b^{4} - 4 \, A a^{6} b^{6} + 6 \, A a^{4} b^{8} - 4 \, A a^{2} b^{10} + A b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(A a^{9} b^{3} - 4 \, A a^{7} b^{5} + 6 \, A a^{5} b^{7} - 4 \, A a^{3} b^{9} + A a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{10} b^{2} - 4 \, A a^{8} b^{4} + 6 \, A a^{6} b^{6} - 4 \, A a^{4} b^{8} + A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{11} b - 4 \, A a^{9} b^{3} + 6 \, A a^{7} b^{5} - 4 \, A a^{5} b^{7} + A a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(6 \, A a^{12} - 24 \, A a^{10} b^{2} + 36 \, A a^{8} b^{4} - 24 \, A a^{6} b^{6} + 6 \, A a^{4} b^{8} + {\left({\left(6 \, A - 11 \, C\right)} a^{9} b^{3} - {\left(71 \, A - 7 \, C\right)} a^{7} b^{5} + {\left(133 \, A + 4 \, C\right)} a^{5} b^{7} - 92 \, A a^{3} b^{9} + 24 \, A a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, {\left(2 \, A - 3 \, C\right)} a^{10} b^{2} - {\left(59 \, A - 8 \, C\right)} a^{8} b^{4} + {\left(110 \, A + C\right)} a^{6} b^{6} - 77 \, A a^{4} b^{8} + 20 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, {\left(A - C\right)} a^{11} b - {\left(132 \, A - 23 \, C\right)} a^{9} b^{3} + {\left(239 \, A - 7 \, C\right)} a^{7} b^{5} - {\left(169 \, A - 2 \, C\right)} a^{5} b^{7} + 44 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{13} b^{3} - 4 \, a^{11} b^{5} + 6 \, a^{9} b^{7} - 4 \, a^{7} b^{9} + a^{5} b^{11}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{14} b^{2} - 4 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 4 \, a^{8} b^{8} + a^{6} b^{10}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{15} b - 4 \, a^{13} b^{3} + 6 \, a^{11} b^{5} - 4 \, a^{9} b^{7} + a^{7} b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{16} - 4 \, a^{14} b^{2} + 6 \, a^{12} b^{4} - 4 \, a^{10} b^{6} + a^{8} b^{8}\right)} d \cos\left(d x + c\right)\right)}}, \frac{3 \, {\left({\left(2 \, C a^{8} b^{3} + {\left(20 \, A + 3 \, C\right)} a^{6} b^{5} - 35 \, A a^{4} b^{7} + 28 \, A a^{2} b^{9} - 8 \, A b^{11}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, C a^{9} b^{2} + {\left(20 \, A + 3 \, C\right)} a^{7} b^{4} - 35 \, A a^{5} b^{6} + 28 \, A a^{3} b^{8} - 8 \, A a b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{10} b + {\left(20 \, A + 3 \, C\right)} a^{8} b^{3} - 35 \, A a^{6} b^{5} + 28 \, A a^{4} b^{7} - 8 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{11} + {\left(20 \, A + 3 \, C\right)} a^{9} b^{2} - 35 \, A a^{7} b^{4} + 28 \, A a^{5} b^{6} - 8 \, A a^{3} b^{8}\right)} \cos\left(d x + c\right)\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) - 12 \, {\left({\left(A a^{8} b^{4} - 4 \, A a^{6} b^{6} + 6 \, A a^{4} b^{8} - 4 \, A a^{2} b^{10} + A b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(A a^{9} b^{3} - 4 \, A a^{7} b^{5} + 6 \, A a^{5} b^{7} - 4 \, A a^{3} b^{9} + A a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{10} b^{2} - 4 \, A a^{8} b^{4} + 6 \, A a^{6} b^{6} - 4 \, A a^{4} b^{8} + A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{11} b - 4 \, A a^{9} b^{3} + 6 \, A a^{7} b^{5} - 4 \, A a^{5} b^{7} + A a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 12 \, {\left({\left(A a^{8} b^{4} - 4 \, A a^{6} b^{6} + 6 \, A a^{4} b^{8} - 4 \, A a^{2} b^{10} + A b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(A a^{9} b^{3} - 4 \, A a^{7} b^{5} + 6 \, A a^{5} b^{7} - 4 \, A a^{3} b^{9} + A a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(A a^{10} b^{2} - 4 \, A a^{8} b^{4} + 6 \, A a^{6} b^{6} - 4 \, A a^{4} b^{8} + A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(A a^{11} b - 4 \, A a^{9} b^{3} + 6 \, A a^{7} b^{5} - 4 \, A a^{5} b^{7} + A a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, A a^{12} - 24 \, A a^{10} b^{2} + 36 \, A a^{8} b^{4} - 24 \, A a^{6} b^{6} + 6 \, A a^{4} b^{8} + {\left({\left(6 \, A - 11 \, C\right)} a^{9} b^{3} - {\left(71 \, A - 7 \, C\right)} a^{7} b^{5} + {\left(133 \, A + 4 \, C\right)} a^{5} b^{7} - 92 \, A a^{3} b^{9} + 24 \, A a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, {\left(2 \, A - 3 \, C\right)} a^{10} b^{2} - {\left(59 \, A - 8 \, C\right)} a^{8} b^{4} + {\left(110 \, A + C\right)} a^{6} b^{6} - 77 \, A a^{4} b^{8} + 20 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, {\left(A - C\right)} a^{11} b - {\left(132 \, A - 23 \, C\right)} a^{9} b^{3} + {\left(239 \, A - 7 \, C\right)} a^{7} b^{5} - {\left(169 \, A - 2 \, C\right)} a^{5} b^{7} + 44 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{13} b^{3} - 4 \, a^{11} b^{5} + 6 \, a^{9} b^{7} - 4 \, a^{7} b^{9} + a^{5} b^{11}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{14} b^{2} - 4 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 4 \, a^{8} b^{8} + a^{6} b^{10}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{15} b - 4 \, a^{13} b^{3} + 6 \, a^{11} b^{5} - 4 \, a^{9} b^{7} + a^{7} b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{16} - 4 \, a^{14} b^{2} + 6 \, a^{12} b^{4} - 4 \, a^{10} b^{6} + a^{8} b^{8}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/12*(3*((2*C*a^8*b^3 + (20*A + 3*C)*a^6*b^5 - 35*A*a^4*b^7 + 28*A*a^2*b^9 - 8*A*b^11)*cos(d*x + c)^4 + 3*(2*C*a^9*b^2 + (20*A + 3*C)*a^7*b^4 - 35*A*a^5*b^6 + 28*A*a^3*b^8 - 8*A*a*b^10)*cos(d*x + c)^3 + 3*(2*C*a^10*b + (20*A + 3*C)*a^8*b^3 - 35*A*a^6*b^5 + 28*A*a^4*b^7 - 8*A*a^2*b^9)*cos(d*x + c)^2 + (2*C*a^11 + (20*A + 3*C)*a^9*b^2 - 35*A*a^7*b^4 + 28*A*a^5*b^6 - 8*A*a^3*b^8)*cos(d*x + c))*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)) + 24*((A*a^8*b^4 - 4*A*a^6*b^6 + 6*A*a^4*b^8 - 4*A*a^2*b^10 + A*b^12)*cos(d*x + c)^4 + 3*(A*a^9*b^3 - 4*A*a^7*b^5 + 6*A*a^5*b^7 - 4*A*a^3*b^9 + A*a*b^11)*cos(d*x + c)^3 + 3*(A*a^10*b^2 - 4*A*a^8*b^4 + 6*A*a^6*b^6 - 4*A*a^4*b^8 + A*a^2*b^10)*cos(d*x + c)^2 + (A*a^11*b - 4*A*a^9*b^3 + 6*A*a^7*b^5 - 4*A*a^5*b^7 + A*a^3*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) - 24*((A*a^8*b^4 - 4*A*a^6*b^6 + 6*A*a^4*b^8 - 4*A*a^2*b^10 + A*b^12)*cos(d*x + c)^4 + 3*(A*a^9*b^3 - 4*A*a^7*b^5 + 6*A*a^5*b^7 - 4*A*a^3*b^9 + A*a*b^11)*cos(d*x + c)^3 + 3*(A*a^10*b^2 - 4*A*a^8*b^4 + 6*A*a^6*b^6 - 4*A*a^4*b^8 + A*a^2*b^10)*cos(d*x + c)^2 + (A*a^11*b - 4*A*a^9*b^3 + 6*A*a^7*b^5 - 4*A*a^5*b^7 + A*a^3*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(6*A*a^12 - 24*A*a^10*b^2 + 36*A*a^8*b^4 - 24*A*a^6*b^6 + 6*A*a^4*b^8 + ((6*A - 11*C)*a^9*b^3 - (71*A - 7*C)*a^7*b^5 + (133*A + 4*C)*a^5*b^7 - 92*A*a^3*b^9 + 24*A*a*b^11)*cos(d*x + c)^3 + 3*(3*(2*A - 3*C)*a^10*b^2 - (59*A - 8*C)*a^8*b^4 + (110*A + C)*a^6*b^6 - 77*A*a^4*b^8 + 20*A*a^2*b^10)*cos(d*x + c)^2 + (18*(A - C)*a^11*b - (132*A - 23*C)*a^9*b^3 + (239*A - 7*C)*a^7*b^5 - (169*A - 2*C)*a^5*b^7 + 44*A*a^3*b^9)*cos(d*x + c))*sin(d*x + c))/((a^13*b^3 - 4*a^11*b^5 + 6*a^9*b^7 - 4*a^7*b^9 + a^5*b^11)*d*cos(d*x + c)^4 + 3*(a^14*b^2 - 4*a^12*b^4 + 6*a^10*b^6 - 4*a^8*b^8 + a^6*b^10)*d*cos(d*x + c)^3 + 3*(a^15*b - 4*a^13*b^3 + 6*a^11*b^5 - 4*a^9*b^7 + a^7*b^9)*d*cos(d*x + c)^2 + (a^16 - 4*a^14*b^2 + 6*a^12*b^4 - 4*a^10*b^6 + a^8*b^8)*d*cos(d*x + c)), 1/6*(3*((2*C*a^8*b^3 + (20*A + 3*C)*a^6*b^5 - 35*A*a^4*b^7 + 28*A*a^2*b^9 - 8*A*b^11)*cos(d*x + c)^4 + 3*(2*C*a^9*b^2 + (20*A + 3*C)*a^7*b^4 - 35*A*a^5*b^6 + 28*A*a^3*b^8 - 8*A*a*b^10)*cos(d*x + c)^3 + 3*(2*C*a^10*b + (20*A + 3*C)*a^8*b^3 - 35*A*a^6*b^5 + 28*A*a^4*b^7 - 8*A*a^2*b^9)*cos(d*x + c)^2 + (2*C*a^11 + (20*A + 3*C)*a^9*b^2 - 35*A*a^7*b^4 + 28*A*a^5*b^6 - 8*A*a^3*b^8)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 12*((A*a^8*b^4 - 4*A*a^6*b^6 + 6*A*a^4*b^8 - 4*A*a^2*b^10 + A*b^12)*cos(d*x + c)^4 + 3*(A*a^9*b^3 - 4*A*a^7*b^5 + 6*A*a^5*b^7 - 4*A*a^3*b^9 + A*a*b^11)*cos(d*x + c)^3 + 3*(A*a^10*b^2 - 4*A*a^8*b^4 + 6*A*a^6*b^6 - 4*A*a^4*b^8 + A*a^2*b^10)*cos(d*x + c)^2 + (A*a^11*b - 4*A*a^9*b^3 + 6*A*a^7*b^5 - 4*A*a^5*b^7 + A*a^3*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) + 12*((A*a^8*b^4 - 4*A*a^6*b^6 + 6*A*a^4*b^8 - 4*A*a^2*b^10 + A*b^12)*cos(d*x + c)^4 + 3*(A*a^9*b^3 - 4*A*a^7*b^5 + 6*A*a^5*b^7 - 4*A*a^3*b^9 + A*a*b^11)*cos(d*x + c)^3 + 3*(A*a^10*b^2 - 4*A*a^8*b^4 + 6*A*a^6*b^6 - 4*A*a^4*b^8 + A*a^2*b^10)*cos(d*x + c)^2 + (A*a^11*b - 4*A*a^9*b^3 + 6*A*a^7*b^5 - 4*A*a^5*b^7 + A*a^3*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (6*A*a^12 - 24*A*a^10*b^2 + 36*A*a^8*b^4 - 24*A*a^6*b^6 + 6*A*a^4*b^8 + ((6*A - 11*C)*a^9*b^3 - (71*A - 7*C)*a^7*b^5 + (133*A + 4*C)*a^5*b^7 - 92*A*a^3*b^9 + 24*A*a*b^11)*cos(d*x + c)^3 + 3*(3*(2*A - 3*C)*a^10*b^2 - (59*A - 8*C)*a^8*b^4 + (110*A + C)*a^6*b^6 - 77*A*a^4*b^8 + 20*A*a^2*b^10)*cos(d*x + c)^2 + (18*(A - C)*a^11*b - (132*A - 23*C)*a^9*b^3 + (239*A - 7*C)*a^7*b^5 - (169*A - 2*C)*a^5*b^7 + 44*A*a^3*b^9)*cos(d*x + c))*sin(d*x + c))/((a^13*b^3 - 4*a^11*b^5 + 6*a^9*b^7 - 4*a^7*b^9 + a^5*b^11)*d*cos(d*x + c)^4 + 3*(a^14*b^2 - 4*a^12*b^4 + 6*a^10*b^6 - 4*a^8*b^8 + a^6*b^10)*d*cos(d*x + c)^3 + 3*(a^15*b - 4*a^13*b^3 + 6*a^11*b^5 - 4*a^9*b^7 + a^7*b^9)*d*cos(d*x + c)^2 + (a^16 - 4*a^14*b^2 + 6*a^12*b^4 - 4*a^10*b^6 + a^8*b^8)*d*cos(d*x + c))]","B",0
592,1,3269,0,87.112807," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(8 \, C a^{8} b^{4} + 8 \, {\left(5 \, A - C\right)} a^{6} b^{6} - 7 \, {\left(12 \, A - C\right)} a^{4} b^{8} + {\left(69 \, A - 2 \, C\right)} a^{2} b^{10} - 20 \, A b^{12}\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(8 \, C a^{9} b^{3} + 8 \, {\left(5 \, A - C\right)} a^{7} b^{5} - 7 \, {\left(12 \, A - C\right)} a^{5} b^{7} + {\left(69 \, A - 2 \, C\right)} a^{3} b^{9} - 20 \, A a b^{11}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(8 \, C a^{10} b^{2} + 8 \, {\left(5 \, A - C\right)} a^{8} b^{4} - 7 \, {\left(12 \, A - C\right)} a^{6} b^{6} + {\left(69 \, A - 2 \, C\right)} a^{4} b^{8} - 20 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, C a^{11} b + 8 \, {\left(5 \, A - C\right)} a^{9} b^{3} - 7 \, {\left(12 \, A - C\right)} a^{7} b^{5} + {\left(69 \, A - 2 \, C\right)} a^{5} b^{7} - 20 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{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) - 3 \, {\left({\left({\left(A + 2 \, C\right)} a^{10} b^{3} + 8 \, {\left(2 \, A - C\right)} a^{8} b^{5} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{6} b^{7} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{4} b^{9} - {\left(79 \, A - 2 \, C\right)} a^{2} b^{11} + 20 \, A b^{13}\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left({\left(A + 2 \, C\right)} a^{11} b^{2} + 8 \, {\left(2 \, A - C\right)} a^{9} b^{4} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{7} b^{6} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{5} b^{8} - {\left(79 \, A - 2 \, C\right)} a^{3} b^{10} + 20 \, A a b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left({\left(A + 2 \, C\right)} a^{12} b + 8 \, {\left(2 \, A - C\right)} a^{10} b^{3} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{8} b^{5} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{6} b^{7} - {\left(79 \, A - 2 \, C\right)} a^{4} b^{9} + 20 \, A a^{2} b^{11}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{13} + 8 \, {\left(2 \, A - C\right)} a^{11} b^{2} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{9} b^{4} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{7} b^{6} - {\left(79 \, A - 2 \, C\right)} a^{5} b^{8} + 20 \, A a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left({\left(A + 2 \, C\right)} a^{10} b^{3} + 8 \, {\left(2 \, A - C\right)} a^{8} b^{5} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{6} b^{7} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{4} b^{9} - {\left(79 \, A - 2 \, C\right)} a^{2} b^{11} + 20 \, A b^{13}\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left({\left(A + 2 \, C\right)} a^{11} b^{2} + 8 \, {\left(2 \, A - C\right)} a^{9} b^{4} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{7} b^{6} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{5} b^{8} - {\left(79 \, A - 2 \, C\right)} a^{3} b^{10} + 20 \, A a b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left({\left(A + 2 \, C\right)} a^{12} b + 8 \, {\left(2 \, A - C\right)} a^{10} b^{3} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{8} b^{5} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{6} b^{7} - {\left(79 \, A - 2 \, C\right)} a^{4} b^{9} + 20 \, A a^{2} b^{11}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{13} + 8 \, {\left(2 \, A - C\right)} a^{11} b^{2} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{9} b^{4} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{7} b^{6} - {\left(79 \, A - 2 \, C\right)} a^{5} b^{8} + 20 \, A a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(3 \, A a^{13} - 12 \, A a^{11} b^{2} + 18 \, A a^{9} b^{4} - 12 \, A a^{7} b^{6} + 3 \, A a^{5} b^{8} - {\left(2 \, {\left(12 \, A - 13 \, C\right)} a^{9} b^{4} - {\left(170 \, A - 43 \, C\right)} a^{7} b^{6} + {\left(313 \, A - 23 \, C\right)} a^{5} b^{8} - {\left(227 \, A - 6 \, C\right)} a^{3} b^{10} + 60 \, A a b^{12}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left({\left(23 \, A - 20 \, C\right)} a^{10} b^{3} - {\left(146 \, A - 35 \, C\right)} a^{8} b^{5} + {\left(263 \, A - 20 \, C\right)} a^{6} b^{7} - 5 \, {\left(38 \, A - C\right)} a^{4} b^{9} + 50 \, A a^{2} b^{11}\right)} \cos\left(d x + c\right)^{3} - {\left(9 \, {\left(7 \, A - 4 \, C\right)} a^{11} b^{2} - 2 \, {\left(171 \, A - 34 \, C\right)} a^{9} b^{4} + {\left(590 \, A - 43 \, C\right)} a^{7} b^{6} - {\left(421 \, A - 11 \, C\right)} a^{5} b^{8} + 110 \, A a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left(A a^{12} b - 4 \, A a^{10} b^{3} + 6 \, A a^{8} b^{5} - 4 \, A a^{6} b^{7} + A a^{4} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{14} b^{3} - 4 \, a^{12} b^{5} + 6 \, a^{10} b^{7} - 4 \, a^{8} b^{9} + a^{6} b^{11}\right)} d \cos\left(d x + c\right)^{5} + 3 \, {\left(a^{15} b^{2} - 4 \, a^{13} b^{4} + 6 \, a^{11} b^{6} - 4 \, a^{9} b^{8} + a^{7} b^{10}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{16} b - 4 \, a^{14} b^{3} + 6 \, a^{12} b^{5} - 4 \, a^{10} b^{7} + a^{8} b^{9}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{17} - 4 \, a^{15} b^{2} + 6 \, a^{13} b^{4} - 4 \, a^{11} b^{6} + a^{9} b^{8}\right)} d \cos\left(d x + c\right)^{2}\right)}}, -\frac{6 \, {\left({\left(8 \, C a^{8} b^{4} + 8 \, {\left(5 \, A - C\right)} a^{6} b^{6} - 7 \, {\left(12 \, A - C\right)} a^{4} b^{8} + {\left(69 \, A - 2 \, C\right)} a^{2} b^{10} - 20 \, A b^{12}\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(8 \, C a^{9} b^{3} + 8 \, {\left(5 \, A - C\right)} a^{7} b^{5} - 7 \, {\left(12 \, A - C\right)} a^{5} b^{7} + {\left(69 \, A - 2 \, C\right)} a^{3} b^{9} - 20 \, A a b^{11}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(8 \, C a^{10} b^{2} + 8 \, {\left(5 \, A - C\right)} a^{8} b^{4} - 7 \, {\left(12 \, A - C\right)} a^{6} b^{6} + {\left(69 \, A - 2 \, C\right)} a^{4} b^{8} - 20 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{3} + {\left(8 \, C a^{11} b + 8 \, {\left(5 \, A - C\right)} a^{9} b^{3} - 7 \, {\left(12 \, A - C\right)} a^{7} b^{5} + {\left(69 \, A - 2 \, C\right)} a^{5} b^{7} - 20 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)^{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) - 3 \, {\left({\left({\left(A + 2 \, C\right)} a^{10} b^{3} + 8 \, {\left(2 \, A - C\right)} a^{8} b^{5} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{6} b^{7} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{4} b^{9} - {\left(79 \, A - 2 \, C\right)} a^{2} b^{11} + 20 \, A b^{13}\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left({\left(A + 2 \, C\right)} a^{11} b^{2} + 8 \, {\left(2 \, A - C\right)} a^{9} b^{4} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{7} b^{6} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{5} b^{8} - {\left(79 \, A - 2 \, C\right)} a^{3} b^{10} + 20 \, A a b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left({\left(A + 2 \, C\right)} a^{12} b + 8 \, {\left(2 \, A - C\right)} a^{10} b^{3} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{8} b^{5} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{6} b^{7} - {\left(79 \, A - 2 \, C\right)} a^{4} b^{9} + 20 \, A a^{2} b^{11}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{13} + 8 \, {\left(2 \, A - C\right)} a^{11} b^{2} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{9} b^{4} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{7} b^{6} - {\left(79 \, A - 2 \, C\right)} a^{5} b^{8} + 20 \, A a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left({\left(A + 2 \, C\right)} a^{10} b^{3} + 8 \, {\left(2 \, A - C\right)} a^{8} b^{5} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{6} b^{7} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{4} b^{9} - {\left(79 \, A - 2 \, C\right)} a^{2} b^{11} + 20 \, A b^{13}\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left({\left(A + 2 \, C\right)} a^{11} b^{2} + 8 \, {\left(2 \, A - C\right)} a^{9} b^{4} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{7} b^{6} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{5} b^{8} - {\left(79 \, A - 2 \, C\right)} a^{3} b^{10} + 20 \, A a b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left({\left(A + 2 \, C\right)} a^{12} b + 8 \, {\left(2 \, A - C\right)} a^{10} b^{3} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{8} b^{5} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{6} b^{7} - {\left(79 \, A - 2 \, C\right)} a^{4} b^{9} + 20 \, A a^{2} b^{11}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{13} + 8 \, {\left(2 \, A - C\right)} a^{11} b^{2} - 2 \, {\left(37 \, A - 6 \, C\right)} a^{9} b^{4} + 4 \, {\left(29 \, A - 2 \, C\right)} a^{7} b^{6} - {\left(79 \, A - 2 \, C\right)} a^{5} b^{8} + 20 \, A a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(3 \, A a^{13} - 12 \, A a^{11} b^{2} + 18 \, A a^{9} b^{4} - 12 \, A a^{7} b^{6} + 3 \, A a^{5} b^{8} - {\left(2 \, {\left(12 \, A - 13 \, C\right)} a^{9} b^{4} - {\left(170 \, A - 43 \, C\right)} a^{7} b^{6} + {\left(313 \, A - 23 \, C\right)} a^{5} b^{8} - {\left(227 \, A - 6 \, C\right)} a^{3} b^{10} + 60 \, A a b^{12}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left({\left(23 \, A - 20 \, C\right)} a^{10} b^{3} - {\left(146 \, A - 35 \, C\right)} a^{8} b^{5} + {\left(263 \, A - 20 \, C\right)} a^{6} b^{7} - 5 \, {\left(38 \, A - C\right)} a^{4} b^{9} + 50 \, A a^{2} b^{11}\right)} \cos\left(d x + c\right)^{3} - {\left(9 \, {\left(7 \, A - 4 \, C\right)} a^{11} b^{2} - 2 \, {\left(171 \, A - 34 \, C\right)} a^{9} b^{4} + {\left(590 \, A - 43 \, C\right)} a^{7} b^{6} - {\left(421 \, A - 11 \, C\right)} a^{5} b^{8} + 110 \, A a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left(A a^{12} b - 4 \, A a^{10} b^{3} + 6 \, A a^{8} b^{5} - 4 \, A a^{6} b^{7} + A a^{4} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{14} b^{3} - 4 \, a^{12} b^{5} + 6 \, a^{10} b^{7} - 4 \, a^{8} b^{9} + a^{6} b^{11}\right)} d \cos\left(d x + c\right)^{5} + 3 \, {\left(a^{15} b^{2} - 4 \, a^{13} b^{4} + 6 \, a^{11} b^{6} - 4 \, a^{9} b^{8} + a^{7} b^{10}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{16} b - 4 \, a^{14} b^{3} + 6 \, a^{12} b^{5} - 4 \, a^{10} b^{7} + a^{8} b^{9}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{17} - 4 \, a^{15} b^{2} + 6 \, a^{13} b^{4} - 4 \, a^{11} b^{6} + a^{9} b^{8}\right)} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/12*(3*((8*C*a^8*b^4 + 8*(5*A - C)*a^6*b^6 - 7*(12*A - C)*a^4*b^8 + (69*A - 2*C)*a^2*b^10 - 20*A*b^12)*cos(d*x + c)^5 + 3*(8*C*a^9*b^3 + 8*(5*A - C)*a^7*b^5 - 7*(12*A - C)*a^5*b^7 + (69*A - 2*C)*a^3*b^9 - 20*A*a*b^11)*cos(d*x + c)^4 + 3*(8*C*a^10*b^2 + 8*(5*A - C)*a^8*b^4 - 7*(12*A - C)*a^6*b^6 + (69*A - 2*C)*a^4*b^8 - 20*A*a^2*b^10)*cos(d*x + c)^3 + (8*C*a^11*b + 8*(5*A - C)*a^9*b^3 - 7*(12*A - C)*a^7*b^5 + (69*A - 2*C)*a^5*b^7 - 20*A*a^3*b^9)*cos(d*x + c)^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)) - 3*(((A + 2*C)*a^10*b^3 + 8*(2*A - C)*a^8*b^5 - 2*(37*A - 6*C)*a^6*b^7 + 4*(29*A - 2*C)*a^4*b^9 - (79*A - 2*C)*a^2*b^11 + 20*A*b^13)*cos(d*x + c)^5 + 3*((A + 2*C)*a^11*b^2 + 8*(2*A - C)*a^9*b^4 - 2*(37*A - 6*C)*a^7*b^6 + 4*(29*A - 2*C)*a^5*b^8 - (79*A - 2*C)*a^3*b^10 + 20*A*a*b^12)*cos(d*x + c)^4 + 3*((A + 2*C)*a^12*b + 8*(2*A - C)*a^10*b^3 - 2*(37*A - 6*C)*a^8*b^5 + 4*(29*A - 2*C)*a^6*b^7 - (79*A - 2*C)*a^4*b^9 + 20*A*a^2*b^11)*cos(d*x + c)^3 + ((A + 2*C)*a^13 + 8*(2*A - C)*a^11*b^2 - 2*(37*A - 6*C)*a^9*b^4 + 4*(29*A - 2*C)*a^7*b^6 - (79*A - 2*C)*a^5*b^8 + 20*A*a^3*b^10)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + 3*(((A + 2*C)*a^10*b^3 + 8*(2*A - C)*a^8*b^5 - 2*(37*A - 6*C)*a^6*b^7 + 4*(29*A - 2*C)*a^4*b^9 - (79*A - 2*C)*a^2*b^11 + 20*A*b^13)*cos(d*x + c)^5 + 3*((A + 2*C)*a^11*b^2 + 8*(2*A - C)*a^9*b^4 - 2*(37*A - 6*C)*a^7*b^6 + 4*(29*A - 2*C)*a^5*b^8 - (79*A - 2*C)*a^3*b^10 + 20*A*a*b^12)*cos(d*x + c)^4 + 3*((A + 2*C)*a^12*b + 8*(2*A - C)*a^10*b^3 - 2*(37*A - 6*C)*a^8*b^5 + 4*(29*A - 2*C)*a^6*b^7 - (79*A - 2*C)*a^4*b^9 + 20*A*a^2*b^11)*cos(d*x + c)^3 + ((A + 2*C)*a^13 + 8*(2*A - C)*a^11*b^2 - 2*(37*A - 6*C)*a^9*b^4 + 4*(29*A - 2*C)*a^7*b^6 - (79*A - 2*C)*a^5*b^8 + 20*A*a^3*b^10)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(3*A*a^13 - 12*A*a^11*b^2 + 18*A*a^9*b^4 - 12*A*a^7*b^6 + 3*A*a^5*b^8 - (2*(12*A - 13*C)*a^9*b^4 - (170*A - 43*C)*a^7*b^6 + (313*A - 23*C)*a^5*b^8 - (227*A - 6*C)*a^3*b^10 + 60*A*a*b^12)*cos(d*x + c)^4 - 3*((23*A - 20*C)*a^10*b^3 - (146*A - 35*C)*a^8*b^5 + (263*A - 20*C)*a^6*b^7 - 5*(38*A - C)*a^4*b^9 + 50*A*a^2*b^11)*cos(d*x + c)^3 - (9*(7*A - 4*C)*a^11*b^2 - 2*(171*A - 34*C)*a^9*b^4 + (590*A - 43*C)*a^7*b^6 - (421*A - 11*C)*a^5*b^8 + 110*A*a^3*b^10)*cos(d*x + c)^2 - 15*(A*a^12*b - 4*A*a^10*b^3 + 6*A*a^8*b^5 - 4*A*a^6*b^7 + A*a^4*b^9)*cos(d*x + c))*sin(d*x + c))/((a^14*b^3 - 4*a^12*b^5 + 6*a^10*b^7 - 4*a^8*b^9 + a^6*b^11)*d*cos(d*x + c)^5 + 3*(a^15*b^2 - 4*a^13*b^4 + 6*a^11*b^6 - 4*a^9*b^8 + a^7*b^10)*d*cos(d*x + c)^4 + 3*(a^16*b - 4*a^14*b^3 + 6*a^12*b^5 - 4*a^10*b^7 + a^8*b^9)*d*cos(d*x + c)^3 + (a^17 - 4*a^15*b^2 + 6*a^13*b^4 - 4*a^11*b^6 + a^9*b^8)*d*cos(d*x + c)^2), -1/12*(6*((8*C*a^8*b^4 + 8*(5*A - C)*a^6*b^6 - 7*(12*A - C)*a^4*b^8 + (69*A - 2*C)*a^2*b^10 - 20*A*b^12)*cos(d*x + c)^5 + 3*(8*C*a^9*b^3 + 8*(5*A - C)*a^7*b^5 - 7*(12*A - C)*a^5*b^7 + (69*A - 2*C)*a^3*b^9 - 20*A*a*b^11)*cos(d*x + c)^4 + 3*(8*C*a^10*b^2 + 8*(5*A - C)*a^8*b^4 - 7*(12*A - C)*a^6*b^6 + (69*A - 2*C)*a^4*b^8 - 20*A*a^2*b^10)*cos(d*x + c)^3 + (8*C*a^11*b + 8*(5*A - C)*a^9*b^3 - 7*(12*A - C)*a^7*b^5 + (69*A - 2*C)*a^5*b^7 - 20*A*a^3*b^9)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*(((A + 2*C)*a^10*b^3 + 8*(2*A - C)*a^8*b^5 - 2*(37*A - 6*C)*a^6*b^7 + 4*(29*A - 2*C)*a^4*b^9 - (79*A - 2*C)*a^2*b^11 + 20*A*b^13)*cos(d*x + c)^5 + 3*((A + 2*C)*a^11*b^2 + 8*(2*A - C)*a^9*b^4 - 2*(37*A - 6*C)*a^7*b^6 + 4*(29*A - 2*C)*a^5*b^8 - (79*A - 2*C)*a^3*b^10 + 20*A*a*b^12)*cos(d*x + c)^4 + 3*((A + 2*C)*a^12*b + 8*(2*A - C)*a^10*b^3 - 2*(37*A - 6*C)*a^8*b^5 + 4*(29*A - 2*C)*a^6*b^7 - (79*A - 2*C)*a^4*b^9 + 20*A*a^2*b^11)*cos(d*x + c)^3 + ((A + 2*C)*a^13 + 8*(2*A - C)*a^11*b^2 - 2*(37*A - 6*C)*a^9*b^4 + 4*(29*A - 2*C)*a^7*b^6 - (79*A - 2*C)*a^5*b^8 + 20*A*a^3*b^10)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + 3*(((A + 2*C)*a^10*b^3 + 8*(2*A - C)*a^8*b^5 - 2*(37*A - 6*C)*a^6*b^7 + 4*(29*A - 2*C)*a^4*b^9 - (79*A - 2*C)*a^2*b^11 + 20*A*b^13)*cos(d*x + c)^5 + 3*((A + 2*C)*a^11*b^2 + 8*(2*A - C)*a^9*b^4 - 2*(37*A - 6*C)*a^7*b^6 + 4*(29*A - 2*C)*a^5*b^8 - (79*A - 2*C)*a^3*b^10 + 20*A*a*b^12)*cos(d*x + c)^4 + 3*((A + 2*C)*a^12*b + 8*(2*A - C)*a^10*b^3 - 2*(37*A - 6*C)*a^8*b^5 + 4*(29*A - 2*C)*a^6*b^7 - (79*A - 2*C)*a^4*b^9 + 20*A*a^2*b^11)*cos(d*x + c)^3 + ((A + 2*C)*a^13 + 8*(2*A - C)*a^11*b^2 - 2*(37*A - 6*C)*a^9*b^4 + 4*(29*A - 2*C)*a^7*b^6 - (79*A - 2*C)*a^5*b^8 + 20*A*a^3*b^10)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(3*A*a^13 - 12*A*a^11*b^2 + 18*A*a^9*b^4 - 12*A*a^7*b^6 + 3*A*a^5*b^8 - (2*(12*A - 13*C)*a^9*b^4 - (170*A - 43*C)*a^7*b^6 + (313*A - 23*C)*a^5*b^8 - (227*A - 6*C)*a^3*b^10 + 60*A*a*b^12)*cos(d*x + c)^4 - 3*((23*A - 20*C)*a^10*b^3 - (146*A - 35*C)*a^8*b^5 + (263*A - 20*C)*a^6*b^7 - 5*(38*A - C)*a^4*b^9 + 50*A*a^2*b^11)*cos(d*x + c)^3 - (9*(7*A - 4*C)*a^11*b^2 - 2*(171*A - 34*C)*a^9*b^4 + (590*A - 43*C)*a^7*b^6 - (421*A - 11*C)*a^5*b^8 + 110*A*a^3*b^10)*cos(d*x + c)^2 - 15*(A*a^12*b - 4*A*a^10*b^3 + 6*A*a^8*b^5 - 4*A*a^6*b^7 + A*a^4*b^9)*cos(d*x + c))*sin(d*x + c))/((a^14*b^3 - 4*a^12*b^5 + 6*a^10*b^7 - 4*a^8*b^9 + a^6*b^11)*d*cos(d*x + c)^5 + 3*(a^15*b^2 - 4*a^13*b^4 + 6*a^11*b^6 - 4*a^9*b^8 + a^7*b^10)*d*cos(d*x + c)^4 + 3*(a^16*b - 4*a^14*b^3 + 6*a^12*b^5 - 4*a^10*b^7 + a^8*b^9)*d*cos(d*x + c)^3 + (a^17 - 4*a^15*b^2 + 6*a^13*b^4 - 4*a^11*b^6 + a^9*b^8)*d*cos(d*x + c)^2)]","B",0
593,1,369,0,0.492843," ","integrate(cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{12 \, \sqrt{-a^{2} + b^{2}} 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) - 3 \, {\left(8 \, a^{4} - 4 \, a^{2} b^{2} - b^{4}\right)} d x - {\left(6 \, b^{4} \cos\left(d x + c\right)^{3} - 8 \, a b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{3} b + 8 \, a b^{3} + 3 \, {\left(4 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, b^{5} d}, \frac{24 \, \sqrt{a^{2} - b^{2}} 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) - 3 \, {\left(8 \, a^{4} - 4 \, a^{2} b^{2} - b^{4}\right)} d x - {\left(6 \, b^{4} \cos\left(d x + c\right)^{3} - 8 \, a b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{3} b + 8 \, a b^{3} + 3 \, {\left(4 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, b^{5} d}\right]"," ",0,"[1/24*(12*sqrt(-a^2 + b^2)*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)) - 3*(8*a^4 - 4*a^2*b^2 - b^4)*d*x - (6*b^4*cos(d*x + c)^3 - 8*a*b^3*cos(d*x + c)^2 - 24*a^3*b + 8*a*b^3 + 3*(4*a^2*b^2 - b^4)*cos(d*x + c))*sin(d*x + c))/(b^5*d), 1/24*(24*sqrt(a^2 - b^2)*a^3*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*(8*a^4 - 4*a^2*b^2 - b^4)*d*x - (6*b^4*cos(d*x + c)^3 - 8*a*b^3*cos(d*x + c)^2 - 24*a^3*b + 8*a*b^3 + 3*(4*a^2*b^2 - b^4)*cos(d*x + c))*sin(d*x + c))/(b^5*d)]","A",0
594,1,304,0,0.503922," ","integrate(cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{-a^{2} + b^{2}} 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) + 3 \, {\left(2 \, a^{3} - a b^{2}\right)} d x - {\left(2 \, b^{3} \cos\left(d x + c\right)^{2} - 3 \, a b^{2} \cos\left(d x + c\right) + 6 \, a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right)}{6 \, b^{4} d}, -\frac{6 \, \sqrt{a^{2} - b^{2}} 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) - 3 \, {\left(2 \, a^{3} - a b^{2}\right)} d x + {\left(2 \, b^{3} \cos\left(d x + c\right)^{2} - 3 \, a b^{2} \cos\left(d x + c\right) + 6 \, a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right)}{6 \, b^{4} d}\right]"," ",0,"[1/6*(3*sqrt(-a^2 + b^2)*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)) + 3*(2*a^3 - a*b^2)*d*x - (2*b^3*cos(d*x + c)^2 - 3*a*b^2*cos(d*x + c) + 6*a^2*b - 2*b^3)*sin(d*x + c))/(b^4*d), -1/6*(6*sqrt(a^2 - b^2)*a^2*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*(2*a^3 - a*b^2)*d*x + (2*b^3*cos(d*x + c)^2 - 3*a*b^2*cos(d*x + c) + 6*a^2*b - 2*b^3)*sin(d*x + c))/(b^4*d)]","A",0
595,1,251,0,0.493287," ","integrate(cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a^{2} - b^{2}\right)} d x - \sqrt{-a^{2} + b^{2}} 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) + {\left(b^{2} \cos\left(d x + c\right) - 2 \, a b\right)} \sin\left(d x + c\right)}{2 \, b^{3} d}, -\frac{{\left(2 \, a^{2} - b^{2}\right)} d x - 2 \, \sqrt{a^{2} - b^{2}} 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^{2} \cos\left(d x + c\right) - 2 \, a b\right)} \sin\left(d x + c\right)}{2 \, b^{3} d}\right]"," ",0,"[-1/2*((2*a^2 - b^2)*d*x - sqrt(-a^2 + b^2)*a*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + (b^2*cos(d*x + c) - 2*a*b)*sin(d*x + c))/(b^3*d), -1/2*((2*a^2 - b^2)*d*x - 2*sqrt(a^2 - b^2)*a*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (b^2*cos(d*x + c) - 2*a*b)*sin(d*x + c))/(b^3*d)]","A",0
596,1,202,0,0.511483," ","integrate((1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, a d x - 2 \, b \sin\left(d x + c\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 \, b^{2} d}, \frac{a d x - b \sin\left(d x + c\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)}{b^{2} d}\right]"," ",0,"[1/2*(2*a*d*x - 2*b*sin(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^2*d), (a*d*x - b*sin(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^2*d)]","A",0
597,1,243,0,0.597790," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, a d x - b \log\left(\sin\left(d x + c\right) + 1\right) + b \log\left(-\sin\left(d x + c\right) + 1\right) - \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 \, a b d}, -\frac{2 \, a d x - b \log\left(\sin\left(d x + c\right) + 1\right) + b \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, \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)}{2 \, a b d}\right]"," ",0,"[-1/2*(2*a*d*x - b*log(sin(d*x + c) + 1) + b*log(-sin(d*x + c) + 1) - 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*b*d), -1/2*(2*a*d*x - b*log(sin(d*x + c) + 1) + b*log(-sin(d*x + c) + 1) - 2*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))))/(a*b*d)]","A",0
598,1,297,0,0.641248," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\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) - 2 \, a \sin\left(d x + c\right)}{2 \, a^{2} d \cos\left(d x + c\right)}, -\frac{b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, \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 \, a \sin\left(d x + c\right)}{2 \, a^{2} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*(b*cos(d*x + c)*log(sin(d*x + c) + 1) - b*cos(d*x + c)*log(-sin(d*x + c) + 1) - 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)) - 2*a*sin(d*x + c))/(a^2*d*cos(d*x + c)), -1/2*(b*cos(d*x + c)*log(sin(d*x + c) + 1) - b*cos(d*x + c)*log(-sin(d*x + c) + 1) + 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) - 2*a*sin(d*x + c))/(a^2*d*cos(d*x + c))]","A",0
599,1,373,0,0.515455," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-a^{2} + b^{2}} b \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^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, a b \cos\left(d x + c\right) - a^{2}\right)} \sin\left(d x + c\right)}{4 \, a^{3} d \cos\left(d x + c\right)^{2}}, \frac{4 \, \sqrt{a^{2} - b^{2}} b \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^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, a b \cos\left(d x + c\right) - a^{2}\right)} \sin\left(d x + c\right)}{4 \, a^{3} d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[1/4*(2*sqrt(-a^2 + b^2)*b*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^2 - 2*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (a^2 - 2*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(2*a*b*cos(d*x + c) - a^2)*sin(d*x + c))/(a^3*d*cos(d*x + c)^2), 1/4*(4*sqrt(a^2 - b^2)*b*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))*cos(d*x + c)^2 - (a^2 - 2*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (a^2 - 2*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(2*a*b*cos(d*x + c) - a^2)*sin(d*x + c))/(a^3*d*cos(d*x + c)^2)]","A",0
600,1,431,0,0.669241," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{-a^{2} + b^{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(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(3 \, a^{2} b \cos\left(d x + c\right) - 2 \, a^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, a^{4} d \cos\left(d x + c\right)^{3}}, -\frac{12 \, \sqrt{a^{2} - b^{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(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, a^{2} b \cos\left(d x + c\right) - 2 \, a^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, a^{4} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[1/12*(6*sqrt(-a^2 + b^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*(a^2*b - 2*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(a^2*b - 2*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - 2*(3*a^2*b*cos(d*x + c) - 2*a^3 + 2*(a^3 - 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(a^4*d*cos(d*x + c)^3), -1/12*(12*sqrt(a^2 - b^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*(a^2*b - 2*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(a^2*b - 2*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(3*a^2*b*cos(d*x + c) - 2*a^3 + 2*(a^3 - 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(a^4*d*cos(d*x + c)^3)]","A",0
601,1,731,0,0.550472," ","integrate(cos(d*x+c)^4*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(40 \, a^{6} b - 52 \, a^{4} b^{3} + 11 \, a^{2} b^{5} + b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(40 \, a^{7} - 52 \, a^{5} b^{2} + 11 \, a^{3} b^{4} + a b^{6}\right)} d x - 12 \, {\left(5 \, a^{6} - 4 \, a^{4} b^{2} + {\left(5 \, a^{5} b - 4 \, a^{3} 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) - {\left(120 \, a^{6} b - 136 \, a^{4} b^{3} + 16 \, a^{2} b^{5} - 6 \, {\left(a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} + 10 \, {\left(a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(20 \, a^{4} b^{3} - 23 \, a^{2} b^{5} + 3 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(60 \, a^{5} b^{2} - 73 \, a^{3} b^{4} + 13 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left({\left(a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{3} b^{6} - a b^{8}\right)} d\right)}}, -\frac{3 \, {\left(40 \, a^{6} b - 52 \, a^{4} b^{3} + 11 \, a^{2} b^{5} + b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(40 \, a^{7} - 52 \, a^{5} b^{2} + 11 \, a^{3} b^{4} + a b^{6}\right)} d x - 24 \, {\left(5 \, a^{6} - 4 \, a^{4} b^{2} + {\left(5 \, a^{5} b - 4 \, a^{3} 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(120 \, a^{6} b - 136 \, a^{4} b^{3} + 16 \, a^{2} b^{5} - 6 \, {\left(a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} + 10 \, {\left(a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(20 \, a^{4} b^{3} - 23 \, a^{2} b^{5} + 3 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(60 \, a^{5} b^{2} - 73 \, a^{3} b^{4} + 13 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left({\left(a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{3} b^{6} - a b^{8}\right)} d\right)}}\right]"," ",0,"[-1/24*(3*(40*a^6*b - 52*a^4*b^3 + 11*a^2*b^5 + b^7)*d*x*cos(d*x + c) + 3*(40*a^7 - 52*a^5*b^2 + 11*a^3*b^4 + a*b^6)*d*x - 12*(5*a^6 - 4*a^4*b^2 + (5*a^5*b - 4*a^3*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)) - (120*a^6*b - 136*a^4*b^3 + 16*a^2*b^5 - 6*(a^2*b^5 - b^7)*cos(d*x + c)^4 + 10*(a^3*b^4 - a*b^6)*cos(d*x + c)^3 - (20*a^4*b^3 - 23*a^2*b^5 + 3*b^7)*cos(d*x + c)^2 + (60*a^5*b^2 - 73*a^3*b^4 + 13*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^7 - b^9)*d*cos(d*x + c) + (a^3*b^6 - a*b^8)*d), -1/24*(3*(40*a^6*b - 52*a^4*b^3 + 11*a^2*b^5 + b^7)*d*x*cos(d*x + c) + 3*(40*a^7 - 52*a^5*b^2 + 11*a^3*b^4 + a*b^6)*d*x - 24*(5*a^6 - 4*a^4*b^2 + (5*a^5*b - 4*a^3*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))) - (120*a^6*b - 136*a^4*b^3 + 16*a^2*b^5 - 6*(a^2*b^5 - b^7)*cos(d*x + c)^4 + 10*(a^3*b^4 - a*b^6)*cos(d*x + c)^3 - (20*a^4*b^3 - 23*a^2*b^5 + 3*b^7)*cos(d*x + c)^2 + (60*a^5*b^2 - 73*a^3*b^4 + 13*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^7 - b^9)*d*cos(d*x + c) + (a^3*b^6 - a*b^8)*d)]","A",0
602,1,629,0,0.510741," ","integrate(cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + a b^{5}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(4 \, a^{6} - 5 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x + 3 \, {\left(4 \, a^{5} - 3 \, a^{3} b^{2} + {\left(4 \, a^{4} b - 3 \, a^{2} 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(12 \, a^{5} b - 13 \, a^{3} b^{3} + a b^{5} + {\left(a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, a^{4} b^{2} - 7 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{3} b^{5} - a b^{7}\right)} d\right)}}, \frac{3 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + a b^{5}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(4 \, a^{6} - 5 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x - 3 \, {\left(4 \, a^{5} - 3 \, a^{3} b^{2} + {\left(4 \, a^{4} b - 3 \, a^{2} 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(12 \, a^{5} b - 13 \, a^{3} b^{3} + a b^{5} + {\left(a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, a^{4} b^{2} - 7 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{3} b^{5} - a b^{7}\right)} d\right)}}\right]"," ",0,"[1/6*(6*(4*a^5*b - 5*a^3*b^3 + a*b^5)*d*x*cos(d*x + c) + 6*(4*a^6 - 5*a^4*b^2 + a^2*b^4)*d*x + 3*(4*a^5 - 3*a^3*b^2 + (4*a^4*b - 3*a^2*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*(12*a^5*b - 13*a^3*b^3 + a*b^5 + (a^2*b^4 - b^6)*cos(d*x + c)^3 - 2*(a^3*b^3 - a*b^5)*cos(d*x + c)^2 + (6*a^4*b^2 - 7*a^2*b^4 + b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^6 - b^8)*d*cos(d*x + c) + (a^3*b^5 - a*b^7)*d), 1/3*(3*(4*a^5*b - 5*a^3*b^3 + a*b^5)*d*x*cos(d*x + c) + 3*(4*a^6 - 5*a^4*b^2 + a^2*b^4)*d*x - 3*(4*a^5 - 3*a^3*b^2 + (4*a^4*b - 3*a^2*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))) - (12*a^5*b - 13*a^3*b^3 + a*b^5 + (a^2*b^4 - b^6)*cos(d*x + c)^3 - 2*(a^3*b^3 - a*b^5)*cos(d*x + c)^2 + (6*a^4*b^2 - 7*a^2*b^4 + b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^6 - b^8)*d*cos(d*x + c) + (a^3*b^5 - a*b^7)*d)]","A",0
603,1,547,0,0.497091," ","integrate(cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(6 \, a^{4} b - 7 \, a^{2} b^{3} + b^{5}\right)} d x \cos\left(d x + c\right) + {\left(6 \, a^{5} - 7 \, a^{3} b^{2} + a b^{4}\right)} d x - {\left(3 \, a^{4} - 2 \, a^{2} b^{2} + {\left(3 \, a^{3} b - 2 \, 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) - {\left(6 \, a^{4} b - 6 \, a^{2} b^{3} - {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{3} b^{4} - a b^{6}\right)} d\right)}}, -\frac{{\left(6 \, a^{4} b - 7 \, a^{2} b^{3} + b^{5}\right)} d x \cos\left(d x + c\right) + {\left(6 \, a^{5} - 7 \, a^{3} b^{2} + a b^{4}\right)} d x - 2 \, {\left(3 \, a^{4} - 2 \, a^{2} b^{2} + {\left(3 \, a^{3} b - 2 \, 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(6 \, a^{4} b - 6 \, a^{2} b^{3} - {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{3} b^{4} - a b^{6}\right)} d\right)}}\right]"," ",0,"[-1/2*((6*a^4*b - 7*a^2*b^3 + b^5)*d*x*cos(d*x + c) + (6*a^5 - 7*a^3*b^2 + a*b^4)*d*x - (3*a^4 - 2*a^2*b^2 + (3*a^3*b - 2*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)) - (6*a^4*b - 6*a^2*b^3 - (a^2*b^3 - b^5)*cos(d*x + c)^2 + 3*(a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^5 - b^7)*d*cos(d*x + c) + (a^3*b^4 - a*b^6)*d), -1/2*((6*a^4*b - 7*a^2*b^3 + b^5)*d*x*cos(d*x + c) + (6*a^5 - 7*a^3*b^2 + a*b^4)*d*x - 2*(3*a^4 - 2*a^2*b^2 + (3*a^3*b - 2*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))) - (6*a^4*b - 6*a^2*b^3 - (a^2*b^3 - b^5)*cos(d*x + c)^2 + 3*(a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^5 - b^7)*d*cos(d*x + c) + (a^3*b^4 - a*b^6)*d)]","A",0
604,1,463,0,0.500431," ","integrate(cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{3} b - a b^{3}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d x + {\left(2 \, a^{3} - a b^{2} + {\left(2 \, a^{2} b - 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^{3} b - 2 \, a b^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{3} b^{3} - a b^{5}\right)} d\right)}}, \frac{2 \, {\left(a^{3} b - a b^{3}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} d x - {\left(2 \, a^{3} - a b^{2} + {\left(2 \, a^{2} b - 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^{3} b - 2 \, a b^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{3} b^{3} - a b^{5}\right)} d}\right]"," ",0,"[1/2*(4*(a^3*b - a*b^3)*d*x*cos(d*x + c) + 4*(a^4 - a^2*b^2)*d*x + (2*a^3 - a*b^2 + (2*a^2*b - 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^3*b - 2*a*b^3 + (a^2*b^2 - b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d*cos(d*x + c) + (a^3*b^3 - a*b^5)*d), (2*(a^3*b - a*b^3)*d*x*cos(d*x + c) + 2*(a^4 - a^2*b^2)*d*x - (2*a^3 - a*b^2 + (2*a^2*b - 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^3*b - 2*a*b^3 + (a^2*b^2 - b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d*cos(d*x + c) + (a^3*b^3 - a*b^5)*d)]","A",0
605,1,376,0,0.551424," ","integrate((1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{2} b - b^{3}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{3} - a b^{2}\right)} d x + {\left(a b \cos\left(d x + c\right) + a^{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) - 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{3} - b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{3} b^{2} - a b^{4}\right)} d\right)}}, -\frac{{\left(a^{2} b - b^{3}\right)} d x \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} d x - {\left(a b \cos\left(d x + c\right) + a^{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(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} b^{3} - b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{3} b^{2} - a b^{4}\right)} d}\right]"," ",0,"[-1/2*(2*(a^2*b - b^3)*d*x*cos(d*x + c) + 2*(a^3 - a*b^2)*d*x + (a*b*cos(d*x + c) + a^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)) - 2*(a^2*b - b^3)*sin(d*x + c))/((a^2*b^3 - b^5)*d*cos(d*x + c) + (a^3*b^2 - a*b^4)*d), -((a^2*b - b^3)*d*x*cos(d*x + c) + (a^3 - a*b^2)*d*x - (a*b*cos(d*x + c) + a^2)*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)*sin(d*x + c))/((a^2*b^3 - b^5)*d*cos(d*x + c) + (a^3*b^2 - a*b^4)*d)]","B",0
606,1,464,0,0.593126," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} \cos\left(d x + c\right) + 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^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b - a^{2} b^{3}\right)} d \cos\left(d x + c\right) + {\left(a^{5} - a^{3} b^{2}\right)} d\right)}}, -\frac{2 \, {\left(b^{2} \cos\left(d x + c\right) + 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^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b - a^{2} b^{3}\right)} d \cos\left(d x + c\right) + {\left(a^{5} - a^{3} b^{2}\right)} d\right)}}\right]"," ",0,"[-1/2*((b^2*cos(d*x + c) + 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^3 - a*b^2 + (a^2*b - b^3)*cos(d*x + c))*log(sin(d*x + c) + 1) + (a^3 - a*b^2 + (a^2*b - b^3)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4*b - a^2*b^3)*d*cos(d*x + c) + (a^5 - a^3*b^2)*d), -1/2*(2*(b^2*cos(d*x + c) + a*b)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (a^3 - a*b^2 + (a^2*b - b^3)*cos(d*x + c))*log(sin(d*x + c) + 1) + (a^3 - a*b^2 + (a^2*b - b^3)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4*b - a^2*b^3)*d*cos(d*x + c) + (a^5 - a^3*b^2)*d)]","B",0
607,1,628,0,0.630967," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} - 2 \, a 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({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{4} - a^{2} b^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{{\left({\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} - 2 \, a 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({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(a^{4} - a^{2} b^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{5} b - a^{3} b^{3}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(((a^2*b - 2*b^3)*cos(d*x + c)^2 + (a^3 - 2*a*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*((a^2*b^2 - b^4)*cos(d*x + c)^2 + (a^3*b - a*b^3)*cos(d*x + c))*log(sin(d*x + c) + 1) + 2*((a^2*b^2 - b^4)*cos(d*x + c)^2 + (a^3*b - a*b^3)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(a^4 - a^2*b^2 + 2*(a^3*b - a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^5*b - a^3*b^3)*d*cos(d*x + c)^2 + (a^6 - a^4*b^2)*d*cos(d*x + c)), -(((a^2*b - 2*b^3)*cos(d*x + c)^2 + (a^3 - 2*a*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))) + ((a^2*b^2 - b^4)*cos(d*x + c)^2 + (a^3*b - a*b^3)*cos(d*x + c))*log(sin(d*x + c) + 1) - ((a^2*b^2 - b^4)*cos(d*x + c)^2 + (a^3*b - a*b^3)*cos(d*x + c))*log(-sin(d*x + c) + 1) - (a^4 - a^2*b^2 + 2*(a^3*b - a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^5*b - a^3*b^3)*d*cos(d*x + c)^2 + (a^6 - a^4*b^2)*d*cos(d*x + c))]","B",0
608,1,757,0,0.763576," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(2 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - 3 \, a b^{3}\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^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{5} - a^{3} b^{2} - 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b - a^{4} b^{3}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{7} - a^{5} b^{2}\right)} d \cos\left(d x + c\right)^{2}\right)}}, \frac{4 \, {\left({\left(2 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - 3 \, a b^{3}\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^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{5} - a^{3} b^{2} - 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b - a^{4} b^{3}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{7} - a^{5} b^{2}\right)} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/4*(2*((2*a^2*b^2 - 3*b^4)*cos(d*x + c)^3 + (2*a^3*b - 3*a*b^3)*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^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^3 + (a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^3 + (a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(a^5 - a^3*b^2 - 6*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 - 3*(a^4*b - a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6*b - a^4*b^3)*d*cos(d*x + c)^3 + (a^7 - a^5*b^2)*d*cos(d*x + c)^2), 1/4*(4*((2*a^2*b^2 - 3*b^4)*cos(d*x + c)^3 + (2*a^3*b - 3*a*b^3)*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^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^3 + (a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^3 + (a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(a^5 - a^3*b^2 - 6*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 - 3*(a^4*b - a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6*b - a^4*b^3)*d*cos(d*x + c)^3 + (a^7 - a^5*b^2)*d*cos(d*x + c)^2)]","B",0
609,1,851,0,0.743016," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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({\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{6} - a^{4} b^{2} - {\left(a^{5} b - 13 \, a^{3} b^{3} + 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{6} - 7 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{7} b - a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{8} - a^{6} b^{2}\right)} d \cos\left(d x + c\right)^{3}\right)}}, -\frac{6 \, {\left({\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{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) - 3 \, {\left({\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{6} - a^{4} b^{2} - {\left(a^{5} b - 13 \, a^{3} b^{3} + 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{6} - 7 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{7} b - a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{8} - a^{6} b^{2}\right)} d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/6*(3*((3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 + (3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^3)*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)) + 3*((a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 + (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 + (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) + 2*(a^6 - a^4*b^2 - (a^5*b - 13*a^3*b^3 + 12*a*b^5)*cos(d*x + c)^3 - (a^6 - 7*a^4*b^2 + 6*a^2*b^4)*cos(d*x + c)^2 - 2*(a^5*b - a^3*b^3)*cos(d*x + c))*sin(d*x + c))/((a^7*b - a^5*b^3)*d*cos(d*x + c)^4 + (a^8 - a^6*b^2)*d*cos(d*x + c)^3), -1/6*(6*((3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 + (3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^3)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*((a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 + (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) + 3*((a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 + (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(a^6 - a^4*b^2 - (a^5*b - 13*a^3*b^3 + 12*a*b^5)*cos(d*x + c)^3 - (a^6 - 7*a^4*b^2 + 6*a^2*b^4)*cos(d*x + c)^2 - 2*(a^5*b - a^3*b^3)*cos(d*x + c))*sin(d*x + c))/((a^7*b - a^5*b^3)*d*cos(d*x + c)^4 + (a^8 - a^6*b^2)*d*cos(d*x + c)^3)]","B",0
610,1,1103,0,0.607381," ","integrate(cos(d*x+c)^4*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(20 \, a^{7} b^{2} - 43 \, a^{5} b^{4} + 26 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 12 \, {\left(20 \, a^{8} b - 43 \, a^{6} b^{3} + 26 \, a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(20 \, a^{9} - 43 \, a^{7} b^{2} + 26 \, a^{5} b^{4} - 3 \, a^{3} b^{6}\right)} d x + 3 \, {\left(20 \, a^{8} - 33 \, a^{6} b^{2} + 12 \, a^{4} b^{4} + {\left(20 \, a^{6} b^{2} - 33 \, a^{4} b^{4} + 12 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(20 \, a^{7} b - 33 \, a^{5} b^{3} + 12 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(60 \, a^{8} b - 119 \, a^{6} b^{3} + 61 \, a^{4} b^{5} - 2 \, a^{2} b^{7} + 2 \, {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(10 \, a^{6} b^{3} - 21 \, a^{4} b^{5} + 12 \, a^{2} b^{7} - b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(90 \, a^{7} b^{2} - 181 \, a^{5} b^{4} + 95 \, a^{3} b^{6} - 4 \, a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{4} b^{8} - 2 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{7} - 2 \, a^{3} b^{9} + a b^{11}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{6} - 2 \, a^{4} b^{8} + a^{2} b^{10}\right)} d\right)}}, \frac{3 \, {\left(20 \, a^{7} b^{2} - 43 \, a^{5} b^{4} + 26 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 6 \, {\left(20 \, a^{8} b - 43 \, a^{6} b^{3} + 26 \, a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(20 \, a^{9} - 43 \, a^{7} b^{2} + 26 \, a^{5} b^{4} - 3 \, a^{3} b^{6}\right)} d x - 3 \, {\left(20 \, a^{8} - 33 \, a^{6} b^{2} + 12 \, a^{4} b^{4} + {\left(20 \, a^{6} b^{2} - 33 \, a^{4} b^{4} + 12 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(20 \, a^{7} b - 33 \, a^{5} b^{3} + 12 \, a^{3} b^{5}\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(60 \, a^{8} b - 119 \, a^{6} b^{3} + 61 \, a^{4} b^{5} - 2 \, a^{2} b^{7} + 2 \, {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(10 \, a^{6} b^{3} - 21 \, a^{4} b^{5} + 12 \, a^{2} b^{7} - b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(90 \, a^{7} b^{2} - 181 \, a^{5} b^{4} + 95 \, a^{3} b^{6} - 4 \, a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{4} b^{8} - 2 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{7} - 2 \, a^{3} b^{9} + a b^{11}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{6} - 2 \, a^{4} b^{8} + a^{2} b^{10}\right)} d\right)}}\right]"," ",0,"[1/12*(6*(20*a^7*b^2 - 43*a^5*b^4 + 26*a^3*b^6 - 3*a*b^8)*d*x*cos(d*x + c)^2 + 12*(20*a^8*b - 43*a^6*b^3 + 26*a^4*b^5 - 3*a^2*b^7)*d*x*cos(d*x + c) + 6*(20*a^9 - 43*a^7*b^2 + 26*a^5*b^4 - 3*a^3*b^6)*d*x + 3*(20*a^8 - 33*a^6*b^2 + 12*a^4*b^4 + (20*a^6*b^2 - 33*a^4*b^4 + 12*a^2*b^6)*cos(d*x + c)^2 + 2*(20*a^7*b - 33*a^5*b^3 + 12*a^3*b^5)*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*(60*a^8*b - 119*a^6*b^3 + 61*a^4*b^5 - 2*a^2*b^7 + 2*(a^4*b^5 - 2*a^2*b^7 + b^9)*cos(d*x + c)^4 - 5*(a^5*b^4 - 2*a^3*b^6 + a*b^8)*cos(d*x + c)^3 + 2*(10*a^6*b^3 - 21*a^4*b^5 + 12*a^2*b^7 - b^9)*cos(d*x + c)^2 + (90*a^7*b^2 - 181*a^5*b^4 + 95*a^3*b^6 - 4*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^4*b^8 - 2*a^2*b^10 + b^12)*d*cos(d*x + c)^2 + 2*(a^5*b^7 - 2*a^3*b^9 + a*b^11)*d*cos(d*x + c) + (a^6*b^6 - 2*a^4*b^8 + a^2*b^10)*d), 1/6*(3*(20*a^7*b^2 - 43*a^5*b^4 + 26*a^3*b^6 - 3*a*b^8)*d*x*cos(d*x + c)^2 + 6*(20*a^8*b - 43*a^6*b^3 + 26*a^4*b^5 - 3*a^2*b^7)*d*x*cos(d*x + c) + 3*(20*a^9 - 43*a^7*b^2 + 26*a^5*b^4 - 3*a^3*b^6)*d*x - 3*(20*a^8 - 33*a^6*b^2 + 12*a^4*b^4 + (20*a^6*b^2 - 33*a^4*b^4 + 12*a^2*b^6)*cos(d*x + c)^2 + 2*(20*a^7*b - 33*a^5*b^3 + 12*a^3*b^5)*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))) - (60*a^8*b - 119*a^6*b^3 + 61*a^4*b^5 - 2*a^2*b^7 + 2*(a^4*b^5 - 2*a^2*b^7 + b^9)*cos(d*x + c)^4 - 5*(a^5*b^4 - 2*a^3*b^6 + a*b^8)*cos(d*x + c)^3 + 2*(10*a^6*b^3 - 21*a^4*b^5 + 12*a^2*b^7 - b^9)*cos(d*x + c)^2 + (90*a^7*b^2 - 181*a^5*b^4 + 95*a^3*b^6 - 4*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^4*b^8 - 2*a^2*b^10 + b^12)*d*cos(d*x + c)^2 + 2*(a^5*b^7 - 2*a^3*b^9 + a*b^11)*d*cos(d*x + c) + (a^6*b^6 - 2*a^4*b^8 + a^2*b^10)*d)]","A",0
611,1,983,0,0.582974," ","integrate(cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(12 \, a^{6} b^{2} - 25 \, a^{4} b^{4} + 14 \, a^{2} b^{6} - b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(12 \, a^{7} b - 25 \, a^{5} b^{3} + 14 \, a^{3} b^{5} - a b^{7}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(12 \, a^{8} - 25 \, a^{6} b^{2} + 14 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x - {\left(12 \, a^{7} - 19 \, a^{5} b^{2} + 6 \, a^{3} b^{4} + {\left(12 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, a^{6} b - 19 \, a^{4} b^{3} + 6 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, a^{7} b - 23 \, a^{5} b^{3} + 11 \, a^{3} b^{5} - {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, a^{6} b^{2} - 35 \, a^{4} b^{4} + 17 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{4} b^{7} - 2 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{6} - 2 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{5} - 2 \, a^{4} b^{7} + a^{2} b^{9}\right)} d\right)}}, -\frac{{\left(12 \, a^{6} b^{2} - 25 \, a^{4} b^{4} + 14 \, a^{2} b^{6} - b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, a^{7} b - 25 \, a^{5} b^{3} + 14 \, a^{3} b^{5} - a b^{7}\right)} d x \cos\left(d x + c\right) + {\left(12 \, a^{8} - 25 \, a^{6} b^{2} + 14 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x - {\left(12 \, a^{7} - 19 \, a^{5} b^{2} + 6 \, a^{3} b^{4} + {\left(12 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, a^{6} b - 19 \, a^{4} b^{3} + 6 \, a^{2} b^{5}\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 \, a^{7} b - 23 \, a^{5} b^{3} + 11 \, a^{3} b^{5} - {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, a^{6} b^{2} - 35 \, a^{4} b^{4} + 17 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{7} - 2 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{6} - 2 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{5} - 2 \, a^{4} b^{7} + a^{2} b^{9}\right)} d\right)}}\right]"," ",0,"[-1/4*(2*(12*a^6*b^2 - 25*a^4*b^4 + 14*a^2*b^6 - b^8)*d*x*cos(d*x + c)^2 + 4*(12*a^7*b - 25*a^5*b^3 + 14*a^3*b^5 - a*b^7)*d*x*cos(d*x + c) + 2*(12*a^8 - 25*a^6*b^2 + 14*a^4*b^4 - a^2*b^6)*d*x - (12*a^7 - 19*a^5*b^2 + 6*a^3*b^4 + (12*a^5*b^2 - 19*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2 + 2*(12*a^6*b - 19*a^4*b^3 + 6*a^2*b^5)*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*a^7*b - 23*a^5*b^3 + 11*a^3*b^5 - (a^4*b^4 - 2*a^2*b^6 + b^8)*cos(d*x + c)^3 + 4*(a^5*b^3 - 2*a^3*b^5 + a*b^7)*cos(d*x + c)^2 + (18*a^6*b^2 - 35*a^4*b^4 + 17*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^7 - 2*a^2*b^9 + b^11)*d*cos(d*x + c)^2 + 2*(a^5*b^6 - 2*a^3*b^8 + a*b^10)*d*cos(d*x + c) + (a^6*b^5 - 2*a^4*b^7 + a^2*b^9)*d), -1/2*((12*a^6*b^2 - 25*a^4*b^4 + 14*a^2*b^6 - b^8)*d*x*cos(d*x + c)^2 + 2*(12*a^7*b - 25*a^5*b^3 + 14*a^3*b^5 - a*b^7)*d*x*cos(d*x + c) + (12*a^8 - 25*a^6*b^2 + 14*a^4*b^4 - a^2*b^6)*d*x - (12*a^7 - 19*a^5*b^2 + 6*a^3*b^4 + (12*a^5*b^2 - 19*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2 + 2*(12*a^6*b - 19*a^4*b^3 + 6*a^2*b^5)*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*a^7*b - 23*a^5*b^3 + 11*a^3*b^5 - (a^4*b^4 - 2*a^2*b^6 + b^8)*cos(d*x + c)^3 + 4*(a^5*b^3 - 2*a^3*b^5 + a*b^7)*cos(d*x + c)^2 + (18*a^6*b^2 - 35*a^4*b^4 + 17*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^7 - 2*a^2*b^9 + b^11)*d*cos(d*x + c)^2 + 2*(a^5*b^6 - 2*a^3*b^8 + a*b^10)*d*cos(d*x + c) + (a^6*b^5 - 2*a^4*b^7 + a^2*b^9)*d)]","A",0
612,1,856,0,0.571886," ","integrate(cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 24 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d x + {\left(6 \, a^{6} - 9 \, a^{4} b^{2} + 2 \, a^{2} b^{4} + {\left(6 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b - 9 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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^{6} b - 11 \, a^{4} b^{3} + 5 \, a^{2} b^{5} + 2 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, a^{5} b^{2} - 17 \, a^{3} b^{4} + 8 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{4} - 2 \, a^{4} b^{6} + a^{2} b^{8}\right)} d\right)}}, \frac{6 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 12 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d x - {\left(6 \, a^{6} - 9 \, a^{4} b^{2} + 2 \, a^{2} b^{4} + {\left(6 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b - 9 \, a^{3} b^{3} + 2 \, a b^{5}\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^{6} b - 11 \, a^{4} b^{3} + 5 \, a^{2} b^{5} + 2 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, a^{5} b^{2} - 17 \, a^{3} b^{4} + 8 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{4} - 2 \, a^{4} b^{6} + a^{2} b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*(12*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*d*x*cos(d*x + c)^2 + 24*(a^6*b - 2*a^4*b^3 + a^2*b^5)*d*x*cos(d*x + c) + 12*(a^7 - 2*a^5*b^2 + a^3*b^4)*d*x + (6*a^6 - 9*a^4*b^2 + 2*a^2*b^4 + (6*a^4*b^2 - 9*a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(6*a^5*b - 9*a^3*b^3 + 2*a*b^5)*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^6*b - 11*a^4*b^3 + 5*a^2*b^5 + 2*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2 + (9*a^5*b^2 - 17*a^3*b^4 + 8*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c)^2 + 2*(a^5*b^5 - 2*a^3*b^7 + a*b^9)*d*cos(d*x + c) + (a^6*b^4 - 2*a^4*b^6 + a^2*b^8)*d), 1/2*(6*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*d*x*cos(d*x + c)^2 + 12*(a^6*b - 2*a^4*b^3 + a^2*b^5)*d*x*cos(d*x + c) + 6*(a^7 - 2*a^5*b^2 + a^3*b^4)*d*x - (6*a^6 - 9*a^4*b^2 + 2*a^2*b^4 + (6*a^4*b^2 - 9*a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(6*a^5*b - 9*a^3*b^3 + 2*a*b^5)*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^6*b - 11*a^4*b^3 + 5*a^2*b^5 + 2*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2 + (9*a^5*b^2 - 17*a^3*b^4 + 8*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c)^2 + 2*(a^5*b^5 - 2*a^3*b^7 + a*b^9)*d*cos(d*x + c) + (a^6*b^4 - 2*a^4*b^6 + a^2*b^8)*d)]","B",0
613,1,740,0,0.510287," ","integrate(cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x + {\left(2 \, a^{5} - 3 \, a^{3} b^{2} + {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{4} b - 3 \, a^{2} 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^{5} b - 3 \, a^{3} b^{3} + a b^{5} + {\left(3 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{3} - 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} d\right)}}, -\frac{2 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x - {\left(2 \, a^{5} - 3 \, a^{3} b^{2} + {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{4} b - 3 \, a^{2} 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^{5} b - 3 \, a^{3} b^{3} + a b^{5} + {\left(3 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + 2 \, b^{6}\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)^{2} + 2 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b^{3} - 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} d\right)}}\right]"," ",0,"[-1/4*(4*(a^4*b^2 - 2*a^2*b^4 + b^6)*d*x*cos(d*x + c)^2 + 8*(a^5*b - 2*a^3*b^3 + a*b^5)*d*x*cos(d*x + c) + 4*(a^6 - 2*a^4*b^2 + a^2*b^4)*d*x + (2*a^5 - 3*a^3*b^2 + (2*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + 2*(2*a^4*b - 3*a^2*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^5*b - 3*a^3*b^3 + a*b^5 + (3*a^4*b^2 - 5*a^2*b^4 + 2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c)^2 + 2*(a^5*b^4 - 2*a^3*b^6 + a*b^8)*d*cos(d*x + c) + (a^6*b^3 - 2*a^4*b^5 + a^2*b^7)*d), -1/2*(2*(a^4*b^2 - 2*a^2*b^4 + b^6)*d*x*cos(d*x + c)^2 + 4*(a^5*b - 2*a^3*b^3 + a*b^5)*d*x*cos(d*x + c) + 2*(a^6 - 2*a^4*b^2 + a^2*b^4)*d*x - (2*a^5 - 3*a^3*b^2 + (2*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + 2*(2*a^4*b - 3*a^2*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^5*b - 3*a^3*b^3 + a*b^5 + (3*a^4*b^2 - 5*a^2*b^4 + 2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c)^2 + 2*(a^5*b^4 - 2*a^3*b^6 + a*b^8)*d*cos(d*x + c) + (a^6*b^3 - 2*a^4*b^5 + a^2*b^7)*d)]","B",0
614,1,449,0,0.500079," ","integrate((1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{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) - 2 \, {\left(a^{2} b - b^{3} + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d\right)}}, \frac{{\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{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(a^{2} b - b^{3} + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d\right)}}\right]"," ",0,"[1/4*((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^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)) - 2*(a^2*b - b^3 + (a^3 - a*b^2)*cos(d*x + c))*sin(d*x + c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*d*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*d*cos(d*x + c) + (a^6 - 2*a^4*b^2 + a^2*b^4)*d), 1/2*((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*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 + (a^3 - a*b^2)*cos(d*x + c))*sin(d*x + c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*d*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*d*cos(d*x + c) + (a^6 - 2*a^4*b^2 + a^2*b^4)*d)]","A",0
615,1,915,0,0.813732," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, a^{4} b - 2 \, a^{2} b^{3} + {\left(3 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - 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) - 2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} 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(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} 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(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{7} b^{2} - 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d\right)}}, -\frac{{\left(3 \, a^{4} b - 2 \, a^{2} b^{3} + {\left(3 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - 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^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} 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^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} b^{2} - 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d\right)}}\right]"," ",0,"[-1/4*((3*a^4*b - 2*a^2*b^3 + (3*a^2*b^3 - 2*b^5)*cos(d*x + c)^2 + 2*(3*a^3*b^2 - 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)) - 2*(a^6 - 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + 2*(a^6 - 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(2*a^6 - 5*a^4*b^2 + 3*a^2*b^4 + (a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^7*b^2 - 2*a^5*b^4 + a^3*b^6)*d*cos(d*x + c)^2 + 2*(a^8*b - 2*a^6*b^3 + a^4*b^5)*d*cos(d*x + c) + (a^9 - 2*a^7*b^2 + a^5*b^4)*d), -1/2*((3*a^4*b - 2*a^2*b^3 + (3*a^2*b^3 - 2*b^5)*cos(d*x + c)^2 + 2*(3*a^3*b^2 - 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^6 - 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + (a^6 - 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (2*a^6 - 5*a^4*b^2 + 3*a^2*b^4 + (a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^7*b^2 - 2*a^5*b^4 + a^3*b^6)*d*cos(d*x + c)^2 + 2*(a^8*b - 2*a^6*b^3 + a^4*b^5)*d*cos(d*x + c) + (a^9 - 2*a^7*b^2 + a^5*b^4)*d)]","B",0
616,1,1121,0,0.953039," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 6 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{6} - 9 \, a^{4} b^{2} + 6 \, 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) - 6 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, a^{7} - 4 \, a^{5} b^{2} + 2 \, a^{3} b^{4} + {\left(5 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, a^{6} b - 17 \, a^{4} b^{3} + 9 \, 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} - 2 \, a^{6} b^{4} + a^{4} b^{6}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{{\left({\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 6 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{6} - 9 \, a^{4} b^{2} + 6 \, 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) + 3 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(2 \, a^{7} - 4 \, a^{5} b^{2} + 2 \, a^{3} b^{4} + {\left(5 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, a^{6} b - 17 \, a^{4} b^{3} + 9 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b^{2} - 2 \, a^{6} b^{4} + a^{4} b^{6}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(((2*a^4*b^2 - 9*a^2*b^4 + 6*b^6)*cos(d*x + c)^3 + 2*(2*a^5*b - 9*a^3*b^3 + 6*a*b^5)*cos(d*x + c)^2 + (2*a^6 - 9*a^4*b^2 + 6*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*((a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^3 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c)^2 + (a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + 6*((a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^3 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c)^2 + (a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(2*a^7 - 4*a^5*b^2 + 2*a^3*b^4 + (5*a^5*b^2 - 11*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2 + (8*a^6*b - 17*a^4*b^3 + 9*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*b^2 - 2*a^6*b^4 + a^4*b^6)*d*cos(d*x + c)^3 + 2*(a^9*b - 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^2 + (a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c)), -1/2*(((2*a^4*b^2 - 9*a^2*b^4 + 6*b^6)*cos(d*x + c)^3 + 2*(2*a^5*b - 9*a^3*b^3 + 6*a*b^5)*cos(d*x + c)^2 + (2*a^6 - 9*a^4*b^2 + 6*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))) + 3*((a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^3 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c)^2 + (a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) - 3*((a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^3 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c)^2 + (a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - (2*a^7 - 4*a^5*b^2 + 2*a^3*b^4 + (5*a^5*b^2 - 11*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2 + (8*a^6*b - 17*a^4*b^3 + 9*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*b^2 - 2*a^6*b^4 + a^4*b^6)*d*cos(d*x + c)^3 + 2*(a^9*b - 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^2 + (a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c))]","B",0
617,1,1302,0,1.487448," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(6 \, a^{4} b^{3} - 19 \, a^{2} b^{5} + 12 \, b^{7}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(6 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 12 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{6} b - 19 \, a^{4} b^{3} + 12 \, a^{2} 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^{6} b^{2} - 14 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - 12 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{8} - 14 \, a^{6} b^{2} + 25 \, a^{4} b^{4} - 12 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{6} b^{2} - 14 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - 12 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{8} - 14 \, a^{6} b^{2} + 25 \, a^{4} b^{4} - 12 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4} - {\left(11 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(17 \, a^{6} b^{2} - 35 \, a^{4} b^{4} + 18 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{9} b^{2} - 2 \, a^{7} b^{4} + a^{5} b^{6}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{10} b - 2 \, a^{8} b^{3} + a^{6} b^{5}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{11} - 2 \, a^{9} b^{2} + a^{7} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)}}, \frac{2 \, {\left({\left(6 \, a^{4} b^{3} - 19 \, a^{2} b^{5} + 12 \, b^{7}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(6 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 12 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{6} b - 19 \, a^{4} b^{3} + 12 \, a^{2} 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^{6} b^{2} - 14 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - 12 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{8} - 14 \, a^{6} b^{2} + 25 \, a^{4} b^{4} - 12 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{6} b^{2} - 14 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - 12 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{8} - 14 \, a^{6} b^{2} + 25 \, a^{4} b^{4} - 12 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4} - {\left(11 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(17 \, a^{6} b^{2} - 35 \, a^{4} b^{4} + 18 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{9} b^{2} - 2 \, a^{7} b^{4} + a^{5} b^{6}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{10} b - 2 \, a^{8} b^{3} + a^{6} b^{5}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{11} - 2 \, a^{9} b^{2} + a^{7} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/4*(((6*a^4*b^3 - 19*a^2*b^5 + 12*b^7)*cos(d*x + c)^4 + 2*(6*a^5*b^2 - 19*a^3*b^4 + 12*a*b^6)*cos(d*x + c)^3 + (6*a^6*b - 19*a^4*b^3 + 12*a^2*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^6*b^2 - 14*a^4*b^4 + 25*a^2*b^6 - 12*b^8)*cos(d*x + c)^4 + 2*(a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7)*cos(d*x + c)^3 + (a^8 - 14*a^6*b^2 + 25*a^4*b^4 - 12*a^2*b^6)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((a^6*b^2 - 14*a^4*b^4 + 25*a^2*b^6 - 12*b^8)*cos(d*x + c)^4 + 2*(a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7)*cos(d*x + c)^3 + (a^8 - 14*a^6*b^2 + 25*a^4*b^4 - 12*a^2*b^6)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(a^8 - 2*a^6*b^2 + a^4*b^4 - (11*a^5*b^3 - 23*a^3*b^5 + 12*a*b^7)*cos(d*x + c)^3 - (17*a^6*b^2 - 35*a^4*b^4 + 18*a^2*b^6)*cos(d*x + c)^2 - 4*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c))*sin(d*x + c))/((a^9*b^2 - 2*a^7*b^4 + a^5*b^6)*d*cos(d*x + c)^4 + 2*(a^10*b - 2*a^8*b^3 + a^6*b^5)*d*cos(d*x + c)^3 + (a^11 - 2*a^9*b^2 + a^7*b^4)*d*cos(d*x + c)^2), 1/4*(2*((6*a^4*b^3 - 19*a^2*b^5 + 12*b^7)*cos(d*x + c)^4 + 2*(6*a^5*b^2 - 19*a^3*b^4 + 12*a*b^6)*cos(d*x + c)^3 + (6*a^6*b - 19*a^4*b^3 + 12*a^2*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^6*b^2 - 14*a^4*b^4 + 25*a^2*b^6 - 12*b^8)*cos(d*x + c)^4 + 2*(a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7)*cos(d*x + c)^3 + (a^8 - 14*a^6*b^2 + 25*a^4*b^4 - 12*a^2*b^6)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((a^6*b^2 - 14*a^4*b^4 + 25*a^2*b^6 - 12*b^8)*cos(d*x + c)^4 + 2*(a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7)*cos(d*x + c)^3 + (a^8 - 14*a^6*b^2 + 25*a^4*b^4 - 12*a^2*b^6)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(a^8 - 2*a^6*b^2 + a^4*b^4 - (11*a^5*b^3 - 23*a^3*b^5 + 12*a*b^7)*cos(d*x + c)^3 - (17*a^6*b^2 - 35*a^4*b^4 + 18*a^2*b^6)*cos(d*x + c)^2 - 4*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c))*sin(d*x + c))/((a^9*b^2 - 2*a^7*b^4 + a^5*b^6)*d*cos(d*x + c)^4 + 2*(a^10*b - 2*a^8*b^3 + a^6*b^5)*d*cos(d*x + c)^3 + (a^11 - 2*a^9*b^2 + a^7*b^4)*d*cos(d*x + c)^2)]","B",0
618,1,1447,0,1.494419," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(12 \, a^{4} b^{4} - 33 \, a^{2} b^{6} + 20 \, b^{8}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{5} b^{3} - 33 \, a^{3} b^{5} + 20 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(12 \, a^{6} b^{2} - 33 \, a^{4} b^{4} + 20 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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({\left(3 \, a^{6} b^{3} - 26 \, a^{4} b^{5} + 43 \, a^{2} b^{7} - 20 \, b^{9}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{7} b^{2} - 26 \, a^{5} b^{4} + 43 \, a^{3} b^{6} - 20 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{8} b - 26 \, a^{6} b^{3} + 43 \, a^{4} b^{5} - 20 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(3 \, a^{6} b^{3} - 26 \, a^{4} b^{5} + 43 \, a^{2} b^{7} - 20 \, b^{9}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{7} b^{2} - 26 \, a^{5} b^{4} + 43 \, a^{3} b^{6} - 20 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{8} b - 26 \, a^{6} b^{3} + 43 \, a^{4} b^{5} - 20 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, a^{9} - 4 \, a^{7} b^{2} + 2 \, a^{5} b^{4} - {\left(2 \, a^{7} b^{2} - 61 \, a^{5} b^{4} + 119 \, a^{3} b^{6} - 60 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(4 \, a^{8} b - 95 \, a^{6} b^{3} + 181 \, a^{4} b^{5} - 90 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} - 12 \, a^{7} b^{2} + 21 \, a^{5} b^{4} - 10 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{2} - 5 \, {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{10} b^{2} - 2 \, a^{8} b^{4} + a^{6} b^{6}\right)} d \cos\left(d x + c\right)^{5} + 2 \, {\left(a^{11} b - 2 \, a^{9} b^{3} + a^{7} b^{5}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{12} - 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d \cos\left(d x + c\right)^{3}\right)}}, -\frac{6 \, {\left({\left(12 \, a^{4} b^{4} - 33 \, a^{2} b^{6} + 20 \, b^{8}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{5} b^{3} - 33 \, a^{3} b^{5} + 20 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(12 \, a^{6} b^{2} - 33 \, a^{4} b^{4} + 20 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{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) - 3 \, {\left({\left(3 \, a^{6} b^{3} - 26 \, a^{4} b^{5} + 43 \, a^{2} b^{7} - 20 \, b^{9}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{7} b^{2} - 26 \, a^{5} b^{4} + 43 \, a^{3} b^{6} - 20 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{8} b - 26 \, a^{6} b^{3} + 43 \, a^{4} b^{5} - 20 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(3 \, a^{6} b^{3} - 26 \, a^{4} b^{5} + 43 \, a^{2} b^{7} - 20 \, b^{9}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{7} b^{2} - 26 \, a^{5} b^{4} + 43 \, a^{3} b^{6} - 20 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{8} b - 26 \, a^{6} b^{3} + 43 \, a^{4} b^{5} - 20 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, a^{9} - 4 \, a^{7} b^{2} + 2 \, a^{5} b^{4} - {\left(2 \, a^{7} b^{2} - 61 \, a^{5} b^{4} + 119 \, a^{3} b^{6} - 60 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(4 \, a^{8} b - 95 \, a^{6} b^{3} + 181 \, a^{4} b^{5} - 90 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} - 12 \, a^{7} b^{2} + 21 \, a^{5} b^{4} - 10 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{2} - 5 \, {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{10} b^{2} - 2 \, a^{8} b^{4} + a^{6} b^{6}\right)} d \cos\left(d x + c\right)^{5} + 2 \, {\left(a^{11} b - 2 \, a^{9} b^{3} + a^{7} b^{5}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{12} - 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/12*(3*((12*a^4*b^4 - 33*a^2*b^6 + 20*b^8)*cos(d*x + c)^5 + 2*(12*a^5*b^3 - 33*a^3*b^5 + 20*a*b^7)*cos(d*x + c)^4 + (12*a^6*b^2 - 33*a^4*b^4 + 20*a^2*b^6)*cos(d*x + c)^3)*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)) + 3*((3*a^6*b^3 - 26*a^4*b^5 + 43*a^2*b^7 - 20*b^9)*cos(d*x + c)^5 + 2*(3*a^7*b^2 - 26*a^5*b^4 + 43*a^3*b^6 - 20*a*b^8)*cos(d*x + c)^4 + (3*a^8*b - 26*a^6*b^3 + 43*a^4*b^5 - 20*a^2*b^7)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((3*a^6*b^3 - 26*a^4*b^5 + 43*a^2*b^7 - 20*b^9)*cos(d*x + c)^5 + 2*(3*a^7*b^2 - 26*a^5*b^4 + 43*a^3*b^6 - 20*a*b^8)*cos(d*x + c)^4 + (3*a^8*b - 26*a^6*b^3 + 43*a^4*b^5 - 20*a^2*b^7)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) + 2*(2*a^9 - 4*a^7*b^2 + 2*a^5*b^4 - (2*a^7*b^2 - 61*a^5*b^4 + 119*a^3*b^6 - 60*a*b^8)*cos(d*x + c)^4 - (4*a^8*b - 95*a^6*b^3 + 181*a^4*b^5 - 90*a^2*b^7)*cos(d*x + c)^3 - 2*(a^9 - 12*a^7*b^2 + 21*a^5*b^4 - 10*a^3*b^6)*cos(d*x + c)^2 - 5*(a^8*b - 2*a^6*b^3 + a^4*b^5)*cos(d*x + c))*sin(d*x + c))/((a^10*b^2 - 2*a^8*b^4 + a^6*b^6)*d*cos(d*x + c)^5 + 2*(a^11*b - 2*a^9*b^3 + a^7*b^5)*d*cos(d*x + c)^4 + (a^12 - 2*a^10*b^2 + a^8*b^4)*d*cos(d*x + c)^3), -1/12*(6*((12*a^4*b^4 - 33*a^2*b^6 + 20*b^8)*cos(d*x + c)^5 + 2*(12*a^5*b^3 - 33*a^3*b^5 + 20*a*b^7)*cos(d*x + c)^4 + (12*a^6*b^2 - 33*a^4*b^4 + 20*a^2*b^6)*cos(d*x + c)^3)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*((3*a^6*b^3 - 26*a^4*b^5 + 43*a^2*b^7 - 20*b^9)*cos(d*x + c)^5 + 2*(3*a^7*b^2 - 26*a^5*b^4 + 43*a^3*b^6 - 20*a*b^8)*cos(d*x + c)^4 + (3*a^8*b - 26*a^6*b^3 + 43*a^4*b^5 - 20*a^2*b^7)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) + 3*((3*a^6*b^3 - 26*a^4*b^5 + 43*a^2*b^7 - 20*b^9)*cos(d*x + c)^5 + 2*(3*a^7*b^2 - 26*a^5*b^4 + 43*a^3*b^6 - 20*a*b^8)*cos(d*x + c)^4 + (3*a^8*b - 26*a^6*b^3 + 43*a^4*b^5 - 20*a^2*b^7)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(2*a^9 - 4*a^7*b^2 + 2*a^5*b^4 - (2*a^7*b^2 - 61*a^5*b^4 + 119*a^3*b^6 - 60*a*b^8)*cos(d*x + c)^4 - (4*a^8*b - 95*a^6*b^3 + 181*a^4*b^5 - 90*a^2*b^7)*cos(d*x + c)^3 - 2*(a^9 - 12*a^7*b^2 + 21*a^5*b^4 - 10*a^3*b^6)*cos(d*x + c)^2 - 5*(a^8*b - 2*a^6*b^3 + a^4*b^5)*cos(d*x + c))*sin(d*x + c))/((a^10*b^2 - 2*a^8*b^4 + a^6*b^6)*d*cos(d*x + c)^5 + 2*(a^11*b - 2*a^9*b^3 + a^7*b^5)*d*cos(d*x + c)^4 + (a^12 - 2*a^10*b^2 + a^8*b^4)*d*cos(d*x + c)^3)]","B",0
619,1,18,0,0.569737," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{a d x - b \sin\left(d x + c\right)}{d}"," ",0,"(a*d*x - b*sin(d*x + c))/d","A",0
620,1,218,0,0.643803," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(a^{2} - b^{2}\right)} d x + \sqrt{-a^{2} + b^{2}} 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)}{{\left(a^{2} - b^{2}\right)} d}, -\frac{{\left(a^{2} - b^{2}\right)} d x - 2 \, \sqrt{a^{2} - b^{2}} 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(a^{2} - b^{2}\right)} d}\right]"," ",0,"[-((a^2 - b^2)*d*x + sqrt(-a^2 + b^2)*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)))/((a^2 - b^2)*d), -((a^2 - b^2)*d*x - 2*sqrt(a^2 - b^2)*a*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))))/((a^2 - b^2)*d)]","A",0
621,1,346,0,0.552176," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(a^{3} + a b^{2} + {\left(a^{2} b + 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) - 4 \, {\left(a^{3} b - 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^{3} + a b^{2} + {\left(a^{2} b + 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) - 2 \, {\left(a^{3} b - 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^3 + a*b^2 + (a^2*b + 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)) - 4*(a^3*b - 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^3 + a*b^2 + (a^2*b + 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^3*b - 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
622,1,598,0,0.605346," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{{\left(a^{5} + 2 \, a^{3} b^{2} + {\left(a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} 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(3 \, a^{5} b - 3 \, a^{3} b^{3} + {\left(2 \, a^{4} b^{2} - a^{2} b^{4} - b^{6}\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)}}, \frac{{\left(a^{5} + 2 \, a^{3} b^{2} + {\left(a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} 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(3 \, a^{5} b - 3 \, a^{3} b^{3} + {\left(2 \, a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\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]"," ",0,"[-1/2*((a^5 + 2*a^3*b^2 + (a^3*b^2 + 2*a*b^4)*cos(d*x + c)^2 + 2*(a^4*b + 2*a^2*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*(3*a^5*b - 3*a^3*b^3 + (2*a^4*b^2 - a^2*b^4 - b^6)*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), ((a^5 + 2*a^3*b^2 + (a^3*b^2 + 2*a*b^4)*cos(d*x + c)^2 + 2*(a^4*b + 2*a^2*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))) - (3*a^5*b - 3*a^3*b^3 + (2*a^4*b^2 - a^2*b^4 - b^6)*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
623,0,0,0,0.561962," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{4} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^4 + A*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
624,0,0,0,0.472067," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^3 + A*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
625,0,0,0,0.582229," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a), x)","F",0
626,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,0,0,0,2.569534," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
628,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,0,0,0,1.166273," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{5} + C a \cos\left(d x + c\right)^{4} + A b \cos\left(d x + c\right)^{3} + A a \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^5 + C*a*cos(d*x + c)^4 + A*b*cos(d*x + c)^3 + A*a*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
631,0,0,0,1.045189," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} + C a \cos\left(d x + c\right)^{3} + A b \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^4 + C*a*cos(d*x + c)^3 + A*b*cos(d*x + c)^2 + A*a*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
632,0,0,0,0.906635," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a), x)","F",0
633,0,0,0,2.359802," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right), x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
634,0,0,0,4.351521," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
635,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,0,0,0,1.981653," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{6} + 2 \, C a b \cos\left(d x + c\right)^{5} + 2 \, A a b \cos\left(d x + c\right)^{3} + A a^{2} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{4}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^6 + 2*C*a*b*cos(d*x + c)^5 + 2*A*a*b*cos(d*x + c)^3 + A*a^2*cos(d*x + c)^2 + (C*a^2 + A*b^2)*cos(d*x + c)^4)*sqrt(b*cos(d*x + c) + a), x)","F",0
639,0,0,0,0.507056," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{5} + 2 \, C a b \cos\left(d x + c\right)^{4} + 2 \, A a b \cos\left(d x + c\right)^{2} + A a^{2} \cos\left(d x + c\right) + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^5 + 2*C*a*b*cos(d*x + c)^4 + 2*A*a*b*cos(d*x + c)^2 + A*a^2*cos(d*x + c) + (C*a^2 + A*b^2)*cos(d*x + c)^3)*sqrt(b*cos(d*x + c) + a), x)","F",0
640,0,0,0,0.577182," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
641,0,0,0,1.794096," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right), x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
642,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,0,0,0,7.714292," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
644,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
645,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
646,0,0,0,1.250865," ","integrate((a+b*cos(d*x+c))^(3/2)*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{3} \cos\left(d x + c\right)^{3} + a b^{2} \cos\left(d x + c\right)^{2} - a^{2} b \cos\left(d x + c\right) - a^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(b^3*cos(d*x + c)^3 + a*b^2*cos(d*x + c)^2 - a^2*b*cos(d*x + c) - a^3)*sqrt(b*cos(d*x + c) + a), x)","F",0
647,0,0,0,0.946487," ","integrate((a^2-b^2*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^2 - a^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
648,0,0,0,0.834904," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{5} + A \cos\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^5 + A*cos(d*x + c)^3)/sqrt(b*cos(d*x + c) + a), x)","F",0
649,0,0,0,0.778883," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{4} + A \cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^4 + A*cos(d*x + c)^2)/sqrt(b*cos(d*x + c) + a), x)","F",0
650,0,0,0,0.796351," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^3 + A*cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
651,0,0,0,0.957205," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)/sqrt(b*cos(d*x + c) + a), x)","F",0
652,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
653,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
654,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
655,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
656,0,0,0,1.059139," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{5} + 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((C*cos(d*x + c)^5 + 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
657,0,0,0,0.863974," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + 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
658,0,0,0,1.369310," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
659,0,0,0,0.658665," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
660,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
661,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
662,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
663,0,0,0,0.832205," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{5} + 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((C*cos(d*x + c)^5 + 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
664,0,0,0,1.530808," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + 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
665,0,0,0,1.768507," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
666,0,0,0,1.022300," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
667,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
668,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
669,0,0,0,0.948257," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{4} \cos\left(d x + c\right)^{4} + 4 \, a b^{3} \cos\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} + 4 \, a^{3} b \cos\left(d x + c\right) + a^{4}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/(b^4*cos(d*x + c)^4 + 4*a*b^3*cos(d*x + c)^3 + 6*a^2*b^2*cos(d*x + c)^2 + 4*a^3*b*cos(d*x + c) + a^4), x)","F",0
670,0,0,0,0.678877," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\sqrt{b \cos\left(d x + c\right) + a} {\left(b \cos\left(d x + c\right) - a\right)}, x\right)"," ",0,"integral(-sqrt(b*cos(d*x + c) + a)*(b*cos(d*x + c) - a), x)","F",0
671,0,0,0,0.761856," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),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
672,0,0,0,1.901528," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \cos\left(d x + c\right) + a} {\left(b \cos\left(d x + c\right) - a\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(-sqrt(b*cos(d*x + c) + a)*(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
673,0,0,0,1.032550," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \cos\left(d x + c\right) + a} {\left(b \cos\left(d x + c\right) - a\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(-sqrt(b*cos(d*x + c) + a)*(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
674,0,0,0,1.295764," ","integrate(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{5} + C a \cos\left(d x + c\right)^{4} + A b \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((C*b*cos(d*x + c)^5 + C*a*cos(d*x + c)^4 + A*b*cos(d*x + c)^3 + A*a*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
675,0,0,0,0.624273," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} + C a \cos\left(d x + c\right)^{3} + A b \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((C*b*cos(d*x + c)^4 + C*a*cos(d*x + c)^3 + A*b*cos(d*x + c)^2 + A*a*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
676,0,0,0,0.572531," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(cos(d*x + c)), x)","F",0
677,0,0,0,0.666273," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)/sqrt(cos(d*x + c)), x)","F",0
678,0,0,0,0.701120," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)/cos(d*x + c)^(3/2), x)","F",0
679,0,0,0,0.636957," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)/cos(d*x + c)^(5/2), x)","F",0
680,0,0,0,0.531505," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)/cos(d*x + c)^(7/2), x)","F",0
681,0,0,0,0.522882," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)/cos(d*x + c)^(9/2), x)","F",0
682,0,0,0,0.662163," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{5} + 2 \, C a b \cos\left(d x + c\right)^{4} + 2 \, A a b \cos\left(d x + c\right)^{2} + A a^{2} \cos\left(d x + c\right) + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^5 + 2*C*a*b*cos(d*x + c)^4 + 2*A*a*b*cos(d*x + c)^2 + A*a^2*cos(d*x + c) + (C*a^2 + A*b^2)*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
683,0,0,0,0.611878," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
684,0,0,0,0.592626," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)/sqrt(cos(d*x + c)), x)","F",0
685,0,0,0,0.607630," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(3/2), x)","F",0
686,0,0,0,0.564235," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(5/2), x)","F",0
687,0,0,0,0.619608," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(7/2), x)","F",0
688,0,0,0,0.675852," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(9/2), x)","F",0
689,0,0,0,2.404627," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
690,0,0,0,0.614408," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)/sqrt(cos(d*x + c)), x)","F",0
691,0,0,0,0.650362," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(3/2), x)","F",0
692,0,0,0,0.812281," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(5/2), x)","F",0
693,0,0,0,0.734130," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(7/2), x)","F",0
694,0,0,0,0.724789," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(9/2), x)","F",0
695,0,0,0,0.627868," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(11/2), x)","F",0
696,0,0,0,0.743138," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
697,0,0,0,0.803058," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)/sqrt(cos(d*x + c)), x)","F",0
698,0,0,0,0.787717," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(3/2), x)","F",0
699,0,0,0,0.769935," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(5/2), x)","F",0
700,0,0,0,0.858709," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(7/2), x)","F",0
701,0,0,0,0.786424," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(9/2), x)","F",0
702,0,0,0,0.947537," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(11/2), x)","F",0
703,0,0,0,0.708029," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}}{\cos\left(d x + c\right)^{\frac{13}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)/cos(d*x + c)^(13/2), x)","F",0
704,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
706,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
707,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
708,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
709,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
710,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
711,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
712,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
714,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
715,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
716,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
717,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
720,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
721,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
722,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
723,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
724,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,0,0,0,121.327949," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
728,0,0,0,79.204137," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
729,0,0,0,1.205446," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
730,0,0,0,44.993985," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
731,0,0,0,0.713296," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
732,0,0,0,0.815782," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
733,0,0,0,102.189688," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
734,0,0,0,117.615000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
735,0,0,0,2.417428," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
736,0,0,0,57.608003," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
737,0,0,0,0.989386," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
738,0,0,0,0.549426," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
739,0,0,0,0.523939," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(11/2), x)","F",0
740,0,0,0,5.923297," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\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((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
741,0,0,0,91.143226," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\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((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
742,0,0,0,2.798016," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
743,0,0,0,2.476446," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
744,0,0,0,33.900323," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
745,0,0,0,31.601725," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
746,0,0,0,1.228429," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(11/2), x)","F",0
747,0,0,0,0.498420," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{13}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(13/2), x)","F",0
748,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
749,0,0,0,99.501906," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
750,0,0,0,26.847609," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
751,0,0,0,0.817392," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
752,0,0,0,0.544745," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
753,0,0,0,0.495940," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{5} + a \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
754,0,0,0,0.451654," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{6} + a \cos\left(d x + c\right)^{5}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)^6 + a*cos(d*x + c)^5), x)","F",0
755,0,0,0,58.885301," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
756,0,0,0,1.265047," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
757,0,0,0,24.335577," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
758,0,0,0,0.452819," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
759,0,0,0,0.481940," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
760,0,0,0,0.558858," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{6} + 2 \, a b \cos\left(d x + c\right)^{5} + a^{2} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^6 + 2*a*b*cos(d*x + c)^5 + a^2*cos(d*x + c)^4), x)","F",0
761,0,0,0,27.158245," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
762,0,0,0,23.377255," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
763,0,0,0,0.506243," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
764,0,0,0,0.529188," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
765,0,0,0,0.549791," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
766,0,0,0,0.472906," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*cos(d*x + c)^m, x)","F",0
767,0,0,0,0.616999," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*cos(d*x + c)^m, x)","F",0
768,0,0,0,0.453363," ","integrate(cos(d*x+c)^m*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{m}}{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*cos(d*x + c)^m/(b*cos(d*x + c) + a), x)","F",0
769,0,0,0,0.469263," ","integrate(cos(d*x+c)^m*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{m}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*cos(d*x + c)^m/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
770,1,81,0,0.428814," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, B a + 3 \, C b\right)} d x + {\left(6 \, C b \cos\left(d x + c\right)^{3} + 8 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{2} + 16 \, C a + 16 \, B b + 3 \, {\left(4 \, B a + 3 \, C b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*B*a + 3*C*b)*d*x + (6*C*b*cos(d*x + c)^3 + 8*(C*a + B*b)*cos(d*x + c)^2 + 16*C*a + 16*B*b + 3*(4*B*a + 3*C*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
771,1,60,0,0.459411," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(C a + B b\right)} d x + {\left(2 \, C b \cos\left(d x + c\right)^{2} + 6 \, B a + 4 \, C b + 3 \, {\left(C a + B b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(C*a + B*b)*d*x + (2*C*b*cos(d*x + c)^2 + 6*B*a + 4*C*b + 3*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
772,1,42,0,0.429675," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{{\left(2 \, B a + C b\right)} d x + {\left(C b \cos\left(d x + c\right) + 2 \, C a + 2 \, B b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*B*a + C*b)*d*x + (C*b*cos(d*x + c) + 2*C*a + 2*B*b)*sin(d*x + c))/d","A",0
773,1,54,0,0.454818," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(C a + B b\right)} d x + B a \log\left(\sin\left(d x + c\right) + 1\right) - B a \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, C b \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(C*a + B*b)*d*x + B*a*log(sin(d*x + c) + 1) - B*a*log(-sin(d*x + c) + 1) + 2*C*b*sin(d*x + c))/d","A",0
774,1,85,0,0.461558," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, C b d x \cos\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a + B b\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B a \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*C*b*d*x*cos(d*x + c) + (C*a + B*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - (C*a + B*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*B*a*sin(d*x + c))/(d*cos(d*x + c))","B",0
775,1,96,0,0.431465," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{{\left(B a + 2 \, C b\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a + 2 \, C b\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a + 2 \, {\left(C a + B b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((B*a + 2*C*b)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (B*a + 2*C*b)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(B*a + 2*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
776,1,115,0,0.459867," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(2 \, B a + 3 \, C b\right)} \cos\left(d x + c\right)^{2} + 2 \, B a + 3 \, {\left(C a + B b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(C*a + B*b)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(C*a + B*b)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*(2*B*a + 3*C*b)*cos(d*x + c)^2 + 2*B*a + 3*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
777,1,136,0,0.534226," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, B a + 4 \, C b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, B a + 4 \, C b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, B a + 4 \, C b\right)} \cos\left(d x + c\right)^{2} + 6 \, B a + 8 \, {\left(C a + B b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(3*B*a + 4*C*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*B*a + 4*C*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*(C*a + B*b)*cos(d*x + c)^3 + 3*(3*B*a + 4*C*b)*cos(d*x + c)^2 + 6*B*a + 8*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
778,1,142,0,0.428484," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, B a^{2} + 6 \, C a b + 3 \, B b^{2}\right)} d x + {\left(24 \, C b^{2} \cos\left(d x + c\right)^{4} + 30 \, {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + 80 \, C a^{2} + 160 \, B a b + 64 \, C b^{2} + 8 \, {\left(5 \, C a^{2} + 10 \, B a b + 4 \, C b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, B a^{2} + 6 \, C a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*B*a^2 + 6*C*a*b + 3*B*b^2)*d*x + (24*C*b^2*cos(d*x + c)^4 + 30*(2*C*a*b + B*b^2)*cos(d*x + c)^3 + 80*C*a^2 + 160*B*a*b + 64*C*b^2 + 8*(5*C*a^2 + 10*B*a*b + 4*C*b^2)*cos(d*x + c)^2 + 15*(4*B*a^2 + 6*C*a*b + 3*B*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
779,1,114,0,0.503577," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, C a^{2} + 8 \, B a b + 3 \, C b^{2}\right)} d x + {\left(6 \, C b^{2} \cos\left(d x + c\right)^{3} + 24 \, B a^{2} + 32 \, C a b + 16 \, B b^{2} + 8 \, {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, C a^{2} + 8 \, B a b + 3 \, C b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*C*a^2 + 8*B*a*b + 3*C*b^2)*d*x + (6*C*b^2*cos(d*x + c)^3 + 24*B*a^2 + 32*C*a*b + 16*B*b^2 + 8*(2*C*a*b + B*b^2)*cos(d*x + c)^2 + 3*(4*C*a^2 + 8*B*a*b + 3*C*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
780,1,85,0,0.525072," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, B a^{2} + 2 \, C a b + B b^{2}\right)} d x + {\left(2 \, C b^{2} \cos\left(d x + c\right)^{2} + 6 \, C a^{2} + 12 \, B a b + 4 \, C b^{2} + 3 \, {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*B*a^2 + 2*C*a*b + B*b^2)*d*x + (2*C*b^2*cos(d*x + c)^2 + 6*C*a^2 + 12*B*a*b + 4*C*b^2 + 3*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
781,1,87,0,0.725781," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{B a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - B a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, C a^{2} + 4 \, B a b + C b^{2}\right)} d x + {\left(C b^{2} \cos\left(d x + c\right) + 4 \, C a b + 2 \, B b^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*a^2*log(sin(d*x + c) + 1) - B*a^2*log(-sin(d*x + c) + 1) + (2*C*a^2 + 4*B*a*b + C*b^2)*d*x + (C*b^2*cos(d*x + c) + 4*C*a*b + 2*B*b^2)*sin(d*x + c))/d","A",0
782,1,117,0,0.602607," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, C a b + B b^{2}\right)} d x \cos\left(d x + c\right) + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(C b^{2} \cos\left(d x + c\right) + B a^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(2*C*a*b + B*b^2)*d*x*cos(d*x + c) + (C*a^2 + 2*B*a*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - (C*a^2 + 2*B*a*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(C*b^2*cos(d*x + c) + B*a^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
783,1,136,0,0.523191," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{4 \, C b^{2} d x \cos\left(d x + c\right)^{2} + {\left(B a^{2} + 4 \, C a b + 2 \, B b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{2} + 4 \, C a b + 2 \, B b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{2} + 2 \, {\left(C a^{2} + 2 \, B 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*C*b^2*d*x*cos(d*x + c)^2 + (B*a^2 + 4*C*a*b + 2*B*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (B*a^2 + 4*C*a*b + 2*B*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(B*a^2 + 2*(C*a^2 + 2*B*a*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
784,1,150,0,0.479070," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(C a^{2} + 2 \, B a b + 2 \, C b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(C a^{2} + 2 \, B a b + 2 \, C b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B a^{2} + 2 \, {\left(2 \, B a^{2} + 6 \, C a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{2} + 2 \, B 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*(C*a^2 + 2*B*a*b + 2*C*b^2)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(C*a^2 + 2*B*a*b + 2*C*b^2)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*B*a^2 + 2*(2*B*a^2 + 6*C*a*b + 3*B*b^2)*cos(d*x + c)^2 + 3*(C*a^2 + 2*B*a*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
785,1,180,0,0.485376," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, B a^{2} + 8 \, C a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, B a^{2} + 8 \, C a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(2 \, C a^{2} + 4 \, B a b + 3 \, C b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, B a^{2} + 3 \, {\left(3 \, B a^{2} + 8 \, C a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(C a^{2} + 2 \, B 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*B*a^2 + 8*C*a*b + 4*B*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*B*a^2 + 8*C*a*b + 4*B*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(2*C*a^2 + 4*B*a*b + 3*C*b^2)*cos(d*x + c)^3 + 6*B*a^2 + 3*(3*B*a^2 + 8*C*a*b + 4*B*b^2)*cos(d*x + c)^2 + 8*(C*a^2 + 2*B*a*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
786,1,174,0,0.471583," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, C a^{3} + 12 \, B a^{2} b + 9 \, C a b^{2} + 3 \, B b^{3}\right)} d x + {\left(24 \, C b^{3} \cos\left(d x + c\right)^{4} + 120 \, B a^{3} + 240 \, C a^{2} b + 240 \, B a b^{2} + 64 \, C b^{3} + 30 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, C a^{2} b + 15 \, B a b^{2} + 4 \, C b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, C a^{3} + 12 \, B a^{2} b + 9 \, C a b^{2} + 3 \, B b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*C*a^3 + 12*B*a^2*b + 9*C*a*b^2 + 3*B*b^3)*d*x + (24*C*b^3*cos(d*x + c)^4 + 120*B*a^3 + 240*C*a^2*b + 240*B*a*b^2 + 64*C*b^3 + 30*(3*C*a*b^2 + B*b^3)*cos(d*x + c)^3 + 8*(15*C*a^2*b + 15*B*a*b^2 + 4*C*b^3)*cos(d*x + c)^2 + 15*(4*C*a^3 + 12*B*a^2*b + 9*C*a*b^2 + 3*B*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
787,1,136,0,0.479337," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 3 \, C b^{3}\right)} d x + {\left(6 \, C b^{3} \cos\left(d x + c\right)^{3} + 24 \, C a^{3} + 72 \, B a^{2} b + 48 \, C a b^{2} + 16 \, B b^{3} + 8 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(4 \, C a^{2} b + 4 \, B a b^{2} + C b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(8*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 3*C*b^3)*d*x + (6*C*b^3*cos(d*x + c)^3 + 24*C*a^3 + 72*B*a^2*b + 48*C*a*b^2 + 16*B*b^3 + 8*(3*C*a*b^2 + B*b^3)*cos(d*x + c)^2 + 9*(4*C*a^2*b + 4*B*a*b^2 + C*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
788,1,131,0,0.477029," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, B a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, B a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d x + {\left(2 \, C b^{3} \cos\left(d x + c\right)^{2} + 18 \, C a^{2} b + 18 \, B a b^{2} + 4 \, C b^{3} + 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*B*a^3*log(sin(d*x + c) + 1) - 3*B*a^3*log(-sin(d*x + c) + 1) + 3*(2*C*a^3 + 6*B*a^2*b + 3*C*a*b^2 + B*b^3)*d*x + (2*C*b^3*cos(d*x + c)^2 + 18*C*a^2*b + 18*B*a*b^2 + 4*C*b^3 + 3*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
789,1,152,0,0.550043," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(6 \, C a^{2} b + 6 \, B a b^{2} + C b^{3}\right)} d x \cos\left(d x + c\right) + {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(C b^{3} \cos\left(d x + c\right)^{2} + 2 \, B a^{3} + 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*((6*C*a^2*b + 6*B*a*b^2 + C*b^3)*d*x*cos(d*x + c) + (C*a^3 + 3*B*a^2*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - (C*a^3 + 3*B*a^2*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (C*b^3*cos(d*x + c)^2 + 2*B*a^3 + 2*(3*C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
790,1,167,0,0.491508," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, C a b^{2} + B b^{3}\right)} d x \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 6 \, C a^{2} b + 6 \, B a b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{3} + 6 \, C a^{2} b + 6 \, B a b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, C b^{3} \cos\left(d x + c\right)^{2} + B a^{3} + 2 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*(3*C*a*b^2 + B*b^3)*d*x*cos(d*x + c)^2 + (B*a^3 + 6*C*a^2*b + 6*B*a*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (B*a^3 + 6*C*a^2*b + 6*B*a*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*b^3*cos(d*x + c)^2 + B*a^3 + 2*(C*a^3 + 3*B*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
791,1,189,0,0.486387," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{12 \, C b^{3} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{3} + 3 \, B a^{2} b + 6 \, C a b^{2} + 2 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(C a^{3} + 3 \, B a^{2} b + 6 \, C a b^{2} + 2 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B a^{3} + 2 \, {\left(2 \, B a^{3} + 9 \, C a^{2} b + 9 \, B a b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(12*C*b^3*d*x*cos(d*x + c)^3 + 3*(C*a^3 + 3*B*a^2*b + 6*C*a*b^2 + 2*B*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(C*a^3 + 3*B*a^2*b + 6*C*a*b^2 + 2*B*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*B*a^3 + 2*(2*B*a^3 + 9*C*a^2*b + 9*B*a*b^2)*cos(d*x + c)^2 + 3*(C*a^3 + 3*B*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
792,1,211,0,0.468329," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 8 \, C b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, B a^{3} + 12 \, C a^{2} b + 12 \, B a b^{2} + 8 \, C b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, B a^{3} + 8 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 9 \, C a b^{2} + 3 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} + 9 \, {\left(B a^{3} + 4 \, C a^{2} b + 4 \, B a b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(C a^{3} + 3 \, B 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*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 8*C*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*B*a^3 + 12*C*a^2*b + 12*B*a*b^2 + 8*C*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(6*B*a^3 + 8*(2*C*a^3 + 6*B*a^2*b + 9*C*a*b^2 + 3*B*b^3)*cos(d*x + c)^3 + 9*(B*a^3 + 4*C*a^2*b + 4*B*a*b^2)*cos(d*x + c)^2 + 8*(C*a^3 + 3*B*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
793,1,249,0,0.527120," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b + 12 \, C a b^{2} + 4 \, B b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b + 12 \, C a b^{2} + 4 \, B b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(8 \, B a^{3} + 30 \, C a^{2} b + 30 \, B a b^{2} + 15 \, C b^{3}\right)} \cos\left(d x + c\right)^{4} + 24 \, B a^{3} + 15 \, {\left(3 \, C a^{3} + 9 \, B a^{2} b + 12 \, C a b^{2} + 4 \, B b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, B a^{3} + 15 \, C a^{2} b + 15 \, B a b^{2}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(C a^{3} + 3 \, B 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*C*a^3 + 9*B*a^2*b + 12*C*a*b^2 + 4*B*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*C*a^3 + 9*B*a^2*b + 12*C*a*b^2 + 4*B*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(8*B*a^3 + 30*C*a^2*b + 30*B*a*b^2 + 15*C*b^3)*cos(d*x + c)^4 + 24*B*a^3 + 15*(3*C*a^3 + 9*B*a^2*b + 12*C*a*b^2 + 4*B*b^3)*cos(d*x + c)^3 + 8*(4*B*a^3 + 15*C*a^2*b + 15*B*a*b^2)*cos(d*x + c)^2 + 30*(C*a^3 + 3*B*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
794,1,541,0,0.502250," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, C a^{5} - 2 \, B a^{4} b - C a^{3} b^{2} + B a^{2} b^{3} - C a b^{4} + B b^{5}\right)} d x - 3 \, {\left(C a^{4} - B 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 \, C a^{4} b - 6 \, B a^{3} b^{2} - 2 \, C a^{2} b^{3} + 6 \, B a b^{4} - 4 \, C b^{5} + 2 \, {\left(C a^{2} b^{3} - C b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} - C a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} - b^{6}\right)} d}, -\frac{3 \, {\left(2 \, C a^{5} - 2 \, B a^{4} b - C a^{3} b^{2} + B a^{2} b^{3} - C a b^{4} + B b^{5}\right)} d x - 6 \, {\left(C a^{4} - B 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 \, C a^{4} b - 6 \, B a^{3} b^{2} - 2 \, C a^{2} b^{3} + 6 \, B a b^{4} - 4 \, C b^{5} + 2 \, {\left(C a^{2} b^{3} - C b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} - C a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} - b^{6}\right)} d}\right]"," ",0,"[-1/6*(3*(2*C*a^5 - 2*B*a^4*b - C*a^3*b^2 + B*a^2*b^3 - C*a*b^4 + B*b^5)*d*x - 3*(C*a^4 - B*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*C*a^4*b - 6*B*a^3*b^2 - 2*C*a^2*b^3 + 6*B*a*b^4 - 4*C*b^5 + 2*(C*a^2*b^3 - C*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - B*a^2*b^3 - C*a*b^4 + B*b^5)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d), -1/6*(3*(2*C*a^5 - 2*B*a^4*b - C*a^3*b^2 + B*a^2*b^3 - C*a*b^4 + B*b^5)*d*x - 6*(C*a^4 - B*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*C*a^4*b - 6*B*a^3*b^2 - 2*C*a^2*b^3 + 6*B*a*b^4 - 4*C*b^5 + 2*(C*a^2*b^3 - C*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - B*a^2*b^3 - C*a*b^4 + B*b^5)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d)]","A",0
795,1,426,0,0.481214," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, C a^{4} - 2 \, B a^{3} b - C a^{2} b^{2} + 2 \, B a b^{3} - C b^{4}\right)} d x + {\left(C a^{3} - B 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 \, C a^{3} b - 2 \, B a^{2} b^{2} - 2 \, C a b^{3} + 2 \, B b^{4} - {\left(C a^{2} b^{2} - C 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 \, C a^{4} - 2 \, B a^{3} b - C a^{2} b^{2} + 2 \, B a b^{3} - C b^{4}\right)} d x - 2 \, {\left(C a^{3} - B 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 \, C a^{3} b - 2 \, B a^{2} b^{2} - 2 \, C a b^{3} + 2 \, B b^{4} - {\left(C a^{2} b^{2} - C 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*C*a^4 - 2*B*a^3*b - C*a^2*b^2 + 2*B*a*b^3 - C*b^4)*d*x + (C*a^3 - B*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*C*a^3*b - 2*B*a^2*b^2 - 2*C*a*b^3 + 2*B*b^4 - (C*a^2*b^2 - C*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d), 1/2*((2*C*a^4 - 2*B*a^3*b - C*a^2*b^2 + 2*B*a*b^3 - C*b^4)*d*x - 2*(C*a^3 - B*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*C*a^3*b - 2*B*a^2*b^2 - 2*C*a*b^3 + 2*B*b^4 - (C*a^2*b^2 - C*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d)]","A",0
796,1,322,0,0.498629," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} d x - {\left(C a^{2} - B 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(C a^{2} b - C b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d}, -\frac{{\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} d x - {\left(C a^{2} - B 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(C a^{2} b - C b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d}\right]"," ",0,"[-1/2*(2*(C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*d*x - (C*a^2 - B*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*(C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d), -((C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*d*x - (C*a^2 - B*a*b)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d)]","A",0
797,1,242,0,0.450244," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{2} - C b^{2}\right)} d x + {\left(C a - B b\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(C a^{2} - C b^{2}\right)} d x - {\left(C a - B 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*(C*a^2 - C*b^2)*d*x + (C*a - B*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), ((C*a^2 - C*b^2)*d*x - (C*a - B*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
798,1,304,0,1.150681," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(C a - B b\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, {\left(C a - B 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^{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*((C*a - B*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)) + (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*(C*a - B*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^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
799,1,460,0,0.662600," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(C a b - B 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(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(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 \, {\left(C a b - B 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(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(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*((C*a*b - B*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)) + (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) - (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(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*(C*a*b - B*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) - (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) + (C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) - 2*(B*a^3 - B*a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d*cos(d*x + c))]","B",0
800,1,589,0,4.606409," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a b^{2} - B 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(B a^{4} - 2 \, C a^{3} b + B a^{2} b^{2} + 2 \, C a b^{3} - 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} - 2 \, C a^{3} b + B a^{2} b^{2} + 2 \, C a b^{3} - 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(C a^{4} - B a^{3} b - C a^{2} b^{2} + 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 \, {\left(C a b^{2} - B 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(B a^{4} - 2 \, C a^{3} b + B a^{2} b^{2} + 2 \, C a b^{3} - 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} - 2 \, C a^{3} b + B a^{2} b^{2} + 2 \, C a b^{3} - 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(C a^{4} - B a^{3} b - C a^{2} b^{2} + 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*(C*a*b^2 - B*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)) + (B*a^4 - 2*C*a^3*b + B*a^2*b^2 + 2*C*a*b^3 - 2*B*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (B*a^4 - 2*C*a^3*b + B*a^2*b^2 + 2*C*a*b^3 - 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*(C*a^4 - B*a^3*b - C*a^2*b^2 + 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*(C*a*b^2 - B*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 + (B*a^4 - 2*C*a^3*b + B*a^2*b^2 + 2*C*a*b^3 - 2*B*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (B*a^4 - 2*C*a^3*b + B*a^2*b^2 + 2*C*a*b^3 - 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*(C*a^4 - B*a^3*b - C*a^2*b^2 + B*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
801,1,965,0,0.589077," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} - 11 \, C a^{4} b^{3} + 8 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} - 4 \, B a b^{6} + C b^{7}\right)} d x \cos\left(d x + c\right) + {\left(6 \, C a^{7} - 4 \, B a^{6} b - 11 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3} + 4 \, C a^{3} b^{4} - 4 \, B a^{2} b^{5} + C a b^{6}\right)} d x - {\left(3 \, C a^{6} - 2 \, B a^{5} b - 4 \, C a^{4} b^{2} + 3 \, B a^{3} b^{3} + {\left(3 \, C a^{5} b - 2 \, B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 3 \, B a^{2} b^{4}\right)} \cos\left(d x + c\right)\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 \, C a^{6} b - 4 \, B a^{5} b^{2} - 10 \, C a^{4} b^{3} + 6 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} - 2 \, B a b^{6} - {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} - 6 \, C a^{3} b^{4} + 4 \, B a^{2} b^{5} + 3 \, C a b^{6} - 2 \, B b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{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 \, C a^{6} b - 4 \, B a^{5} b^{2} - 11 \, C a^{4} b^{3} + 8 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} - 4 \, B a b^{6} + C b^{7}\right)} d x \cos\left(d x + c\right) + {\left(6 \, C a^{7} - 4 \, B a^{6} b - 11 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3} + 4 \, C a^{3} b^{4} - 4 \, B a^{2} b^{5} + C a b^{6}\right)} d x - 2 \, {\left(3 \, C a^{6} - 2 \, B a^{5} b - 4 \, C a^{4} b^{2} + 3 \, B a^{3} b^{3} + {\left(3 \, C a^{5} b - 2 \, B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 3 \, B a^{2} b^{4}\right)} \cos\left(d x + c\right)\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 \, C a^{6} b - 4 \, B a^{5} b^{2} - 10 \, C a^{4} b^{3} + 6 \, B a^{3} b^{4} + 4 \, C a^{2} b^{5} - 2 \, B a b^{6} - {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} - 6 \, C a^{3} b^{4} + 4 \, B a^{2} b^{5} + 3 \, C a b^{6} - 2 \, B b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{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*C*a^6*b - 4*B*a^5*b^2 - 11*C*a^4*b^3 + 8*B*a^3*b^4 + 4*C*a^2*b^5 - 4*B*a*b^6 + C*b^7)*d*x*cos(d*x + c) + (6*C*a^7 - 4*B*a^6*b - 11*C*a^5*b^2 + 8*B*a^4*b^3 + 4*C*a^3*b^4 - 4*B*a^2*b^5 + C*a*b^6)*d*x - (3*C*a^6 - 2*B*a^5*b - 4*C*a^4*b^2 + 3*B*a^3*b^3 + (3*C*a^5*b - 2*B*a^4*b^2 - 4*C*a^3*b^3 + 3*B*a^2*b^4)*cos(d*x + c))*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*C*a^6*b - 4*B*a^5*b^2 - 10*C*a^4*b^3 + 6*B*a^3*b^4 + 4*C*a^2*b^5 - 2*B*a*b^6 - (C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7)*cos(d*x + c)^2 + (3*C*a^5*b^2 - 2*B*a^4*b^3 - 6*C*a^3*b^4 + 4*B*a^2*b^5 + 3*C*a*b^6 - 2*B*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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*C*a^6*b - 4*B*a^5*b^2 - 11*C*a^4*b^3 + 8*B*a^3*b^4 + 4*C*a^2*b^5 - 4*B*a*b^6 + C*b^7)*d*x*cos(d*x + c) + (6*C*a^7 - 4*B*a^6*b - 11*C*a^5*b^2 + 8*B*a^4*b^3 + 4*C*a^3*b^4 - 4*B*a^2*b^5 + C*a*b^6)*d*x - 2*(3*C*a^6 - 2*B*a^5*b - 4*C*a^4*b^2 + 3*B*a^3*b^3 + (3*C*a^5*b - 2*B*a^4*b^2 - 4*C*a^3*b^3 + 3*B*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*C*a^6*b - 4*B*a^5*b^2 - 10*C*a^4*b^3 + 6*B*a^3*b^4 + 4*C*a^2*b^5 - 2*B*a*b^6 - (C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7)*cos(d*x + c)^2 + (3*C*a^5*b^2 - 2*B*a^4*b^3 - 6*C*a^3*b^4 + 4*B*a^2*b^5 + 3*C*a*b^6 - 2*B*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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
802,1,788,0,0.547141," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(2 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(2 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} d x + {\left(2 \, C a^{5} - B a^{4} b - 3 \, C a^{3} b^{2} + 2 \, B a^{2} b^{3} + {\left(2 \, C a^{4} b - B a^{3} b^{2} - 3 \, C a^{2} b^{3} + 2 \, B a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{5} b - B a^{4} b^{2} - 3 \, C a^{3} b^{3} + B a^{2} b^{4} + C a b^{5} + {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C 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 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} d x \cos\left(d x + c\right) + {\left(2 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} d x - {\left(2 \, C a^{5} - B a^{4} b - 3 \, C a^{3} b^{2} + 2 \, B a^{2} b^{3} + {\left(2 \, C a^{4} b - B a^{3} b^{2} - 3 \, C a^{2} b^{3} + 2 \, B a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, C a^{5} b - B a^{4} b^{2} - 3 \, C a^{3} b^{3} + B a^{2} b^{4} + C a b^{5} + {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C 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*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*d*x*cos(d*x + c) + 2*(2*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*d*x + (2*C*a^5 - B*a^4*b - 3*C*a^3*b^2 + 2*B*a^2*b^3 + (2*C*a^4*b - B*a^3*b^2 - 3*C*a^2*b^3 + 2*B*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*C*a^5*b - B*a^4*b^2 - 3*C*a^3*b^3 + B*a^2*b^4 + C*a*b^5 + (C*a^4*b^2 - 2*C*a^2*b^4 + C*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*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*d*x*cos(d*x + c) + (2*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*d*x - (2*C*a^5 - B*a^4*b - 3*C*a^3*b^2 + 2*B*a^2*b^3 + (2*C*a^4*b - B*a^3*b^2 - 3*C*a^2*b^3 + 2*B*a*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*C*a^5*b - B*a^4*b^2 - 3*C*a^3*b^3 + B*a^2*b^4 + C*a*b^5 + (C*a^4*b^2 - 2*C*a^2*b^4 + C*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
803,1,552,0,0.510046," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} d x - {\left(C a^{4} - 2 \, C a^{2} b^{2} + B a b^{3} + {\left(C a^{3} b - 2 \, C a b^{3} + B 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(C a^{4} b - B a^{3} b^{2} - C a^{2} b^{3} + B a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5}\right)} d x \cos\left(d x + c\right) + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} d x - {\left(C a^{4} - 2 \, C a^{2} b^{2} + B a b^{3} + {\left(C a^{3} b - 2 \, C a b^{3} + B 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(C a^{4} b - B a^{3} b^{2} - C a^{2} b^{3} + B a b^{4}\right)} \sin\left(d x + c\right)}{{\left(a^{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*(C*a^4*b - 2*C*a^2*b^3 + C*b^5)*d*x*cos(d*x + c) + 2*(C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*d*x - (C*a^4 - 2*C*a^2*b^2 + B*a*b^3 + (C*a^3*b - 2*C*a*b^3 + B*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*(C*a^4*b - B*a^3*b^2 - C*a^2*b^3 + B*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), ((C*a^4*b - 2*C*a^2*b^3 + C*b^5)*d*x*cos(d*x + c) + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*d*x - (C*a^4 - 2*C*a^2*b^2 + B*a*b^3 + (C*a^3*b - 2*C*a*b^3 + B*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))) - (C*a^4*b - B*a^3*b^2 - C*a^2*b^3 + B*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
804,1,379,0,0.519645," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{2} - C a b + {\left(B a b - C 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(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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(B a^{2} - C a b + {\left(B a b - C 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(C a^{3} - B a^{2} b - C a b^{2} + B 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*((B*a^2 - C*a*b + (B*a*b - C*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*(C*a^3 - B*a^2*b - C*a*b^2 + B*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), ((B*a^2 - C*a*b + (B*a*b - C*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))) + (C*a^3 - B*a^2*b - C*a*b^2 + B*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
805,1,684,0,5.056102," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(C a^{4} - 2 \, B a^{3} b + B a b^{3} + {\left(C a^{3} b - 2 \, B a^{2} b^{2} + B 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(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4} + {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4} + {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{4} b - B a^{3} b^{2} - C a^{2} b^{3} + B a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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(C a^{4} - 2 \, B a^{3} b + B a b^{3} + {\left(C a^{3} b - 2 \, B a^{2} b^{2} + B 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^{5} - 2 \, B a^{3} b^{2} + B a b^{4} + {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{5} - 2 \, B a^{3} b^{2} + B a b^{4} + {\left(B a^{4} b - 2 \, B a^{2} b^{3} + B b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(C a^{4} b - B a^{3} b^{2} - C a^{2} b^{3} + B a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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*((C*a^4 - 2*B*a^3*b + B*a*b^3 + (C*a^3*b - 2*B*a^2*b^2 + B*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 - 2*B*a^3*b^2 + B*a*b^4 + (B*a^4*b - 2*B*a^2*b^3 + B*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) - (B*a^5 - 2*B*a^3*b^2 + B*a*b^4 + (B*a^4*b - 2*B*a^2*b^3 + B*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(C*a^4*b - B*a^3*b^2 - C*a^2*b^3 + B*a*b^4)*sin(d*x + c))/((a^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*(C*a^4 - 2*B*a^3*b + B*a*b^3 + (C*a^3*b - 2*B*a^2*b^2 + B*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 - 2*B*a^3*b^2 + B*a*b^4 + (B*a^4*b - 2*B*a^2*b^3 + B*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) - (B*a^5 - 2*B*a^3*b^2 + B*a*b^4 + (B*a^4*b - 2*B*a^2*b^3 + B*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(C*a^4*b - B*a^3*b^2 - C*a^2*b^3 + B*a*b^4)*sin(d*x + c))/((a^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
806,1,1088,0,12.363724," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - C a b^{4} + 2 \, B b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{4} b - 3 \, B a^{3} b^{2} - C a^{2} b^{3} + 2 \, B a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(C a^{5} b - 2 \, B a^{4} b^{2} - 2 \, C a^{3} b^{3} + 4 \, B a^{2} b^{4} + C a b^{5} - 2 \, B b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{6} - 2 \, B a^{5} b - 2 \, C a^{4} b^{2} + 4 \, B a^{3} b^{3} + C a^{2} b^{4} - 2 \, B a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(C a^{5} b - 2 \, B a^{4} b^{2} - 2 \, C a^{3} b^{3} + 4 \, B a^{2} b^{4} + C a b^{5} - 2 \, B b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{6} - 2 \, B a^{5} b - 2 \, C a^{4} b^{2} + 4 \, B a^{3} b^{3} + C a^{2} b^{4} - 2 \, B a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{6} - 2 \, B a^{4} b^{2} + B a^{2} b^{4} + {\left(B a^{5} b + C a^{4} b^{2} - 3 \, B a^{3} b^{3} - C a^{2} b^{4} + 2 \, B a b^{5}\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 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3} - C a b^{4} + 2 \, B b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{4} b - 3 \, B a^{3} b^{2} - C a^{2} b^{3} + 2 \, B a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left({\left(C a^{5} b - 2 \, B a^{4} b^{2} - 2 \, C a^{3} b^{3} + 4 \, B a^{2} b^{4} + C a b^{5} - 2 \, B b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{6} - 2 \, B a^{5} b - 2 \, C a^{4} b^{2} + 4 \, B a^{3} b^{3} + C a^{2} b^{4} - 2 \, B a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(C a^{5} b - 2 \, B a^{4} b^{2} - 2 \, C a^{3} b^{3} + 4 \, B a^{2} b^{4} + C a b^{5} - 2 \, B b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{6} - 2 \, B a^{5} b - 2 \, C a^{4} b^{2} + 4 \, B a^{3} b^{3} + C a^{2} b^{4} - 2 \, B a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{6} - 2 \, B a^{4} b^{2} + B a^{2} b^{4} + {\left(B a^{5} b + C a^{4} b^{2} - 3 \, B a^{3} b^{3} - C a^{2} b^{4} + 2 \, B a b^{5}\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*C*a^3*b^2 - 3*B*a^2*b^3 - C*a*b^4 + 2*B*b^5)*cos(d*x + c)^2 + (2*C*a^4*b - 3*B*a^3*b^2 - C*a^2*b^3 + 2*B*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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)) - ((C*a^5*b - 2*B*a^4*b^2 - 2*C*a^3*b^3 + 4*B*a^2*b^4 + C*a*b^5 - 2*B*b^6)*cos(d*x + c)^2 + (C*a^6 - 2*B*a^5*b - 2*C*a^4*b^2 + 4*B*a^3*b^3 + C*a^2*b^4 - 2*B*a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((C*a^5*b - 2*B*a^4*b^2 - 2*C*a^3*b^3 + 4*B*a^2*b^4 + C*a*b^5 - 2*B*b^6)*cos(d*x + c)^2 + (C*a^6 - 2*B*a^5*b - 2*C*a^4*b^2 + 4*B*a^3*b^3 + C*a^2*b^4 - 2*B*a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(B*a^6 - 2*B*a^4*b^2 + B*a^2*b^4 + (B*a^5*b + C*a^4*b^2 - 3*B*a^3*b^3 - C*a^2*b^4 + 2*B*a*b^5)*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*C*a^3*b^2 - 3*B*a^2*b^3 - C*a*b^4 + 2*B*b^5)*cos(d*x + c)^2 + (2*C*a^4*b - 3*B*a^3*b^2 - C*a^2*b^3 + 2*B*a*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - ((C*a^5*b - 2*B*a^4*b^2 - 2*C*a^3*b^3 + 4*B*a^2*b^4 + C*a*b^5 - 2*B*b^6)*cos(d*x + c)^2 + (C*a^6 - 2*B*a^5*b - 2*C*a^4*b^2 + 4*B*a^3*b^3 + C*a^2*b^4 - 2*B*a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((C*a^5*b - 2*B*a^4*b^2 - 2*C*a^3*b^3 + 4*B*a^2*b^4 + C*a*b^5 - 2*B*b^6)*cos(d*x + c)^2 + (C*a^6 - 2*B*a^5*b - 2*C*a^4*b^2 + 4*B*a^3*b^3 + C*a^2*b^4 - 2*B*a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(B*a^6 - 2*B*a^4*b^2 + B*a^2*b^4 + (B*a^5*b + C*a^4*b^2 - 3*B*a^3*b^3 - C*a^2*b^4 + 2*B*a*b^5)*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
807,1,1812,0,0.672122," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(12 \, C a^{8} b^{2} - 6 \, B a^{7} b^{3} - 35 \, C a^{6} b^{4} + 18 \, B a^{5} b^{5} + 33 \, C a^{4} b^{6} - 18 \, B a^{3} b^{7} - 9 \, C a^{2} b^{8} + 6 \, B a b^{9} - C b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(12 \, C a^{9} b - 6 \, B a^{8} b^{2} - 35 \, C a^{7} b^{3} + 18 \, B a^{6} b^{4} + 33 \, C a^{5} b^{5} - 18 \, B a^{4} b^{6} - 9 \, C a^{3} b^{7} + 6 \, B a^{2} b^{8} - C a b^{9}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(12 \, C a^{10} - 6 \, B a^{9} b - 35 \, C a^{8} b^{2} + 18 \, B a^{7} b^{3} + 33 \, C a^{6} b^{4} - 18 \, B a^{5} b^{5} - 9 \, C a^{4} b^{6} + 6 \, B a^{3} b^{7} - C a^{2} b^{8}\right)} d x + {\left(12 \, C a^{9} - 6 \, B a^{8} b - 29 \, C a^{7} b^{2} + 15 \, B a^{6} b^{3} + 20 \, C a^{5} b^{4} - 12 \, B a^{4} b^{5} + {\left(12 \, C a^{7} b^{2} - 6 \, B a^{6} b^{3} - 29 \, C a^{5} b^{4} + 15 \, B a^{4} b^{5} + 20 \, C a^{3} b^{6} - 12 \, B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, C a^{8} b - 6 \, B a^{7} b^{2} - 29 \, C a^{6} b^{3} + 15 \, B a^{5} b^{4} + 20 \, C a^{4} b^{5} - 12 \, B 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 \, C a^{9} b - 6 \, B a^{8} b^{2} - 33 \, C a^{7} b^{3} + 17 \, B a^{6} b^{4} + 27 \, C a^{5} b^{5} - 13 \, B a^{4} b^{6} - 6 \, C a^{3} b^{7} + 2 \, B a^{2} b^{8} - {\left(C a^{6} b^{4} - 3 \, C a^{4} b^{6} + 3 \, C a^{2} b^{8} - C b^{10}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, C a^{7} b^{3} - B a^{6} b^{4} - 6 \, C a^{5} b^{5} + 3 \, B a^{4} b^{6} + 6 \, C a^{3} b^{7} - 3 \, B a^{2} b^{8} - 2 \, C a b^{9} + B b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, C a^{8} b^{2} - 9 \, B a^{7} b^{3} - 50 \, C a^{6} b^{4} + 25 \, B a^{5} b^{5} + 43 \, C a^{4} b^{6} - 20 \, B a^{3} b^{7} - 11 \, C a^{2} b^{8} + 4 \, B 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 \, C a^{8} b^{2} - 6 \, B a^{7} b^{3} - 35 \, C a^{6} b^{4} + 18 \, B a^{5} b^{5} + 33 \, C a^{4} b^{6} - 18 \, B a^{3} b^{7} - 9 \, C a^{2} b^{8} + 6 \, B a b^{9} - C b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, C a^{9} b - 6 \, B a^{8} b^{2} - 35 \, C a^{7} b^{3} + 18 \, B a^{6} b^{4} + 33 \, C a^{5} b^{5} - 18 \, B a^{4} b^{6} - 9 \, C a^{3} b^{7} + 6 \, B a^{2} b^{8} - C a b^{9}\right)} d x \cos\left(d x + c\right) + {\left(12 \, C a^{10} - 6 \, B a^{9} b - 35 \, C a^{8} b^{2} + 18 \, B a^{7} b^{3} + 33 \, C a^{6} b^{4} - 18 \, B a^{5} b^{5} - 9 \, C a^{4} b^{6} + 6 \, B a^{3} b^{7} - C a^{2} b^{8}\right)} d x - {\left(12 \, C a^{9} - 6 \, B a^{8} b - 29 \, C a^{7} b^{2} + 15 \, B a^{6} b^{3} + 20 \, C a^{5} b^{4} - 12 \, B a^{4} b^{5} + {\left(12 \, C a^{7} b^{2} - 6 \, B a^{6} b^{3} - 29 \, C a^{5} b^{4} + 15 \, B a^{4} b^{5} + 20 \, C a^{3} b^{6} - 12 \, B a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, C a^{8} b - 6 \, B a^{7} b^{2} - 29 \, C a^{6} b^{3} + 15 \, B a^{5} b^{4} + 20 \, C a^{4} b^{5} - 12 \, B 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 \, C a^{9} b - 6 \, B a^{8} b^{2} - 33 \, C a^{7} b^{3} + 17 \, B a^{6} b^{4} + 27 \, C a^{5} b^{5} - 13 \, B a^{4} b^{6} - 6 \, C a^{3} b^{7} + 2 \, B a^{2} b^{8} - {\left(C a^{6} b^{4} - 3 \, C a^{4} b^{6} + 3 \, C a^{2} b^{8} - C b^{10}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, C a^{7} b^{3} - B a^{6} b^{4} - 6 \, C a^{5} b^{5} + 3 \, B a^{4} b^{6} + 6 \, C a^{3} b^{7} - 3 \, B a^{2} b^{8} - 2 \, C a b^{9} + B b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, C a^{8} b^{2} - 9 \, B a^{7} b^{3} - 50 \, C a^{6} b^{4} + 25 \, B a^{5} b^{5} + 43 \, C a^{4} b^{6} - 20 \, B a^{3} b^{7} - 11 \, C a^{2} b^{8} + 4 \, B 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*C*a^8*b^2 - 6*B*a^7*b^3 - 35*C*a^6*b^4 + 18*B*a^5*b^5 + 33*C*a^4*b^6 - 18*B*a^3*b^7 - 9*C*a^2*b^8 + 6*B*a*b^9 - C*b^10)*d*x*cos(d*x + c)^2 + 4*(12*C*a^9*b - 6*B*a^8*b^2 - 35*C*a^7*b^3 + 18*B*a^6*b^4 + 33*C*a^5*b^5 - 18*B*a^4*b^6 - 9*C*a^3*b^7 + 6*B*a^2*b^8 - C*a*b^9)*d*x*cos(d*x + c) + 2*(12*C*a^10 - 6*B*a^9*b - 35*C*a^8*b^2 + 18*B*a^7*b^3 + 33*C*a^6*b^4 - 18*B*a^5*b^5 - 9*C*a^4*b^6 + 6*B*a^3*b^7 - C*a^2*b^8)*d*x + (12*C*a^9 - 6*B*a^8*b - 29*C*a^7*b^2 + 15*B*a^6*b^3 + 20*C*a^5*b^4 - 12*B*a^4*b^5 + (12*C*a^7*b^2 - 6*B*a^6*b^3 - 29*C*a^5*b^4 + 15*B*a^4*b^5 + 20*C*a^3*b^6 - 12*B*a^2*b^7)*cos(d*x + c)^2 + 2*(12*C*a^8*b - 6*B*a^7*b^2 - 29*C*a^6*b^3 + 15*B*a^5*b^4 + 20*C*a^4*b^5 - 12*B*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*C*a^9*b - 6*B*a^8*b^2 - 33*C*a^7*b^3 + 17*B*a^6*b^4 + 27*C*a^5*b^5 - 13*B*a^4*b^6 - 6*C*a^3*b^7 + 2*B*a^2*b^8 - (C*a^6*b^4 - 3*C*a^4*b^6 + 3*C*a^2*b^8 - C*b^10)*cos(d*x + c)^3 + 2*(2*C*a^7*b^3 - B*a^6*b^4 - 6*C*a^5*b^5 + 3*B*a^4*b^6 + 6*C*a^3*b^7 - 3*B*a^2*b^8 - 2*C*a*b^9 + B*b^10)*cos(d*x + c)^2 + (18*C*a^8*b^2 - 9*B*a^7*b^3 - 50*C*a^6*b^4 + 25*B*a^5*b^5 + 43*C*a^4*b^6 - 20*B*a^3*b^7 - 11*C*a^2*b^8 + 4*B*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*C*a^8*b^2 - 6*B*a^7*b^3 - 35*C*a^6*b^4 + 18*B*a^5*b^5 + 33*C*a^4*b^6 - 18*B*a^3*b^7 - 9*C*a^2*b^8 + 6*B*a*b^9 - C*b^10)*d*x*cos(d*x + c)^2 + 2*(12*C*a^9*b - 6*B*a^8*b^2 - 35*C*a^7*b^3 + 18*B*a^6*b^4 + 33*C*a^5*b^5 - 18*B*a^4*b^6 - 9*C*a^3*b^7 + 6*B*a^2*b^8 - C*a*b^9)*d*x*cos(d*x + c) + (12*C*a^10 - 6*B*a^9*b - 35*C*a^8*b^2 + 18*B*a^7*b^3 + 33*C*a^6*b^4 - 18*B*a^5*b^5 - 9*C*a^4*b^6 + 6*B*a^3*b^7 - C*a^2*b^8)*d*x - (12*C*a^9 - 6*B*a^8*b - 29*C*a^7*b^2 + 15*B*a^6*b^3 + 20*C*a^5*b^4 - 12*B*a^4*b^5 + (12*C*a^7*b^2 - 6*B*a^6*b^3 - 29*C*a^5*b^4 + 15*B*a^4*b^5 + 20*C*a^3*b^6 - 12*B*a^2*b^7)*cos(d*x + c)^2 + 2*(12*C*a^8*b - 6*B*a^7*b^2 - 29*C*a^6*b^3 + 15*B*a^5*b^4 + 20*C*a^4*b^5 - 12*B*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*C*a^9*b - 6*B*a^8*b^2 - 33*C*a^7*b^3 + 17*B*a^6*b^4 + 27*C*a^5*b^5 - 13*B*a^4*b^6 - 6*C*a^3*b^7 + 2*B*a^2*b^8 - (C*a^6*b^4 - 3*C*a^4*b^6 + 3*C*a^2*b^8 - C*b^10)*cos(d*x + c)^3 + 2*(2*C*a^7*b^3 - B*a^6*b^4 - 6*C*a^5*b^5 + 3*B*a^4*b^6 + 6*C*a^3*b^7 - 3*B*a^2*b^8 - 2*C*a*b^9 + B*b^10)*cos(d*x + c)^2 + (18*C*a^8*b^2 - 9*B*a^7*b^3 - 50*C*a^6*b^4 + 25*B*a^5*b^5 + 43*C*a^4*b^6 - 20*B*a^3*b^7 - 11*C*a^2*b^8 + 4*B*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
808,1,1561,0,0.655902," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(3 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} d x - {\left(6 \, C a^{8} - 2 \, B a^{7} b - 15 \, C a^{6} b^{2} + 5 \, B a^{5} b^{3} + 12 \, C a^{4} b^{4} - 6 \, B a^{3} b^{5} + {\left(6 \, C a^{6} b^{2} - 2 \, B a^{5} b^{3} - 15 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 12 \, C a^{2} b^{6} - 6 \, B a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, C a^{7} b - 2 \, B a^{6} b^{2} - 15 \, C a^{5} b^{3} + 5 \, B a^{4} b^{4} + 12 \, C a^{3} b^{5} - 6 \, B a^{2} b^{6}\right)} \cos\left(d x + c\right)\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 \, C a^{8} b - 2 \, B a^{7} b^{2} - 17 \, C a^{6} b^{3} + 7 \, B a^{5} b^{4} + 13 \, C a^{4} b^{5} - 5 \, B a^{3} b^{6} - 2 \, C a^{2} b^{7} + 2 \, {\left(C a^{6} b^{3} - 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} - C b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} - 25 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 20 \, C a^{3} b^{6} - 6 \, B a^{2} b^{7} - 4 \, C a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{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 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(3 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} d x - {\left(6 \, C a^{8} - 2 \, B a^{7} b - 15 \, C a^{6} b^{2} + 5 \, B a^{5} b^{3} + 12 \, C a^{4} b^{4} - 6 \, B a^{3} b^{5} + {\left(6 \, C a^{6} b^{2} - 2 \, B a^{5} b^{3} - 15 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 12 \, C a^{2} b^{6} - 6 \, B a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, C a^{7} b - 2 \, B a^{6} b^{2} - 15 \, C a^{5} b^{3} + 5 \, B a^{4} b^{4} + 12 \, C a^{3} b^{5} - 6 \, B a^{2} b^{6}\right)} \cos\left(d x + c\right)\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 \, C a^{8} b - 2 \, B a^{7} b^{2} - 17 \, C a^{6} b^{3} + 7 \, B a^{5} b^{4} + 13 \, C a^{4} b^{5} - 5 \, B a^{3} b^{6} - 2 \, C a^{2} b^{7} + 2 \, {\left(C a^{6} b^{3} - 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} - C b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} - 25 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 20 \, C a^{3} b^{6} - 6 \, B a^{2} b^{7} - 4 \, C a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*d*x*cos(d*x + c)^2 + 8*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*d*x*cos(d*x + c) + 4*(3*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*d*x - (6*C*a^8 - 2*B*a^7*b - 15*C*a^6*b^2 + 5*B*a^5*b^3 + 12*C*a^4*b^4 - 6*B*a^3*b^5 + (6*C*a^6*b^2 - 2*B*a^5*b^3 - 15*C*a^4*b^4 + 5*B*a^3*b^5 + 12*C*a^2*b^6 - 6*B*a*b^7)*cos(d*x + c)^2 + 2*(6*C*a^7*b - 2*B*a^6*b^2 - 15*C*a^5*b^3 + 5*B*a^4*b^4 + 12*C*a^3*b^5 - 6*B*a^2*b^6)*cos(d*x + c))*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*C*a^8*b - 2*B*a^7*b^2 - 17*C*a^6*b^3 + 7*B*a^5*b^4 + 13*C*a^4*b^5 - 5*B*a^3*b^6 - 2*C*a^2*b^7 + 2*(C*a^6*b^3 - 3*C*a^4*b^5 + 3*C*a^2*b^7 - C*b^9)*cos(d*x + c)^2 + (9*C*a^7*b^2 - 3*B*a^6*b^3 - 25*C*a^5*b^4 + 9*B*a^4*b^5 + 20*C*a^3*b^6 - 6*B*a^2*b^7 - 4*C*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^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*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*d*x*cos(d*x + c)^2 + 4*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*d*x*cos(d*x + c) + 2*(3*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*d*x - (6*C*a^8 - 2*B*a^7*b - 15*C*a^6*b^2 + 5*B*a^5*b^3 + 12*C*a^4*b^4 - 6*B*a^3*b^5 + (6*C*a^6*b^2 - 2*B*a^5*b^3 - 15*C*a^4*b^4 + 5*B*a^3*b^5 + 12*C*a^2*b^6 - 6*B*a*b^7)*cos(d*x + c)^2 + 2*(6*C*a^7*b - 2*B*a^6*b^2 - 15*C*a^5*b^3 + 5*B*a^4*b^4 + 12*C*a^3*b^5 - 6*B*a^2*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*C*a^8*b - 2*B*a^7*b^2 - 17*C*a^6*b^3 + 7*B*a^5*b^4 + 13*C*a^4*b^5 - 5*B*a^3*b^6 - 2*C*a^2*b^7 + 2*(C*a^6*b^3 - 3*C*a^4*b^5 + 3*C*a^2*b^7 - C*b^9)*cos(d*x + c)^2 + (9*C*a^7*b^2 - 3*B*a^6*b^3 - 25*C*a^5*b^4 + 9*B*a^4*b^5 + 20*C*a^3*b^6 - 6*B*a^2*b^7 - 4*C*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^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
809,1,1152,0,0.682820," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} d x + {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} - B a^{4} b^{3} + 6 \, C a^{3} b^{4} - 2 \, B a^{2} b^{5} + {\left(2 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} - B a^{2} b^{5} + 6 \, C a b^{6} - 2 \, B b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} - B a^{3} b^{4} + 6 \, C a^{2} b^{5} - 2 \, B a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{7} b - 7 \, C a^{5} b^{3} + 3 \, B a^{4} b^{4} + 5 \, C a^{3} b^{5} - 3 \, B a^{2} b^{6} + {\left(3 \, C a^{6} b^{2} - B a^{5} b^{3} - 9 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 6 \, C a^{2} b^{6} - 4 \, B a b^{7}\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(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} d x - {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} - B a^{4} b^{3} + 6 \, C a^{3} b^{4} - 2 \, B a^{2} b^{5} + {\left(2 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} - B a^{2} b^{5} + 6 \, C a b^{6} - 2 \, B b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} - B a^{3} b^{4} + 6 \, C a^{2} b^{5} - 2 \, B a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, C a^{7} b - 7 \, C a^{5} b^{3} + 3 \, B a^{4} b^{4} + 5 \, C a^{3} b^{5} - 3 \, B a^{2} b^{6} + {\left(3 \, C a^{6} b^{2} - B a^{5} b^{3} - 9 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + 6 \, C a^{2} b^{6} - 4 \, B a b^{7}\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*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8)*d*x*cos(d*x + c)^2 + 8*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*d*x*cos(d*x + c) + 4*(C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*d*x + (2*C*a^7 - 5*C*a^5*b^2 - B*a^4*b^3 + 6*C*a^3*b^4 - 2*B*a^2*b^5 + (2*C*a^5*b^2 - 5*C*a^3*b^4 - B*a^2*b^5 + 6*C*a*b^6 - 2*B*b^7)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 - B*a^3*b^4 + 6*C*a^2*b^5 - 2*B*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*C*a^7*b - 7*C*a^5*b^3 + 3*B*a^4*b^4 + 5*C*a^3*b^5 - 3*B*a^2*b^6 + (3*C*a^6*b^2 - B*a^5*b^3 - 9*C*a^4*b^4 + 5*B*a^3*b^5 + 6*C*a^2*b^6 - 4*B*a*b^7)*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*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8)*d*x*cos(d*x + c)^2 + 4*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*d*x*cos(d*x + c) + 2*(C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*d*x - (2*C*a^7 - 5*C*a^5*b^2 - B*a^4*b^3 + 6*C*a^3*b^4 - 2*B*a^2*b^5 + (2*C*a^5*b^2 - 5*C*a^3*b^4 - B*a^2*b^5 + 6*C*a*b^6 - 2*B*b^7)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 - B*a^3*b^4 + 6*C*a^2*b^5 - 2*B*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*C*a^7*b - 7*C*a^5*b^3 + 3*B*a^4*b^4 + 5*C*a^3*b^5 - 3*B*a^2*b^6 + (3*C*a^6*b^2 - B*a^5*b^3 - 9*C*a^4*b^4 + 5*B*a^3*b^5 + 6*C*a^2*b^6 - 4*B*a*b^7)*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
810,1,740,0,0.524873," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(C a^{4} - 3 \, B a^{3} b + 2 \, C a^{2} b^{2} + {\left(C a^{2} b^{2} - 3 \, B a b^{3} + 2 \, C b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{3} b - 3 \, B a^{2} b^{2} + 2 \, C a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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} - 3 \, C a^{4} b - B a^{3} b^{2} + 3 \, C a^{2} b^{3} - B a b^{4} + {\left(C a^{5} + B a^{4} b - 5 \, C a^{3} b^{2} + B a^{2} b^{3} + 4 \, C a b^{4} - 2 \, B b^{5}\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(C a^{4} - 3 \, B a^{3} b + 2 \, C a^{2} b^{2} + {\left(C a^{2} b^{2} - 3 \, B a b^{3} + 2 \, C b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(C a^{3} b - 3 \, B a^{2} b^{2} + 2 \, C a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{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} - 3 \, C a^{4} b - B a^{3} b^{2} + 3 \, C a^{2} b^{3} - B a b^{4} + {\left(C a^{5} + B a^{4} b - 5 \, C a^{3} b^{2} + B a^{2} b^{3} + 4 \, C a b^{4} - 2 \, B b^{5}\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*((C*a^4 - 3*B*a^3*b + 2*C*a^2*b^2 + (C*a^2*b^2 - 3*B*a*b^3 + 2*C*b^4)*cos(d*x + c)^2 + 2*(C*a^3*b - 3*B*a^2*b^2 + 2*C*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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 - 3*C*a^4*b - B*a^3*b^2 + 3*C*a^2*b^3 - B*a*b^4 + (C*a^5 + B*a^4*b - 5*C*a^3*b^2 + B*a^2*b^3 + 4*C*a*b^4 - 2*B*b^5)*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*((C*a^4 - 3*B*a^3*b + 2*C*a^2*b^2 + (C*a^2*b^2 - 3*B*a*b^3 + 2*C*b^4)*cos(d*x + c)^2 + 2*(C*a^3*b - 3*B*a^2*b^2 + 2*C*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (2*B*a^5 - 3*C*a^4*b - B*a^3*b^2 + 3*C*a^2*b^3 - B*a*b^4 + (C*a^5 + B*a^4*b - 5*C*a^3*b^2 + B*a^2*b^3 + 4*C*a*b^4 - 2*B*b^5)*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
811,1,742,0,0.617646," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B a^{4} - 3 \, C a^{3} b + B a^{2} b^{2} + {\left(2 \, B a^{2} b^{2} - 3 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{3} b - 3 \, C a^{2} b^{2} + B a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{5} - 4 \, B a^{4} b - C a^{3} b^{2} + 5 \, B a^{2} b^{3} - C a b^{4} - B b^{5} + {\left(C a^{4} b - 3 \, B a^{3} b^{2} + C a^{2} b^{3} + 3 \, B a b^{4} - 2 \, C b^{5}\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 \, B a^{4} - 3 \, C a^{3} b + B a^{2} b^{2} + {\left(2 \, B a^{2} b^{2} - 3 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{3} b - 3 \, C a^{2} b^{2} + B a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(2 \, C a^{5} - 4 \, B a^{4} b - C a^{3} b^{2} + 5 \, B a^{2} b^{3} - C a b^{4} - B b^{5} + {\left(C a^{4} b - 3 \, B a^{3} b^{2} + C a^{2} b^{3} + 3 \, B a b^{4} - 2 \, C b^{5}\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*B*a^4 - 3*C*a^3*b + B*a^2*b^2 + (2*B*a^2*b^2 - 3*C*a*b^3 + B*b^4)*cos(d*x + c)^2 + 2*(2*B*a^3*b - 3*C*a^2*b^2 + B*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*C*a^5 - 4*B*a^4*b - C*a^3*b^2 + 5*B*a^2*b^3 - C*a*b^4 - B*b^5 + (C*a^4*b - 3*B*a^3*b^2 + C*a^2*b^3 + 3*B*a*b^4 - 2*C*b^5)*cos(d*x + c))*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*B*a^4 - 3*C*a^3*b + B*a^2*b^2 + (2*B*a^2*b^2 - 3*C*a*b^3 + B*b^4)*cos(d*x + c)^2 + 2*(2*B*a^3*b - 3*C*a^2*b^2 + B*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (2*C*a^5 - 4*B*a^4*b - C*a^3*b^2 + 5*B*a^2*b^3 - C*a*b^4 - B*b^5 + (C*a^4*b - 3*B*a^3*b^2 + C*a^2*b^3 + 3*B*a*b^4 - 2*C*b^5)*cos(d*x + c))*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
812,1,1400,0,22.220105," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, C a^{7} - 6 \, B a^{6} b + C a^{5} b^{2} + 5 \, B a^{4} b^{3} - 2 \, B a^{2} b^{5} + {\left(2 \, C a^{5} b^{2} - 6 \, B a^{4} b^{3} + C a^{3} b^{4} + 5 \, B a^{2} b^{5} - 2 \, B b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 6 \, B a^{5} b^{2} + C a^{4} b^{3} + 5 \, B a^{3} b^{4} - 2 \, B a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6} + {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6} + {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, C a^{7} b - 6 \, B a^{6} b^{2} - 5 \, C a^{5} b^{3} + 9 \, B a^{4} b^{4} + C a^{3} b^{5} - 3 \, B a^{2} b^{6} + {\left(3 \, C a^{6} b^{2} - 5 \, B a^{5} b^{3} - 3 \, C a^{4} b^{4} + 7 \, B a^{3} b^{5} - 2 \, B a b^{7}\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 \, C a^{7} - 6 \, B a^{6} b + C a^{5} b^{2} + 5 \, B a^{4} b^{3} - 2 \, B a^{2} b^{5} + {\left(2 \, C a^{5} b^{2} - 6 \, B a^{4} b^{3} + C a^{3} b^{4} + 5 \, B a^{2} b^{5} - 2 \, B b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 6 \, B a^{5} b^{2} + C a^{4} b^{3} + 5 \, B a^{3} b^{4} - 2 \, B a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) + {\left(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6} + {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(B a^{8} - 3 \, B a^{6} b^{2} + 3 \, B a^{4} b^{4} - B a^{2} b^{6} + {\left(B a^{6} b^{2} - 3 \, B a^{4} b^{4} + 3 \, B a^{2} b^{6} - B b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} b - 3 \, B a^{5} b^{3} + 3 \, B a^{3} b^{5} - B a b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(4 \, C a^{7} b - 6 \, B a^{6} b^{2} - 5 \, C a^{5} b^{3} + 9 \, B a^{4} b^{4} + C a^{3} b^{5} - 3 \, B a^{2} b^{6} + {\left(3 \, C a^{6} b^{2} - 5 \, B a^{5} b^{3} - 3 \, C a^{4} b^{4} + 7 \, B a^{3} b^{5} - 2 \, B a b^{7}\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*C*a^7 - 6*B*a^6*b + C*a^5*b^2 + 5*B*a^4*b^3 - 2*B*a^2*b^5 + (2*C*a^5*b^2 - 6*B*a^4*b^3 + C*a^3*b^4 + 5*B*a^2*b^5 - 2*B*b^7)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 6*B*a^5*b^2 + C*a^4*b^3 + 5*B*a^3*b^4 - 2*B*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6 + (B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8)*cos(d*x + c)^2 + 2*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) - 2*(B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6 + (B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8)*cos(d*x + c)^2 + 2*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(4*C*a^7*b - 6*B*a^6*b^2 - 5*C*a^5*b^3 + 9*B*a^4*b^4 + C*a^3*b^5 - 3*B*a^2*b^6 + (3*C*a^6*b^2 - 5*B*a^5*b^3 - 3*C*a^4*b^4 + 7*B*a^3*b^5 - 2*B*a*b^7)*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*C*a^7 - 6*B*a^6*b + C*a^5*b^2 + 5*B*a^4*b^3 - 2*B*a^2*b^5 + (2*C*a^5*b^2 - 6*B*a^4*b^3 + C*a^3*b^4 + 5*B*a^2*b^5 - 2*B*b^7)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 6*B*a^5*b^2 + C*a^4*b^3 + 5*B*a^3*b^4 - 2*B*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6 + (B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8)*cos(d*x + c)^2 + 2*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) - (B*a^8 - 3*B*a^6*b^2 + 3*B*a^4*b^4 - B*a^2*b^6 + (B*a^6*b^2 - 3*B*a^4*b^4 + 3*B*a^2*b^6 - B*b^8)*cos(d*x + c)^2 + 2*(B*a^7*b - 3*B*a^5*b^3 + 3*B*a^3*b^5 - B*a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) - (4*C*a^7*b - 6*B*a^6*b^2 - 5*C*a^5*b^3 + 9*B*a^4*b^4 + C*a^3*b^5 - 3*B*a^2*b^6 + (3*C*a^6*b^2 - 5*B*a^5*b^3 - 3*C*a^4*b^4 + 7*B*a^3*b^5 - 2*B*a*b^7)*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
813,1,2100,0,47.694199," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(6 \, C a^{5} b^{3} - 12 \, B a^{4} b^{4} - 5 \, C a^{3} b^{5} + 15 \, B a^{2} b^{6} + 2 \, C a b^{7} - 6 \, B b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, C a^{6} b^{2} - 12 \, B a^{5} b^{3} - 5 \, C a^{4} b^{4} + 15 \, B a^{3} b^{5} + 2 \, C a^{2} b^{6} - 6 \, B a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{7} b - 12 \, B a^{6} b^{2} - 5 \, C a^{5} b^{3} + 15 \, B a^{4} b^{4} + 2 \, C a^{3} b^{5} - 6 \, B a^{2} b^{6}\right)} \cos\left(d x + c\right)\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(C a^{7} b^{2} - 3 \, B a^{6} b^{3} - 3 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B a^{2} b^{7} - C a b^{8} + 3 \, B b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(C a^{8} b - 3 \, B a^{7} b^{2} - 3 \, C a^{6} b^{3} + 9 \, B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 9 \, B a^{3} b^{6} - C a^{2} b^{7} + 3 \, B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{9} - 3 \, B a^{8} b - 3 \, C a^{7} b^{2} + 9 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} - C a^{3} b^{6} + 3 \, B a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(C a^{7} b^{2} - 3 \, B a^{6} b^{3} - 3 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B a^{2} b^{7} - C a b^{8} + 3 \, B b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(C a^{8} b - 3 \, B a^{7} b^{2} - 3 \, C a^{6} b^{3} + 9 \, B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 9 \, B a^{3} b^{6} - C a^{2} b^{7} + 3 \, B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{9} - 3 \, B a^{8} b - 3 \, C a^{7} b^{2} + 9 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} - C a^{3} b^{6} + 3 \, B a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, B a^{9} - 6 \, B a^{7} b^{2} + 6 \, B a^{5} b^{4} - 2 \, B a^{3} b^{6} + {\left(2 \, B a^{7} b^{2} + 5 \, C a^{6} b^{3} - 13 \, B a^{5} b^{4} - 7 \, C a^{4} b^{5} + 17 \, B a^{3} b^{6} + 2 \, C a^{2} b^{7} - 6 \, B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, B a^{8} b + 6 \, C a^{7} b^{2} - 20 \, B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 25 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{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 \, C a^{5} b^{3} - 12 \, B a^{4} b^{4} - 5 \, C a^{3} b^{5} + 15 \, B a^{2} b^{6} + 2 \, C a b^{7} - 6 \, B b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, C a^{6} b^{2} - 12 \, B a^{5} b^{3} - 5 \, C a^{4} b^{4} + 15 \, B a^{3} b^{5} + 2 \, C a^{2} b^{6} - 6 \, B a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, C a^{7} b - 12 \, B a^{6} b^{2} - 5 \, C a^{5} b^{3} + 15 \, B a^{4} b^{4} + 2 \, C a^{3} b^{5} - 6 \, B a^{2} b^{6}\right)} \cos\left(d x + c\right)\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(C a^{7} b^{2} - 3 \, B a^{6} b^{3} - 3 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B a^{2} b^{7} - C a b^{8} + 3 \, B b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(C a^{8} b - 3 \, B a^{7} b^{2} - 3 \, C a^{6} b^{3} + 9 \, B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 9 \, B a^{3} b^{6} - C a^{2} b^{7} + 3 \, B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{9} - 3 \, B a^{8} b - 3 \, C a^{7} b^{2} + 9 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} - C a^{3} b^{6} + 3 \, B a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(C a^{7} b^{2} - 3 \, B a^{6} b^{3} - 3 \, C a^{5} b^{4} + 9 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B a^{2} b^{7} - C a b^{8} + 3 \, B b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(C a^{8} b - 3 \, B a^{7} b^{2} - 3 \, C a^{6} b^{3} + 9 \, B a^{5} b^{4} + 3 \, C a^{4} b^{5} - 9 \, B a^{3} b^{6} - C a^{2} b^{7} + 3 \, B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{9} - 3 \, B a^{8} b - 3 \, C a^{7} b^{2} + 9 \, B a^{6} b^{3} + 3 \, C a^{5} b^{4} - 9 \, B a^{4} b^{5} - C a^{3} b^{6} + 3 \, B a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(2 \, B a^{9} - 6 \, B a^{7} b^{2} + 6 \, B a^{5} b^{4} - 2 \, B a^{3} b^{6} + {\left(2 \, B a^{7} b^{2} + 5 \, C a^{6} b^{3} - 13 \, B a^{5} b^{4} - 7 \, C a^{4} b^{5} + 17 \, B a^{3} b^{6} + 2 \, C a^{2} b^{7} - 6 \, B a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, B a^{8} b + 6 \, C a^{7} b^{2} - 20 \, B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 25 \, B a^{4} b^{5} + 3 \, C a^{3} b^{6} - 9 \, B a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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*C*a^5*b^3 - 12*B*a^4*b^4 - 5*C*a^3*b^5 + 15*B*a^2*b^6 + 2*C*a*b^7 - 6*B*b^8)*cos(d*x + c)^3 + 2*(6*C*a^6*b^2 - 12*B*a^5*b^3 - 5*C*a^4*b^4 + 15*B*a^3*b^5 + 2*C*a^2*b^6 - 6*B*a*b^7)*cos(d*x + c)^2 + (6*C*a^7*b - 12*B*a^6*b^2 - 5*C*a^5*b^3 + 15*B*a^4*b^4 + 2*C*a^3*b^5 - 6*B*a^2*b^6)*cos(d*x + c))*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*((C*a^7*b^2 - 3*B*a^6*b^3 - 3*C*a^5*b^4 + 9*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*a^2*b^7 - C*a*b^8 + 3*B*b^9)*cos(d*x + c)^3 + 2*(C*a^8*b - 3*B*a^7*b^2 - 3*C*a^6*b^3 + 9*B*a^5*b^4 + 3*C*a^4*b^5 - 9*B*a^3*b^6 - C*a^2*b^7 + 3*B*a*b^8)*cos(d*x + c)^2 + (C*a^9 - 3*B*a^8*b - 3*C*a^7*b^2 + 9*B*a^6*b^3 + 3*C*a^5*b^4 - 9*B*a^4*b^5 - C*a^3*b^6 + 3*B*a^2*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) - 2*((C*a^7*b^2 - 3*B*a^6*b^3 - 3*C*a^5*b^4 + 9*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*a^2*b^7 - C*a*b^8 + 3*B*b^9)*cos(d*x + c)^3 + 2*(C*a^8*b - 3*B*a^7*b^2 - 3*C*a^6*b^3 + 9*B*a^5*b^4 + 3*C*a^4*b^5 - 9*B*a^3*b^6 - C*a^2*b^7 + 3*B*a*b^8)*cos(d*x + c)^2 + (C*a^9 - 3*B*a^8*b - 3*C*a^7*b^2 + 9*B*a^6*b^3 + 3*C*a^5*b^4 - 9*B*a^4*b^5 - C*a^3*b^6 + 3*B*a^2*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(2*B*a^9 - 6*B*a^7*b^2 + 6*B*a^5*b^4 - 2*B*a^3*b^6 + (2*B*a^7*b^2 + 5*C*a^6*b^3 - 13*B*a^5*b^4 - 7*C*a^4*b^5 + 17*B*a^3*b^6 + 2*C*a^2*b^7 - 6*B*a*b^8)*cos(d*x + c)^2 + (4*B*a^8*b + 6*C*a^7*b^2 - 20*B*a^6*b^3 - 9*C*a^5*b^4 + 25*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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*C*a^5*b^3 - 12*B*a^4*b^4 - 5*C*a^3*b^5 + 15*B*a^2*b^6 + 2*C*a*b^7 - 6*B*b^8)*cos(d*x + c)^3 + 2*(6*C*a^6*b^2 - 12*B*a^5*b^3 - 5*C*a^4*b^4 + 15*B*a^3*b^5 + 2*C*a^2*b^6 - 6*B*a*b^7)*cos(d*x + c)^2 + (6*C*a^7*b - 12*B*a^6*b^2 - 5*C*a^5*b^3 + 15*B*a^4*b^4 + 2*C*a^3*b^5 - 6*B*a^2*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - ((C*a^7*b^2 - 3*B*a^6*b^3 - 3*C*a^5*b^4 + 9*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*a^2*b^7 - C*a*b^8 + 3*B*b^9)*cos(d*x + c)^3 + 2*(C*a^8*b - 3*B*a^7*b^2 - 3*C*a^6*b^3 + 9*B*a^5*b^4 + 3*C*a^4*b^5 - 9*B*a^3*b^6 - C*a^2*b^7 + 3*B*a*b^8)*cos(d*x + c)^2 + (C*a^9 - 3*B*a^8*b - 3*C*a^7*b^2 + 9*B*a^6*b^3 + 3*C*a^5*b^4 - 9*B*a^4*b^5 - C*a^3*b^6 + 3*B*a^2*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((C*a^7*b^2 - 3*B*a^6*b^3 - 3*C*a^5*b^4 + 9*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*a^2*b^7 - C*a*b^8 + 3*B*b^9)*cos(d*x + c)^3 + 2*(C*a^8*b - 3*B*a^7*b^2 - 3*C*a^6*b^3 + 9*B*a^5*b^4 + 3*C*a^4*b^5 - 9*B*a^3*b^6 - C*a^2*b^7 + 3*B*a*b^8)*cos(d*x + c)^2 + (C*a^9 - 3*B*a^8*b - 3*C*a^7*b^2 + 9*B*a^6*b^3 + 3*C*a^5*b^4 - 9*B*a^4*b^5 - C*a^3*b^6 + 3*B*a^2*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) - (2*B*a^9 - 6*B*a^7*b^2 + 6*B*a^5*b^4 - 2*B*a^3*b^6 + (2*B*a^7*b^2 + 5*C*a^6*b^3 - 13*B*a^5*b^4 - 7*C*a^4*b^5 + 17*B*a^3*b^6 + 2*C*a^2*b^7 - 6*B*a*b^8)*cos(d*x + c)^2 + (4*B*a^8*b + 6*C*a^7*b^2 - 20*B*a^6*b^3 - 9*C*a^5*b^4 + 25*B*a^4*b^5 + 3*C*a^3*b^6 - 9*B*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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
814,0,0,0,0.497894," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} + B \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^3 + B*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
815,0,0,0,0.449459," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
816,0,0,0,0.509116," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right), x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
817,0,0,0,1.727853," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
818,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
820,0,0,0,0.936612," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} + B a \cos\left(d x + c\right)^{2} + {\left(C a + B b\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^4 + B*a*cos(d*x + c)^2 + (C*a + B*b)*cos(d*x + c)^3)*sqrt(b*cos(d*x + c) + a), x)","F",0
821,0,0,0,0.812378," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + B a \cos\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + B*a*cos(d*x + c) + (C*a + B*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
822,0,0,0,0.682357," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + B a \cos\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right), x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + B*a*cos(d*x + c) + (C*a + B*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
823,0,0,0,2.623391," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + B a \cos\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + B*a*cos(d*x + c) + (C*a + B*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
824,0,0,0,6.412567," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + B a \cos\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + B*a*cos(d*x + c) + (C*a + B*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
825,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
826,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
827,0,0,0,0.768544," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{5} + B a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^5 + B*a^2*cos(d*x + c)^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^4 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^3)*sqrt(b*cos(d*x + c) + a), x)","F",0
828,0,0,0,0.899731," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + B*a^2*cos(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
829,0,0,0,1.917800," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right), x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + B*a^2*cos(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
830,0,0,0,2.334080," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + B*a^2*cos(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
831,0,0,0,4.489247," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + B*a^2*cos(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
832,0,0,0,5.723058," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + B*a^2*cos(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
833,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
834,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
835,0,0,0,1.151851," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{3} + B \cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^3 + B*cos(d*x + c)^2)/sqrt(b*cos(d*x + c) + a), x)","F",0
836,0,0,0,1.844320," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
837,0,0,0,1.881224," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
838,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
839,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
840,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
841,0,0,0,0.875703," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + B \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((C*cos(d*x + c)^4 + B*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
842,0,0,0,0.605052," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + B \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((C*cos(d*x + c)^3 + B*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
843,0,0,0,0.462590," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*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
844,0,0,0,0.470735," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \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((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
845,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
846,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
847,0,0,0,1.166612," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + B \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((C*cos(d*x + c)^4 + B*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
848,0,0,0,1.167236," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + B \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((C*cos(d*x + c)^3 + B*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
849,0,0,0,0.701841," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{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((C*cos(d*x + c)^2 + B*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
850,0,0,0,0.743245," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \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((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*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
851,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
852,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,0,0,0,0.938258," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} + B a \cos\left(d x + c\right)^{2} + {\left(C a + B b\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^4 + B*a*cos(d*x + c)^2 + (C*a + B*b)*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
854,0,0,0,0.900162," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + B a \cos\left(d x + c\right) + {\left(C a + B b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + B*a*cos(d*x + c) + (C*a + B*b)*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
855,0,0,0,0.561829," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B b\right)} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
856,0,0,0,0.461763," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B b\right)} \cos\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
857,0,0,0,0.504917," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
858,0,0,0,0.439396," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))/cos(d*x + c)^(5/2), x)","F",0
859,0,0,0,0.460526," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))/cos(d*x + c)^(7/2), x)","F",0
860,0,0,0,0.494152," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{5} + B a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^5 + B*a^2*cos(d*x + c)^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^4 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
861,0,0,0,0.509259," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + B*a^2*cos(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
862,0,0,0,0.520643," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
863,0,0,0,0.649536," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
864,0,0,0,0.586366," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
865,0,0,0,0.637599," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))/cos(d*x + c)^(5/2), x)","F",0
866,0,0,0,0.521493," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))/cos(d*x + c)^(7/2), x)","F",0
867,0,0,0,0.577899," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B a b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))/cos(d*x + c)^(9/2), x)","F",0
868,0,0,0,0.647653," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + B a^{3} \cos\left(d x + c\right) + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(C a^{2} b + B a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + B*a^3*cos(d*x + c) + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + 3*(C*a^2*b + B*a*b^2)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b)*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
869,0,0,0,0.832501," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{4} + B a^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{2} b + B a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^4 + B*a^3 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^3 + 3*(C*a^2*b + B*a*b^2)*cos(d*x + c)^2 + (C*a^3 + 3*B*a^2*b)*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
870,0,0,0,0.501448," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{4} + B a^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{2} b + B a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^4 + B*a^3 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^3 + 3*(C*a^2*b + B*a*b^2)*cos(d*x + c)^2 + (C*a^3 + 3*B*a^2*b)*cos(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
871,0,0,0,0.517272," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{4} + B a^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{2} b + B a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^4 + B*a^3 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^3 + 3*(C*a^2*b + B*a*b^2)*cos(d*x + c)^2 + (C*a^3 + 3*B*a^2*b)*cos(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
872,0,0,0,0.507690," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{4} + B a^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{2} b + B a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^4 + B*a^3 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^3 + 3*(C*a^2*b + B*a*b^2)*cos(d*x + c)^2 + (C*a^3 + 3*B*a^2*b)*cos(d*x + c))/cos(d*x + c)^(5/2), x)","F",0
873,0,0,0,0.481418," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{4} + B a^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{2} b + B a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^4 + B*a^3 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^3 + 3*(C*a^2*b + B*a*b^2)*cos(d*x + c)^2 + (C*a^3 + 3*B*a^2*b)*cos(d*x + c))/cos(d*x + c)^(7/2), x)","F",0
874,0,0,0,0.466133," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{4} + B a^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{2} b + B a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^4 + B*a^3 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^3 + 3*(C*a^2*b + B*a*b^2)*cos(d*x + c)^2 + (C*a^3 + 3*B*a^2*b)*cos(d*x + c))/cos(d*x + c)^(9/2), x)","F",0
875,0,0,0,0.615904," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{4} + B a^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(C a^{2} b + B a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{3} + 3 \, B a^{2} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^4 + B*a^3 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^3 + 3*(C*a^2*b + B*a*b^2)*cos(d*x + c)^2 + (C*a^3 + 3*B*a^2*b)*cos(d*x + c))/cos(d*x + c)^(11/2), x)","F",0
876,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
877,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
878,0,0,0,155.262306," ","integrate(cos(d*x+c)^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
879,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
881,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
882,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
883,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
884,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
885,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
886,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
887,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
888,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
889,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
890,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
891,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
892,0,0,0,175.514998," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + B \cos\left(d x + c\right)^{2}\right)} \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((C*cos(d*x + c)^3 + B*cos(d*x + c)^2)*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
893,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
894,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
895,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
896,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,0,0,0,3.871614," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right) + B\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
899,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
900,0,0,0,41.154473," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
901,0,0,0,0.771566," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
902,0,0,0,0.958784," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
903,0,0,0,1.139560," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
904,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
905,0,0,0,64.307703," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B 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((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
906,0,0,0,1.519992," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B 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((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
907,0,0,0,1.378931," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B 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((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
908,0,0,0,0.974956," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B 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((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
909,0,0,0,0.514067," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B 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((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
910,0,0,0,0.506947," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{2} + B a + {\left(C a + B 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((C*b*cos(d*x + c)^2 + B*a + (C*a + B*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
911,0,0,0,4.756609," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + B a^{2} \cos\left(d x + c\right) + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{2} + 2 \, B 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((C*b^2*cos(d*x + c)^4 + B*a^2*cos(d*x + c) + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + (C*a^2 + 2*B*a*b)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
912,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
913,0,0,0,110.445927," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B 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((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
914,0,0,0,2.832381," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B 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((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
915,0,0,0,2.327604," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B 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((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
916,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
917,0,0,0,0.740163," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B 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((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
918,0,0,0,1.191497," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B 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((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(11/2), x)","F",0
919,0,0,0,0.849127," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{3} + B a^{2} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B 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((C*b^2*cos(d*x + c)^3 + B*a^2 + (2*C*a*b + B*b^2)*cos(d*x + c)^2 + (C*a^2 + 2*B*a*b)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(13/2), x)","F",0
920,0,0,0,68.524158," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + B \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^3 + B*cos(d*x + c)^2)*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
921,0,0,0,1.938848," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
922,0,0,0,1.252792," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c) + B)*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
923,0,0,0,0.857244," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
924,0,0,0,0.450445," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
925,0,0,0,0.440993," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
926,0,0,0,0.451498," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
927,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
928,0,0,0,83.960454," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*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
929,0,0,0,1.060731," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
930,0,0,0,0.555520," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
931,0,0,0,0.473731," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
932,0,0,0,0.511198," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
933,0,0,0,1.383697," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + B \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((C*cos(d*x + c)^3 + B*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
934,0,0,0,0.898352," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + B*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
935,0,0,0,0.483579," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
936,0,0,0,0.488614," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
937,0,0,0,0.519645," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right) + B\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((C*cos(d*x + c) + B)*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
938,1,121,0,0.428032," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left({\left(4 \, A + 3 \, C\right)} a + 3 \, B b\right)} d x + {\left(24 \, C b \cos\left(d x + c\right)^{4} + 30 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(5 \, B a + {\left(5 \, A + 4 \, C\right)} b\right)} \cos\left(d x + c\right)^{2} + 80 \, B a + 16 \, {\left(5 \, A + 4 \, C\right)} b + 15 \, {\left({\left(4 \, A + 3 \, C\right)} a + 3 \, B b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*((4*A + 3*C)*a + 3*B*b)*d*x + (24*C*b*cos(d*x + c)^4 + 30*(C*a + B*b)*cos(d*x + c)^3 + 8*(5*B*a + (5*A + 4*C)*b)*cos(d*x + c)^2 + 80*B*a + 16*(5*A + 4*C)*b + 15*((4*A + 3*C)*a + 3*B*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
939,1,97,0,0.428279," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, B a + {\left(4 \, A + 3 \, C\right)} b\right)} d x + {\left(6 \, C b \cos\left(d x + c\right)^{3} + 8 \, {\left(C a + B b\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, A + 2 \, C\right)} a + 16 \, B b + 3 \, {\left(4 \, B a + {\left(4 \, A + 3 \, C\right)} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*B*a + (4*A + 3*C)*b)*d*x + (6*C*b*cos(d*x + c)^3 + 8*(C*a + B*b)*cos(d*x + c)^2 + 8*(3*A + 2*C)*a + 16*B*b + 3*(4*B*a + (4*A + 3*C)*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
940,1,70,0,0.421982," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(2 \, A + C\right)} a + B b\right)} d x + {\left(2 \, C b \cos\left(d x + c\right)^{2} + 6 \, B a + 2 \, {\left(3 \, A + 2 \, C\right)} b + 3 \, {\left(C a + B b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*((2*A + C)*a + B*b)*d*x + (2*C*b*cos(d*x + c)^2 + 6*B*a + 2*(3*A + 2*C)*b + 3*(C*a + B*b)*cos(d*x + c))*sin(d*x + c))/d","A",0
941,1,73,0,0.443340," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{{\left(2 \, B a + {\left(2 \, A + C\right)} 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) + {\left(C b \cos\left(d x + c\right) + 2 \, C a + 2 \, B b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*B*a + (2*A + C)*b)*d*x + A*a*log(sin(d*x + c) + 1) - A*a*log(-sin(d*x + c) + 1) + (C*b*cos(d*x + c) + 2*C*a + 2*B*b)*sin(d*x + c))/d","A",0
942,1,101,0,0.446931," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(C a + B b\right)} 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 \, {\left(C b \cos\left(d x + c\right) + A a\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(2*(C*a + 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*(C*b*cos(d*x + c) + A*a)*sin(d*x + c))/(d*cos(d*x + c))","A",0
943,1,118,0,0.450049," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, C b d x \cos\left(d x + c\right)^{2} + {\left({\left(A + 2 \, C\right)} a + 2 \, B b\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A + 2 \, C\right)} 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*(4*C*b*d*x*cos(d*x + c)^2 + ((A + 2*C)*a + 2*B*b)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - ((A + 2*C)*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
944,1,128,0,0.434747," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(B a + {\left(A + 2 \, C\right)} b\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B a + {\left(A + 2 \, C\right)} b\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left({\left(2 \, A + 3 \, C\right)} 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 + 2*C)*b)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B*a + (A + 2*C)*b)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*((2*A + 3*C)*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
945,1,158,0,0.439600," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(3 \, A + 4 \, C\right)} a + 4 \, B b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(3 \, A + 4 \, C\right)} a + 4 \, B b\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 + {\left(2 \, A + 3 \, C\right)} b\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} 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 + 4*C)*a + 4*B*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*((3*A + 4*C)*a + 4*B*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(2*B*a + (2*A + 3*C)*b)*cos(d*x + c)^3 + 3*((3*A + 4*C)*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
946,1,182,0,0.441448," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a + {\left(3 \, A + 4 \, C\right)} b\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, B a + {\left(3 \, A + 4 \, C\right)} b\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left({\left(4 \, A + 5 \, C\right)} a + 5 \, B b\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(3 \, B a + {\left(3 \, A + 4 \, C\right)} b\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left({\left(4 \, A + 5 \, C\right)} a + 5 \, B b\right)} \cos\left(d x + c\right)^{2} + 24 \, A a + 30 \, {\left(B a + A 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*A + 4*C)*b)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*B*a + (3*A + 4*C)*b)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*((4*A + 5*C)*a + 5*B*b)*cos(d*x + c)^4 + 15*(3*B*a + (3*A + 4*C)*b)*cos(d*x + c)^3 + 8*((4*A + 5*C)*a + 5*B*b)*cos(d*x + c)^2 + 24*A*a + 30*(B*a + A*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
947,1,171,0,0.459284," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, B a^{2} + 2 \, {\left(4 \, A + 3 \, C\right)} a b + 3 \, B b^{2}\right)} d x + {\left(24 \, C b^{2} \cos\left(d x + c\right)^{4} + 30 \, {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + 40 \, {\left(3 \, A + 2 \, C\right)} a^{2} + 160 \, B a b + 16 \, {\left(5 \, A + 4 \, C\right)} b^{2} + 8 \, {\left(5 \, C a^{2} + 10 \, B a b + {\left(5 \, A + 4 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, B a^{2} + 2 \, {\left(4 \, A + 3 \, C\right)} a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*B*a^2 + 2*(4*A + 3*C)*a*b + 3*B*b^2)*d*x + (24*C*b^2*cos(d*x + c)^4 + 30*(2*C*a*b + B*b^2)*cos(d*x + c)^3 + 40*(3*A + 2*C)*a^2 + 160*B*a*b + 16*(5*A + 4*C)*b^2 + 8*(5*C*a^2 + 10*B*a*b + (5*A + 4*C)*b^2)*cos(d*x + c)^2 + 15*(4*B*a^2 + 2*(4*A + 3*C)*a*b + 3*B*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
948,1,134,0,0.454662," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, {\left(2 \, A + C\right)} a^{2} + 8 \, B a b + {\left(4 \, A + 3 \, C\right)} b^{2}\right)} d x + {\left(6 \, C b^{2} \cos\left(d x + c\right)^{3} + 24 \, B a^{2} + 16 \, {\left(3 \, A + 2 \, C\right)} a b + 16 \, B b^{2} + 8 \, {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, C a^{2} + 8 \, B a b + {\left(4 \, A + 3 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*(2*A + C)*a^2 + 8*B*a*b + (4*A + 3*C)*b^2)*d*x + (6*C*b^2*cos(d*x + c)^3 + 24*B*a^2 + 16*(3*A + 2*C)*a*b + 16*B*b^2 + 8*(2*C*a*b + B*b^2)*cos(d*x + c)^2 + 3*(4*C*a^2 + 8*B*a*b + (4*A + 3*C)*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
949,1,127,0,0.476258," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, A a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, A a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, B a^{2} + 2 \, {\left(2 \, A + C\right)} a b + B b^{2}\right)} d x + {\left(2 \, C b^{2} \cos\left(d x + c\right)^{2} + 6 \, C a^{2} + 12 \, B a b + 2 \, {\left(3 \, A + 2 \, C\right)} b^{2} + 3 \, {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*A*a^2*log(sin(d*x + c) + 1) - 3*A*a^2*log(-sin(d*x + c) + 1) + 3*(2*B*a^2 + 2*(2*A + C)*a*b + B*b^2)*d*x + (2*C*b^2*cos(d*x + c)^2 + 6*C*a^2 + 12*B*a*b + 2*(3*A + 2*C)*b^2 + 3*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
950,1,147,0,0.461080," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, C a^{2} + 4 \, B a b + {\left(2 \, A + C\right)} 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) + {\left(C b^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} + 2 \, {\left(2 \, C a b + B b^{2}\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*((2*C*a^2 + 4*B*a*b + (2*A + C)*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) + (C*b^2*cos(d*x + c)^2 + 2*A*a^2 + 2*(2*C*a*b + B*b^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
951,1,165,0,0.464048," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(2 \, C a b + B b^{2}\right)} d x \cos\left(d x + c\right)^{2} + {\left({\left(A + 2 \, C\right)} 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({\left(A + 2 \, C\right)} 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(2 \, C b^{2} \cos\left(d x + c\right)^{2} + 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*(2*C*a*b + B*b^2)*d*x*cos(d*x + c)^2 + ((A + 2*C)*a^2 + 4*B*a*b + 2*A*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - ((A + 2*C)*a^2 + 4*B*a*b + 2*A*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*C*b^2*cos(d*x + c)^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
952,1,179,0,0.453952," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{12 \, C b^{2} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{2} + 2 \, {\left(A + 2 \, C\right)} 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 \, {\left(A + 2 \, C\right)} 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({\left(2 \, A + 3 \, C\right)} 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*(12*C*b^2*d*x*cos(d*x + c)^3 + 3*(B*a^2 + 2*(A + 2*C)*a*b + 2*B*b^2)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B*a^2 + 2*(A + 2*C)*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 + 3*C)*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
953,1,209,0,0.443722," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{2} + 8 \, B a b + 4 \, {\left(A + 2 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{2} + 8 \, B a b + 4 \, {\left(A + 2 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(2 \, B a^{2} + 2 \, {\left(2 \, A + 3 \, C\right)} a b + 3 \, B b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, A a^{2} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{2} + 8 \, B a b + 4 \, A b^{2}\right)} \cos\left(d x + c\right)^{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 + 4*C)*a^2 + 8*B*a*b + 4*(A + 2*C)*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*((3*A + 4*C)*a^2 + 8*B*a*b + 4*(A + 2*C)*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*(2*B*a^2 + 2*(2*A + 3*C)*a*b + 3*B*b^2)*cos(d*x + c)^3 + 6*A*a^2 + 3*((3*A + 4*C)*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
954,1,243,0,0.453300," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a^{2} + 2 \, {\left(3 \, A + 4 \, C\right)} a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, B a^{2} + 2 \, {\left(3 \, A + 4 \, C\right)} a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(2 \, {\left(4 \, A + 5 \, C\right)} a^{2} + 20 \, B a b + 5 \, {\left(2 \, A + 3 \, C\right)} b^{2}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(3 \, B a^{2} + 2 \, {\left(3 \, A + 4 \, C\right)} a b + 4 \, B b^{2}\right)} \cos\left(d x + c\right)^{3} + 24 \, A a^{2} + 8 \, {\left({\left(4 \, A + 5 \, C\right)} a^{2} + 10 \, B a b + 5 \, A b^{2}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(B a^{2} + 2 \, A a 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^2 + 2*(3*A + 4*C)*a*b + 4*B*b^2)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*B*a^2 + 2*(3*A + 4*C)*a*b + 4*B*b^2)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(2*(4*A + 5*C)*a^2 + 20*B*a*b + 5*(2*A + 3*C)*b^2)*cos(d*x + c)^4 + 15*(3*B*a^2 + 2*(3*A + 4*C)*a*b + 4*B*b^2)*cos(d*x + c)^3 + 24*A*a^2 + 8*((4*A + 5*C)*a^2 + 10*B*a*b + 5*A*b^2)*cos(d*x + c)^2 + 30*(B*a^2 + 2*A*a*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
955,1,256,0,0.453991," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, B a^{3} + 6 \, {\left(4 \, A + 3 \, C\right)} a^{2} b + 18 \, B a b^{2} + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} d x + {\left(40 \, C b^{3} \cos\left(d x + c\right)^{5} + 48 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + 80 \, {\left(3 \, A + 2 \, C\right)} a^{3} + 480 \, B a^{2} b + 96 \, {\left(5 \, A + 4 \, C\right)} a b^{2} + 128 \, B b^{3} + 10 \, {\left(18 \, C a^{2} b + 18 \, B a b^{2} + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(5 \, C a^{3} + 15 \, B a^{2} b + 3 \, {\left(5 \, A + 4 \, C\right)} a b^{2} + 4 \, B b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(8 \, B a^{3} + 6 \, {\left(4 \, A + 3 \, C\right)} a^{2} b + 18 \, B a b^{2} + {\left(6 \, A + 5 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(8*B*a^3 + 6*(4*A + 3*C)*a^2*b + 18*B*a*b^2 + (6*A + 5*C)*b^3)*d*x + (40*C*b^3*cos(d*x + c)^5 + 48*(3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + 80*(3*A + 2*C)*a^3 + 480*B*a^2*b + 96*(5*A + 4*C)*a*b^2 + 128*B*b^3 + 10*(18*C*a^2*b + 18*B*a*b^2 + (6*A + 5*C)*b^3)*cos(d*x + c)^3 + 16*(5*C*a^3 + 15*B*a^2*b + 3*(5*A + 4*C)*a*b^2 + 4*B*b^3)*cos(d*x + c)^2 + 15*(8*B*a^3 + 6*(4*A + 3*C)*a^2*b + 18*B*a*b^2 + (6*A + 5*C)*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
956,1,207,0,0.443628," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, {\left(2 \, A + C\right)} a^{3} + 12 \, B a^{2} b + 3 \, {\left(4 \, A + 3 \, C\right)} a b^{2} + 3 \, B b^{3}\right)} d x + {\left(24 \, C b^{3} \cos\left(d x + c\right)^{4} + 120 \, B a^{3} + 120 \, {\left(3 \, A + 2 \, C\right)} a^{2} b + 240 \, B a b^{2} + 16 \, {\left(5 \, A + 4 \, C\right)} b^{3} + 30 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(15 \, C a^{2} b + 15 \, B a b^{2} + {\left(5 \, A + 4 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, C a^{3} + 12 \, B a^{2} b + 3 \, {\left(4 \, A + 3 \, C\right)} a b^{2} + 3 \, B b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*(2*A + C)*a^3 + 12*B*a^2*b + 3*(4*A + 3*C)*a*b^2 + 3*B*b^3)*d*x + (24*C*b^3*cos(d*x + c)^4 + 120*B*a^3 + 120*(3*A + 2*C)*a^2*b + 240*B*a*b^2 + 16*(5*A + 4*C)*b^3 + 30*(3*C*a*b^2 + B*b^3)*cos(d*x + c)^3 + 8*(15*C*a^2*b + 15*B*a*b^2 + (5*A + 4*C)*b^3)*cos(d*x + c)^2 + 15*(4*C*a^3 + 12*B*a^2*b + 3*(4*A + 3*C)*a*b^2 + 3*B*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
957,1,189,0,0.470614," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{12 \, A a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 12 \, A a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(8 \, B a^{3} + 12 \, {\left(2 \, A + C\right)} a^{2} b + 12 \, B a b^{2} + {\left(4 \, A + 3 \, C\right)} b^{3}\right)} d x + {\left(6 \, C b^{3} \cos\left(d x + c\right)^{3} + 24 \, C a^{3} + 72 \, B a^{2} b + 24 \, {\left(3 \, A + 2 \, C\right)} a b^{2} + 16 \, B b^{3} + 8 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(12 \, C a^{2} b + 12 \, B a b^{2} + {\left(4 \, A + 3 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(12*A*a^3*log(sin(d*x + c) + 1) - 12*A*a^3*log(-sin(d*x + c) + 1) + 3*(8*B*a^3 + 12*(2*A + C)*a^2*b + 12*B*a*b^2 + (4*A + 3*C)*b^3)*d*x + (6*C*b^3*cos(d*x + c)^3 + 24*C*a^3 + 72*B*a^2*b + 24*(3*A + 2*C)*a*b^2 + 16*B*b^3 + 8*(3*C*a*b^2 + B*b^3)*cos(d*x + c)^2 + 3*(12*C*a^2*b + 12*B*a*b^2 + (4*A + 3*C)*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
958,1,201,0,0.460345," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, C a^{3} + 6 \, B a^{2} b + 3 \, {\left(2 \, A + C\right)} a b^{2} + B b^{3}\right)} d x \cos\left(d x + c\right) + 3 \, {\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) - 3 \, {\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(2 \, C b^{3} \cos\left(d x + c\right)^{3} + 6 \, A a^{3} + 3 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(9 \, C a^{2} b + 9 \, B a b^{2} + {\left(3 \, A + 2 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"1/6*(3*(2*C*a^3 + 6*B*a^2*b + 3*(2*A + C)*a*b^2 + B*b^3)*d*x*cos(d*x + c) + 3*(B*a^3 + 3*A*a^2*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*(B*a^3 + 3*A*a^2*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (2*C*b^3*cos(d*x + c)^3 + 6*A*a^3 + 3*(3*C*a*b^2 + B*b^3)*cos(d*x + c)^2 + 2*(9*C*a^2*b + 9*B*a*b^2 + (3*A + 2*C)*b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
959,1,208,0,0.448733," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, C a^{2} b + 6 \, B a b^{2} + {\left(2 \, A + C\right)} b^{3}\right)} d x \cos\left(d x + c\right)^{2} + {\left({\left(A + 2 \, C\right)} 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({\left(A + 2 \, C\right)} 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(C b^{3} \cos\left(d x + c\right)^{3} + A a^{3} + 2 \, {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{2} + 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*(2*(6*C*a^2*b + 6*B*a*b^2 + (2*A + C)*b^3)*d*x*cos(d*x + c)^2 + ((A + 2*C)*a^3 + 6*B*a^2*b + 6*A*a*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - ((A + 2*C)*a^3 + 6*B*a^2*b + 6*A*a*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(C*b^3*cos(d*x + c)^3 + A*a^3 + 2*(3*C*a*b^2 + B*b^3)*cos(d*x + c)^2 + 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
960,1,225,0,0.462707," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{12 \, {\left(3 \, C a b^{2} + B b^{3}\right)} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{3} + 3 \, {\left(A + 2 \, C\right)} 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 \, {\left(A + 2 \, C\right)} 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(6 \, C b^{3} \cos\left(d x + c\right)^{3} + 2 \, A a^{3} + 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{3} + 9 \, B a^{2} b + 9 \, A a b^{2}\right)} \cos\left(d x + c\right)^{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*(3*C*a*b^2 + B*b^3)*d*x*cos(d*x + c)^3 + 3*(B*a^3 + 3*(A + 2*C)*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 + 2*C)*a^2*b + 6*B*a*b^2 + 2*A*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(6*C*b^3*cos(d*x + c)^3 + 2*A*a^3 + 2*((2*A + 3*C)*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
961,1,257,0,0.458380," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{48 \, C b^{3} d x \cos\left(d x + c\right)^{4} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{3} + 12 \, B a^{2} b + 12 \, {\left(A + 2 \, C\right)} a b^{2} + 8 \, B b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{3} + 12 \, B a^{2} b + 12 \, {\left(A + 2 \, C\right)} a b^{2} + 8 \, B b^{3}\right)} \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} + 3 \, {\left(2 \, A + 3 \, C\right)} a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2}\right)} \cos\left(d x + c\right)^{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*(48*C*b^3*d*x*cos(d*x + c)^4 + 3*((3*A + 4*C)*a^3 + 12*B*a^2*b + 12*(A + 2*C)*a*b^2 + 8*B*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*((3*A + 4*C)*a^3 + 12*B*a^2*b + 12*(A + 2*C)*a*b^2 + 8*B*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(6*A*a^3 + 8*(2*B*a^3 + 3*(2*A + 3*C)*a^2*b + 9*B*a*b^2 + 3*A*b^3)*cos(d*x + c)^3 + 3*((3*A + 4*C)*a^3 + 12*B*a^2*b + 12*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
962,1,292,0,0.462977," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, B a^{3} + 3 \, {\left(3 \, A + 4 \, C\right)} a^{2} b + 12 \, B a b^{2} + 4 \, {\left(A + 2 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, B a^{3} + 3 \, {\left(3 \, A + 4 \, C\right)} a^{2} b + 12 \, B a b^{2} + 4 \, {\left(A + 2 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, {\left(2 \, {\left(4 \, A + 5 \, C\right)} a^{3} + 30 \, B a^{2} b + 15 \, {\left(2 \, A + 3 \, C\right)} 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} + 3 \, {\left(3 \, A + 4 \, C\right)} a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left({\left(4 \, A + 5 \, C\right)} a^{3} + 15 \, B a^{2} b + 15 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + 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 + 3*(3*A + 4*C)*a^2*b + 12*B*a*b^2 + 4*(A + 2*C)*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*B*a^3 + 3*(3*A + 4*C)*a^2*b + 12*B*a*b^2 + 4*(A + 2*C)*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(8*(2*(4*A + 5*C)*a^3 + 30*B*a^2*b + 15*(2*A + 3*C)*a*b^2 + 15*B*b^3)*cos(d*x + c)^4 + 24*A*a^3 + 15*(3*B*a^3 + 3*(3*A + 4*C)*a^2*b + 12*B*a*b^2 + 4*A*b^3)*cos(d*x + c)^3 + 8*((4*A + 5*C)*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
963,1,342,0,0.476236," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 18 \, B a^{2} b + 6 \, {\left(3 \, A + 4 \, C\right)} a b^{2} + 8 \, B b^{3}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 18 \, B a^{2} b + 6 \, {\left(3 \, A + 4 \, C\right)} a b^{2} + 8 \, B b^{3}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(8 \, B a^{3} + 6 \, {\left(4 \, A + 5 \, C\right)} a^{2} b + 30 \, B a b^{2} + 5 \, {\left(2 \, A + 3 \, C\right)} b^{3}\right)} \cos\left(d x + c\right)^{5} + 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 18 \, B a^{2} b + 6 \, {\left(3 \, A + 4 \, C\right)} a b^{2} + 8 \, B b^{3}\right)} \cos\left(d x + c\right)^{4} + 40 \, A a^{3} + 16 \, {\left(4 \, B a^{3} + 3 \, {\left(4 \, A + 5 \, C\right)} a^{2} b + 15 \, B a b^{2} + 5 \, A b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left({\left(5 \, A + 6 \, C\right)} a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + 48 \, {\left(B a^{3} + 3 \, A a^{2} 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 + 6*C)*a^3 + 18*B*a^2*b + 6*(3*A + 4*C)*a*b^2 + 8*B*b^3)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*((5*A + 6*C)*a^3 + 18*B*a^2*b + 6*(3*A + 4*C)*a*b^2 + 8*B*b^3)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(8*B*a^3 + 6*(4*A + 5*C)*a^2*b + 30*B*a*b^2 + 5*(2*A + 3*C)*b^3)*cos(d*x + c)^5 + 15*((5*A + 6*C)*a^3 + 18*B*a^2*b + 6*(3*A + 4*C)*a*b^2 + 8*B*b^3)*cos(d*x + c)^4 + 40*A*a^3 + 16*(4*B*a^3 + 3*(4*A + 5*C)*a^2*b + 15*B*a*b^2 + 5*A*b^3)*cos(d*x + c)^3 + 10*((5*A + 6*C)*a^3 + 18*B*a^2*b + 18*A*a*b^2)*cos(d*x + c)^2 + 48*(B*a^3 + 3*A*a^2*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
964,1,354,0,0.489841," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{105 \, {\left(8 \, B a^{4} + 8 \, {\left(4 \, A + 3 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 4 \, {\left(6 \, A + 5 \, C\right)} a b^{3} + 5 \, B b^{4}\right)} d x + {\left(240 \, C b^{4} \cos\left(d x + c\right)^{6} + 280 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + 560 \, {\left(3 \, A + 2 \, C\right)} a^{4} + 4480 \, B a^{3} b + 1344 \, {\left(5 \, A + 4 \, C\right)} a^{2} b^{2} + 3584 \, B a b^{3} + 128 \, {\left(7 \, A + 6 \, C\right)} b^{4} + 48 \, {\left(42 \, C a^{2} b^{2} + 28 \, B a b^{3} + {\left(7 \, A + 6 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left(24 \, C a^{3} b + 36 \, B a^{2} b^{2} + 4 \, {\left(6 \, A + 5 \, C\right)} a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(35 \, C a^{4} + 140 \, B a^{3} b + 42 \, {\left(5 \, A + 4 \, C\right)} a^{2} b^{2} + 112 \, B a b^{3} + 4 \, {\left(7 \, A + 6 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 105 \, {\left(8 \, B a^{4} + 8 \, {\left(4 \, A + 3 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 4 \, {\left(6 \, A + 5 \, C\right)} a b^{3} + 5 \, B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(105*(8*B*a^4 + 8*(4*A + 3*C)*a^3*b + 36*B*a^2*b^2 + 4*(6*A + 5*C)*a*b^3 + 5*B*b^4)*d*x + (240*C*b^4*cos(d*x + c)^6 + 280*(4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + 560*(3*A + 2*C)*a^4 + 4480*B*a^3*b + 1344*(5*A + 4*C)*a^2*b^2 + 3584*B*a*b^3 + 128*(7*A + 6*C)*b^4 + 48*(42*C*a^2*b^2 + 28*B*a*b^3 + (7*A + 6*C)*b^4)*cos(d*x + c)^4 + 70*(24*C*a^3*b + 36*B*a^2*b^2 + 4*(6*A + 5*C)*a*b^3 + 5*B*b^4)*cos(d*x + c)^3 + 16*(35*C*a^4 + 140*B*a^3*b + 42*(5*A + 4*C)*a^2*b^2 + 112*B*a*b^3 + 4*(7*A + 6*C)*b^4)*cos(d*x + c)^2 + 105*(8*B*a^4 + 8*(4*A + 3*C)*a^3*b + 36*B*a^2*b^2 + 4*(6*A + 5*C)*a*b^3 + 5*B*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
965,1,292,0,0.492275," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, {\left(2 \, A + C\right)} a^{4} + 32 \, B a^{3} b + 12 \, {\left(4 \, A + 3 \, C\right)} a^{2} b^{2} + 24 \, B a b^{3} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} d x + {\left(40 \, C b^{4} \cos\left(d x + c\right)^{5} + 240 \, B a^{4} + 320 \, {\left(3 \, A + 2 \, C\right)} a^{3} b + 960 \, B a^{2} b^{2} + 128 \, {\left(5 \, A + 4 \, C\right)} a b^{3} + 128 \, B b^{4} + 48 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{4} + 10 \, {\left(36 \, C a^{2} b^{2} + 24 \, B a b^{3} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(10 \, C a^{3} b + 15 \, B a^{2} b^{2} + 2 \, {\left(5 \, A + 4 \, C\right)} a b^{3} + 2 \, B b^{4}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(8 \, C a^{4} + 32 \, B a^{3} b + 12 \, {\left(4 \, A + 3 \, C\right)} a^{2} b^{2} + 24 \, B a b^{3} + {\left(6 \, A + 5 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(8*(2*A + C)*a^4 + 32*B*a^3*b + 12*(4*A + 3*C)*a^2*b^2 + 24*B*a*b^3 + (6*A + 5*C)*b^4)*d*x + (40*C*b^4*cos(d*x + c)^5 + 240*B*a^4 + 320*(3*A + 2*C)*a^3*b + 960*B*a^2*b^2 + 128*(5*A + 4*C)*a*b^3 + 128*B*b^4 + 48*(4*C*a*b^3 + B*b^4)*cos(d*x + c)^4 + 10*(36*C*a^2*b^2 + 24*B*a*b^3 + (6*A + 5*C)*b^4)*cos(d*x + c)^3 + 32*(10*C*a^3*b + 15*B*a^2*b^2 + 2*(5*A + 4*C)*a*b^3 + 2*B*b^4)*cos(d*x + c)^2 + 15*(8*C*a^4 + 32*B*a^3*b + 12*(4*A + 3*C)*a^2*b^2 + 24*B*a*b^3 + (6*A + 5*C)*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
966,1,262,0,0.473335," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{60 \, A a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 60 \, A a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 15 \, {\left(8 \, B a^{4} + 16 \, {\left(2 \, A + C\right)} a^{3} b + 24 \, B a^{2} b^{2} + 4 \, {\left(4 \, A + 3 \, C\right)} a b^{3} + 3 \, B b^{4}\right)} d x + {\left(24 \, C b^{4} \cos\left(d x + c\right)^{4} + 120 \, C a^{4} + 480 \, B a^{3} b + 240 \, {\left(3 \, A + 2 \, C\right)} a^{2} b^{2} + 320 \, B a b^{3} + 16 \, {\left(5 \, A + 4 \, C\right)} b^{4} + 30 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(30 \, C a^{2} b^{2} + 20 \, B a b^{3} + {\left(5 \, A + 4 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 4 \, {\left(4 \, A + 3 \, C\right)} a b^{3} + 3 \, B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(60*A*a^4*log(sin(d*x + c) + 1) - 60*A*a^4*log(-sin(d*x + c) + 1) + 15*(8*B*a^4 + 16*(2*A + C)*a^3*b + 24*B*a^2*b^2 + 4*(4*A + 3*C)*a*b^3 + 3*B*b^4)*d*x + (24*C*b^4*cos(d*x + c)^4 + 120*C*a^4 + 480*B*a^3*b + 240*(3*A + 2*C)*a^2*b^2 + 320*B*a*b^3 + 16*(5*A + 4*C)*b^4 + 30*(4*C*a*b^3 + B*b^4)*cos(d*x + c)^3 + 8*(30*C*a^2*b^2 + 20*B*a*b^3 + (5*A + 4*C)*b^4)*cos(d*x + c)^2 + 15*(16*C*a^3*b + 24*B*a^2*b^2 + 4*(4*A + 3*C)*a*b^3 + 3*B*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
967,1,263,0,0.484163," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, C a^{4} + 32 \, B a^{3} b + 24 \, {\left(2 \, A + C\right)} a^{2} b^{2} + 16 \, B a b^{3} + {\left(4 \, A + 3 \, C\right)} b^{4}\right)} d x \cos\left(d x + c\right) + 12 \, {\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) - 12 \, {\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(6 \, C b^{4} \cos\left(d x + c\right)^{4} + 24 \, A a^{4} + 8 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(24 \, C a^{2} b^{2} + 16 \, B a b^{3} + {\left(4 \, A + 3 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 16 \, {\left(6 \, C a^{3} b + 9 \, B a^{2} b^{2} + 2 \, {\left(3 \, A + 2 \, C\right)} a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}"," ",0,"1/24*(3*(8*C*a^4 + 32*B*a^3*b + 24*(2*A + C)*a^2*b^2 + 16*B*a*b^3 + (4*A + 3*C)*b^4)*d*x*cos(d*x + c) + 12*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)*log(sin(d*x + c) + 1) - 12*(B*a^4 + 4*A*a^3*b)*cos(d*x + c)*log(-sin(d*x + c) + 1) + (6*C*b^4*cos(d*x + c)^4 + 24*A*a^4 + 8*(4*C*a*b^3 + B*b^4)*cos(d*x + c)^3 + 3*(24*C*a^2*b^2 + 16*B*a*b^3 + (4*A + 3*C)*b^4)*cos(d*x + c)^2 + 16*(6*C*a^3*b + 9*B*a^2*b^2 + 2*(3*A + 2*C)*a*b^3 + B*b^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A",0
968,1,262,0,0.471351," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{6 \, {\left(8 \, C a^{3} b + 12 \, B a^{2} b^{2} + 4 \, {\left(2 \, A + C\right)} a b^{3} + B b^{4}\right)} d x \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(A + 2 \, C\right)} 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) - 3 \, {\left({\left(A + 2 \, C\right)} 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(2 \, C b^{4} \cos\left(d x + c\right)^{4} + 3 \, A a^{4} + 3 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(18 \, C a^{2} b^{2} + 12 \, B a b^{3} + {\left(3 \, A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\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)^{2}}"," ",0,"1/12*(6*(8*C*a^3*b + 12*B*a^2*b^2 + 4*(2*A + C)*a*b^3 + B*b^4)*d*x*cos(d*x + c)^2 + 3*((A + 2*C)*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*((A + 2*C)*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*(2*C*b^4*cos(d*x + c)^4 + 3*A*a^4 + 3*(4*C*a*b^3 + B*b^4)*cos(d*x + c)^3 + 2*(18*C*a^2*b^2 + 12*B*a*b^3 + (3*A + 2*C)*b^4)*cos(d*x + c)^2 + 6*(B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
969,1,269,0,0.489802," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{6 \, {\left(12 \, C a^{2} b^{2} + 8 \, B a b^{3} + {\left(2 \, A + C\right)} b^{4}\right)} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{4} + 4 \, {\left(A + 2 \, C\right)} a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B a^{4} + 4 \, {\left(A + 2 \, C\right)} a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, C b^{4} \cos\left(d x + c\right)^{4} + 2 \, A a^{4} + 6 \, {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{4} + 12 \, B a^{3} b + 18 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 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*(6*(12*C*a^2*b^2 + 8*B*a*b^3 + (2*A + C)*b^4)*d*x*cos(d*x + c)^3 + 3*(B*a^4 + 4*(A + 2*C)*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 + 2*C)*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*(3*C*b^4*cos(d*x + c)^4 + 2*A*a^4 + 6*(4*C*a*b^3 + B*b^4)*cos(d*x + c)^3 + 2*((2*A + 3*C)*a^4 + 12*B*a^3*b + 18*A*a^2*b^2)*cos(d*x + c)^2 + 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
970,1,302,0,0.478951," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{48 \, {\left(4 \, C a b^{3} + B b^{4}\right)} d x \cos\left(d x + c\right)^{4} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{4} + 16 \, B a^{3} b + 24 \, {\left(A + 2 \, C\right)} a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{4} + 16 \, B a^{3} b + 24 \, {\left(A + 2 \, C\right)} a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, C b^{4} \cos\left(d x + c\right)^{4} + 6 \, A a^{4} + 16 \, {\left(B a^{4} + 2 \, {\left(2 \, A + 3 \, C\right)} a^{3} b + 9 \, B a^{2} b^{2} + 6 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 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*(4*C*a*b^3 + B*b^4)*d*x*cos(d*x + c)^4 + 3*((3*A + 4*C)*a^4 + 16*B*a^3*b + 24*(A + 2*C)*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*((3*A + 4*C)*a^4 + 16*B*a^3*b + 24*(A + 2*C)*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*C*b^4*cos(d*x + c)^4 + 6*A*a^4 + 16*(B*a^4 + 2*(2*A + 3*C)*a^3*b + 9*B*a^2*b^2 + 6*A*a*b^3)*cos(d*x + c)^3 + 3*((3*A + 4*C)*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
971,1,340,0,0.494679," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{240 \, C b^{4} d x \cos\left(d x + c\right)^{5} + 15 \, {\left(3 \, B a^{4} + 4 \, {\left(3 \, A + 4 \, C\right)} a^{3} b + 24 \, B a^{2} b^{2} + 16 \, {\left(A + 2 \, C\right)} a b^{3} + 8 \, B b^{4}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, B a^{4} + 4 \, {\left(3 \, A + 4 \, C\right)} a^{3} b + 24 \, B a^{2} b^{2} + 16 \, {\left(A + 2 \, C\right)} a b^{3} + 8 \, B b^{4}\right)} \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(2 \, {\left(4 \, A + 5 \, C\right)} a^{4} + 40 \, B a^{3} b + 30 \, {\left(2 \, A + 3 \, C\right)} 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} + 4 \, {\left(3 \, A + 4 \, C\right)} a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left({\left(4 \, A + 5 \, C\right)} a^{4} + 20 \, B a^{3} b + 30 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 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*(240*C*b^4*d*x*cos(d*x + c)^5 + 15*(3*B*a^4 + 4*(3*A + 4*C)*a^3*b + 24*B*a^2*b^2 + 16*(A + 2*C)*a*b^3 + 8*B*b^4)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*B*a^4 + 4*(3*A + 4*C)*a^3*b + 24*B*a^2*b^2 + 16*(A + 2*C)*a*b^3 + 8*B*b^4)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(24*A*a^4 + 8*(2*(4*A + 5*C)*a^4 + 40*B*a^3*b + 30*(2*A + 3*C)*a^2*b^2 + 60*B*a*b^3 + 15*A*b^4)*cos(d*x + c)^4 + 15*(3*B*a^4 + 4*(3*A + 4*C)*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3)*cos(d*x + c)^3 + 8*((4*A + 5*C)*a^4 + 20*B*a^3*b + 30*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
972,1,391,0,0.502767," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 24 \, B a^{3} b + 12 \, {\left(3 \, A + 4 \, C\right)} a^{2} b^{2} + 32 \, B a b^{3} + 8 \, {\left(A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 24 \, B a^{3} b + 12 \, {\left(3 \, A + 4 \, C\right)} a^{2} b^{2} + 32 \, B a b^{3} + 8 \, {\left(A + 2 \, C\right)} b^{4}\right)} \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} + 8 \, {\left(4 \, A + 5 \, C\right)} a^{3} b + 60 \, B a^{2} b^{2} + 20 \, {\left(2 \, A + 3 \, C\right)} a b^{3} + 15 \, B b^{4}\right)} \cos\left(d x + c\right)^{5} + 40 \, A a^{4} + 15 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 24 \, B a^{3} b + 12 \, {\left(3 \, A + 4 \, C\right)} a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} + 32 \, {\left(2 \, B a^{4} + 2 \, {\left(4 \, A + 5 \, C\right)} a^{3} b + 15 \, B a^{2} b^{2} + 10 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left({\left(5 \, A + 6 \, C\right)} a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{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 + 6*C)*a^4 + 24*B*a^3*b + 12*(3*A + 4*C)*a^2*b^2 + 32*B*a*b^3 + 8*(A + 2*C)*b^4)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*((5*A + 6*C)*a^4 + 24*B*a^3*b + 12*(3*A + 4*C)*a^2*b^2 + 32*B*a*b^3 + 8*(A + 2*C)*b^4)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(16*(8*B*a^4 + 8*(4*A + 5*C)*a^3*b + 60*B*a^2*b^2 + 20*(2*A + 3*C)*a*b^3 + 15*B*b^4)*cos(d*x + c)^5 + 40*A*a^4 + 15*((5*A + 6*C)*a^4 + 24*B*a^3*b + 12*(3*A + 4*C)*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*cos(d*x + c)^4 + 32*(2*B*a^4 + 2*(4*A + 5*C)*a^3*b + 15*B*a^2*b^2 + 10*A*a*b^3)*cos(d*x + c)^3 + 10*((5*A + 6*C)*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
973,1,450,0,0.524318," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^8,x, algorithm=""fricas"")","\frac{105 \, {\left(5 \, B a^{4} + 4 \, {\left(5 \, A + 6 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 8 \, {\left(3 \, A + 4 \, C\right)} a b^{3} + 8 \, B b^{4}\right)} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(5 \, B a^{4} + 4 \, {\left(5 \, A + 6 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 8 \, {\left(3 \, A + 4 \, C\right)} a b^{3} + 8 \, B b^{4}\right)} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(8 \, {\left(6 \, A + 7 \, C\right)} a^{4} + 224 \, B a^{3} b + 84 \, {\left(4 \, A + 5 \, C\right)} a^{2} b^{2} + 280 \, B a b^{3} + 35 \, {\left(2 \, A + 3 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{6} + 105 \, {\left(5 \, B a^{4} + 4 \, {\left(5 \, A + 6 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 8 \, {\left(3 \, A + 4 \, C\right)} a b^{3} + 8 \, B b^{4}\right)} \cos\left(d x + c\right)^{5} + 240 \, A a^{4} + 16 \, {\left(4 \, {\left(6 \, A + 7 \, C\right)} a^{4} + 112 \, B a^{3} b + 42 \, {\left(4 \, A + 5 \, C\right)} a^{2} b^{2} + 140 \, B a b^{3} + 35 \, A b^{4}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left(5 \, B a^{4} + 4 \, {\left(5 \, A + 6 \, C\right)} a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + 48 \, {\left({\left(6 \, A + 7 \, C\right)} a^{4} + 28 \, B a^{3} b + 42 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 280 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3360 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/3360*(105*(5*B*a^4 + 4*(5*A + 6*C)*a^3*b + 36*B*a^2*b^2 + 8*(3*A + 4*C)*a*b^3 + 8*B*b^4)*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(5*B*a^4 + 4*(5*A + 6*C)*a^3*b + 36*B*a^2*b^2 + 8*(3*A + 4*C)*a*b^3 + 8*B*b^4)*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 2*(16*(8*(6*A + 7*C)*a^4 + 224*B*a^3*b + 84*(4*A + 5*C)*a^2*b^2 + 280*B*a*b^3 + 35*(2*A + 3*C)*b^4)*cos(d*x + c)^6 + 105*(5*B*a^4 + 4*(5*A + 6*C)*a^3*b + 36*B*a^2*b^2 + 8*(3*A + 4*C)*a*b^3 + 8*B*b^4)*cos(d*x + c)^5 + 240*A*a^4 + 16*(4*(6*A + 7*C)*a^4 + 112*B*a^3*b + 42*(4*A + 5*C)*a^2*b^2 + 140*B*a*b^3 + 35*A*b^4)*cos(d*x + c)^4 + 70*(5*B*a^4 + 4*(5*A + 6*C)*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3)*cos(d*x + c)^3 + 48*((6*A + 7*C)*a^4 + 28*B*a^3*b + 42*A*a^2*b^2)*cos(d*x + c)^2 + 280*(B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
974,1,212,0,0.447084," ","integrate((a+b*cos(d*x+c))^3*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""fricas"")","-\frac{15 \, {\left(8 \, C a^{5} - 8 \, B a^{4} b + 8 \, C a^{3} b^{2} - 24 \, B a^{2} b^{3} - 9 \, C a b^{4} - 3 \, B b^{5}\right)} d x - {\left(24 \, C b^{5} \cos\left(d x + c\right)^{4} - 360 \, C a^{4} b + 480 \, B a^{3} b^{2} + 160 \, C a^{2} b^{3} + 320 \, B a b^{4} + 64 \, C b^{5} + 30 \, {\left(3 \, C a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)^{3} + 16 \, {\left(5 \, C a^{2} b^{3} + 10 \, B a b^{4} + 2 \, C b^{5}\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left(8 \, C a^{3} b^{2} - 24 \, B a^{2} b^{3} - 9 \, C a b^{4} - 3 \, B b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"-1/120*(15*(8*C*a^5 - 8*B*a^4*b + 8*C*a^3*b^2 - 24*B*a^2*b^3 - 9*C*a*b^4 - 3*B*b^5)*d*x - (24*C*b^5*cos(d*x + c)^4 - 360*C*a^4*b + 480*B*a^3*b^2 + 160*C*a^2*b^3 + 320*B*a*b^4 + 64*C*b^5 + 30*(3*C*a*b^4 + B*b^5)*cos(d*x + c)^3 + 16*(5*C*a^2*b^3 + 10*B*a*b^4 + 2*C*b^5)*cos(d*x + c)^2 - 15*(8*C*a^3*b^2 - 24*B*a^2*b^3 - 9*C*a*b^4 - 3*B*b^5)*cos(d*x + c))*sin(d*x + c))/d","A",0
975,1,133,0,0.458249," ","integrate((a+b*cos(d*x+c))^2*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""fricas"")","-\frac{3 \, {\left(8 \, C a^{4} - 8 \, B a^{3} b - 12 \, B a b^{3} - 3 \, C b^{4}\right)} d x - {\left(6 \, C b^{4} \cos\left(d x + c\right)^{3} - 48 \, C a^{3} b + 72 \, B a^{2} b^{2} + 32 \, C a b^{3} + 16 \, B b^{4} + 8 \, {\left(2 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(4 \, B a b^{3} + C b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"-1/24*(3*(8*C*a^4 - 8*B*a^3*b - 12*B*a*b^3 - 3*C*b^4)*d*x - (6*C*b^4*cos(d*x + c)^3 - 48*C*a^3*b + 72*B*a^2*b^2 + 32*C*a*b^3 + 16*B*b^4 + 8*(2*C*a*b^3 + B*b^4)*cos(d*x + c)^2 + 9*(4*B*a*b^3 + C*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
976,1,100,0,0.415446," ","integrate((a+b*cos(d*x+c))*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""fricas"")","-\frac{3 \, {\left(2 \, C a^{3} - 2 \, B a^{2} b - C a b^{2} - B b^{3}\right)} d x - {\left(2 \, C b^{3} \cos\left(d x + c\right)^{2} - 6 \, C a^{2} b + 12 \, B a b^{2} + 4 \, C b^{3} + 3 \, {\left(C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(3*(2*C*a^3 - 2*B*a^2*b - C*a*b^2 - B*b^3)*d*x - (2*C*b^3*cos(d*x + c)^2 - 6*C*a^2*b + 12*B*a*b^2 + 4*C*b^3 + 3*(C*a*b^2 + B*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
977,1,777,0,0.549070," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, C a^{6} - 8 \, B a^{5} b + 4 \, {\left(2 \, A - C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} - {\left(4 \, A + C\right)} a^{2} b^{4} + 4 \, B a b^{5} - {\left(4 \, A + 3 \, C\right)} b^{6}\right)} d x - 12 \, {\left(C a^{5} - B a^{4} b + A a^{3} b^{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(24 \, C a^{5} b - 24 \, B a^{4} b^{2} + 8 \, {\left(3 \, A - C\right)} a^{3} b^{3} + 8 \, B a^{2} b^{4} - 8 \, {\left(3 \, A + 2 \, C\right)} a b^{5} + 16 \, B b^{6} - 6 \, {\left(C a^{2} b^{4} - C b^{6}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(C a^{3} b^{3} - B a^{2} b^{4} - C a b^{5} + B b^{6}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(4 \, C a^{4} b^{2} - 4 \, B a^{3} b^{3} + {\left(4 \, A - C\right)} a^{2} b^{4} + 4 \, B a b^{5} - {\left(4 \, A + 3 \, C\right)} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{2} b^{5} - b^{7}\right)} d}, \frac{3 \, {\left(8 \, C a^{6} - 8 \, B a^{5} b + 4 \, {\left(2 \, A - C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} - {\left(4 \, A + C\right)} a^{2} b^{4} + 4 \, B a b^{5} - {\left(4 \, A + 3 \, C\right)} b^{6}\right)} d x - 24 \, {\left(C a^{5} - B a^{4} b + A a^{3} 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) - {\left(24 \, C a^{5} b - 24 \, B a^{4} b^{2} + 8 \, {\left(3 \, A - C\right)} a^{3} b^{3} + 8 \, B a^{2} b^{4} - 8 \, {\left(3 \, A + 2 \, C\right)} a b^{5} + 16 \, B b^{6} - 6 \, {\left(C a^{2} b^{4} - C b^{6}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(C a^{3} b^{3} - B a^{2} b^{4} - C a b^{5} + B b^{6}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(4 \, C a^{4} b^{2} - 4 \, B a^{3} b^{3} + {\left(4 \, A - C\right)} a^{2} b^{4} + 4 \, B a b^{5} - {\left(4 \, A + 3 \, C\right)} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{2} b^{5} - b^{7}\right)} d}\right]"," ",0,"[1/24*(3*(8*C*a^6 - 8*B*a^5*b + 4*(2*A - C)*a^4*b^2 + 4*B*a^3*b^3 - (4*A + C)*a^2*b^4 + 4*B*a*b^5 - (4*A + 3*C)*b^6)*d*x - 12*(C*a^5 - B*a^4*b + A*a^3*b^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)) - (24*C*a^5*b - 24*B*a^4*b^2 + 8*(3*A - C)*a^3*b^3 + 8*B*a^2*b^4 - 8*(3*A + 2*C)*a*b^5 + 16*B*b^6 - 6*(C*a^2*b^4 - C*b^6)*cos(d*x + c)^3 + 8*(C*a^3*b^3 - B*a^2*b^4 - C*a*b^5 + B*b^6)*cos(d*x + c)^2 - 3*(4*C*a^4*b^2 - 4*B*a^3*b^3 + (4*A - C)*a^2*b^4 + 4*B*a*b^5 - (4*A + 3*C)*b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^5 - b^7)*d), 1/24*(3*(8*C*a^6 - 8*B*a^5*b + 4*(2*A - C)*a^4*b^2 + 4*B*a^3*b^3 - (4*A + C)*a^2*b^4 + 4*B*a*b^5 - (4*A + 3*C)*b^6)*d*x - 24*(C*a^5 - B*a^4*b + A*a^3*b^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (24*C*a^5*b - 24*B*a^4*b^2 + 8*(3*A - C)*a^3*b^3 + 8*B*a^2*b^4 - 8*(3*A + 2*C)*a*b^5 + 16*B*b^6 - 6*(C*a^2*b^4 - C*b^6)*cos(d*x + c)^3 + 8*(C*a^3*b^3 - B*a^2*b^4 - C*a*b^5 + B*b^6)*cos(d*x + c)^2 - 3*(4*C*a^4*b^2 - 4*B*a^3*b^3 + (4*A - C)*a^2*b^4 + 4*B*a*b^5 - (4*A + 3*C)*b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^5 - b^7)*d)]","A",0
978,1,599,0,0.521839," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, C a^{5} - 2 \, B a^{4} b + {\left(2 \, A - C\right)} a^{3} b^{2} + B a^{2} b^{3} - {\left(2 \, A + C\right)} a b^{4} + B b^{5}\right)} d x + 3 \, {\left(C a^{4} - B a^{3} b + A a^{2} b^{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(6 \, C a^{4} b - 6 \, B a^{3} b^{2} + 2 \, {\left(3 \, A - C\right)} a^{2} b^{3} + 6 \, B a b^{4} - 2 \, {\left(3 \, A + 2 \, C\right)} b^{5} + 2 \, {\left(C a^{2} b^{3} - C b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} - C a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} - b^{6}\right)} d}, -\frac{3 \, {\left(2 \, C a^{5} - 2 \, B a^{4} b + {\left(2 \, A - C\right)} a^{3} b^{2} + B a^{2} b^{3} - {\left(2 \, A + C\right)} a b^{4} + B b^{5}\right)} d x - 6 \, {\left(C a^{4} - B a^{3} b + A a^{2} 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) - {\left(6 \, C a^{4} b - 6 \, B a^{3} b^{2} + 2 \, {\left(3 \, A - C\right)} a^{2} b^{3} + 6 \, B a b^{4} - 2 \, {\left(3 \, A + 2 \, C\right)} b^{5} + 2 \, {\left(C a^{2} b^{3} - C b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(C a^{3} b^{2} - B a^{2} b^{3} - C a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} - b^{6}\right)} d}\right]"," ",0,"[-1/6*(3*(2*C*a^5 - 2*B*a^4*b + (2*A - C)*a^3*b^2 + B*a^2*b^3 - (2*A + C)*a*b^4 + B*b^5)*d*x + 3*(C*a^4 - B*a^3*b + A*a^2*b^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)) - (6*C*a^4*b - 6*B*a^3*b^2 + 2*(3*A - C)*a^2*b^3 + 6*B*a*b^4 - 2*(3*A + 2*C)*b^5 + 2*(C*a^2*b^3 - C*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - B*a^2*b^3 - C*a*b^4 + B*b^5)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d), -1/6*(3*(2*C*a^5 - 2*B*a^4*b + (2*A - C)*a^3*b^2 + B*a^2*b^3 - (2*A + C)*a*b^4 + B*b^5)*d*x - 6*(C*a^4 - B*a^3*b + A*a^2*b^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*C*a^4*b - 6*B*a^3*b^2 + 2*(3*A - C)*a^2*b^3 + 6*B*a*b^4 - 2*(3*A + 2*C)*b^5 + 2*(C*a^2*b^3 - C*b^5)*cos(d*x + c)^2 - 3*(C*a^3*b^2 - B*a^2*b^3 - C*a*b^4 + B*b^5)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d)]","A",0
979,1,457,0,0.482681," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, C a^{4} - 2 \, B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} + 2 \, B a b^{3} - {\left(2 \, A + C\right)} b^{4}\right)} d x - {\left(C a^{3} - B a^{2} b + A a b^{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(2 \, C a^{3} b - 2 \, B a^{2} b^{2} - 2 \, C a b^{3} + 2 \, B b^{4} - {\left(C a^{2} b^{2} - C 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 \, C a^{4} - 2 \, B a^{3} b + {\left(2 \, A - C\right)} a^{2} b^{2} + 2 \, B a b^{3} - {\left(2 \, A + C\right)} b^{4}\right)} d x - 2 \, {\left(C a^{3} - B a^{2} b + A 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) - {\left(2 \, C a^{3} b - 2 \, B a^{2} b^{2} - 2 \, C a b^{3} + 2 \, B b^{4} - {\left(C a^{2} b^{2} - C 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*C*a^4 - 2*B*a^3*b + (2*A - C)*a^2*b^2 + 2*B*a*b^3 - (2*A + C)*b^4)*d*x - (C*a^3 - B*a^2*b + A*a*b^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)) - (2*C*a^3*b - 2*B*a^2*b^2 - 2*C*a*b^3 + 2*B*b^4 - (C*a^2*b^2 - C*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d), 1/2*((2*C*a^4 - 2*B*a^3*b + (2*A - C)*a^2*b^2 + 2*B*a*b^3 - (2*A + C)*b^4)*d*x - 2*(C*a^3 - B*a^2*b + A*a*b^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*C*a^3*b - 2*B*a^2*b^2 - 2*C*a*b^3 + 2*B*b^4 - (C*a^2*b^2 - C*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d)]","A",0
980,1,331,0,0.473178," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} d x + {\left(C a^{2} - B a b + A b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(C a^{2} b - C b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d}, -\frac{{\left(C a^{3} - B a^{2} b - C a b^{2} + B b^{3}\right)} d x - {\left(C a^{2} - 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) - {\left(C a^{2} b - C b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d}\right]"," ",0,"[-1/2*(2*(C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*d*x + (C*a^2 - B*a*b + A*b^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)) - 2*(C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d), -((C*a^3 - B*a^2*b - C*a*b^2 + B*b^3)*d*x - (C*a^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))) - (C*a^2*b - C*b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d)]","A",0
981,1,363,0,2.774661," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{3} - C a b^{2}\right)} d x - {\left(C a^{2} - B a b + A b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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} b - A b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{2} b - A b^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} b - a b^{3}\right)} d}, \frac{2 \, {\left(C a^{3} - C a b^{2}\right)} d x - 2 \, {\left(C a^{2} - 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) + {\left(A a^{2} b - A b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{2} b - A b^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} b - a b^{3}\right)} d}\right]"," ",0,"[1/2*(2*(C*a^3 - C*a*b^2)*d*x - (C*a^2 - B*a*b + A*b^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^2*b - A*b^3)*log(sin(d*x + c) + 1) - (A*a^2*b - A*b^3)*log(-sin(d*x + c) + 1))/((a^3*b - a*b^3)*d), 1/2*(2*(C*a^3 - C*a*b^2)*d*x - 2*(C*a^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))) + (A*a^2*b - A*b^3)*log(sin(d*x + c) + 1) - (A*a^2*b - A*b^3)*log(-sin(d*x + c) + 1))/((a^3*b - a*b^3)*d)]","A",0
982,1,470,0,5.128286," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{{\left(C a^{2} - B a b + A b^{2}\right)} \sqrt{-a^{2} + b^{2}} \cos\left(d x + c\right) \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(C a^{2} - 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*((C*a^2 - B*a*b + A*b^2)*sqrt(-a^2 + b^2)*cos(d*x + c)*log((2*a*b*cos(d*x + c) + (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*(C*a^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
983,1,633,0,12.153755," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(C a^{2} b - 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({\left(A + 2 \, C\right)} a^{4} - 2 \, B a^{3} b + {\left(A - 2 \, C\right)} a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(A + 2 \, C\right)} a^{4} - 2 \, B a^{3} b + {\left(A - 2 \, C\right)} a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} \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(C a^{2} b - 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({\left(A + 2 \, C\right)} a^{4} - 2 \, B a^{3} b + {\left(A - 2 \, C\right)} a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(A + 2 \, C\right)} a^{4} - 2 \, B a^{3} b + {\left(A - 2 \, C\right)} a^{2} b^{2} + 2 \, B a b^{3} - 2 \, A b^{4}\right)} \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*(C*a^2*b - 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 + 2*C)*a^4 - 2*B*a^3*b + (A - 2*C)*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + ((A + 2*C)*a^4 - 2*B*a^3*b + (A - 2*C)*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*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*(C*a^2*b - 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 + 2*C)*a^4 - 2*B*a^3*b + (A - 2*C)*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + ((A + 2*C)*a^4 - 2*B*a^3*b + (A - 2*C)*a^2*b^2 + 2*B*a*b^3 - 2*A*b^4)*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
984,1,795,0,24.948448," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(C a^{2} b^{2} - 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} - {\left(A + 2 \, C\right)} a^{4} b + B a^{3} b^{2} - {\left(A - 2 \, C\right)} a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(B a^{5} - {\left(A + 2 \, C\right)} a^{4} b + B a^{3} b^{2} - {\left(A - 2 \, C\right)} a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} \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({\left(2 \, A + 3 \, C\right)} a^{5} - 3 \, B a^{4} b + {\left(A - 3 \, C\right)} 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(C a^{2} b^{2} - 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} - {\left(A + 2 \, C\right)} a^{4} b + B a^{3} b^{2} - {\left(A - 2 \, C\right)} a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(B a^{5} - {\left(A + 2 \, C\right)} a^{4} b + B a^{3} b^{2} - {\left(A - 2 \, C\right)} a^{2} b^{3} - 2 \, B a b^{4} + 2 \, A b^{5}\right)} \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({\left(2 \, A + 3 \, C\right)} a^{5} - 3 \, B a^{4} b + {\left(A - 3 \, C\right)} 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*(C*a^2*b^2 - 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 + 2*C)*a^4*b + B*a^3*b^2 - (A - 2*C)*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(B*a^5 - (A + 2*C)*a^4*b + B*a^3*b^2 - (A - 2*C)*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*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 + 3*C)*a^5 - 3*B*a^4*b + (A - 3*C)*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*(C*a^2*b^2 - 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 + 2*C)*a^4*b + B*a^3*b^2 - (A - 2*C)*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(B*a^5 - (A + 2*C)*a^4*b + B*a^3*b^2 - (A - 2*C)*a^2*b^3 - 2*B*a*b^4 + 2*A*b^5)*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 + 3*C)*a^5 - 3*B*a^4*b + (A - 3*C)*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
985,1,993,0,59.488188," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{24 \, {\left(C a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \sqrt{-a^{2} + b^{2}} \cos\left(d x + c\right)^{4} \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({\left(3 \, A + 4 \, C\right)} a^{6} - 4 \, B a^{5} b + {\left(A + 4 \, C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + 4 \, {\left(A - 2 \, C\right)} a^{2} b^{4} + 8 \, B a b^{5} - 8 \, A b^{6}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{6} - 4 \, B a^{5} b + {\left(A + 4 \, C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + 4 \, {\left(A - 2 \, C\right)} a^{2} b^{4} + 8 \, B a b^{5} - 8 \, A b^{6}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(6 \, A a^{6} - 6 \, A a^{4} b^{2} + 8 \, {\left(2 \, B a^{6} - {\left(2 \, A + 3 \, C\right)} a^{5} b + B a^{4} b^{2} - {\left(A - 3 \, C\right)} a^{3} b^{3} - 3 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{6} - 4 \, B a^{5} b + {\left(A - 4 \, C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(B a^{6} - A a^{5} b - B a^{4} b^{2} + A a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{7} - a^{5} b^{2}\right)} d \cos\left(d x + c\right)^{4}}, -\frac{48 \, {\left(C a^{2} b^{3} - B a b^{4} + A b^{5}\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)^{4} - 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{6} - 4 \, B a^{5} b + {\left(A + 4 \, C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + 4 \, {\left(A - 2 \, C\right)} a^{2} b^{4} + 8 \, B a b^{5} - 8 \, A b^{6}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{6} - 4 \, B a^{5} b + {\left(A + 4 \, C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + 4 \, {\left(A - 2 \, C\right)} a^{2} b^{4} + 8 \, B a b^{5} - 8 \, A b^{6}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(6 \, A a^{6} - 6 \, A a^{4} b^{2} + 8 \, {\left(2 \, B a^{6} - {\left(2 \, A + 3 \, C\right)} a^{5} b + B a^{4} b^{2} - {\left(A - 3 \, C\right)} a^{3} b^{3} - 3 \, B a^{2} b^{4} + 3 \, A a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(3 \, A + 4 \, C\right)} a^{6} - 4 \, B a^{5} b + {\left(A - 4 \, C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(B a^{6} - A a^{5} b - B a^{4} b^{2} + A a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{7} - a^{5} b^{2}\right)} d \cos\left(d x + c\right)^{4}}\right]"," ",0,"[-1/48*(24*(C*a^2*b^3 - B*a*b^4 + A*b^5)*sqrt(-a^2 + b^2)*cos(d*x + c)^4*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*((3*A + 4*C)*a^6 - 4*B*a^5*b + (A + 4*C)*a^4*b^2 - 4*B*a^3*b^3 + 4*(A - 2*C)*a^2*b^4 + 8*B*a*b^5 - 8*A*b^6)*cos(d*x + c)^4*log(sin(d*x + c) + 1) + 3*((3*A + 4*C)*a^6 - 4*B*a^5*b + (A + 4*C)*a^4*b^2 - 4*B*a^3*b^3 + 4*(A - 2*C)*a^2*b^4 + 8*B*a*b^5 - 8*A*b^6)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 2*(6*A*a^6 - 6*A*a^4*b^2 + 8*(2*B*a^6 - (2*A + 3*C)*a^5*b + B*a^4*b^2 - (A - 3*C)*a^3*b^3 - 3*B*a^2*b^4 + 3*A*a*b^5)*cos(d*x + c)^3 + 3*((3*A + 4*C)*a^6 - 4*B*a^5*b + (A - 4*C)*a^4*b^2 + 4*B*a^3*b^3 - 4*A*a^2*b^4)*cos(d*x + c)^2 + 8*(B*a^6 - A*a^5*b - B*a^4*b^2 + A*a^3*b^3)*cos(d*x + c))*sin(d*x + c))/((a^7 - a^5*b^2)*d*cos(d*x + c)^4), -1/48*(48*(C*a^2*b^3 - B*a*b^4 + A*b^5)*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)^4 - 3*((3*A + 4*C)*a^6 - 4*B*a^5*b + (A + 4*C)*a^4*b^2 - 4*B*a^3*b^3 + 4*(A - 2*C)*a^2*b^4 + 8*B*a*b^5 - 8*A*b^6)*cos(d*x + c)^4*log(sin(d*x + c) + 1) + 3*((3*A + 4*C)*a^6 - 4*B*a^5*b + (A + 4*C)*a^4*b^2 - 4*B*a^3*b^3 + 4*(A - 2*C)*a^2*b^4 + 8*B*a*b^5 - 8*A*b^6)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 2*(6*A*a^6 - 6*A*a^4*b^2 + 8*(2*B*a^6 - (2*A + 3*C)*a^5*b + B*a^4*b^2 - (A - 3*C)*a^3*b^3 - 3*B*a^2*b^4 + 3*A*a*b^5)*cos(d*x + c)^3 + 3*((3*A + 4*C)*a^6 - 4*B*a^5*b + (A - 4*C)*a^4*b^2 + 4*B*a^3*b^3 - 4*A*a^2*b^4)*cos(d*x + c)^2 + 8*(B*a^6 - A*a^5*b - B*a^4*b^2 + A*a^3*b^3)*cos(d*x + c))*sin(d*x + c))/((a^7 - a^5*b^2)*d*cos(d*x + c)^4)]","A",0
986,1,1357,0,0.697073," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, C a^{7} b - 6 \, B a^{6} b^{2} + 2 \, {\left(2 \, A - 7 \, C\right)} a^{5} b^{3} + 11 \, B a^{4} b^{4} - 4 \, {\left(2 \, A - C\right)} a^{3} b^{5} - 4 \, B a^{2} b^{6} + 2 \, {\left(2 \, A + C\right)} a b^{7} - B b^{8}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(8 \, C a^{8} - 6 \, B a^{7} b + 2 \, {\left(2 \, A - 7 \, C\right)} a^{6} b^{2} + 11 \, B a^{5} b^{3} - 4 \, {\left(2 \, A - C\right)} a^{4} b^{4} - 4 \, B a^{3} b^{5} + 2 \, {\left(2 \, A + C\right)} a^{2} b^{6} - B a b^{7}\right)} d x + 3 \, {\left(4 \, C a^{7} - 3 \, B a^{6} b + {\left(2 \, A - 5 \, C\right)} a^{5} b^{2} + 4 \, B a^{4} b^{3} - 3 \, A a^{3} b^{4} + {\left(4 \, C a^{6} b - 3 \, B a^{5} b^{2} + {\left(2 \, A - 5 \, C\right)} a^{4} b^{3} + 4 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)\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(24 \, C a^{7} b - 18 \, B a^{6} b^{2} + 2 \, {\left(6 \, A - 19 \, C\right)} a^{5} b^{3} + 30 \, B a^{4} b^{4} - 2 \, {\left(9 \, A - 5 \, C\right)} a^{3} b^{5} - 12 \, B a^{2} b^{6} + 2 \, {\left(3 \, A + 2 \, C\right)} a b^{7} + 2 \, {\left(C a^{4} b^{4} - 2 \, C a^{2} b^{6} + C b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(4 \, C a^{5} b^{3} - 3 \, B a^{4} b^{4} - 8 \, C a^{3} b^{5} + 6 \, B a^{2} b^{6} + 4 \, C a b^{7} - 3 \, B b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(12 \, C a^{6} b^{2} - 9 \, B a^{5} b^{3} + 2 \, {\left(3 \, A - 10 \, C\right)} a^{4} b^{4} + 18 \, B a^{3} b^{5} - 4 \, {\left(3 \, A - C\right)} a^{2} b^{6} - 9 \, B a b^{7} + 2 \, {\left(3 \, A + 2 \, C\right)} b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d\right)}}, -\frac{3 \, {\left(8 \, C a^{7} b - 6 \, B a^{6} b^{2} + 2 \, {\left(2 \, A - 7 \, C\right)} a^{5} b^{3} + 11 \, B a^{4} b^{4} - 4 \, {\left(2 \, A - C\right)} a^{3} b^{5} - 4 \, B a^{2} b^{6} + 2 \, {\left(2 \, A + C\right)} a b^{7} - B b^{8}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(8 \, C a^{8} - 6 \, B a^{7} b + 2 \, {\left(2 \, A - 7 \, C\right)} a^{6} b^{2} + 11 \, B a^{5} b^{3} - 4 \, {\left(2 \, A - C\right)} a^{4} b^{4} - 4 \, B a^{3} b^{5} + 2 \, {\left(2 \, A + C\right)} a^{2} b^{6} - B a b^{7}\right)} d x - 6 \, {\left(4 \, C a^{7} - 3 \, B a^{6} b + {\left(2 \, A - 5 \, C\right)} a^{5} b^{2} + 4 \, B a^{4} b^{3} - 3 \, A a^{3} b^{4} + {\left(4 \, C a^{6} b - 3 \, B a^{5} b^{2} + {\left(2 \, A - 5 \, C\right)} a^{4} b^{3} + 4 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} \cos\left(d x + c\right)\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 \, C a^{7} b - 18 \, B a^{6} b^{2} + 2 \, {\left(6 \, A - 19 \, C\right)} a^{5} b^{3} + 30 \, B a^{4} b^{4} - 2 \, {\left(9 \, A - 5 \, C\right)} a^{3} b^{5} - 12 \, B a^{2} b^{6} + 2 \, {\left(3 \, A + 2 \, C\right)} a b^{7} + 2 \, {\left(C a^{4} b^{4} - 2 \, C a^{2} b^{6} + C b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(4 \, C a^{5} b^{3} - 3 \, B a^{4} b^{4} - 8 \, C a^{3} b^{5} + 6 \, B a^{2} b^{6} + 4 \, C a b^{7} - 3 \, B b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(12 \, C a^{6} b^{2} - 9 \, B a^{5} b^{3} + 2 \, {\left(3 \, A - 10 \, C\right)} a^{4} b^{4} + 18 \, B a^{3} b^{5} - 4 \, {\left(3 \, A - C\right)} a^{2} b^{6} - 9 \, B a b^{7} + 2 \, {\left(3 \, A + 2 \, C\right)} b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d\right)}}\right]"," ",0,"[-1/6*(3*(8*C*a^7*b - 6*B*a^6*b^2 + 2*(2*A - 7*C)*a^5*b^3 + 11*B*a^4*b^4 - 4*(2*A - C)*a^3*b^5 - 4*B*a^2*b^6 + 2*(2*A + C)*a*b^7 - B*b^8)*d*x*cos(d*x + c) + 3*(8*C*a^8 - 6*B*a^7*b + 2*(2*A - 7*C)*a^6*b^2 + 11*B*a^5*b^3 - 4*(2*A - C)*a^4*b^4 - 4*B*a^3*b^5 + 2*(2*A + C)*a^2*b^6 - B*a*b^7)*d*x + 3*(4*C*a^7 - 3*B*a^6*b + (2*A - 5*C)*a^5*b^2 + 4*B*a^4*b^3 - 3*A*a^3*b^4 + (4*C*a^6*b - 3*B*a^5*b^2 + (2*A - 5*C)*a^4*b^3 + 4*B*a^3*b^4 - 3*A*a^2*b^5)*cos(d*x + c))*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)) - (24*C*a^7*b - 18*B*a^6*b^2 + 2*(6*A - 19*C)*a^5*b^3 + 30*B*a^4*b^4 - 2*(9*A - 5*C)*a^3*b^5 - 12*B*a^2*b^6 + 2*(3*A + 2*C)*a*b^7 + 2*(C*a^4*b^4 - 2*C*a^2*b^6 + C*b^8)*cos(d*x + c)^3 - (4*C*a^5*b^3 - 3*B*a^4*b^4 - 8*C*a^3*b^5 + 6*B*a^2*b^6 + 4*C*a*b^7 - 3*B*b^8)*cos(d*x + c)^2 + (12*C*a^6*b^2 - 9*B*a^5*b^3 + 2*(3*A - 10*C)*a^4*b^4 + 18*B*a^3*b^5 - 4*(3*A - C)*a^2*b^6 - 9*B*a*b^7 + 2*(3*A + 2*C)*b^8)*cos(d*x + c))*sin(d*x + c))/((a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c) + (a^5*b^5 - 2*a^3*b^7 + a*b^9)*d), -1/6*(3*(8*C*a^7*b - 6*B*a^6*b^2 + 2*(2*A - 7*C)*a^5*b^3 + 11*B*a^4*b^4 - 4*(2*A - C)*a^3*b^5 - 4*B*a^2*b^6 + 2*(2*A + C)*a*b^7 - B*b^8)*d*x*cos(d*x + c) + 3*(8*C*a^8 - 6*B*a^7*b + 2*(2*A - 7*C)*a^6*b^2 + 11*B*a^5*b^3 - 4*(2*A - C)*a^4*b^4 - 4*B*a^3*b^5 + 2*(2*A + C)*a^2*b^6 - B*a*b^7)*d*x - 6*(4*C*a^7 - 3*B*a^6*b + (2*A - 5*C)*a^5*b^2 + 4*B*a^4*b^3 - 3*A*a^3*b^4 + (4*C*a^6*b - 3*B*a^5*b^2 + (2*A - 5*C)*a^4*b^3 + 4*B*a^3*b^4 - 3*A*a^2*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (24*C*a^7*b - 18*B*a^6*b^2 + 2*(6*A - 19*C)*a^5*b^3 + 30*B*a^4*b^4 - 2*(9*A - 5*C)*a^3*b^5 - 12*B*a^2*b^6 + 2*(3*A + 2*C)*a*b^7 + 2*(C*a^4*b^4 - 2*C*a^2*b^6 + C*b^8)*cos(d*x + c)^3 - (4*C*a^5*b^3 - 3*B*a^4*b^4 - 8*C*a^3*b^5 + 6*B*a^2*b^6 + 4*C*a*b^7 - 3*B*b^8)*cos(d*x + c)^2 + (12*C*a^6*b^2 - 9*B*a^5*b^3 + 2*(3*A - 10*C)*a^4*b^4 + 18*B*a^3*b^5 - 4*(3*A - C)*a^2*b^6 - 9*B*a*b^7 + 2*(3*A + 2*C)*b^8)*cos(d*x + c))*sin(d*x + c))/((a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c) + (a^5*b^5 - 2*a^3*b^7 + a*b^9)*d)]","A",0
987,1,1077,0,1.068964," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(6 \, C a^{6} b - 4 \, B a^{5} b^{2} + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - 4 \, {\left(A - C\right)} a^{2} b^{5} - 4 \, B a b^{6} + {\left(2 \, A + C\right)} b^{7}\right)} d x \cos\left(d x + c\right) + {\left(6 \, C a^{7} - 4 \, B a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + {\left(2 \, A + C\right)} a b^{6}\right)} d x - {\left(3 \, C a^{6} - 2 \, B a^{5} b + {\left(A - 4 \, C\right)} a^{4} b^{2} + 3 \, B a^{3} b^{3} - 2 \, A a^{2} b^{4} + {\left(3 \, C a^{5} b - 2 \, B a^{4} b^{2} + {\left(A - 4 \, C\right)} a^{3} b^{3} + 3 \, B a^{2} b^{4} - 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\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 \, C a^{6} b - 4 \, B a^{5} b^{2} + 2 \, {\left(A - 5 \, C\right)} a^{4} b^{3} + 6 \, B a^{3} b^{4} - 2 \, {\left(A - 2 \, C\right)} a^{2} b^{5} - 2 \, B a b^{6} - {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} - 6 \, C a^{3} b^{4} + 4 \, B a^{2} b^{5} + 3 \, C a b^{6} - 2 \, B b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{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 \, C a^{6} b - 4 \, B a^{5} b^{2} + {\left(2 \, A - 11 \, C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - 4 \, {\left(A - C\right)} a^{2} b^{5} - 4 \, B a b^{6} + {\left(2 \, A + C\right)} b^{7}\right)} d x \cos\left(d x + c\right) + {\left(6 \, C a^{7} - 4 \, B a^{6} b + {\left(2 \, A - 11 \, C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - 4 \, {\left(A - C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + {\left(2 \, A + C\right)} a b^{6}\right)} d x - 2 \, {\left(3 \, C a^{6} - 2 \, B a^{5} b + {\left(A - 4 \, C\right)} a^{4} b^{2} + 3 \, B a^{3} b^{3} - 2 \, A a^{2} b^{4} + {\left(3 \, C a^{5} b - 2 \, B a^{4} b^{2} + {\left(A - 4 \, C\right)} a^{3} b^{3} + 3 \, B a^{2} b^{4} - 2 \, A a b^{5}\right)} \cos\left(d x + c\right)\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 \, C a^{6} b - 4 \, B a^{5} b^{2} + 2 \, {\left(A - 5 \, C\right)} a^{4} b^{3} + 6 \, B a^{3} b^{4} - 2 \, {\left(A - 2 \, C\right)} a^{2} b^{5} - 2 \, B a b^{6} - {\left(C a^{4} b^{3} - 2 \, C a^{2} b^{5} + C b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} - 6 \, C a^{3} b^{4} + 4 \, B a^{2} b^{5} + 3 \, C a b^{6} - 2 \, B b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{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*C*a^6*b - 4*B*a^5*b^2 + (2*A - 11*C)*a^4*b^3 + 8*B*a^3*b^4 - 4*(A - C)*a^2*b^5 - 4*B*a*b^6 + (2*A + C)*b^7)*d*x*cos(d*x + c) + (6*C*a^7 - 4*B*a^6*b + (2*A - 11*C)*a^5*b^2 + 8*B*a^4*b^3 - 4*(A - C)*a^3*b^4 - 4*B*a^2*b^5 + (2*A + C)*a*b^6)*d*x - (3*C*a^6 - 2*B*a^5*b + (A - 4*C)*a^4*b^2 + 3*B*a^3*b^3 - 2*A*a^2*b^4 + (3*C*a^5*b - 2*B*a^4*b^2 + (A - 4*C)*a^3*b^3 + 3*B*a^2*b^4 - 2*A*a*b^5)*cos(d*x + c))*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*C*a^6*b - 4*B*a^5*b^2 + 2*(A - 5*C)*a^4*b^3 + 6*B*a^3*b^4 - 2*(A - 2*C)*a^2*b^5 - 2*B*a*b^6 - (C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7)*cos(d*x + c)^2 + (3*C*a^5*b^2 - 2*B*a^4*b^3 - 6*C*a^3*b^4 + 4*B*a^2*b^5 + 3*C*a*b^6 - 2*B*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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*C*a^6*b - 4*B*a^5*b^2 + (2*A - 11*C)*a^4*b^3 + 8*B*a^3*b^4 - 4*(A - C)*a^2*b^5 - 4*B*a*b^6 + (2*A + C)*b^7)*d*x*cos(d*x + c) + (6*C*a^7 - 4*B*a^6*b + (2*A - 11*C)*a^5*b^2 + 8*B*a^4*b^3 - 4*(A - C)*a^3*b^4 - 4*B*a^2*b^5 + (2*A + C)*a*b^6)*d*x - 2*(3*C*a^6 - 2*B*a^5*b + (A - 4*C)*a^4*b^2 + 3*B*a^3*b^3 - 2*A*a^2*b^4 + (3*C*a^5*b - 2*B*a^4*b^2 + (A - 4*C)*a^3*b^3 + 3*B*a^2*b^4 - 2*A*a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*C*a^6*b - 4*B*a^5*b^2 + 2*(A - 5*C)*a^4*b^3 + 6*B*a^3*b^4 - 2*(A - 2*C)*a^2*b^5 - 2*B*a*b^6 - (C*a^4*b^3 - 2*C*a^2*b^5 + C*b^7)*cos(d*x + c)^2 + (3*C*a^5*b^2 - 2*B*a^4*b^3 - 6*C*a^3*b^4 + 4*B*a^2*b^5 + 3*C*a*b^6 - 2*B*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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
988,1,830,0,0.911209," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(2 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(2 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} d x + {\left(2 \, C a^{5} - B a^{4} b - 3 \, C a^{3} b^{2} + 2 \, B a^{2} b^{3} - A a b^{4} + {\left(2 \, C a^{4} b - B a^{3} b^{2} - 3 \, C a^{2} b^{3} + 2 \, B a b^{4} - A b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{5} b - B a^{4} b^{2} + {\left(A - 3 \, C\right)} a^{3} b^{3} + B a^{2} b^{4} - {\left(A - C\right)} a b^{5} + {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C 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 \, C a^{5} b - B a^{4} b^{2} - 4 \, C a^{3} b^{3} + 2 \, B a^{2} b^{4} + 2 \, C a b^{5} - B b^{6}\right)} d x \cos\left(d x + c\right) + {\left(2 \, C a^{6} - B a^{5} b - 4 \, C a^{4} b^{2} + 2 \, B a^{3} b^{3} + 2 \, C a^{2} b^{4} - B a b^{5}\right)} d x - {\left(2 \, C a^{5} - B a^{4} b - 3 \, C a^{3} b^{2} + 2 \, B a^{2} b^{3} - A a b^{4} + {\left(2 \, C a^{4} b - B a^{3} b^{2} - 3 \, C a^{2} b^{3} + 2 \, B a b^{4} - A b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, C a^{5} b - B a^{4} b^{2} + {\left(A - 3 \, C\right)} a^{3} b^{3} + B a^{2} b^{4} - {\left(A - C\right)} a b^{5} + {\left(C a^{4} b^{2} - 2 \, C a^{2} b^{4} + C 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*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*d*x*cos(d*x + c) + 2*(2*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*d*x + (2*C*a^5 - B*a^4*b - 3*C*a^3*b^2 + 2*B*a^2*b^3 - A*a*b^4 + (2*C*a^4*b - B*a^3*b^2 - 3*C*a^2*b^3 + 2*B*a*b^4 - A*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*C*a^5*b - B*a^4*b^2 + (A - 3*C)*a^3*b^3 + B*a^2*b^4 - (A - C)*a*b^5 + (C*a^4*b^2 - 2*C*a^2*b^4 + C*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*C*a^5*b - B*a^4*b^2 - 4*C*a^3*b^3 + 2*B*a^2*b^4 + 2*C*a*b^5 - B*b^6)*d*x*cos(d*x + c) + (2*C*a^6 - B*a^5*b - 4*C*a^4*b^2 + 2*B*a^3*b^3 + 2*C*a^2*b^4 - B*a*b^5)*d*x - (2*C*a^5 - B*a^4*b - 3*C*a^3*b^2 + 2*B*a^2*b^3 - A*a*b^4 + (2*C*a^4*b - B*a^3*b^2 - 3*C*a^2*b^3 + 2*B*a*b^4 - A*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*C*a^5*b - B*a^4*b^2 + (A - 3*C)*a^3*b^3 + B*a^2*b^4 - (A - C)*a*b^5 + (C*a^4*b^2 - 2*C*a^2*b^4 + C*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
989,1,586,0,0.702580," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} d x - {\left(C a^{4} - {\left(A + 2 \, C\right)} a^{2} b^{2} + B a b^{3} + {\left(C a^{3} b - {\left(A + 2 \, C\right)} a b^{3} + B 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(C a^{4} b - B a^{3} b^{2} + {\left(A - C\right)} a^{2} b^{3} + B a b^{4} - A b^{5}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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(C a^{4} b - 2 \, C a^{2} b^{3} + C b^{5}\right)} d x \cos\left(d x + c\right) + {\left(C a^{5} - 2 \, C a^{3} b^{2} + C a b^{4}\right)} d x - {\left(C a^{4} - {\left(A + 2 \, C\right)} a^{2} b^{2} + B a b^{3} + {\left(C a^{3} b - {\left(A + 2 \, C\right)} a b^{3} + B 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(C a^{4} b - B a^{3} b^{2} + {\left(A - C\right)} a^{2} b^{3} + B a b^{4} - A b^{5}\right)} \sin\left(d x + c\right)}{{\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*(C*a^4*b - 2*C*a^2*b^3 + C*b^5)*d*x*cos(d*x + c) + 2*(C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*d*x - (C*a^4 - (A + 2*C)*a^2*b^2 + B*a*b^3 + (C*a^3*b - (A + 2*C)*a*b^3 + B*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*(C*a^4*b - B*a^3*b^2 + (A - C)*a^2*b^3 + B*a*b^4 - A*b^5)*sin(d*x + c))/((a^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), ((C*a^4*b - 2*C*a^2*b^3 + C*b^5)*d*x*cos(d*x + c) + (C*a^5 - 2*C*a^3*b^2 + C*a*b^4)*d*x - (C*a^4 - (A + 2*C)*a^2*b^2 + B*a*b^3 + (C*a^3*b - (A + 2*C)*a*b^3 + B*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))) - (C*a^4*b - B*a^3*b^2 + (A - C)*a^2*b^3 + B*a*b^4 - A*b^5)*sin(d*x + c))/((a^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
990,1,718,0,10.260243," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{4} - {\left(2 \, A + C\right)} a^{3} b + A a b^{3} + {\left(B a^{3} b - {\left(2 \, A + C\right)} 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(C a^{5} - B a^{4} b + {\left(A - C\right)} a^{3} b^{2} + B a^{2} b^{3} - A a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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} - {\left(2 \, A + C\right)} a^{3} b + A a b^{3} + {\left(B a^{3} b - {\left(2 \, A + C\right)} 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(C a^{5} - B a^{4} b + {\left(A - C\right)} a^{3} b^{2} + B a^{2} b^{3} - A a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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 + C)*a^3*b + A*a*b^3 + (B*a^3*b - (2*A + C)*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*(C*a^5 - B*a^4*b + (A - C)*a^3*b^2 + B*a^2*b^3 - A*a*b^4)*sin(d*x + c))/((a^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 + C)*a^3*b + A*a*b^3 + (B*a^3*b - (2*A + C)*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*(C*a^5 - B*a^4*b + (A - C)*a^3*b^2 + B*a^2*b^3 - A*a*b^4)*sin(d*x + c))/((a^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
991,1,1126,0,36.879716," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(C a^{4} b - 2 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3} + B a b^{4} - 2 \, A b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(C a^{5} - 2 \, B a^{4} b + 3 \, A a^{3} b^{2} + B a^{2} b^{3} - 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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({\left(A - C\right)} a^{5} b + B a^{4} b^{2} - {\left(3 \, A - C\right)} a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5}\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(C a^{4} b - 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(C a^{5} - 2 \, B a^{4} b + 3 \, A a^{3} b^{2} + B a^{2} b^{3} - 2 \, A a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{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({\left(A - C\right)} a^{5} b + B a^{4} b^{2} - {\left(3 \, A - C\right)} a^{3} b^{3} - B a^{2} b^{4} + 2 \, A a b^{5}\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*(((C*a^4*b - 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 + (C*a^5 - 2*B*a^4*b + 3*A*a^3*b^2 + B*a^2*b^3 - 2*A*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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 - C)*a^5*b + B*a^4*b^2 - (3*A - C)*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*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*((C*a^4*b - 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 + (C*a^5 - 2*B*a^4*b + 3*A*a^3*b^2 + B*a^2*b^3 - 2*A*a*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(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 - C)*a^5*b + B*a^4*b^2 - (3*A - C)*a^3*b^3 - B*a^2*b^4 + 2*A*a*b^5)*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
992,1,1515,0,77.592777," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left({\left(2 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} + {\left(4 \, A - C\right)} a^{2} b^{4} + 2 \, B a b^{5} - 3 \, A b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, C a^{5} b - 3 \, B a^{4} b^{2} + {\left(4 \, A - C\right)} a^{3} b^{3} + 2 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} \cos\left(d x + c\right)^{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({\left(A + 2 \, C\right)} a^{6} b - 4 \, B a^{5} b^{2} + 4 \, {\left(A - C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{7} - 4 \, B a^{6} b + 4 \, {\left(A - C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left({\left(A + 2 \, C\right)} a^{6} b - 4 \, B a^{5} b^{2} + 4 \, {\left(A - C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{7} - 4 \, B a^{6} b + 4 \, {\left(A - C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} \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 - {\left(2 \, A - C\right)} a^{5} b^{2} - 3 \, B a^{4} b^{3} + {\left(5 \, A - C\right)} 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(2 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} + {\left(4 \, A - C\right)} a^{2} b^{4} + 2 \, B a b^{5} - 3 \, A b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, C a^{5} b - 3 \, B a^{4} b^{2} + {\left(4 \, A - C\right)} a^{3} b^{3} + 2 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} \cos\left(d x + c\right)^{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({\left(A + 2 \, C\right)} a^{6} b - 4 \, B a^{5} b^{2} + 4 \, {\left(A - C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{7} - 4 \, B a^{6} b + 4 \, {\left(A - C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left({\left(A + 2 \, C\right)} a^{6} b - 4 \, B a^{5} b^{2} + 4 \, {\left(A - C\right)} a^{4} b^{3} + 8 \, B a^{3} b^{4} - {\left(11 \, A - 2 \, C\right)} a^{2} b^{5} - 4 \, B a b^{6} + 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(A + 2 \, C\right)} a^{7} - 4 \, B a^{6} b + 4 \, {\left(A - C\right)} a^{5} b^{2} + 8 \, B a^{4} b^{3} - {\left(11 \, A - 2 \, C\right)} a^{3} b^{4} - 4 \, B a^{2} b^{5} + 6 \, A a b^{6}\right)} \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 - {\left(2 \, A - C\right)} a^{5} b^{2} - 3 \, B a^{4} b^{3} + {\left(5 \, A - C\right)} 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*((2*C*a^4*b^2 - 3*B*a^3*b^3 + (4*A - C)*a^2*b^4 + 2*B*a*b^5 - 3*A*b^6)*cos(d*x + c)^3 + (2*C*a^5*b - 3*B*a^4*b^2 + (4*A - C)*a^3*b^3 + 2*B*a^2*b^4 - 3*A*a*b^5)*cos(d*x + c)^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 + 2*C)*a^6*b - 4*B*a^5*b^2 + 4*(A - C)*a^4*b^3 + 8*B*a^3*b^4 - (11*A - 2*C)*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*cos(d*x + c)^3 + ((A + 2*C)*a^7 - 4*B*a^6*b + 4*(A - C)*a^5*b^2 + 8*B*a^4*b^3 - (11*A - 2*C)*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + (((A + 2*C)*a^6*b - 4*B*a^5*b^2 + 4*(A - C)*a^4*b^3 + 8*B*a^3*b^4 - (11*A - 2*C)*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*cos(d*x + c)^3 + ((A + 2*C)*a^7 - 4*B*a^6*b + 4*(A - C)*a^5*b^2 + 8*B*a^4*b^3 - (11*A - 2*C)*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*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 - C)*a^5*b^2 - 3*B*a^4*b^3 + (5*A - C)*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*((2*C*a^4*b^2 - 3*B*a^3*b^3 + (4*A - C)*a^2*b^4 + 2*B*a*b^5 - 3*A*b^6)*cos(d*x + c)^3 + (2*C*a^5*b - 3*B*a^4*b^2 + (4*A - C)*a^3*b^3 + 2*B*a^2*b^4 - 3*A*a*b^5)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (((A + 2*C)*a^6*b - 4*B*a^5*b^2 + 4*(A - C)*a^4*b^3 + 8*B*a^3*b^4 - (11*A - 2*C)*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*cos(d*x + c)^3 + ((A + 2*C)*a^7 - 4*B*a^6*b + 4*(A - C)*a^5*b^2 + 8*B*a^4*b^3 - (11*A - 2*C)*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + (((A + 2*C)*a^6*b - 4*B*a^5*b^2 + 4*(A - C)*a^4*b^3 + 8*B*a^3*b^4 - (11*A - 2*C)*a^2*b^5 - 4*B*a*b^6 + 6*A*b^7)*cos(d*x + c)^3 + ((A + 2*C)*a^7 - 4*B*a^6*b + 4*(A - C)*a^5*b^2 + 8*B*a^4*b^3 - (11*A - 2*C)*a^3*b^4 - 4*B*a^2*b^5 + 6*A*a*b^6)*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 - C)*a^5*b^2 - 3*B*a^4*b^3 + (5*A - C)*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
993,1,1795,0,121.506901," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left({\left(3 \, C a^{4} b^{3} - 4 \, B a^{3} b^{4} + {\left(5 \, A - 2 \, C\right)} a^{2} b^{5} + 3 \, B a b^{6} - 4 \, A b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A - 2 \, C\right)} a^{3} b^{4} + 3 \, B a^{2} b^{5} - 4 \, A a b^{6}\right)} \cos\left(d x + c\right)^{3}\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) - 3 \, {\left({\left(B a^{7} b - 2 \, {\left(A + 2 \, C\right)} a^{6} b^{2} + 4 \, B a^{5} b^{3} - 4 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - 11 \, B a^{3} b^{5} + 2 \, {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 6 \, B a b^{7} - 8 \, A b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(B a^{8} - 2 \, {\left(A + 2 \, C\right)} a^{7} b + 4 \, B a^{6} b^{2} - 4 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - 11 \, B a^{4} b^{4} + 2 \, {\left(7 \, A - 2 \, C\right)} a^{3} b^{5} + 6 \, B a^{2} b^{6} - 8 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(B a^{7} b - 2 \, {\left(A + 2 \, C\right)} a^{6} b^{2} + 4 \, B a^{5} b^{3} - 4 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - 11 \, B a^{3} b^{5} + 2 \, {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 6 \, B a b^{7} - 8 \, A b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(B a^{8} - 2 \, {\left(A + 2 \, C\right)} a^{7} b + 4 \, B a^{6} b^{2} - 4 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - 11 \, B a^{4} b^{4} + 2 \, {\left(7 \, A - 2 \, C\right)} a^{3} b^{5} + 6 \, B a^{2} b^{6} - 8 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, A a^{8} - 4 \, A a^{6} b^{2} + 2 \, A a^{4} b^{4} + 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{7} b - 6 \, B a^{6} b^{2} + {\left(5 \, A - 9 \, C\right)} a^{5} b^{3} + 15 \, B a^{4} b^{4} - {\left(19 \, A - 6 \, C\right)} a^{3} b^{5} - 9 \, B a^{2} b^{6} + 12 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, {\left(2 \, A + 3 \, C\right)} a^{8} - 9 \, B a^{7} b + 4 \, {\left(A - 3 \, C\right)} a^{6} b^{2} + 18 \, B a^{5} b^{3} - 2 \, {\left(10 \, A - 3 \, C\right)} a^{4} b^{4} - 9 \, B a^{3} b^{5} + 12 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B a^{8} - 4 \, A a^{7} b - 6 \, B a^{6} b^{2} + 8 \, A a^{5} b^{3} + 3 \, B a^{4} b^{4} - 4 \, A a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{3}\right)}}, \frac{12 \, {\left({\left(3 \, C a^{4} b^{3} - 4 \, B a^{3} b^{4} + {\left(5 \, A - 2 \, C\right)} a^{2} b^{5} + 3 \, B a b^{6} - 4 \, A b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, C a^{5} b^{2} - 4 \, B a^{4} b^{3} + {\left(5 \, A - 2 \, C\right)} a^{3} b^{4} + 3 \, B a^{2} b^{5} - 4 \, A a b^{6}\right)} \cos\left(d x + c\right)^{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) + 3 \, {\left({\left(B a^{7} b - 2 \, {\left(A + 2 \, C\right)} a^{6} b^{2} + 4 \, B a^{5} b^{3} - 4 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - 11 \, B a^{3} b^{5} + 2 \, {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 6 \, B a b^{7} - 8 \, A b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(B a^{8} - 2 \, {\left(A + 2 \, C\right)} a^{7} b + 4 \, B a^{6} b^{2} - 4 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - 11 \, B a^{4} b^{4} + 2 \, {\left(7 \, A - 2 \, C\right)} a^{3} b^{5} + 6 \, B a^{2} b^{6} - 8 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(B a^{7} b - 2 \, {\left(A + 2 \, C\right)} a^{6} b^{2} + 4 \, B a^{5} b^{3} - 4 \, {\left(A - 2 \, C\right)} a^{4} b^{4} - 11 \, B a^{3} b^{5} + 2 \, {\left(7 \, A - 2 \, C\right)} a^{2} b^{6} + 6 \, B a b^{7} - 8 \, A b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(B a^{8} - 2 \, {\left(A + 2 \, C\right)} a^{7} b + 4 \, B a^{6} b^{2} - 4 \, {\left(A - 2 \, C\right)} a^{5} b^{3} - 11 \, B a^{4} b^{4} + 2 \, {\left(7 \, A - 2 \, C\right)} a^{3} b^{5} + 6 \, B a^{2} b^{6} - 8 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{8} - 4 \, A a^{6} b^{2} + 2 \, A a^{4} b^{4} + 2 \, {\left({\left(2 \, A + 3 \, C\right)} a^{7} b - 6 \, B a^{6} b^{2} + {\left(5 \, A - 9 \, C\right)} a^{5} b^{3} + 15 \, B a^{4} b^{4} - {\left(19 \, A - 6 \, C\right)} a^{3} b^{5} - 9 \, B a^{2} b^{6} + 12 \, A a b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, {\left(2 \, A + 3 \, C\right)} a^{8} - 9 \, B a^{7} b + 4 \, {\left(A - 3 \, C\right)} a^{6} b^{2} + 18 \, B a^{5} b^{3} - 2 \, {\left(10 \, A - 3 \, C\right)} a^{4} b^{4} - 9 \, B a^{3} b^{5} + 12 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B a^{8} - 4 \, A a^{7} b - 6 \, B a^{6} b^{2} + 8 \, A a^{5} b^{3} + 3 \, B a^{4} b^{4} - 4 \, A a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[-1/12*(6*((3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A - 2*C)*a^2*b^5 + 3*B*a*b^6 - 4*A*b^7)*cos(d*x + c)^4 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A - 2*C)*a^3*b^4 + 3*B*a^2*b^5 - 4*A*a*b^6)*cos(d*x + c)^3)*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)) - 3*((B*a^7*b - 2*(A + 2*C)*a^6*b^2 + 4*B*a^5*b^3 - 4*(A - 2*C)*a^4*b^4 - 11*B*a^3*b^5 + 2*(7*A - 2*C)*a^2*b^6 + 6*B*a*b^7 - 8*A*b^8)*cos(d*x + c)^4 + (B*a^8 - 2*(A + 2*C)*a^7*b + 4*B*a^6*b^2 - 4*(A - 2*C)*a^5*b^3 - 11*B*a^4*b^4 + 2*(7*A - 2*C)*a^3*b^5 + 6*B*a^2*b^6 - 8*A*a*b^7)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) + 3*((B*a^7*b - 2*(A + 2*C)*a^6*b^2 + 4*B*a^5*b^3 - 4*(A - 2*C)*a^4*b^4 - 11*B*a^3*b^5 + 2*(7*A - 2*C)*a^2*b^6 + 6*B*a*b^7 - 8*A*b^8)*cos(d*x + c)^4 + (B*a^8 - 2*(A + 2*C)*a^7*b + 4*B*a^6*b^2 - 4*(A - 2*C)*a^5*b^3 - 11*B*a^4*b^4 + 2*(7*A - 2*C)*a^3*b^5 + 6*B*a^2*b^6 - 8*A*a*b^7)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(2*A*a^8 - 4*A*a^6*b^2 + 2*A*a^4*b^4 + 2*((2*A + 3*C)*a^7*b - 6*B*a^6*b^2 + (5*A - 9*C)*a^5*b^3 + 15*B*a^4*b^4 - (19*A - 6*C)*a^3*b^5 - 9*B*a^2*b^6 + 12*A*a*b^7)*cos(d*x + c)^3 + (2*(2*A + 3*C)*a^8 - 9*B*a^7*b + 4*(A - 3*C)*a^6*b^2 + 18*B*a^5*b^3 - 2*(10*A - 3*C)*a^4*b^4 - 9*B*a^3*b^5 + 12*A*a^2*b^6)*cos(d*x + c)^2 + (3*B*a^8 - 4*A*a^7*b - 6*B*a^6*b^2 + 8*A*a^5*b^3 + 3*B*a^4*b^4 - 4*A*a^3*b^5)*cos(d*x + c))*sin(d*x + c))/((a^9*b - 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^4 + (a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c)^3), 1/12*(12*((3*C*a^4*b^3 - 4*B*a^3*b^4 + (5*A - 2*C)*a^2*b^5 + 3*B*a*b^6 - 4*A*b^7)*cos(d*x + c)^4 + (3*C*a^5*b^2 - 4*B*a^4*b^3 + (5*A - 2*C)*a^3*b^4 + 3*B*a^2*b^5 - 4*A*a*b^6)*cos(d*x + c)^3)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + 3*((B*a^7*b - 2*(A + 2*C)*a^6*b^2 + 4*B*a^5*b^3 - 4*(A - 2*C)*a^4*b^4 - 11*B*a^3*b^5 + 2*(7*A - 2*C)*a^2*b^6 + 6*B*a*b^7 - 8*A*b^8)*cos(d*x + c)^4 + (B*a^8 - 2*(A + 2*C)*a^7*b + 4*B*a^6*b^2 - 4*(A - 2*C)*a^5*b^3 - 11*B*a^4*b^4 + 2*(7*A - 2*C)*a^3*b^5 + 6*B*a^2*b^6 - 8*A*a*b^7)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((B*a^7*b - 2*(A + 2*C)*a^6*b^2 + 4*B*a^5*b^3 - 4*(A - 2*C)*a^4*b^4 - 11*B*a^3*b^5 + 2*(7*A - 2*C)*a^2*b^6 + 6*B*a*b^7 - 8*A*b^8)*cos(d*x + c)^4 + (B*a^8 - 2*(A + 2*C)*a^7*b + 4*B*a^6*b^2 - 4*(A - 2*C)*a^5*b^3 - 11*B*a^4*b^4 + 2*(7*A - 2*C)*a^3*b^5 + 6*B*a^2*b^6 - 8*A*a*b^7)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) + 2*(2*A*a^8 - 4*A*a^6*b^2 + 2*A*a^4*b^4 + 2*((2*A + 3*C)*a^7*b - 6*B*a^6*b^2 + (5*A - 9*C)*a^5*b^3 + 15*B*a^4*b^4 - (19*A - 6*C)*a^3*b^5 - 9*B*a^2*b^6 + 12*A*a*b^7)*cos(d*x + c)^3 + (2*(2*A + 3*C)*a^8 - 9*B*a^7*b + 4*(A - 3*C)*a^6*b^2 + 18*B*a^5*b^3 - 2*(10*A - 3*C)*a^4*b^4 - 9*B*a^3*b^5 + 12*A*a^2*b^6)*cos(d*x + c)^2 + (3*B*a^8 - 4*A*a^7*b - 6*B*a^6*b^2 + 8*A*a^5*b^3 + 3*B*a^4*b^4 - 4*A*a^3*b^5)*cos(d*x + c))*sin(d*x + c))/((a^9*b - 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^4 + (a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c)^3)]","B",0
994,1,2107,0,1.336224," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(12 \, C a^{8} b^{2} - 6 \, B a^{7} b^{3} + {\left(2 \, A - 35 \, C\right)} a^{6} b^{4} + 18 \, B a^{5} b^{5} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{4} b^{6} - 18 \, B a^{3} b^{7} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{2} b^{8} + 6 \, B a b^{9} - {\left(2 \, A + C\right)} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(12 \, C a^{9} b - 6 \, B a^{8} b^{2} + {\left(2 \, A - 35 \, C\right)} a^{7} b^{3} + 18 \, B a^{6} b^{4} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{5} b^{5} - 18 \, B a^{4} b^{6} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{3} b^{7} + 6 \, B a^{2} b^{8} - {\left(2 \, A + C\right)} a b^{9}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(12 \, C a^{10} - 6 \, B a^{9} b + {\left(2 \, A - 35 \, C\right)} a^{8} b^{2} + 18 \, B a^{7} b^{3} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{6} b^{4} - 18 \, B a^{5} b^{5} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{4} b^{6} + 6 \, B a^{3} b^{7} - {\left(2 \, A + C\right)} a^{2} b^{8}\right)} d x - {\left(12 \, C a^{9} - 6 \, B a^{8} b + {\left(2 \, A - 29 \, C\right)} a^{7} b^{2} + 15 \, B a^{6} b^{3} - 5 \, {\left(A - 4 \, C\right)} a^{5} b^{4} - 12 \, B a^{4} b^{5} + 6 \, A a^{3} b^{6} + {\left(12 \, C a^{7} b^{2} - 6 \, B a^{6} b^{3} + {\left(2 \, A - 29 \, C\right)} a^{5} b^{4} + 15 \, B a^{4} b^{5} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} - 12 \, B a^{2} b^{7} + 6 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, C a^{8} b - 6 \, B a^{7} b^{2} + {\left(2 \, A - 29 \, C\right)} a^{6} b^{3} + 15 \, B a^{5} b^{4} - 5 \, {\left(A - 4 \, C\right)} a^{4} b^{5} - 12 \, B a^{3} b^{6} + 6 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{9} b - 6 \, B a^{8} b^{2} + {\left(2 \, A - 33 \, C\right)} a^{7} b^{3} + 17 \, B a^{6} b^{4} - {\left(7 \, A - 27 \, C\right)} a^{5} b^{5} - 13 \, B a^{4} b^{6} + {\left(5 \, A - 6 \, C\right)} a^{3} b^{7} + 2 \, B a^{2} b^{8} - {\left(C a^{6} b^{4} - 3 \, C a^{4} b^{6} + 3 \, C a^{2} b^{8} - C b^{10}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, C a^{7} b^{3} - B a^{6} b^{4} - 6 \, C a^{5} b^{5} + 3 \, B a^{4} b^{6} + 6 \, C a^{3} b^{7} - 3 \, B a^{2} b^{8} - 2 \, C a b^{9} + B b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, C a^{8} b^{2} - 9 \, B a^{7} b^{3} + {\left(3 \, A - 50 \, C\right)} a^{6} b^{4} + 25 \, B a^{5} b^{5} - {\left(9 \, A - 43 \, C\right)} a^{4} b^{6} - 20 \, B a^{3} b^{7} + {\left(6 \, A - 11 \, C\right)} a^{2} b^{8} + 4 \, B 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 \, C a^{8} b^{2} - 6 \, B a^{7} b^{3} + {\left(2 \, A - 35 \, C\right)} a^{6} b^{4} + 18 \, B a^{5} b^{5} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{4} b^{6} - 18 \, B a^{3} b^{7} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{2} b^{8} + 6 \, B a b^{9} - {\left(2 \, A + C\right)} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, C a^{9} b - 6 \, B a^{8} b^{2} + {\left(2 \, A - 35 \, C\right)} a^{7} b^{3} + 18 \, B a^{6} b^{4} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{5} b^{5} - 18 \, B a^{4} b^{6} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{3} b^{7} + 6 \, B a^{2} b^{8} - {\left(2 \, A + C\right)} a b^{9}\right)} d x \cos\left(d x + c\right) + {\left(12 \, C a^{10} - 6 \, B a^{9} b + {\left(2 \, A - 35 \, C\right)} a^{8} b^{2} + 18 \, B a^{7} b^{3} - 3 \, {\left(2 \, A - 11 \, C\right)} a^{6} b^{4} - 18 \, B a^{5} b^{5} + 3 \, {\left(2 \, A - 3 \, C\right)} a^{4} b^{6} + 6 \, B a^{3} b^{7} - {\left(2 \, A + C\right)} a^{2} b^{8}\right)} d x - {\left(12 \, C a^{9} - 6 \, B a^{8} b + {\left(2 \, A - 29 \, C\right)} a^{7} b^{2} + 15 \, B a^{6} b^{3} - 5 \, {\left(A - 4 \, C\right)} a^{5} b^{4} - 12 \, B a^{4} b^{5} + 6 \, A a^{3} b^{6} + {\left(12 \, C a^{7} b^{2} - 6 \, B a^{6} b^{3} + {\left(2 \, A - 29 \, C\right)} a^{5} b^{4} + 15 \, B a^{4} b^{5} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} - 12 \, B a^{2} b^{7} + 6 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, C a^{8} b - 6 \, B a^{7} b^{2} + {\left(2 \, A - 29 \, C\right)} a^{6} b^{3} + 15 \, B a^{5} b^{4} - 5 \, {\left(A - 4 \, C\right)} a^{4} b^{5} - 12 \, B a^{3} b^{6} + 6 \, A a^{2} b^{7}\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 \, C a^{9} b - 6 \, B a^{8} b^{2} + {\left(2 \, A - 33 \, C\right)} a^{7} b^{3} + 17 \, B a^{6} b^{4} - {\left(7 \, A - 27 \, C\right)} a^{5} b^{5} - 13 \, B a^{4} b^{6} + {\left(5 \, A - 6 \, C\right)} a^{3} b^{7} + 2 \, B a^{2} b^{8} - {\left(C a^{6} b^{4} - 3 \, C a^{4} b^{6} + 3 \, C a^{2} b^{8} - C b^{10}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, C a^{7} b^{3} - B a^{6} b^{4} - 6 \, C a^{5} b^{5} + 3 \, B a^{4} b^{6} + 6 \, C a^{3} b^{7} - 3 \, B a^{2} b^{8} - 2 \, C a b^{9} + B b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, C a^{8} b^{2} - 9 \, B a^{7} b^{3} + {\left(3 \, A - 50 \, C\right)} a^{6} b^{4} + 25 \, B a^{5} b^{5} - {\left(9 \, A - 43 \, C\right)} a^{4} b^{6} - 20 \, B a^{3} b^{7} + {\left(6 \, A - 11 \, C\right)} a^{2} b^{8} + 4 \, B 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*C*a^8*b^2 - 6*B*a^7*b^3 + (2*A - 35*C)*a^6*b^4 + 18*B*a^5*b^5 - 3*(2*A - 11*C)*a^4*b^6 - 18*B*a^3*b^7 + 3*(2*A - 3*C)*a^2*b^8 + 6*B*a*b^9 - (2*A + C)*b^10)*d*x*cos(d*x + c)^2 + 4*(12*C*a^9*b - 6*B*a^8*b^2 + (2*A - 35*C)*a^7*b^3 + 18*B*a^6*b^4 - 3*(2*A - 11*C)*a^5*b^5 - 18*B*a^4*b^6 + 3*(2*A - 3*C)*a^3*b^7 + 6*B*a^2*b^8 - (2*A + C)*a*b^9)*d*x*cos(d*x + c) + 2*(12*C*a^10 - 6*B*a^9*b + (2*A - 35*C)*a^8*b^2 + 18*B*a^7*b^3 - 3*(2*A - 11*C)*a^6*b^4 - 18*B*a^5*b^5 + 3*(2*A - 3*C)*a^4*b^6 + 6*B*a^3*b^7 - (2*A + C)*a^2*b^8)*d*x - (12*C*a^9 - 6*B*a^8*b + (2*A - 29*C)*a^7*b^2 + 15*B*a^6*b^3 - 5*(A - 4*C)*a^5*b^4 - 12*B*a^4*b^5 + 6*A*a^3*b^6 + (12*C*a^7*b^2 - 6*B*a^6*b^3 + (2*A - 29*C)*a^5*b^4 + 15*B*a^4*b^5 - 5*(A - 4*C)*a^3*b^6 - 12*B*a^2*b^7 + 6*A*a*b^8)*cos(d*x + c)^2 + 2*(12*C*a^8*b - 6*B*a^7*b^2 + (2*A - 29*C)*a^6*b^3 + 15*B*a^5*b^4 - 5*(A - 4*C)*a^4*b^5 - 12*B*a^3*b^6 + 6*A*a^2*b^7)*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*C*a^9*b - 6*B*a^8*b^2 + (2*A - 33*C)*a^7*b^3 + 17*B*a^6*b^4 - (7*A - 27*C)*a^5*b^5 - 13*B*a^4*b^6 + (5*A - 6*C)*a^3*b^7 + 2*B*a^2*b^8 - (C*a^6*b^4 - 3*C*a^4*b^6 + 3*C*a^2*b^8 - C*b^10)*cos(d*x + c)^3 + 2*(2*C*a^7*b^3 - B*a^6*b^4 - 6*C*a^5*b^5 + 3*B*a^4*b^6 + 6*C*a^3*b^7 - 3*B*a^2*b^8 - 2*C*a*b^9 + B*b^10)*cos(d*x + c)^2 + (18*C*a^8*b^2 - 9*B*a^7*b^3 + (3*A - 50*C)*a^6*b^4 + 25*B*a^5*b^5 - (9*A - 43*C)*a^4*b^6 - 20*B*a^3*b^7 + (6*A - 11*C)*a^2*b^8 + 4*B*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*C*a^8*b^2 - 6*B*a^7*b^3 + (2*A - 35*C)*a^6*b^4 + 18*B*a^5*b^5 - 3*(2*A - 11*C)*a^4*b^6 - 18*B*a^3*b^7 + 3*(2*A - 3*C)*a^2*b^8 + 6*B*a*b^9 - (2*A + C)*b^10)*d*x*cos(d*x + c)^2 + 2*(12*C*a^9*b - 6*B*a^8*b^2 + (2*A - 35*C)*a^7*b^3 + 18*B*a^6*b^4 - 3*(2*A - 11*C)*a^5*b^5 - 18*B*a^4*b^6 + 3*(2*A - 3*C)*a^3*b^7 + 6*B*a^2*b^8 - (2*A + C)*a*b^9)*d*x*cos(d*x + c) + (12*C*a^10 - 6*B*a^9*b + (2*A - 35*C)*a^8*b^2 + 18*B*a^7*b^3 - 3*(2*A - 11*C)*a^6*b^4 - 18*B*a^5*b^5 + 3*(2*A - 3*C)*a^4*b^6 + 6*B*a^3*b^7 - (2*A + C)*a^2*b^8)*d*x - (12*C*a^9 - 6*B*a^8*b + (2*A - 29*C)*a^7*b^2 + 15*B*a^6*b^3 - 5*(A - 4*C)*a^5*b^4 - 12*B*a^4*b^5 + 6*A*a^3*b^6 + (12*C*a^7*b^2 - 6*B*a^6*b^3 + (2*A - 29*C)*a^5*b^4 + 15*B*a^4*b^5 - 5*(A - 4*C)*a^3*b^6 - 12*B*a^2*b^7 + 6*A*a*b^8)*cos(d*x + c)^2 + 2*(12*C*a^8*b - 6*B*a^7*b^2 + (2*A - 29*C)*a^6*b^3 + 15*B*a^5*b^4 - 5*(A - 4*C)*a^4*b^5 - 12*B*a^3*b^6 + 6*A*a^2*b^7)*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*C*a^9*b - 6*B*a^8*b^2 + (2*A - 33*C)*a^7*b^3 + 17*B*a^6*b^4 - (7*A - 27*C)*a^5*b^5 - 13*B*a^4*b^6 + (5*A - 6*C)*a^3*b^7 + 2*B*a^2*b^8 - (C*a^6*b^4 - 3*C*a^4*b^6 + 3*C*a^2*b^8 - C*b^10)*cos(d*x + c)^3 + 2*(2*C*a^7*b^3 - B*a^6*b^4 - 6*C*a^5*b^5 + 3*B*a^4*b^6 + 6*C*a^3*b^7 - 3*B*a^2*b^8 - 2*C*a*b^9 + B*b^10)*cos(d*x + c)^2 + (18*C*a^8*b^2 - 9*B*a^7*b^3 + (3*A - 50*C)*a^6*b^4 + 25*B*a^5*b^5 - (9*A - 43*C)*a^4*b^6 - 20*B*a^3*b^7 + (6*A - 11*C)*a^2*b^8 + 4*B*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
995,1,1666,0,1.277661," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(3 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(3 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} d x + {\left(6 \, C a^{8} - 2 \, B a^{7} b - 15 \, C a^{6} b^{2} + 5 \, B a^{5} b^{3} + {\left(A + 12 \, C\right)} a^{4} b^{4} - 6 \, B a^{3} b^{5} + 2 \, A a^{2} b^{6} + {\left(6 \, C a^{6} b^{2} - 2 \, B a^{5} b^{3} - 15 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + {\left(A + 12 \, C\right)} a^{2} b^{6} - 6 \, B a b^{7} + 2 \, A b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, C a^{7} b - 2 \, B a^{6} b^{2} - 15 \, C a^{5} b^{3} + 5 \, B a^{4} b^{4} + {\left(A + 12 \, C\right)} a^{3} b^{5} - 6 \, B a^{2} b^{6} + 2 \, A a b^{7}\right)} \cos\left(d x + c\right)\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 \, C a^{8} b - 2 \, B a^{7} b^{2} - 17 \, C a^{6} b^{3} + 7 \, B a^{5} b^{4} - {\left(3 \, A - 13 \, C\right)} a^{4} b^{5} - 5 \, B a^{3} b^{6} + {\left(3 \, A - 2 \, C\right)} a^{2} b^{7} + 2 \, {\left(C a^{6} b^{3} - 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} - C b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} + {\left(A - 25 \, C\right)} a^{5} b^{4} + 9 \, B a^{4} b^{5} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} - 6 \, B a^{2} b^{7} + 4 \, {\left(A - C\right)} a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{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 \, C a^{7} b^{2} - B a^{6} b^{3} - 9 \, C a^{5} b^{4} + 3 \, B a^{4} b^{5} + 9 \, C a^{3} b^{6} - 3 \, B a^{2} b^{7} - 3 \, C a b^{8} + B b^{9}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(3 \, C a^{8} b - B a^{7} b^{2} - 9 \, C a^{6} b^{3} + 3 \, B a^{5} b^{4} + 9 \, C a^{4} b^{5} - 3 \, B a^{3} b^{6} - 3 \, C a^{2} b^{7} + B a b^{8}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(3 \, C a^{9} - B a^{8} b - 9 \, C a^{7} b^{2} + 3 \, B a^{6} b^{3} + 9 \, C a^{5} b^{4} - 3 \, B a^{4} b^{5} - 3 \, C a^{3} b^{6} + B a^{2} b^{7}\right)} d x - {\left(6 \, C a^{8} - 2 \, B a^{7} b - 15 \, C a^{6} b^{2} + 5 \, B a^{5} b^{3} + {\left(A + 12 \, C\right)} a^{4} b^{4} - 6 \, B a^{3} b^{5} + 2 \, A a^{2} b^{6} + {\left(6 \, C a^{6} b^{2} - 2 \, B a^{5} b^{3} - 15 \, C a^{4} b^{4} + 5 \, B a^{3} b^{5} + {\left(A + 12 \, C\right)} a^{2} b^{6} - 6 \, B a b^{7} + 2 \, A b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, C a^{7} b - 2 \, B a^{6} b^{2} - 15 \, C a^{5} b^{3} + 5 \, B a^{4} b^{4} + {\left(A + 12 \, C\right)} a^{3} b^{5} - 6 \, B a^{2} b^{6} + 2 \, A a b^{7}\right)} \cos\left(d x + c\right)\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 \, C a^{8} b - 2 \, B a^{7} b^{2} - 17 \, C a^{6} b^{3} + 7 \, B a^{5} b^{4} - {\left(3 \, A - 13 \, C\right)} a^{4} b^{5} - 5 \, B a^{3} b^{6} + {\left(3 \, A - 2 \, C\right)} a^{2} b^{7} + 2 \, {\left(C a^{6} b^{3} - 3 \, C a^{4} b^{5} + 3 \, C a^{2} b^{7} - C b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, C a^{7} b^{2} - 3 \, B a^{6} b^{3} + {\left(A - 25 \, C\right)} a^{5} b^{4} + 9 \, B a^{4} b^{5} - 5 \, {\left(A - 4 \, C\right)} a^{3} b^{6} - 6 \, B a^{2} b^{7} + 4 \, {\left(A - C\right)} a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*d*x*cos(d*x + c)^2 + 8*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*d*x*cos(d*x + c) + 4*(3*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*d*x + (6*C*a^8 - 2*B*a^7*b - 15*C*a^6*b^2 + 5*B*a^5*b^3 + (A + 12*C)*a^4*b^4 - 6*B*a^3*b^5 + 2*A*a^2*b^6 + (6*C*a^6*b^2 - 2*B*a^5*b^3 - 15*C*a^4*b^4 + 5*B*a^3*b^5 + (A + 12*C)*a^2*b^6 - 6*B*a*b^7 + 2*A*b^8)*cos(d*x + c)^2 + 2*(6*C*a^7*b - 2*B*a^6*b^2 - 15*C*a^5*b^3 + 5*B*a^4*b^4 + (A + 12*C)*a^3*b^5 - 6*B*a^2*b^6 + 2*A*a*b^7)*cos(d*x + c))*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*C*a^8*b - 2*B*a^7*b^2 - 17*C*a^6*b^3 + 7*B*a^5*b^4 - (3*A - 13*C)*a^4*b^5 - 5*B*a^3*b^6 + (3*A - 2*C)*a^2*b^7 + 2*(C*a^6*b^3 - 3*C*a^4*b^5 + 3*C*a^2*b^7 - C*b^9)*cos(d*x + c)^2 + (9*C*a^7*b^2 - 3*B*a^6*b^3 + (A - 25*C)*a^5*b^4 + 9*B*a^4*b^5 - 5*(A - 4*C)*a^3*b^6 - 6*B*a^2*b^7 + 4*(A - C)*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^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*C*a^7*b^2 - B*a^6*b^3 - 9*C*a^5*b^4 + 3*B*a^4*b^5 + 9*C*a^3*b^6 - 3*B*a^2*b^7 - 3*C*a*b^8 + B*b^9)*d*x*cos(d*x + c)^2 + 4*(3*C*a^8*b - B*a^7*b^2 - 9*C*a^6*b^3 + 3*B*a^5*b^4 + 9*C*a^4*b^5 - 3*B*a^3*b^6 - 3*C*a^2*b^7 + B*a*b^8)*d*x*cos(d*x + c) + 2*(3*C*a^9 - B*a^8*b - 9*C*a^7*b^2 + 3*B*a^6*b^3 + 9*C*a^5*b^4 - 3*B*a^4*b^5 - 3*C*a^3*b^6 + B*a^2*b^7)*d*x - (6*C*a^8 - 2*B*a^7*b - 15*C*a^6*b^2 + 5*B*a^5*b^3 + (A + 12*C)*a^4*b^4 - 6*B*a^3*b^5 + 2*A*a^2*b^6 + (6*C*a^6*b^2 - 2*B*a^5*b^3 - 15*C*a^4*b^4 + 5*B*a^3*b^5 + (A + 12*C)*a^2*b^6 - 6*B*a*b^7 + 2*A*b^8)*cos(d*x + c)^2 + 2*(6*C*a^7*b - 2*B*a^6*b^2 - 15*C*a^5*b^3 + 5*B*a^4*b^4 + (A + 12*C)*a^3*b^5 - 6*B*a^2*b^6 + 2*A*a*b^7)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*C*a^8*b - 2*B*a^7*b^2 - 17*C*a^6*b^3 + 7*B*a^5*b^4 - (3*A - 13*C)*a^4*b^5 - 5*B*a^3*b^6 + (3*A - 2*C)*a^2*b^7 + 2*(C*a^6*b^3 - 3*C*a^4*b^5 + 3*C*a^2*b^7 - C*b^9)*cos(d*x + c)^2 + (9*C*a^7*b^2 - 3*B*a^6*b^3 + (A - 25*C)*a^5*b^4 + 9*B*a^4*b^5 - 5*(A - 4*C)*a^3*b^6 - 6*B*a^2*b^7 + 4*(A - C)*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^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
996,1,1234,0,1.296798," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} d x + {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} - B a^{4} b^{3} + 3 \, {\left(A + 2 \, C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + {\left(2 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} - B a^{2} b^{5} + 3 \, {\left(A + 2 \, C\right)} a b^{6} - 2 \, B b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} - B a^{3} b^{4} + 3 \, {\left(A + 2 \, C\right)} a^{2} b^{5} - 2 \, B a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{7} b - {\left(2 \, A + 7 \, C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} + {\left(A + 5 \, C\right)} a^{3} b^{5} - 3 \, B a^{2} b^{6} + A a b^{7} + {\left(3 \, C a^{6} b^{2} - B a^{5} b^{3} - {\left(A + 9 \, C\right)} a^{4} b^{4} + 5 \, B a^{3} b^{5} - {\left(A - 6 \, C\right)} a^{2} b^{6} - 4 \, B a b^{7} + 2 \, A b^{8}\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(C a^{6} b^{2} - 3 \, C a^{4} b^{4} + 3 \, C a^{2} b^{6} - C b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(C a^{7} b - 3 \, C a^{5} b^{3} + 3 \, C a^{3} b^{5} - C a b^{7}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(C a^{8} - 3 \, C a^{6} b^{2} + 3 \, C a^{4} b^{4} - C a^{2} b^{6}\right)} d x - {\left(2 \, C a^{7} - 5 \, C a^{5} b^{2} - B a^{4} b^{3} + 3 \, {\left(A + 2 \, C\right)} a^{3} b^{4} - 2 \, B a^{2} b^{5} + {\left(2 \, C a^{5} b^{2} - 5 \, C a^{3} b^{4} - B a^{2} b^{5} + 3 \, {\left(A + 2 \, C\right)} a b^{6} - 2 \, B b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{6} b - 5 \, C a^{4} b^{3} - B a^{3} b^{4} + 3 \, {\left(A + 2 \, C\right)} a^{2} b^{5} - 2 \, B a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, C a^{7} b - {\left(2 \, A + 7 \, C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} + {\left(A + 5 \, C\right)} a^{3} b^{5} - 3 \, B a^{2} b^{6} + A a b^{7} + {\left(3 \, C a^{6} b^{2} - B a^{5} b^{3} - {\left(A + 9 \, C\right)} a^{4} b^{4} + 5 \, B a^{3} b^{5} - {\left(A - 6 \, C\right)} a^{2} b^{6} - 4 \, B a b^{7} + 2 \, A b^{8}\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*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8)*d*x*cos(d*x + c)^2 + 8*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*d*x*cos(d*x + c) + 4*(C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*d*x + (2*C*a^7 - 5*C*a^5*b^2 - B*a^4*b^3 + 3*(A + 2*C)*a^3*b^4 - 2*B*a^2*b^5 + (2*C*a^5*b^2 - 5*C*a^3*b^4 - B*a^2*b^5 + 3*(A + 2*C)*a*b^6 - 2*B*b^7)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 - B*a^3*b^4 + 3*(A + 2*C)*a^2*b^5 - 2*B*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*C*a^7*b - (2*A + 7*C)*a^5*b^3 + 3*B*a^4*b^4 + (A + 5*C)*a^3*b^5 - 3*B*a^2*b^6 + A*a*b^7 + (3*C*a^6*b^2 - B*a^5*b^3 - (A + 9*C)*a^4*b^4 + 5*B*a^3*b^5 - (A - 6*C)*a^2*b^6 - 4*B*a*b^7 + 2*A*b^8)*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*(C*a^6*b^2 - 3*C*a^4*b^4 + 3*C*a^2*b^6 - C*b^8)*d*x*cos(d*x + c)^2 + 4*(C*a^7*b - 3*C*a^5*b^3 + 3*C*a^3*b^5 - C*a*b^7)*d*x*cos(d*x + c) + 2*(C*a^8 - 3*C*a^6*b^2 + 3*C*a^4*b^4 - C*a^2*b^6)*d*x - (2*C*a^7 - 5*C*a^5*b^2 - B*a^4*b^3 + 3*(A + 2*C)*a^3*b^4 - 2*B*a^2*b^5 + (2*C*a^5*b^2 - 5*C*a^3*b^4 - B*a^2*b^5 + 3*(A + 2*C)*a*b^6 - 2*B*b^7)*cos(d*x + c)^2 + 2*(2*C*a^6*b - 5*C*a^4*b^3 - B*a^3*b^4 + 3*(A + 2*C)*a^2*b^5 - 2*B*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*C*a^7*b - (2*A + 7*C)*a^5*b^3 + 3*B*a^4*b^4 + (A + 5*C)*a^3*b^5 - 3*B*a^2*b^6 + A*a*b^7 + (3*C*a^6*b^2 - B*a^5*b^3 - (A + 9*C)*a^4*b^4 + 5*B*a^3*b^5 - (A - 6*C)*a^2*b^6 - 4*B*a*b^7 + 2*A*b^8)*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
997,1,838,0,0.555773," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, A + C\right)} a^{4} - 3 \, B a^{3} b + {\left(A + 2 \, C\right)} a^{2} b^{2} + {\left({\left(2 \, A + C\right)} a^{2} b^{2} - 3 \, B a b^{3} + {\left(A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, A + C\right)} a^{3} b - 3 \, B a^{2} b^{2} + {\left(A + 2 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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} - {\left(4 \, A + 3 \, C\right)} a^{4} b - B a^{3} b^{2} + {\left(5 \, A + 3 \, C\right)} a^{2} b^{3} - B a b^{4} - A b^{5} + {\left(C a^{5} + B a^{4} b - {\left(3 \, A + 5 \, C\right)} a^{3} b^{2} + B a^{2} b^{3} + {\left(3 \, A + 4 \, C\right)} a b^{4} - 2 \, B b^{5}\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({\left(2 \, A + C\right)} a^{4} - 3 \, B a^{3} b + {\left(A + 2 \, C\right)} a^{2} b^{2} + {\left({\left(2 \, A + C\right)} a^{2} b^{2} - 3 \, B a b^{3} + {\left(A + 2 \, C\right)} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, A + C\right)} a^{3} b - 3 \, B a^{2} b^{2} + {\left(A + 2 \, C\right)} a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{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} - {\left(4 \, A + 3 \, C\right)} a^{4} b - B a^{3} b^{2} + {\left(5 \, A + 3 \, C\right)} a^{2} b^{3} - B a b^{4} - A b^{5} + {\left(C a^{5} + B a^{4} b - {\left(3 \, A + 5 \, C\right)} a^{3} b^{2} + B a^{2} b^{3} + {\left(3 \, A + 4 \, C\right)} a b^{4} - 2 \, B b^{5}\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 + C)*a^4 - 3*B*a^3*b + (A + 2*C)*a^2*b^2 + ((2*A + C)*a^2*b^2 - 3*B*a*b^3 + (A + 2*C)*b^4)*cos(d*x + c)^2 + 2*((2*A + C)*a^3*b - 3*B*a^2*b^2 + (A + 2*C)*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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 + 3*C)*a^4*b - B*a^3*b^2 + (5*A + 3*C)*a^2*b^3 - B*a*b^4 - A*b^5 + (C*a^5 + B*a^4*b - (3*A + 5*C)*a^3*b^2 + B*a^2*b^3 + (3*A + 4*C)*a*b^4 - 2*B*b^5)*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 + C)*a^4 - 3*B*a^3*b + (A + 2*C)*a^2*b^2 + ((2*A + C)*a^2*b^2 - 3*B*a*b^3 + (A + 2*C)*b^4)*cos(d*x + c)^2 + 2*((2*A + C)*a^3*b - 3*B*a^2*b^2 + (A + 2*C)*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (2*B*a^5 - (4*A + 3*C)*a^4*b - B*a^3*b^2 + (5*A + 3*C)*a^2*b^3 - B*a*b^4 - A*b^5 + (C*a^5 + B*a^4*b - (3*A + 5*C)*a^3*b^2 + B*a^2*b^3 + (3*A + 4*C)*a*b^4 - 2*B*b^5)*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
998,1,1485,0,47.701320," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a^{7} - 3 \, {\left(2 \, A + C\right)} a^{6} b + B a^{5} b^{2} + 5 \, A a^{4} b^{3} - 2 \, A a^{2} b^{5} + {\left(2 \, B a^{5} b^{2} - 3 \, {\left(2 \, A + C\right)} a^{4} b^{3} + B a^{3} b^{4} + 5 \, A a^{2} b^{5} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{6} b - 3 \, {\left(2 \, A + C\right)} a^{5} b^{2} + B a^{4} b^{3} + 5 \, A a^{3} b^{4} - 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(2 \, C a^{8} - 4 \, B a^{7} b + {\left(6 \, A - C\right)} a^{6} b^{2} + 5 \, B a^{5} b^{3} - {\left(9 \, A + C\right)} a^{4} b^{4} - B a^{3} b^{5} + 3 \, A a^{2} b^{6} + {\left(C a^{7} b - 3 \, B a^{6} b^{2} + {\left(5 \, A + C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} - {\left(7 \, A + 2 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7}\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} - 3 \, {\left(2 \, A + C\right)} a^{6} b + B a^{5} b^{2} + 5 \, A a^{4} b^{3} - 2 \, A a^{2} b^{5} + {\left(2 \, B a^{5} b^{2} - 3 \, {\left(2 \, A + C\right)} a^{4} b^{3} + B a^{3} b^{4} + 5 \, A a^{2} b^{5} - 2 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B a^{6} b - 3 \, {\left(2 \, A + C\right)} a^{5} b^{2} + B a^{4} b^{3} + 5 \, A a^{3} b^{4} - 2 \, A a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{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(2 \, C a^{8} - 4 \, B a^{7} b + {\left(6 \, A - C\right)} a^{6} b^{2} + 5 \, B a^{5} b^{3} - {\left(9 \, A + C\right)} a^{4} b^{4} - B a^{3} b^{5} + 3 \, A a^{2} b^{6} + {\left(C a^{7} b - 3 \, B a^{6} b^{2} + {\left(5 \, A + C\right)} a^{5} b^{3} + 3 \, B a^{4} b^{4} - {\left(7 \, A + 2 \, C\right)} a^{3} b^{5} + 2 \, A a b^{7}\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 - 3*(2*A + C)*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 - 3*(2*A + C)*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 - 3*(2*A + C)*a^5*b^2 + B*a^4*b^3 + 5*A*a^3*b^4 - 2*A*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*(2*C*a^8 - 4*B*a^7*b + (6*A - C)*a^6*b^2 + 5*B*a^5*b^3 - (9*A + C)*a^4*b^4 - B*a^3*b^5 + 3*A*a^2*b^6 + (C*a^7*b - 3*B*a^6*b^2 + (5*A + C)*a^5*b^3 + 3*B*a^4*b^4 - (7*A + 2*C)*a^3*b^5 + 2*A*a*b^7)*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 - 3*(2*A + C)*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 - 3*(2*A + C)*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 - 3*(2*A + C)*a^5*b^2 + B*a^4*b^3 + 5*A*a^3*b^4 - 2*A*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(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) + (2*C*a^8 - 4*B*a^7*b + (6*A - C)*a^6*b^2 + 5*B*a^5*b^3 - (9*A + C)*a^4*b^4 - B*a^3*b^5 + 3*A*a^2*b^6 + (C*a^7*b - 3*B*a^6*b^2 + (5*A + C)*a^5*b^3 + 3*B*a^4*b^4 - (7*A + 2*C)*a^3*b^5 + 2*A*a*b^7)*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
999,1,2213,0,123.361218," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, C a^{6} b^{2} - 6 \, B a^{5} b^{3} + {\left(12 \, A + C\right)} a^{4} b^{4} + 5 \, B a^{3} b^{5} - 15 \, A a^{2} b^{6} - 2 \, B a b^{7} + 6 \, A b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, C a^{7} b - 6 \, B a^{6} b^{2} + {\left(12 \, A + C\right)} a^{5} b^{3} + 5 \, B a^{4} b^{4} - 15 \, A a^{3} b^{5} - 2 \, B a^{2} b^{6} + 6 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{8} - 6 \, B a^{7} b + {\left(12 \, A + C\right)} a^{6} b^{2} + 5 \, B a^{5} b^{3} - 15 \, A a^{4} b^{4} - 2 \, B a^{3} b^{5} + 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\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({\left(2 \, A - 3 \, C\right)} a^{7} b^{2} + 5 \, B a^{6} b^{3} - {\left(13 \, A - 3 \, C\right)} a^{5} b^{4} - 7 \, B a^{4} b^{5} + 17 \, A a^{3} b^{6} + 2 \, B a^{2} b^{7} - 6 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, {\left(A - C\right)} a^{8} b + 6 \, B a^{7} b^{2} - 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} - 9 \, B a^{5} b^{4} + {\left(25 \, A - C\right)} a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{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(2 \, C a^{6} b^{2} - 6 \, B a^{5} b^{3} + {\left(12 \, A + C\right)} a^{4} b^{4} + 5 \, B a^{3} b^{5} - 15 \, A a^{2} b^{6} - 2 \, B a b^{7} + 6 \, A b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, C a^{7} b - 6 \, B a^{6} b^{2} + {\left(12 \, A + C\right)} a^{5} b^{3} + 5 \, B a^{4} b^{4} - 15 \, A a^{3} b^{5} - 2 \, B a^{2} b^{6} + 6 \, A a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, C a^{8} - 6 \, B a^{7} b + {\left(12 \, A + C\right)} a^{6} b^{2} + 5 \, B a^{5} b^{3} - 15 \, A a^{4} b^{4} - 2 \, B a^{3} b^{5} + 6 \, A a^{2} b^{6}\right)} \cos\left(d x + c\right)\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({\left(2 \, A - 3 \, C\right)} a^{7} b^{2} + 5 \, B a^{6} b^{3} - {\left(13 \, A - 3 \, C\right)} a^{5} b^{4} - 7 \, B a^{4} b^{5} + 17 \, A a^{3} b^{6} + 2 \, B a^{2} b^{7} - 6 \, A a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, {\left(A - C\right)} a^{8} b + 6 \, B a^{7} b^{2} - 5 \, {\left(4 \, A - C\right)} a^{6} b^{3} - 9 \, B a^{5} b^{4} + {\left(25 \, A - C\right)} a^{4} b^{5} + 3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{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*(((2*C*a^6*b^2 - 6*B*a^5*b^3 + (12*A + C)*a^4*b^4 + 5*B*a^3*b^5 - 15*A*a^2*b^6 - 2*B*a*b^7 + 6*A*b^8)*cos(d*x + c)^3 + 2*(2*C*a^7*b - 6*B*a^6*b^2 + (12*A + C)*a^5*b^3 + 5*B*a^4*b^4 - 15*A*a^3*b^5 - 2*B*a^2*b^6 + 6*A*a*b^7)*cos(d*x + c)^2 + (2*C*a^8 - 6*B*a^7*b + (12*A + C)*a^6*b^2 + 5*B*a^5*b^3 - 15*A*a^4*b^4 - 2*B*a^3*b^5 + 6*A*a^2*b^6)*cos(d*x + c))*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 - 3*C)*a^7*b^2 + 5*B*a^6*b^3 - (13*A - 3*C)*a^5*b^4 - 7*B*a^4*b^5 + 17*A*a^3*b^6 + 2*B*a^2*b^7 - 6*A*a*b^8)*cos(d*x + c)^2 + (4*(A - C)*a^8*b + 6*B*a^7*b^2 - 5*(4*A - C)*a^6*b^3 - 9*B*a^5*b^4 + (25*A - C)*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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*(((2*C*a^6*b^2 - 6*B*a^5*b^3 + (12*A + C)*a^4*b^4 + 5*B*a^3*b^5 - 15*A*a^2*b^6 - 2*B*a*b^7 + 6*A*b^8)*cos(d*x + c)^3 + 2*(2*C*a^7*b - 6*B*a^6*b^2 + (12*A + C)*a^5*b^3 + 5*B*a^4*b^4 - 15*A*a^3*b^5 - 2*B*a^2*b^6 + 6*A*a*b^7)*cos(d*x + c)^2 + (2*C*a^8 - 6*B*a^7*b + (12*A + C)*a^6*b^2 + 5*B*a^5*b^3 - 15*A*a^4*b^4 - 2*B*a^3*b^5 + 6*A*a^2*b^6)*cos(d*x + c))*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 - 3*C)*a^7*b^2 + 5*B*a^6*b^3 - (13*A - 3*C)*a^5*b^4 - 7*B*a^4*b^5 + 17*A*a^3*b^6 + 2*B*a^2*b^7 - 6*A*a*b^8)*cos(d*x + c)^2 + (4*(A - C)*a^8*b + 6*B*a^7*b^2 - 5*(4*A - C)*a^6*b^3 - 9*B*a^5*b^4 + (25*A - C)*a^4*b^5 + 3*B*a^3*b^6 - 9*A*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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
1000,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1001,1,3385,0,2.427359," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(20 \, C a^{10} b^{3} - 8 \, B a^{9} b^{4} + {\left(2 \, A - 79 \, C\right)} a^{8} b^{5} + 32 \, B a^{7} b^{6} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{6} b^{7} - 48 \, B a^{5} b^{8} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{4} b^{9} + 32 \, B a^{3} b^{10} - 8 \, {\left(A - 2 \, C\right)} a^{2} b^{11} - 8 \, B a b^{12} + {\left(2 \, A + C\right)} b^{13}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(20 \, C a^{11} b^{2} - 8 \, B a^{10} b^{3} + {\left(2 \, A - 79 \, C\right)} a^{9} b^{4} + 32 \, B a^{8} b^{5} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{7} b^{6} - 48 \, B a^{6} b^{7} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{5} b^{8} + 32 \, B a^{4} b^{9} - 8 \, {\left(A - 2 \, C\right)} a^{3} b^{10} - 8 \, B a^{2} b^{11} + {\left(2 \, A + C\right)} a b^{12}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(20 \, C a^{12} b - 8 \, B a^{11} b^{2} + {\left(2 \, A - 79 \, C\right)} a^{10} b^{3} + 32 \, B a^{9} b^{4} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{8} b^{5} - 48 \, B a^{7} b^{6} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{6} b^{7} + 32 \, B a^{5} b^{8} - 8 \, {\left(A - 2 \, C\right)} a^{4} b^{9} - 8 \, B a^{3} b^{10} + {\left(2 \, A + C\right)} a^{2} b^{11}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(20 \, C a^{13} - 8 \, B a^{12} b + {\left(2 \, A - 79 \, C\right)} a^{11} b^{2} + 32 \, B a^{10} b^{3} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{9} b^{4} - 48 \, B a^{8} b^{5} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{7} b^{6} + 32 \, B a^{6} b^{7} - 8 \, {\left(A - 2 \, C\right)} a^{5} b^{8} - 8 \, B a^{4} b^{9} + {\left(2 \, A + C\right)} a^{3} b^{10}\right)} d x - 3 \, {\left(20 \, C a^{12} - 8 \, B a^{11} b + {\left(2 \, A - 69 \, C\right)} a^{10} b^{2} + 28 \, B a^{9} b^{3} - 7 \, {\left(A - 12 \, C\right)} a^{8} b^{4} - 35 \, B a^{7} b^{5} + 8 \, {\left(A - 5 \, C\right)} a^{6} b^{6} + 20 \, B a^{5} b^{7} - 8 \, A a^{4} b^{8} + {\left(20 \, C a^{9} b^{3} - 8 \, B a^{8} b^{4} + {\left(2 \, A - 69 \, C\right)} a^{7} b^{5} + 28 \, B a^{6} b^{6} - 7 \, {\left(A - 12 \, C\right)} a^{5} b^{7} - 35 \, B a^{4} b^{8} + 8 \, {\left(A - 5 \, C\right)} a^{3} b^{9} + 20 \, B a^{2} b^{10} - 8 \, A a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, C a^{10} b^{2} - 8 \, B a^{9} b^{3} + {\left(2 \, A - 69 \, C\right)} a^{8} b^{4} + 28 \, B a^{7} b^{5} - 7 \, {\left(A - 12 \, C\right)} a^{6} b^{6} - 35 \, B a^{5} b^{7} + 8 \, {\left(A - 5 \, C\right)} a^{4} b^{8} + 20 \, B a^{3} b^{9} - 8 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, C a^{11} b - 8 \, B a^{10} b^{2} + {\left(2 \, A - 69 \, C\right)} a^{9} b^{3} + 28 \, B a^{8} b^{4} - 7 \, {\left(A - 12 \, C\right)} a^{7} b^{5} - 35 \, B a^{6} b^{6} + 8 \, {\left(A - 5 \, C\right)} a^{5} b^{7} + 20 \, B a^{4} b^{8} - 8 \, A a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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(60 \, C a^{12} b - 24 \, B a^{11} b^{2} + {\left(6 \, A - 227 \, C\right)} a^{10} b^{3} + 92 \, B a^{9} b^{4} - {\left(23 \, A - 313 \, C\right)} a^{8} b^{5} - 133 \, B a^{7} b^{6} + {\left(43 \, A - 170 \, C\right)} a^{6} b^{7} + 71 \, B a^{5} b^{8} - 2 \, {\left(13 \, A - 12 \, C\right)} a^{4} b^{9} - 6 \, B a^{3} b^{10} - 3 \, {\left(C a^{8} b^{5} - 4 \, C a^{6} b^{7} + 6 \, C a^{4} b^{9} - 4 \, C a^{2} b^{11} + C b^{13}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, C a^{9} b^{4} - 2 \, B a^{8} b^{5} - 20 \, C a^{7} b^{6} + 8 \, B a^{6} b^{7} + 30 \, C a^{5} b^{8} - 12 \, B a^{4} b^{9} - 20 \, C a^{3} b^{10} + 8 \, B a^{2} b^{11} + 5 \, C a b^{12} - 2 \, B b^{13}\right)} \cos\left(d x + c\right)^{3} + {\left(110 \, C a^{10} b^{3} - 44 \, B a^{9} b^{4} + {\left(11 \, A - 421 \, C\right)} a^{8} b^{5} + 169 \, B a^{7} b^{6} - {\left(43 \, A - 590 \, C\right)} a^{6} b^{7} - 239 \, B a^{5} b^{8} + 2 \, {\left(34 \, A - 171 \, C\right)} a^{4} b^{9} + 132 \, B a^{3} b^{10} - 9 \, {\left(4 \, A - 7 \, C\right)} a^{2} b^{11} - 18 \, B a b^{12}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(50 \, C a^{11} b^{2} - 20 \, B a^{10} b^{3} + 5 \, {\left(A - 38 \, C\right)} a^{9} b^{4} + 77 \, B a^{8} b^{5} - {\left(20 \, A - 263 \, C\right)} a^{7} b^{6} - 110 \, B a^{6} b^{7} + {\left(35 \, A - 146 \, C\right)} a^{5} b^{8} + 59 \, B a^{4} b^{9} - {\left(20 \, A - 23 \, C\right)} a^{3} b^{10} - 6 \, B a^{2} b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{9} - 4 \, a^{6} b^{11} + 6 \, a^{4} b^{13} - 4 \, a^{2} b^{15} + b^{17}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{8} - 4 \, a^{7} b^{10} + 6 \, a^{5} b^{12} - 4 \, a^{3} b^{14} + a b^{16}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{7} - 4 \, a^{8} b^{9} + 6 \, a^{6} b^{11} - 4 \, a^{4} b^{13} + a^{2} b^{15}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{6} - 4 \, a^{9} b^{8} + 6 \, a^{7} b^{10} - 4 \, a^{5} b^{12} + a^{3} b^{14}\right)} d\right)}}, \frac{3 \, {\left(20 \, C a^{10} b^{3} - 8 \, B a^{9} b^{4} + {\left(2 \, A - 79 \, C\right)} a^{8} b^{5} + 32 \, B a^{7} b^{6} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{6} b^{7} - 48 \, B a^{5} b^{8} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{4} b^{9} + 32 \, B a^{3} b^{10} - 8 \, {\left(A - 2 \, C\right)} a^{2} b^{11} - 8 \, B a b^{12} + {\left(2 \, A + C\right)} b^{13}\right)} d x \cos\left(d x + c\right)^{3} + 9 \, {\left(20 \, C a^{11} b^{2} - 8 \, B a^{10} b^{3} + {\left(2 \, A - 79 \, C\right)} a^{9} b^{4} + 32 \, B a^{8} b^{5} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{7} b^{6} - 48 \, B a^{6} b^{7} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{5} b^{8} + 32 \, B a^{4} b^{9} - 8 \, {\left(A - 2 \, C\right)} a^{3} b^{10} - 8 \, B a^{2} b^{11} + {\left(2 \, A + C\right)} a b^{12}\right)} d x \cos\left(d x + c\right)^{2} + 9 \, {\left(20 \, C a^{12} b - 8 \, B a^{11} b^{2} + {\left(2 \, A - 79 \, C\right)} a^{10} b^{3} + 32 \, B a^{9} b^{4} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{8} b^{5} - 48 \, B a^{7} b^{6} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{6} b^{7} + 32 \, B a^{5} b^{8} - 8 \, {\left(A - 2 \, C\right)} a^{4} b^{9} - 8 \, B a^{3} b^{10} + {\left(2 \, A + C\right)} a^{2} b^{11}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(20 \, C a^{13} - 8 \, B a^{12} b + {\left(2 \, A - 79 \, C\right)} a^{11} b^{2} + 32 \, B a^{10} b^{3} - 4 \, {\left(2 \, A - 29 \, C\right)} a^{9} b^{4} - 48 \, B a^{8} b^{5} + 2 \, {\left(6 \, A - 37 \, C\right)} a^{7} b^{6} + 32 \, B a^{6} b^{7} - 8 \, {\left(A - 2 \, C\right)} a^{5} b^{8} - 8 \, B a^{4} b^{9} + {\left(2 \, A + C\right)} a^{3} b^{10}\right)} d x - 3 \, {\left(20 \, C a^{12} - 8 \, B a^{11} b + {\left(2 \, A - 69 \, C\right)} a^{10} b^{2} + 28 \, B a^{9} b^{3} - 7 \, {\left(A - 12 \, C\right)} a^{8} b^{4} - 35 \, B a^{7} b^{5} + 8 \, {\left(A - 5 \, C\right)} a^{6} b^{6} + 20 \, B a^{5} b^{7} - 8 \, A a^{4} b^{8} + {\left(20 \, C a^{9} b^{3} - 8 \, B a^{8} b^{4} + {\left(2 \, A - 69 \, C\right)} a^{7} b^{5} + 28 \, B a^{6} b^{6} - 7 \, {\left(A - 12 \, C\right)} a^{5} b^{7} - 35 \, B a^{4} b^{8} + 8 \, {\left(A - 5 \, C\right)} a^{3} b^{9} + 20 \, B a^{2} b^{10} - 8 \, A a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, C a^{10} b^{2} - 8 \, B a^{9} b^{3} + {\left(2 \, A - 69 \, C\right)} a^{8} b^{4} + 28 \, B a^{7} b^{5} - 7 \, {\left(A - 12 \, C\right)} a^{6} b^{6} - 35 \, B a^{5} b^{7} + 8 \, {\left(A - 5 \, C\right)} a^{4} b^{8} + 20 \, B a^{3} b^{9} - 8 \, A a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, C a^{11} b - 8 \, B a^{10} b^{2} + {\left(2 \, A - 69 \, C\right)} a^{9} b^{3} + 28 \, B a^{8} b^{4} - 7 \, {\left(A - 12 \, C\right)} a^{7} b^{5} - 35 \, B a^{6} b^{6} + 8 \, {\left(A - 5 \, C\right)} a^{5} b^{7} + 20 \, B a^{4} b^{8} - 8 \, A a^{3} b^{9}\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(60 \, C a^{12} b - 24 \, B a^{11} b^{2} + {\left(6 \, A - 227 \, C\right)} a^{10} b^{3} + 92 \, B a^{9} b^{4} - {\left(23 \, A - 313 \, C\right)} a^{8} b^{5} - 133 \, B a^{7} b^{6} + {\left(43 \, A - 170 \, C\right)} a^{6} b^{7} + 71 \, B a^{5} b^{8} - 2 \, {\left(13 \, A - 12 \, C\right)} a^{4} b^{9} - 6 \, B a^{3} b^{10} - 3 \, {\left(C a^{8} b^{5} - 4 \, C a^{6} b^{7} + 6 \, C a^{4} b^{9} - 4 \, C a^{2} b^{11} + C b^{13}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, C a^{9} b^{4} - 2 \, B a^{8} b^{5} - 20 \, C a^{7} b^{6} + 8 \, B a^{6} b^{7} + 30 \, C a^{5} b^{8} - 12 \, B a^{4} b^{9} - 20 \, C a^{3} b^{10} + 8 \, B a^{2} b^{11} + 5 \, C a b^{12} - 2 \, B b^{13}\right)} \cos\left(d x + c\right)^{3} + {\left(110 \, C a^{10} b^{3} - 44 \, B a^{9} b^{4} + {\left(11 \, A - 421 \, C\right)} a^{8} b^{5} + 169 \, B a^{7} b^{6} - {\left(43 \, A - 590 \, C\right)} a^{6} b^{7} - 239 \, B a^{5} b^{8} + 2 \, {\left(34 \, A - 171 \, C\right)} a^{4} b^{9} + 132 \, B a^{3} b^{10} - 9 \, {\left(4 \, A - 7 \, C\right)} a^{2} b^{11} - 18 \, B a b^{12}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(50 \, C a^{11} b^{2} - 20 \, B a^{10} b^{3} + 5 \, {\left(A - 38 \, C\right)} a^{9} b^{4} + 77 \, B a^{8} b^{5} - {\left(20 \, A - 263 \, C\right)} a^{7} b^{6} - 110 \, B a^{6} b^{7} + {\left(35 \, A - 146 \, C\right)} a^{5} b^{8} + 59 \, B a^{4} b^{9} - {\left(20 \, A - 23 \, C\right)} a^{3} b^{10} - 6 \, B a^{2} b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{9} - 4 \, a^{6} b^{11} + 6 \, a^{4} b^{13} - 4 \, a^{2} b^{15} + b^{17}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{8} - 4 \, a^{7} b^{10} + 6 \, a^{5} b^{12} - 4 \, a^{3} b^{14} + a b^{16}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{7} - 4 \, a^{8} b^{9} + 6 \, a^{6} b^{11} - 4 \, a^{4} b^{13} + a^{2} b^{15}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{6} - 4 \, a^{9} b^{8} + 6 \, a^{7} b^{10} - 4 \, a^{5} b^{12} + a^{3} b^{14}\right)} d\right)}}\right]"," ",0,"[1/12*(6*(20*C*a^10*b^3 - 8*B*a^9*b^4 + (2*A - 79*C)*a^8*b^5 + 32*B*a^7*b^6 - 4*(2*A - 29*C)*a^6*b^7 - 48*B*a^5*b^8 + 2*(6*A - 37*C)*a^4*b^9 + 32*B*a^3*b^10 - 8*(A - 2*C)*a^2*b^11 - 8*B*a*b^12 + (2*A + C)*b^13)*d*x*cos(d*x + c)^3 + 18*(20*C*a^11*b^2 - 8*B*a^10*b^3 + (2*A - 79*C)*a^9*b^4 + 32*B*a^8*b^5 - 4*(2*A - 29*C)*a^7*b^6 - 48*B*a^6*b^7 + 2*(6*A - 37*C)*a^5*b^8 + 32*B*a^4*b^9 - 8*(A - 2*C)*a^3*b^10 - 8*B*a^2*b^11 + (2*A + C)*a*b^12)*d*x*cos(d*x + c)^2 + 18*(20*C*a^12*b - 8*B*a^11*b^2 + (2*A - 79*C)*a^10*b^3 + 32*B*a^9*b^4 - 4*(2*A - 29*C)*a^8*b^5 - 48*B*a^7*b^6 + 2*(6*A - 37*C)*a^6*b^7 + 32*B*a^5*b^8 - 8*(A - 2*C)*a^4*b^9 - 8*B*a^3*b^10 + (2*A + C)*a^2*b^11)*d*x*cos(d*x + c) + 6*(20*C*a^13 - 8*B*a^12*b + (2*A - 79*C)*a^11*b^2 + 32*B*a^10*b^3 - 4*(2*A - 29*C)*a^9*b^4 - 48*B*a^8*b^5 + 2*(6*A - 37*C)*a^7*b^6 + 32*B*a^6*b^7 - 8*(A - 2*C)*a^5*b^8 - 8*B*a^4*b^9 + (2*A + C)*a^3*b^10)*d*x - 3*(20*C*a^12 - 8*B*a^11*b + (2*A - 69*C)*a^10*b^2 + 28*B*a^9*b^3 - 7*(A - 12*C)*a^8*b^4 - 35*B*a^7*b^5 + 8*(A - 5*C)*a^6*b^6 + 20*B*a^5*b^7 - 8*A*a^4*b^8 + (20*C*a^9*b^3 - 8*B*a^8*b^4 + (2*A - 69*C)*a^7*b^5 + 28*B*a^6*b^6 - 7*(A - 12*C)*a^5*b^7 - 35*B*a^4*b^8 + 8*(A - 5*C)*a^3*b^9 + 20*B*a^2*b^10 - 8*A*a*b^11)*cos(d*x + c)^3 + 3*(20*C*a^10*b^2 - 8*B*a^9*b^3 + (2*A - 69*C)*a^8*b^4 + 28*B*a^7*b^5 - 7*(A - 12*C)*a^6*b^6 - 35*B*a^5*b^7 + 8*(A - 5*C)*a^4*b^8 + 20*B*a^3*b^9 - 8*A*a^2*b^10)*cos(d*x + c)^2 + 3*(20*C*a^11*b - 8*B*a^10*b^2 + (2*A - 69*C)*a^9*b^3 + 28*B*a^8*b^4 - 7*(A - 12*C)*a^7*b^5 - 35*B*a^6*b^6 + 8*(A - 5*C)*a^5*b^7 + 20*B*a^4*b^8 - 8*A*a^3*b^9)*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*(60*C*a^12*b - 24*B*a^11*b^2 + (6*A - 227*C)*a^10*b^3 + 92*B*a^9*b^4 - (23*A - 313*C)*a^8*b^5 - 133*B*a^7*b^6 + (43*A - 170*C)*a^6*b^7 + 71*B*a^5*b^8 - 2*(13*A - 12*C)*a^4*b^9 - 6*B*a^3*b^10 - 3*(C*a^8*b^5 - 4*C*a^6*b^7 + 6*C*a^4*b^9 - 4*C*a^2*b^11 + C*b^13)*cos(d*x + c)^4 + 3*(5*C*a^9*b^4 - 2*B*a^8*b^5 - 20*C*a^7*b^6 + 8*B*a^6*b^7 + 30*C*a^5*b^8 - 12*B*a^4*b^9 - 20*C*a^3*b^10 + 8*B*a^2*b^11 + 5*C*a*b^12 - 2*B*b^13)*cos(d*x + c)^3 + (110*C*a^10*b^3 - 44*B*a^9*b^4 + (11*A - 421*C)*a^8*b^5 + 169*B*a^7*b^6 - (43*A - 590*C)*a^6*b^7 - 239*B*a^5*b^8 + 2*(34*A - 171*C)*a^4*b^9 + 132*B*a^3*b^10 - 9*(4*A - 7*C)*a^2*b^11 - 18*B*a*b^12)*cos(d*x + c)^2 + 3*(50*C*a^11*b^2 - 20*B*a^10*b^3 + 5*(A - 38*C)*a^9*b^4 + 77*B*a^8*b^5 - (20*A - 263*C)*a^7*b^6 - 110*B*a^6*b^7 + (35*A - 146*C)*a^5*b^8 + 59*B*a^4*b^9 - (20*A - 23*C)*a^3*b^10 - 6*B*a^2*b^11)*cos(d*x + c))*sin(d*x + c))/((a^8*b^9 - 4*a^6*b^11 + 6*a^4*b^13 - 4*a^2*b^15 + b^17)*d*cos(d*x + c)^3 + 3*(a^9*b^8 - 4*a^7*b^10 + 6*a^5*b^12 - 4*a^3*b^14 + a*b^16)*d*cos(d*x + c)^2 + 3*(a^10*b^7 - 4*a^8*b^9 + 6*a^6*b^11 - 4*a^4*b^13 + a^2*b^15)*d*cos(d*x + c) + (a^11*b^6 - 4*a^9*b^8 + 6*a^7*b^10 - 4*a^5*b^12 + a^3*b^14)*d), 1/6*(3*(20*C*a^10*b^3 - 8*B*a^9*b^4 + (2*A - 79*C)*a^8*b^5 + 32*B*a^7*b^6 - 4*(2*A - 29*C)*a^6*b^7 - 48*B*a^5*b^8 + 2*(6*A - 37*C)*a^4*b^9 + 32*B*a^3*b^10 - 8*(A - 2*C)*a^2*b^11 - 8*B*a*b^12 + (2*A + C)*b^13)*d*x*cos(d*x + c)^3 + 9*(20*C*a^11*b^2 - 8*B*a^10*b^3 + (2*A - 79*C)*a^9*b^4 + 32*B*a^8*b^5 - 4*(2*A - 29*C)*a^7*b^6 - 48*B*a^6*b^7 + 2*(6*A - 37*C)*a^5*b^8 + 32*B*a^4*b^9 - 8*(A - 2*C)*a^3*b^10 - 8*B*a^2*b^11 + (2*A + C)*a*b^12)*d*x*cos(d*x + c)^2 + 9*(20*C*a^12*b - 8*B*a^11*b^2 + (2*A - 79*C)*a^10*b^3 + 32*B*a^9*b^4 - 4*(2*A - 29*C)*a^8*b^5 - 48*B*a^7*b^6 + 2*(6*A - 37*C)*a^6*b^7 + 32*B*a^5*b^8 - 8*(A - 2*C)*a^4*b^9 - 8*B*a^3*b^10 + (2*A + C)*a^2*b^11)*d*x*cos(d*x + c) + 3*(20*C*a^13 - 8*B*a^12*b + (2*A - 79*C)*a^11*b^2 + 32*B*a^10*b^3 - 4*(2*A - 29*C)*a^9*b^4 - 48*B*a^8*b^5 + 2*(6*A - 37*C)*a^7*b^6 + 32*B*a^6*b^7 - 8*(A - 2*C)*a^5*b^8 - 8*B*a^4*b^9 + (2*A + C)*a^3*b^10)*d*x - 3*(20*C*a^12 - 8*B*a^11*b + (2*A - 69*C)*a^10*b^2 + 28*B*a^9*b^3 - 7*(A - 12*C)*a^8*b^4 - 35*B*a^7*b^5 + 8*(A - 5*C)*a^6*b^6 + 20*B*a^5*b^7 - 8*A*a^4*b^8 + (20*C*a^9*b^3 - 8*B*a^8*b^4 + (2*A - 69*C)*a^7*b^5 + 28*B*a^6*b^6 - 7*(A - 12*C)*a^5*b^7 - 35*B*a^4*b^8 + 8*(A - 5*C)*a^3*b^9 + 20*B*a^2*b^10 - 8*A*a*b^11)*cos(d*x + c)^3 + 3*(20*C*a^10*b^2 - 8*B*a^9*b^3 + (2*A - 69*C)*a^8*b^4 + 28*B*a^7*b^5 - 7*(A - 12*C)*a^6*b^6 - 35*B*a^5*b^7 + 8*(A - 5*C)*a^4*b^8 + 20*B*a^3*b^9 - 8*A*a^2*b^10)*cos(d*x + c)^2 + 3*(20*C*a^11*b - 8*B*a^10*b^2 + (2*A - 69*C)*a^9*b^3 + 28*B*a^8*b^4 - 7*(A - 12*C)*a^7*b^5 - 35*B*a^6*b^6 + 8*(A - 5*C)*a^5*b^7 + 20*B*a^4*b^8 - 8*A*a^3*b^9)*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))) - (60*C*a^12*b - 24*B*a^11*b^2 + (6*A - 227*C)*a^10*b^3 + 92*B*a^9*b^4 - (23*A - 313*C)*a^8*b^5 - 133*B*a^7*b^6 + (43*A - 170*C)*a^6*b^7 + 71*B*a^5*b^8 - 2*(13*A - 12*C)*a^4*b^9 - 6*B*a^3*b^10 - 3*(C*a^8*b^5 - 4*C*a^6*b^7 + 6*C*a^4*b^9 - 4*C*a^2*b^11 + C*b^13)*cos(d*x + c)^4 + 3*(5*C*a^9*b^4 - 2*B*a^8*b^5 - 20*C*a^7*b^6 + 8*B*a^6*b^7 + 30*C*a^5*b^8 - 12*B*a^4*b^9 - 20*C*a^3*b^10 + 8*B*a^2*b^11 + 5*C*a*b^12 - 2*B*b^13)*cos(d*x + c)^3 + (110*C*a^10*b^3 - 44*B*a^9*b^4 + (11*A - 421*C)*a^8*b^5 + 169*B*a^7*b^6 - (43*A - 590*C)*a^6*b^7 - 239*B*a^5*b^8 + 2*(34*A - 171*C)*a^4*b^9 + 132*B*a^3*b^10 - 9*(4*A - 7*C)*a^2*b^11 - 18*B*a*b^12)*cos(d*x + c)^2 + 3*(50*C*a^11*b^2 - 20*B*a^10*b^3 + 5*(A - 38*C)*a^9*b^4 + 77*B*a^8*b^5 - (20*A - 263*C)*a^7*b^6 - 110*B*a^6*b^7 + (35*A - 146*C)*a^5*b^8 + 59*B*a^4*b^9 - (20*A - 23*C)*a^3*b^10 - 6*B*a^2*b^11)*cos(d*x + c))*sin(d*x + c))/((a^8*b^9 - 4*a^6*b^11 + 6*a^4*b^13 - 4*a^2*b^15 + b^17)*d*cos(d*x + c)^3 + 3*(a^9*b^8 - 4*a^7*b^10 + 6*a^5*b^12 - 4*a^3*b^14 + a*b^16)*d*cos(d*x + c)^2 + 3*(a^10*b^7 - 4*a^8*b^9 + 6*a^6*b^11 - 4*a^4*b^13 + a^2*b^15)*d*cos(d*x + c) + (a^11*b^6 - 4*a^9*b^8 + 6*a^7*b^10 - 4*a^5*b^12 + a^3*b^14)*d)]","B",0
1002,1,2777,0,1.956163," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(4 \, C a^{9} b^{3} - B a^{8} b^{4} - 16 \, C a^{7} b^{5} + 4 \, B a^{6} b^{6} + 24 \, C a^{5} b^{7} - 6 \, B a^{4} b^{8} - 16 \, C a^{3} b^{9} + 4 \, B a^{2} b^{10} + 4 \, C a b^{11} - B b^{12}\right)} d x \cos\left(d x + c\right)^{3} + 36 \, {\left(4 \, C a^{10} b^{2} - B a^{9} b^{3} - 16 \, C a^{8} b^{4} + 4 \, B a^{7} b^{5} + 24 \, C a^{6} b^{6} - 6 \, B a^{5} b^{7} - 16 \, C a^{4} b^{8} + 4 \, B a^{3} b^{9} + 4 \, C a^{2} b^{10} - B a b^{11}\right)} d x \cos\left(d x + c\right)^{2} + 36 \, {\left(4 \, C a^{11} b - B a^{10} b^{2} - 16 \, C a^{9} b^{3} + 4 \, B a^{8} b^{4} + 24 \, C a^{7} b^{5} - 6 \, B a^{6} b^{6} - 16 \, C a^{5} b^{7} + 4 \, B a^{4} b^{8} + 4 \, C a^{3} b^{9} - B a^{2} b^{10}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(4 \, C a^{12} - B a^{11} b - 16 \, C a^{10} b^{2} + 4 \, B a^{9} b^{3} + 24 \, C a^{8} b^{4} - 6 \, B a^{7} b^{5} - 16 \, C a^{6} b^{6} + 4 \, B a^{5} b^{7} + 4 \, C a^{4} b^{8} - B a^{3} b^{9}\right)} d x + 3 \, {\left(8 \, C a^{11} - 2 \, B a^{10} b - 28 \, C a^{9} b^{2} + 7 \, B a^{8} b^{3} + 35 \, C a^{7} b^{4} - 8 \, B a^{6} b^{5} - {\left(3 \, A + 20 \, C\right)} a^{5} b^{6} + 8 \, B a^{4} b^{7} - 2 \, A a^{3} b^{8} + {\left(8 \, C a^{8} b^{3} - 2 \, B a^{7} b^{4} - 28 \, C a^{6} b^{5} + 7 \, B a^{5} b^{6} + 35 \, C a^{4} b^{7} - 8 \, B a^{3} b^{8} - {\left(3 \, A + 20 \, C\right)} a^{2} b^{9} + 8 \, B a b^{10} - 2 \, A b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, C a^{9} b^{2} - 2 \, B a^{8} b^{3} - 28 \, C a^{7} b^{4} + 7 \, B a^{6} b^{5} + 35 \, C a^{5} b^{6} - 8 \, B a^{4} b^{7} - {\left(3 \, A + 20 \, C\right)} a^{3} b^{8} + 8 \, B a^{2} b^{9} - 2 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, C a^{10} b - 2 \, B a^{9} b^{2} - 28 \, C a^{8} b^{3} + 7 \, B a^{7} b^{4} + 35 \, C a^{6} b^{5} - 8 \, B a^{5} b^{6} - {\left(3 \, A + 20 \, C\right)} a^{4} b^{7} + 8 \, B a^{3} b^{8} - 2 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{11} b - 6 \, B a^{10} b^{2} - 92 \, C a^{9} b^{3} + 23 \, B a^{8} b^{4} + {\left(4 \, A + 133 \, C\right)} a^{7} b^{5} - 43 \, B a^{6} b^{6} + {\left(7 \, A - 71 \, C\right)} a^{5} b^{7} + 26 \, B a^{4} b^{8} - {\left(11 \, A - 6 \, C\right)} a^{3} b^{9} + 6 \, {\left(C a^{8} b^{4} - 4 \, C a^{6} b^{6} + 6 \, C a^{4} b^{8} - 4 \, C a^{2} b^{10} + C b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(44 \, C a^{9} b^{3} - 11 \, B a^{8} b^{4} + {\left(2 \, A - 169 \, C\right)} a^{7} b^{5} + 43 \, B a^{6} b^{6} - {\left(7 \, A - 239 \, C\right)} a^{5} b^{7} - 68 \, B a^{4} b^{8} + {\left(23 \, A - 132 \, C\right)} a^{3} b^{9} + 36 \, B a^{2} b^{10} - 18 \, {\left(A - C\right)} a b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, C a^{10} b^{2} - 5 \, B a^{9} b^{3} - 77 \, C a^{8} b^{4} + 20 \, B a^{7} b^{5} + {\left(A + 110 \, C\right)} a^{6} b^{6} - 35 \, B a^{5} b^{7} + {\left(8 \, A - 59 \, C\right)} a^{4} b^{8} + 20 \, B a^{3} b^{9} - 3 \, {\left(3 \, A - 2 \, C\right)} 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 \, C a^{9} b^{3} - B a^{8} b^{4} - 16 \, C a^{7} b^{5} + 4 \, B a^{6} b^{6} + 24 \, C a^{5} b^{7} - 6 \, B a^{4} b^{8} - 16 \, C a^{3} b^{9} + 4 \, B a^{2} b^{10} + 4 \, C a b^{11} - B b^{12}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(4 \, C a^{10} b^{2} - B a^{9} b^{3} - 16 \, C a^{8} b^{4} + 4 \, B a^{7} b^{5} + 24 \, C a^{6} b^{6} - 6 \, B a^{5} b^{7} - 16 \, C a^{4} b^{8} + 4 \, B a^{3} b^{9} + 4 \, C a^{2} b^{10} - B a b^{11}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(4 \, C a^{11} b - B a^{10} b^{2} - 16 \, C a^{9} b^{3} + 4 \, B a^{8} b^{4} + 24 \, C a^{7} b^{5} - 6 \, B a^{6} b^{6} - 16 \, C a^{5} b^{7} + 4 \, B a^{4} b^{8} + 4 \, C a^{3} b^{9} - B a^{2} b^{10}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(4 \, C a^{12} - B a^{11} b - 16 \, C a^{10} b^{2} + 4 \, B a^{9} b^{3} + 24 \, C a^{8} b^{4} - 6 \, B a^{7} b^{5} - 16 \, C a^{6} b^{6} + 4 \, B a^{5} b^{7} + 4 \, C a^{4} b^{8} - B a^{3} b^{9}\right)} d x - 3 \, {\left(8 \, C a^{11} - 2 \, B a^{10} b - 28 \, C a^{9} b^{2} + 7 \, B a^{8} b^{3} + 35 \, C a^{7} b^{4} - 8 \, B a^{6} b^{5} - {\left(3 \, A + 20 \, C\right)} a^{5} b^{6} + 8 \, B a^{4} b^{7} - 2 \, A a^{3} b^{8} + {\left(8 \, C a^{8} b^{3} - 2 \, B a^{7} b^{4} - 28 \, C a^{6} b^{5} + 7 \, B a^{5} b^{6} + 35 \, C a^{4} b^{7} - 8 \, B a^{3} b^{8} - {\left(3 \, A + 20 \, C\right)} a^{2} b^{9} + 8 \, B a b^{10} - 2 \, A b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, C a^{9} b^{2} - 2 \, B a^{8} b^{3} - 28 \, C a^{7} b^{4} + 7 \, B a^{6} b^{5} + 35 \, C a^{5} b^{6} - 8 \, B a^{4} b^{7} - {\left(3 \, A + 20 \, C\right)} a^{3} b^{8} + 8 \, B a^{2} b^{9} - 2 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, C a^{10} b - 2 \, B a^{9} b^{2} - 28 \, C a^{8} b^{3} + 7 \, B a^{7} b^{4} + 35 \, C a^{6} b^{5} - 8 \, B a^{5} b^{6} - {\left(3 \, A + 20 \, C\right)} a^{4} b^{7} + 8 \, B a^{3} b^{8} - 2 \, A a^{2} b^{9}\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 \, C a^{11} b - 6 \, B a^{10} b^{2} - 92 \, C a^{9} b^{3} + 23 \, B a^{8} b^{4} + {\left(4 \, A + 133 \, C\right)} a^{7} b^{5} - 43 \, B a^{6} b^{6} + {\left(7 \, A - 71 \, C\right)} a^{5} b^{7} + 26 \, B a^{4} b^{8} - {\left(11 \, A - 6 \, C\right)} a^{3} b^{9} + 6 \, {\left(C a^{8} b^{4} - 4 \, C a^{6} b^{6} + 6 \, C a^{4} b^{8} - 4 \, C a^{2} b^{10} + C b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(44 \, C a^{9} b^{3} - 11 \, B a^{8} b^{4} + {\left(2 \, A - 169 \, C\right)} a^{7} b^{5} + 43 \, B a^{6} b^{6} - {\left(7 \, A - 239 \, C\right)} a^{5} b^{7} - 68 \, B a^{4} b^{8} + {\left(23 \, A - 132 \, C\right)} a^{3} b^{9} + 36 \, B a^{2} b^{10} - 18 \, {\left(A - C\right)} a b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, C a^{10} b^{2} - 5 \, B a^{9} b^{3} - 77 \, C a^{8} b^{4} + 20 \, B a^{7} b^{5} + {\left(A + 110 \, C\right)} a^{6} b^{6} - 35 \, B a^{5} b^{7} + {\left(8 \, A - 59 \, C\right)} a^{4} b^{8} + 20 \, B a^{3} b^{9} - 3 \, {\left(3 \, A - 2 \, C\right)} 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*C*a^9*b^3 - B*a^8*b^4 - 16*C*a^7*b^5 + 4*B*a^6*b^6 + 24*C*a^5*b^7 - 6*B*a^4*b^8 - 16*C*a^3*b^9 + 4*B*a^2*b^10 + 4*C*a*b^11 - B*b^12)*d*x*cos(d*x + c)^3 + 36*(4*C*a^10*b^2 - B*a^9*b^3 - 16*C*a^8*b^4 + 4*B*a^7*b^5 + 24*C*a^6*b^6 - 6*B*a^5*b^7 - 16*C*a^4*b^8 + 4*B*a^3*b^9 + 4*C*a^2*b^10 - B*a*b^11)*d*x*cos(d*x + c)^2 + 36*(4*C*a^11*b - B*a^10*b^2 - 16*C*a^9*b^3 + 4*B*a^8*b^4 + 24*C*a^7*b^5 - 6*B*a^6*b^6 - 16*C*a^5*b^7 + 4*B*a^4*b^8 + 4*C*a^3*b^9 - B*a^2*b^10)*d*x*cos(d*x + c) + 12*(4*C*a^12 - B*a^11*b - 16*C*a^10*b^2 + 4*B*a^9*b^3 + 24*C*a^8*b^4 - 6*B*a^7*b^5 - 16*C*a^6*b^6 + 4*B*a^5*b^7 + 4*C*a^4*b^8 - B*a^3*b^9)*d*x + 3*(8*C*a^11 - 2*B*a^10*b - 28*C*a^9*b^2 + 7*B*a^8*b^3 + 35*C*a^7*b^4 - 8*B*a^6*b^5 - (3*A + 20*C)*a^5*b^6 + 8*B*a^4*b^7 - 2*A*a^3*b^8 + (8*C*a^8*b^3 - 2*B*a^7*b^4 - 28*C*a^6*b^5 + 7*B*a^5*b^6 + 35*C*a^4*b^7 - 8*B*a^3*b^8 - (3*A + 20*C)*a^2*b^9 + 8*B*a*b^10 - 2*A*b^11)*cos(d*x + c)^3 + 3*(8*C*a^9*b^2 - 2*B*a^8*b^3 - 28*C*a^7*b^4 + 7*B*a^6*b^5 + 35*C*a^5*b^6 - 8*B*a^4*b^7 - (3*A + 20*C)*a^3*b^8 + 8*B*a^2*b^9 - 2*A*a*b^10)*cos(d*x + c)^2 + 3*(8*C*a^10*b - 2*B*a^9*b^2 - 28*C*a^8*b^3 + 7*B*a^7*b^4 + 35*C*a^6*b^5 - 8*B*a^5*b^6 - (3*A + 20*C)*a^4*b^7 + 8*B*a^3*b^8 - 2*A*a^2*b^9)*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*C*a^11*b - 6*B*a^10*b^2 - 92*C*a^9*b^3 + 23*B*a^8*b^4 + (4*A + 133*C)*a^7*b^5 - 43*B*a^6*b^6 + (7*A - 71*C)*a^5*b^7 + 26*B*a^4*b^8 - (11*A - 6*C)*a^3*b^9 + 6*(C*a^8*b^4 - 4*C*a^6*b^6 + 6*C*a^4*b^8 - 4*C*a^2*b^10 + C*b^12)*cos(d*x + c)^3 + (44*C*a^9*b^3 - 11*B*a^8*b^4 + (2*A - 169*C)*a^7*b^5 + 43*B*a^6*b^6 - (7*A - 239*C)*a^5*b^7 - 68*B*a^4*b^8 + (23*A - 132*C)*a^3*b^9 + 36*B*a^2*b^10 - 18*(A - C)*a*b^11)*cos(d*x + c)^2 + 3*(20*C*a^10*b^2 - 5*B*a^9*b^3 - 77*C*a^8*b^4 + 20*B*a^7*b^5 + (A + 110*C)*a^6*b^6 - 35*B*a^5*b^7 + (8*A - 59*C)*a^4*b^8 + 20*B*a^3*b^9 - 3*(3*A - 2*C)*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*C*a^9*b^3 - B*a^8*b^4 - 16*C*a^7*b^5 + 4*B*a^6*b^6 + 24*C*a^5*b^7 - 6*B*a^4*b^8 - 16*C*a^3*b^9 + 4*B*a^2*b^10 + 4*C*a*b^11 - B*b^12)*d*x*cos(d*x + c)^3 + 18*(4*C*a^10*b^2 - B*a^9*b^3 - 16*C*a^8*b^4 + 4*B*a^7*b^5 + 24*C*a^6*b^6 - 6*B*a^5*b^7 - 16*C*a^4*b^8 + 4*B*a^3*b^9 + 4*C*a^2*b^10 - B*a*b^11)*d*x*cos(d*x + c)^2 + 18*(4*C*a^11*b - B*a^10*b^2 - 16*C*a^9*b^3 + 4*B*a^8*b^4 + 24*C*a^7*b^5 - 6*B*a^6*b^6 - 16*C*a^5*b^7 + 4*B*a^4*b^8 + 4*C*a^3*b^9 - B*a^2*b^10)*d*x*cos(d*x + c) + 6*(4*C*a^12 - B*a^11*b - 16*C*a^10*b^2 + 4*B*a^9*b^3 + 24*C*a^8*b^4 - 6*B*a^7*b^5 - 16*C*a^6*b^6 + 4*B*a^5*b^7 + 4*C*a^4*b^8 - B*a^3*b^9)*d*x - 3*(8*C*a^11 - 2*B*a^10*b - 28*C*a^9*b^2 + 7*B*a^8*b^3 + 35*C*a^7*b^4 - 8*B*a^6*b^5 - (3*A + 20*C)*a^5*b^6 + 8*B*a^4*b^7 - 2*A*a^3*b^8 + (8*C*a^8*b^3 - 2*B*a^7*b^4 - 28*C*a^6*b^5 + 7*B*a^5*b^6 + 35*C*a^4*b^7 - 8*B*a^3*b^8 - (3*A + 20*C)*a^2*b^9 + 8*B*a*b^10 - 2*A*b^11)*cos(d*x + c)^3 + 3*(8*C*a^9*b^2 - 2*B*a^8*b^3 - 28*C*a^7*b^4 + 7*B*a^6*b^5 + 35*C*a^5*b^6 - 8*B*a^4*b^7 - (3*A + 20*C)*a^3*b^8 + 8*B*a^2*b^9 - 2*A*a*b^10)*cos(d*x + c)^2 + 3*(8*C*a^10*b - 2*B*a^9*b^2 - 28*C*a^8*b^3 + 7*B*a^7*b^4 + 35*C*a^6*b^5 - 8*B*a^5*b^6 - (3*A + 20*C)*a^4*b^7 + 8*B*a^3*b^8 - 2*A*a^2*b^9)*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*C*a^11*b - 6*B*a^10*b^2 - 92*C*a^9*b^3 + 23*B*a^8*b^4 + (4*A + 133*C)*a^7*b^5 - 43*B*a^6*b^6 + (7*A - 71*C)*a^5*b^7 + 26*B*a^4*b^8 - (11*A - 6*C)*a^3*b^9 + 6*(C*a^8*b^4 - 4*C*a^6*b^6 + 6*C*a^4*b^8 - 4*C*a^2*b^10 + C*b^12)*cos(d*x + c)^3 + (44*C*a^9*b^3 - 11*B*a^8*b^4 + (2*A - 169*C)*a^7*b^5 + 43*B*a^6*b^6 - (7*A - 239*C)*a^5*b^7 - 68*B*a^4*b^8 + (23*A - 132*C)*a^3*b^9 + 36*B*a^2*b^10 - 18*(A - C)*a*b^11)*cos(d*x + c)^2 + 3*(20*C*a^10*b^2 - 5*B*a^9*b^3 - 77*C*a^8*b^4 + 20*B*a^7*b^5 + (A + 110*C)*a^6*b^6 - 35*B*a^5*b^7 + (8*A - 59*C)*a^4*b^8 + 20*B*a^3*b^9 - 3*(3*A - 2*C)*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
1003,1,2045,0,1.407111," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 36 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 36 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} d x + 3 \, {\left(2 \, C a^{10} - 7 \, C a^{8} b^{2} - {\left(A - 8 \, C\right)} a^{6} b^{4} + 3 \, B a^{5} b^{5} - 4 \, {\left(A + 2 \, C\right)} a^{4} b^{6} + 2 \, B a^{3} b^{7} + {\left(2 \, C a^{7} b^{3} - 7 \, C a^{5} b^{5} - {\left(A - 8 \, C\right)} a^{3} b^{7} + 3 \, B a^{2} b^{8} - 4 \, {\left(A + 2 \, C\right)} a b^{9} + 2 \, B b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{8} b^{2} - 7 \, C a^{6} b^{4} - {\left(A - 8 \, C\right)} a^{4} b^{6} + 3 \, B a^{3} b^{7} - 4 \, {\left(A + 2 \, C\right)} a^{2} b^{8} + 2 \, B a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{9} b - 7 \, C a^{7} b^{3} - {\left(A - 8 \, C\right)} a^{5} b^{5} + 3 \, B a^{4} b^{6} - 4 \, {\left(A + 2 \, C\right)} a^{3} b^{7} + 2 \, B a^{2} b^{8}\right)} \cos\left(d x + c\right)\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 \, C a^{10} b - 23 \, C a^{8} b^{3} - 4 \, B a^{7} b^{4} + {\left(13 \, A + 43 \, C\right)} a^{6} b^{5} - 7 \, B a^{5} b^{6} - {\left(11 \, A + 26 \, C\right)} a^{4} b^{7} + 11 \, B a^{3} b^{8} - 2 \, A a^{2} b^{9} + {\left(11 \, C a^{8} b^{3} - 2 \, B a^{7} b^{4} - {\left(A + 43 \, C\right)} a^{6} b^{5} + 7 \, B a^{5} b^{6} + {\left(11 \, A + 68 \, C\right)} a^{4} b^{7} - 23 \, B a^{3} b^{8} - 4 \, {\left(A + 9 \, C\right)} a^{2} b^{9} + 18 \, B a b^{10} - 6 \, A b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, C a^{9} b^{2} - {\left(A + 20 \, C\right)} a^{7} b^{4} - B a^{6} b^{5} + 5 \, {\left(2 \, A + 7 \, C\right)} a^{5} b^{6} - 8 \, B a^{4} b^{7} - {\left(7 \, A + 20 \, C\right)} a^{3} b^{8} + 9 \, B a^{2} b^{9} - 2 \, A a b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{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(C a^{8} b^{3} - 4 \, C a^{6} b^{5} + 6 \, C a^{4} b^{7} - 4 \, C a^{2} b^{9} + C b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(C a^{9} b^{2} - 4 \, C a^{7} b^{4} + 6 \, C a^{5} b^{6} - 4 \, C a^{3} b^{8} + C a b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(C a^{10} b - 4 \, C a^{8} b^{3} + 6 \, C a^{6} b^{5} - 4 \, C a^{4} b^{7} + C a^{2} b^{9}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(C a^{11} - 4 \, C a^{9} b^{2} + 6 \, C a^{7} b^{4} - 4 \, C a^{5} b^{6} + C a^{3} b^{8}\right)} d x - 3 \, {\left(2 \, C a^{10} - 7 \, C a^{8} b^{2} - {\left(A - 8 \, C\right)} a^{6} b^{4} + 3 \, B a^{5} b^{5} - 4 \, {\left(A + 2 \, C\right)} a^{4} b^{6} + 2 \, B a^{3} b^{7} + {\left(2 \, C a^{7} b^{3} - 7 \, C a^{5} b^{5} - {\left(A - 8 \, C\right)} a^{3} b^{7} + 3 \, B a^{2} b^{8} - 4 \, {\left(A + 2 \, C\right)} a b^{9} + 2 \, B b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{8} b^{2} - 7 \, C a^{6} b^{4} - {\left(A - 8 \, C\right)} a^{4} b^{6} + 3 \, B a^{3} b^{7} - 4 \, {\left(A + 2 \, C\right)} a^{2} b^{8} + 2 \, B a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{9} b - 7 \, C a^{7} b^{3} - {\left(A - 8 \, C\right)} a^{5} b^{5} + 3 \, B a^{4} b^{6} - 4 \, {\left(A + 2 \, C\right)} a^{3} b^{7} + 2 \, B a^{2} b^{8}\right)} \cos\left(d x + c\right)\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 \, C a^{10} b - 23 \, C a^{8} b^{3} - 4 \, B a^{7} b^{4} + {\left(13 \, A + 43 \, C\right)} a^{6} b^{5} - 7 \, B a^{5} b^{6} - {\left(11 \, A + 26 \, C\right)} a^{4} b^{7} + 11 \, B a^{3} b^{8} - 2 \, A a^{2} b^{9} + {\left(11 \, C a^{8} b^{3} - 2 \, B a^{7} b^{4} - {\left(A + 43 \, C\right)} a^{6} b^{5} + 7 \, B a^{5} b^{6} + {\left(11 \, A + 68 \, C\right)} a^{4} b^{7} - 23 \, B a^{3} b^{8} - 4 \, {\left(A + 9 \, C\right)} a^{2} b^{9} + 18 \, B a b^{10} - 6 \, A b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, C a^{9} b^{2} - {\left(A + 20 \, C\right)} a^{7} b^{4} - B a^{6} b^{5} + 5 \, {\left(2 \, A + 7 \, C\right)} a^{5} b^{6} - 8 \, B a^{4} b^{7} - {\left(7 \, A + 20 \, C\right)} a^{3} b^{8} + 9 \, B a^{2} b^{9} - 2 \, A a b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{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*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11)*d*x*cos(d*x + c)^3 + 36*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*d*x*cos(d*x + c)^2 + 36*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*d*x*cos(d*x + c) + 12*(C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*d*x + 3*(2*C*a^10 - 7*C*a^8*b^2 - (A - 8*C)*a^6*b^4 + 3*B*a^5*b^5 - 4*(A + 2*C)*a^4*b^6 + 2*B*a^3*b^7 + (2*C*a^7*b^3 - 7*C*a^5*b^5 - (A - 8*C)*a^3*b^7 + 3*B*a^2*b^8 - 4*(A + 2*C)*a*b^9 + 2*B*b^10)*cos(d*x + c)^3 + 3*(2*C*a^8*b^2 - 7*C*a^6*b^4 - (A - 8*C)*a^4*b^6 + 3*B*a^3*b^7 - 4*(A + 2*C)*a^2*b^8 + 2*B*a*b^9)*cos(d*x + c)^2 + 3*(2*C*a^9*b - 7*C*a^7*b^3 - (A - 8*C)*a^5*b^5 + 3*B*a^4*b^6 - 4*(A + 2*C)*a^3*b^7 + 2*B*a^2*b^8)*cos(d*x + c))*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*C*a^10*b - 23*C*a^8*b^3 - 4*B*a^7*b^4 + (13*A + 43*C)*a^6*b^5 - 7*B*a^5*b^6 - (11*A + 26*C)*a^4*b^7 + 11*B*a^3*b^8 - 2*A*a^2*b^9 + (11*C*a^8*b^3 - 2*B*a^7*b^4 - (A + 43*C)*a^6*b^5 + 7*B*a^5*b^6 + (11*A + 68*C)*a^4*b^7 - 23*B*a^3*b^8 - 4*(A + 9*C)*a^2*b^9 + 18*B*a*b^10 - 6*A*b^11)*cos(d*x + c)^2 + 3*(5*C*a^9*b^2 - (A + 20*C)*a^7*b^4 - B*a^6*b^5 + 5*(2*A + 7*C)*a^5*b^6 - 8*B*a^4*b^7 - (7*A + 20*C)*a^3*b^8 + 9*B*a^2*b^9 - 2*A*a*b^10)*cos(d*x + c))*sin(d*x + c))/((a^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*(C*a^8*b^3 - 4*C*a^6*b^5 + 6*C*a^4*b^7 - 4*C*a^2*b^9 + C*b^11)*d*x*cos(d*x + c)^3 + 18*(C*a^9*b^2 - 4*C*a^7*b^4 + 6*C*a^5*b^6 - 4*C*a^3*b^8 + C*a*b^10)*d*x*cos(d*x + c)^2 + 18*(C*a^10*b - 4*C*a^8*b^3 + 6*C*a^6*b^5 - 4*C*a^4*b^7 + C*a^2*b^9)*d*x*cos(d*x + c) + 6*(C*a^11 - 4*C*a^9*b^2 + 6*C*a^7*b^4 - 4*C*a^5*b^6 + C*a^3*b^8)*d*x - 3*(2*C*a^10 - 7*C*a^8*b^2 - (A - 8*C)*a^6*b^4 + 3*B*a^5*b^5 - 4*(A + 2*C)*a^4*b^6 + 2*B*a^3*b^7 + (2*C*a^7*b^3 - 7*C*a^5*b^5 - (A - 8*C)*a^3*b^7 + 3*B*a^2*b^8 - 4*(A + 2*C)*a*b^9 + 2*B*b^10)*cos(d*x + c)^3 + 3*(2*C*a^8*b^2 - 7*C*a^6*b^4 - (A - 8*C)*a^4*b^6 + 3*B*a^3*b^7 - 4*(A + 2*C)*a^2*b^8 + 2*B*a*b^9)*cos(d*x + c)^2 + 3*(2*C*a^9*b - 7*C*a^7*b^3 - (A - 8*C)*a^5*b^5 + 3*B*a^4*b^6 - 4*(A + 2*C)*a^3*b^7 + 2*B*a^2*b^8)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*C*a^10*b - 23*C*a^8*b^3 - 4*B*a^7*b^4 + (13*A + 43*C)*a^6*b^5 - 7*B*a^5*b^6 - (11*A + 26*C)*a^4*b^7 + 11*B*a^3*b^8 - 2*A*a^2*b^9 + (11*C*a^8*b^3 - 2*B*a^7*b^4 - (A + 43*C)*a^6*b^5 + 7*B*a^5*b^6 + (11*A + 68*C)*a^4*b^7 - 23*B*a^3*b^8 - 4*(A + 9*C)*a^2*b^9 + 18*B*a*b^10 - 6*A*b^11)*cos(d*x + c)^2 + 3*(5*C*a^9*b^2 - (A + 20*C)*a^7*b^4 - B*a^6*b^5 + 5*(2*A + 7*C)*a^5*b^6 - 8*B*a^4*b^7 - (7*A + 20*C)*a^3*b^8 + 9*B*a^2*b^9 - 2*A*a*b^10)*cos(d*x + c))*sin(d*x + c))/((a^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
1004,1,1410,0,1.052868," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{6} - {\left(4 \, A + 3 \, C\right)} a^{5} b + 4 \, B a^{4} b^{2} - {\left(A + 2 \, C\right)} a^{3} b^{3} + {\left(B a^{3} b^{3} - {\left(4 \, A + 3 \, C\right)} a^{2} b^{4} + 4 \, B a b^{5} - {\left(A + 2 \, C\right)} b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{4} b^{2} - {\left(4 \, A + 3 \, C\right)} a^{3} b^{3} + 4 \, B a^{2} b^{4} - {\left(A + 2 \, C\right)} a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{5} b - {\left(4 \, A + 3 \, C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} - {\left(A + 2 \, C\right)} a^{2} b^{4}\right)} \cos\left(d x + c\right)\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 \, {\left(3 \, A + 2 \, C\right)} a^{7} - 13 \, B a^{6} b + {\left(4 \, A + 7 \, C\right)} a^{5} b^{2} + 11 \, B a^{4} b^{3} - 11 \, {\left(A + C\right)} a^{3} b^{4} + 2 \, B a^{2} b^{5} + A a b^{6} + {\left(2 \, C a^{7} + B a^{6} b + {\left(2 \, A - 7 \, C\right)} a^{5} b^{2} - 11 \, B a^{4} b^{3} + {\left(11 \, A + 23 \, C\right)} a^{3} b^{4} + 4 \, B a^{2} b^{5} - {\left(13 \, A + 18 \, C\right)} a b^{6} + 6 \, B b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{7} + {\left(2 \, A + C\right)} a^{6} b - 10 \, B a^{5} b^{2} + {\left(7 \, A + 8 \, C\right)} a^{4} b^{3} + 7 \, B a^{3} b^{4} - {\left(10 \, A + 9 \, C\right)} a^{2} b^{5} + 2 \, B a b^{6} + A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{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} - {\left(4 \, A + 3 \, C\right)} a^{5} b + 4 \, B a^{4} b^{2} - {\left(A + 2 \, C\right)} a^{3} b^{3} + {\left(B a^{3} b^{3} - {\left(4 \, A + 3 \, C\right)} a^{2} b^{4} + 4 \, B a b^{5} - {\left(A + 2 \, C\right)} b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(B a^{4} b^{2} - {\left(4 \, A + 3 \, C\right)} a^{3} b^{3} + 4 \, B a^{2} b^{4} - {\left(A + 2 \, C\right)} a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{5} b - {\left(4 \, A + 3 \, C\right)} a^{4} b^{2} + 4 \, B a^{3} b^{3} - {\left(A + 2 \, C\right)} a^{2} b^{4}\right)} \cos\left(d x + c\right)\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 \, {\left(3 \, A + 2 \, C\right)} a^{7} - 13 \, B a^{6} b + {\left(4 \, A + 7 \, C\right)} a^{5} b^{2} + 11 \, B a^{4} b^{3} - 11 \, {\left(A + C\right)} a^{3} b^{4} + 2 \, B a^{2} b^{5} + A a b^{6} + {\left(2 \, C a^{7} + B a^{6} b + {\left(2 \, A - 7 \, C\right)} a^{5} b^{2} - 11 \, B a^{4} b^{3} + {\left(11 \, A + 23 \, C\right)} a^{3} b^{4} + 4 \, B a^{2} b^{5} - {\left(13 \, A + 18 \, C\right)} a b^{6} + 6 \, B b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(B a^{7} + {\left(2 \, A + C\right)} a^{6} b - 10 \, B a^{5} b^{2} + {\left(7 \, A + 8 \, C\right)} a^{4} b^{3} + 7 \, B a^{3} b^{4} - {\left(10 \, A + 9 \, C\right)} a^{2} b^{5} + 2 \, B a b^{6} + A b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{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 + 3*C)*a^5*b + 4*B*a^4*b^2 - (A + 2*C)*a^3*b^3 + (B*a^3*b^3 - (4*A + 3*C)*a^2*b^4 + 4*B*a*b^5 - (A + 2*C)*b^6)*cos(d*x + c)^3 + 3*(B*a^4*b^2 - (4*A + 3*C)*a^3*b^3 + 4*B*a^2*b^4 - (A + 2*C)*a*b^5)*cos(d*x + c)^2 + 3*(B*a^5*b - (4*A + 3*C)*a^4*b^2 + 4*B*a^3*b^3 - (A + 2*C)*a^2*b^4)*cos(d*x + c))*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*(3*A + 2*C)*a^7 - 13*B*a^6*b + (4*A + 7*C)*a^5*b^2 + 11*B*a^4*b^3 - 11*(A + C)*a^3*b^4 + 2*B*a^2*b^5 + A*a*b^6 + (2*C*a^7 + B*a^6*b + (2*A - 7*C)*a^5*b^2 - 11*B*a^4*b^3 + (11*A + 23*C)*a^3*b^4 + 4*B*a^2*b^5 - (13*A + 18*C)*a*b^6 + 6*B*b^7)*cos(d*x + c)^2 + 3*(B*a^7 + (2*A + C)*a^6*b - 10*B*a^5*b^2 + (7*A + 8*C)*a^4*b^3 + 7*B*a^3*b^4 - (10*A + 9*C)*a^2*b^5 + 2*B*a*b^6 + A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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 + 3*C)*a^5*b + 4*B*a^4*b^2 - (A + 2*C)*a^3*b^3 + (B*a^3*b^3 - (4*A + 3*C)*a^2*b^4 + 4*B*a*b^5 - (A + 2*C)*b^6)*cos(d*x + c)^3 + 3*(B*a^4*b^2 - (4*A + 3*C)*a^3*b^3 + 4*B*a^2*b^4 - (A + 2*C)*a*b^5)*cos(d*x + c)^2 + 3*(B*a^5*b - (4*A + 3*C)*a^4*b^2 + 4*B*a^3*b^3 - (A + 2*C)*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) + (2*(3*A + 2*C)*a^7 - 13*B*a^6*b + (4*A + 7*C)*a^5*b^2 + 11*B*a^4*b^3 - 11*(A + C)*a^3*b^4 + 2*B*a^2*b^5 + A*a*b^6 + (2*C*a^7 + B*a^6*b + (2*A - 7*C)*a^5*b^2 - 11*B*a^4*b^3 + (11*A + 23*C)*a^3*b^4 + 4*B*a^2*b^5 - (13*A + 18*C)*a*b^6 + 6*B*b^7)*cos(d*x + c)^2 + 3*(B*a^7 + (2*A + C)*a^6*b - 10*B*a^5*b^2 + (7*A + 8*C)*a^4*b^3 + 7*B*a^3*b^4 - (10*A + 9*C)*a^2*b^5 + 2*B*a*b^6 + A*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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
1005,1,1404,0,0.749377," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, A + C\right)} a^{6} - 4 \, B a^{5} b + {\left(3 \, A + 4 \, C\right)} a^{4} b^{2} - B a^{3} b^{3} + {\left({\left(2 \, A + C\right)} a^{3} b^{3} - 4 \, B a^{2} b^{4} + {\left(3 \, A + 4 \, C\right)} a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(2 \, A + C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + {\left(3 \, A + 4 \, C\right)} a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{5} b - 4 \, B a^{4} b^{2} + {\left(3 \, A + 4 \, C\right)} a^{3} b^{3} - B a^{2} b^{4}\right)} \cos\left(d x + c\right)\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} - {\left(18 \, A + 13 \, C\right)} a^{6} b + 4 \, B a^{5} b^{2} + {\left(23 \, A + 11 \, C\right)} a^{4} b^{3} - 11 \, B a^{3} b^{4} - {\left(7 \, A - 2 \, C\right)} a^{2} b^{5} + B a b^{6} + 2 \, A b^{7} + {\left(C a^{6} b + 2 \, B a^{5} b^{2} - 11 \, {\left(A + C\right)} a^{4} b^{3} + 11 \, B a^{3} b^{4} + {\left(7 \, A + 4 \, C\right)} a^{2} b^{5} - 13 \, B a b^{6} + 2 \, {\left(2 \, A + 3 \, C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{7} + 2 \, B a^{6} b - {\left(9 \, A + 10 \, C\right)} a^{5} b^{2} + 7 \, B a^{4} b^{3} + {\left(8 \, A + 7 \, C\right)} a^{3} b^{4} - 10 \, B a^{2} b^{5} + {\left(A + 2 \, C\right)} a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{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({\left(2 \, A + C\right)} a^{6} - 4 \, B a^{5} b + {\left(3 \, A + 4 \, C\right)} a^{4} b^{2} - B a^{3} b^{3} + {\left({\left(2 \, A + C\right)} a^{3} b^{3} - 4 \, B a^{2} b^{4} + {\left(3 \, A + 4 \, C\right)} a b^{5} - B b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(2 \, A + C\right)} a^{4} b^{2} - 4 \, B a^{3} b^{3} + {\left(3 \, A + 4 \, C\right)} a^{2} b^{4} - B a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + C\right)} a^{5} b - 4 \, B a^{4} b^{2} + {\left(3 \, A + 4 \, C\right)} a^{3} b^{3} - B a^{2} b^{4}\right)} \cos\left(d x + c\right)\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} - {\left(18 \, A + 13 \, C\right)} a^{6} b + 4 \, B a^{5} b^{2} + {\left(23 \, A + 11 \, C\right)} a^{4} b^{3} - 11 \, B a^{3} b^{4} - {\left(7 \, A - 2 \, C\right)} a^{2} b^{5} + B a b^{6} + 2 \, A b^{7} + {\left(C a^{6} b + 2 \, B a^{5} b^{2} - 11 \, {\left(A + C\right)} a^{4} b^{3} + 11 \, B a^{3} b^{4} + {\left(7 \, A + 4 \, C\right)} a^{2} b^{5} - 13 \, B a b^{6} + 2 \, {\left(2 \, A + 3 \, C\right)} b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(C a^{7} + 2 \, B a^{6} b - {\left(9 \, A + 10 \, C\right)} a^{5} b^{2} + 7 \, B a^{4} b^{3} + {\left(8 \, A + 7 \, C\right)} a^{3} b^{4} - 10 \, B a^{2} b^{5} + {\left(A + 2 \, C\right)} a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{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 + C)*a^6 - 4*B*a^5*b + (3*A + 4*C)*a^4*b^2 - B*a^3*b^3 + ((2*A + C)*a^3*b^3 - 4*B*a^2*b^4 + (3*A + 4*C)*a*b^5 - B*b^6)*cos(d*x + c)^3 + 3*((2*A + C)*a^4*b^2 - 4*B*a^3*b^3 + (3*A + 4*C)*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + 3*((2*A + C)*a^5*b - 4*B*a^4*b^2 + (3*A + 4*C)*a^3*b^3 - B*a^2*b^4)*cos(d*x + c))*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 + 13*C)*a^6*b + 4*B*a^5*b^2 + (23*A + 11*C)*a^4*b^3 - 11*B*a^3*b^4 - (7*A - 2*C)*a^2*b^5 + B*a*b^6 + 2*A*b^7 + (C*a^6*b + 2*B*a^5*b^2 - 11*(A + C)*a^4*b^3 + 11*B*a^3*b^4 + (7*A + 4*C)*a^2*b^5 - 13*B*a*b^6 + 2*(2*A + 3*C)*b^7)*cos(d*x + c)^2 + 3*(C*a^7 + 2*B*a^6*b - (9*A + 10*C)*a^5*b^2 + 7*B*a^4*b^3 + (8*A + 7*C)*a^3*b^4 - 10*B*a^2*b^5 + (A + 2*C)*a*b^6 + B*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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 + C)*a^6 - 4*B*a^5*b + (3*A + 4*C)*a^4*b^2 - B*a^3*b^3 + ((2*A + C)*a^3*b^3 - 4*B*a^2*b^4 + (3*A + 4*C)*a*b^5 - B*b^6)*cos(d*x + c)^3 + 3*((2*A + C)*a^4*b^2 - 4*B*a^3*b^3 + (3*A + 4*C)*a^2*b^4 - B*a*b^5)*cos(d*x + c)^2 + 3*((2*A + C)*a^5*b - 4*B*a^4*b^2 + (3*A + 4*C)*a^3*b^3 - B*a^2*b^4)*cos(d*x + c))*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 + 13*C)*a^6*b + 4*B*a^5*b^2 + (23*A + 11*C)*a^4*b^3 - 11*B*a^3*b^4 - (7*A - 2*C)*a^2*b^5 + B*a*b^6 + 2*A*b^7 + (C*a^6*b + 2*B*a^5*b^2 - 11*(A + C)*a^4*b^3 + 11*B*a^3*b^4 + (7*A + 4*C)*a^2*b^5 - 13*B*a*b^6 + 2*(2*A + 3*C)*b^7)*cos(d*x + c)^2 + 3*(C*a^7 + 2*B*a^6*b - (9*A + 10*C)*a^5*b^2 + 7*B*a^4*b^3 + (8*A + 7*C)*a^3*b^4 - 10*B*a^2*b^5 + (A + 2*C)*a*b^6 + B*b^7)*cos(d*x + c))*sin(d*x + c))/((a^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
1006,1,2458,0,134.921175," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B a^{10} - 4 \, {\left(2 \, A + C\right)} a^{9} b + 3 \, B a^{8} b^{2} + {\left(8 \, A - C\right)} a^{7} b^{3} - 7 \, A a^{5} b^{5} + 2 \, A a^{3} b^{7} + {\left(2 \, B a^{7} b^{3} - 4 \, {\left(2 \, A + C\right)} a^{6} b^{4} + 3 \, B a^{5} b^{5} + {\left(8 \, A - C\right)} a^{4} b^{6} - 7 \, A a^{2} b^{8} + 2 \, A b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{8} b^{2} - 4 \, {\left(2 \, A + C\right)} a^{7} b^{3} + 3 \, B a^{6} b^{4} + {\left(8 \, A - C\right)} a^{5} b^{5} - 7 \, A a^{3} b^{7} + 2 \, A a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{9} b - 4 \, {\left(2 \, A + C\right)} a^{8} b^{2} + 3 \, B a^{7} b^{3} + {\left(8 \, A - C\right)} a^{6} b^{4} - 7 \, A a^{4} b^{6} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)\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(6 \, C a^{11} - 18 \, B a^{10} b + 4 \, {\left(9 \, A + C\right)} a^{9} b^{2} + 23 \, B a^{8} b^{3} - {\left(68 \, A + 11 \, C\right)} a^{7} b^{4} - 7 \, B a^{6} b^{5} + {\left(43 \, A + C\right)} a^{5} b^{6} + 2 \, B a^{4} b^{7} - 11 \, A a^{3} b^{8} + {\left(2 \, C a^{9} b^{2} - 11 \, B a^{8} b^{3} + {\left(26 \, A + 11 \, C\right)} a^{7} b^{4} + 7 \, B a^{6} b^{5} - {\left(43 \, A + 13 \, C\right)} a^{5} b^{6} + 4 \, B a^{4} b^{7} + 23 \, A a^{3} b^{8} - 6 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{10} b - 9 \, B a^{9} b^{2} + {\left(20 \, A + 7 \, C\right)} a^{8} b^{3} + 8 \, B a^{7} b^{4} - 5 \, {\left(7 \, A + 2 \, C\right)} a^{6} b^{5} + B a^{5} b^{6} + {\left(20 \, A + C\right)} a^{4} b^{7} - 5 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{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} - 4 \, {\left(2 \, A + C\right)} a^{9} b + 3 \, B a^{8} b^{2} + {\left(8 \, A - C\right)} a^{7} b^{3} - 7 \, A a^{5} b^{5} + 2 \, A a^{3} b^{7} + {\left(2 \, B a^{7} b^{3} - 4 \, {\left(2 \, A + C\right)} a^{6} b^{4} + 3 \, B a^{5} b^{5} + {\left(8 \, A - C\right)} a^{4} b^{6} - 7 \, A a^{2} b^{8} + 2 \, A b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a^{8} b^{2} - 4 \, {\left(2 \, A + C\right)} a^{7} b^{3} + 3 \, B a^{6} b^{4} + {\left(8 \, A - C\right)} a^{5} b^{5} - 7 \, A a^{3} b^{7} + 2 \, A a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{9} b - 4 \, {\left(2 \, A + C\right)} a^{8} b^{2} + 3 \, B a^{7} b^{3} + {\left(8 \, A - C\right)} a^{6} b^{4} - 7 \, A a^{4} b^{6} + 2 \, A a^{2} b^{8}\right)} \cos\left(d x + c\right)\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(6 \, C a^{11} - 18 \, B a^{10} b + 4 \, {\left(9 \, A + C\right)} a^{9} b^{2} + 23 \, B a^{8} b^{3} - {\left(68 \, A + 11 \, C\right)} a^{7} b^{4} - 7 \, B a^{6} b^{5} + {\left(43 \, A + C\right)} a^{5} b^{6} + 2 \, B a^{4} b^{7} - 11 \, A a^{3} b^{8} + {\left(2 \, C a^{9} b^{2} - 11 \, B a^{8} b^{3} + {\left(26 \, A + 11 \, C\right)} a^{7} b^{4} + 7 \, B a^{6} b^{5} - {\left(43 \, A + 13 \, C\right)} a^{5} b^{6} + 4 \, B a^{4} b^{7} + 23 \, A a^{3} b^{8} - 6 \, A a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{10} b - 9 \, B a^{9} b^{2} + {\left(20 \, A + 7 \, C\right)} a^{8} b^{3} + 8 \, B a^{7} b^{4} - 5 \, {\left(7 \, A + 2 \, C\right)} a^{6} b^{5} + B a^{5} b^{6} + {\left(20 \, A + C\right)} a^{4} b^{7} - 5 \, A a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{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 - 4*(2*A + C)*a^9*b + 3*B*a^8*b^2 + (8*A - C)*a^7*b^3 - 7*A*a^5*b^5 + 2*A*a^3*b^7 + (2*B*a^7*b^3 - 4*(2*A + C)*a^6*b^4 + 3*B*a^5*b^5 + (8*A - C)*a^4*b^6 - 7*A*a^2*b^8 + 2*A*b^10)*cos(d*x + c)^3 + 3*(2*B*a^8*b^2 - 4*(2*A + C)*a^7*b^3 + 3*B*a^6*b^4 + (8*A - C)*a^5*b^5 - 7*A*a^3*b^7 + 2*A*a*b^9)*cos(d*x + c)^2 + 3*(2*B*a^9*b - 4*(2*A + C)*a^8*b^2 + 3*B*a^7*b^3 + (8*A - C)*a^6*b^4 - 7*A*a^4*b^6 + 2*A*a^2*b^8)*cos(d*x + c))*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*(6*C*a^11 - 18*B*a^10*b + 4*(9*A + C)*a^9*b^2 + 23*B*a^8*b^3 - (68*A + 11*C)*a^7*b^4 - 7*B*a^6*b^5 + (43*A + C)*a^5*b^6 + 2*B*a^4*b^7 - 11*A*a^3*b^8 + (2*C*a^9*b^2 - 11*B*a^8*b^3 + (26*A + 11*C)*a^7*b^4 + 7*B*a^6*b^5 - (43*A + 13*C)*a^5*b^6 + 4*B*a^4*b^7 + 23*A*a^3*b^8 - 6*A*a*b^10)*cos(d*x + c)^2 + 3*(2*C*a^10*b - 9*B*a^9*b^2 + (20*A + 7*C)*a^8*b^3 + 8*B*a^7*b^4 - 5*(7*A + 2*C)*a^6*b^5 + B*a^5*b^6 + (20*A + C)*a^4*b^7 - 5*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^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 - 4*(2*A + C)*a^9*b + 3*B*a^8*b^2 + (8*A - C)*a^7*b^3 - 7*A*a^5*b^5 + 2*A*a^3*b^7 + (2*B*a^7*b^3 - 4*(2*A + C)*a^6*b^4 + 3*B*a^5*b^5 + (8*A - C)*a^4*b^6 - 7*A*a^2*b^8 + 2*A*b^10)*cos(d*x + c)^3 + 3*(2*B*a^8*b^2 - 4*(2*A + C)*a^7*b^3 + 3*B*a^6*b^4 + (8*A - C)*a^5*b^5 - 7*A*a^3*b^7 + 2*A*a*b^9)*cos(d*x + c)^2 + 3*(2*B*a^9*b - 4*(2*A + C)*a^8*b^2 + 3*B*a^7*b^3 + (8*A - C)*a^6*b^4 - 7*A*a^4*b^6 + 2*A*a^2*b^8)*cos(d*x + c))*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) + (6*C*a^11 - 18*B*a^10*b + 4*(9*A + C)*a^9*b^2 + 23*B*a^8*b^3 - (68*A + 11*C)*a^7*b^4 - 7*B*a^6*b^5 + (43*A + C)*a^5*b^6 + 2*B*a^4*b^7 - 11*A*a^3*b^8 + (2*C*a^9*b^2 - 11*B*a^8*b^3 + (26*A + 11*C)*a^7*b^4 + 7*B*a^6*b^5 - (43*A + 13*C)*a^5*b^6 + 4*B*a^4*b^7 + 23*A*a^3*b^8 - 6*A*a*b^10)*cos(d*x + c)^2 + 3*(2*C*a^10*b - 9*B*a^9*b^2 + (20*A + 7*C)*a^8*b^3 + 8*B*a^7*b^4 - 5*(7*A + 2*C)*a^6*b^5 + B*a^5*b^6 + (20*A + C)*a^4*b^7 - 5*A*a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^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
1007,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1008,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1009,1,27,0,0.879510," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(C a - B b\right)} d x - C b \sin\left(d x + c\right)}{d}"," ",0,"-((C*a - B*b)*d*x - C*b*sin(d*x + c))/d","A",0
1010,1,240,0,1.073428," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(C a^{2} - C b^{2}\right)} d x + {\left(2 \, C a - B 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^{2}\right)} d}, \frac{{\left(C a^{2} - C b^{2}\right)} d x - {\left(2 \, C a - B 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^{2}\right)} d}\right]"," ",0,"[1/2*(2*(C*a^2 - C*b^2)*d*x + (2*C*a - B*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^2)*d), ((C*a^2 - C*b^2)*d*x - (2*C*a - B*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^2)*d)]","A",0
1011,1,421,0,0.768861," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(C a^{3} - B a^{2} b + C a b^{2} + {\left(C a^{2} b - B a b^{2} + C 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 \, C a^{3} b - B a^{2} b^{2} - 2 \, C a b^{3} + B b^{4}\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(C a^{3} - B a^{2} b + C a b^{2} + {\left(C a^{2} b - B a b^{2} + C 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 \, C a^{3} b - B a^{2} b^{2} - 2 \, C a b^{3} + B b^{4}\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*((C*a^3 - B*a^2*b + C*a*b^2 + (C*a^2*b - B*a*b^2 + C*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*C*a^3*b - B*a^2*b^2 - 2*C*a*b^3 + B*b^4)*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), -((C*a^3 - B*a^2*b + C*a*b^2 + (C*a^2*b - B*a*b^2 + C*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*C*a^3*b - B*a^2*b^2 - 2*C*a*b^3 + B*b^4)*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
1012,1,803,0,1.507965," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, C a^{5} - 2 \, B a^{4} b + 4 \, C a^{3} b^{2} - B a^{2} b^{3} + {\left(2 \, C a^{3} b^{2} - 2 \, B a^{2} b^{3} + 4 \, C a b^{4} - B b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{4} b - 2 \, B a^{3} b^{2} + 4 \, C a^{2} b^{3} - B a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{5} b - 4 \, B a^{4} b^{2} - 6 \, C a^{3} b^{3} + 5 \, B a^{2} b^{4} - B b^{6} + {\left(4 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} - 2 \, C a^{2} b^{4} + 3 \, B a b^{5} - 2 \, C b^{6}\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 \, C a^{5} - 2 \, B a^{4} b + 4 \, C a^{3} b^{2} - B a^{2} b^{3} + {\left(2 \, C a^{3} b^{2} - 2 \, B a^{2} b^{3} + 4 \, C a b^{4} - B b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, C a^{4} b - 2 \, B a^{3} b^{2} + 4 \, C a^{2} b^{3} - B a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(6 \, C a^{5} b - 4 \, B a^{4} b^{2} - 6 \, C a^{3} b^{3} + 5 \, B a^{2} b^{4} - B b^{6} + {\left(4 \, C a^{4} b^{2} - 3 \, B a^{3} b^{3} - 2 \, C a^{2} b^{4} + 3 \, B a b^{5} - 2 \, C b^{6}\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*C*a^5 - 2*B*a^4*b + 4*C*a^3*b^2 - B*a^2*b^3 + (2*C*a^3*b^2 - 2*B*a^2*b^3 + 4*C*a*b^4 - B*b^5)*cos(d*x + c)^2 + 2*(2*C*a^4*b - 2*B*a^3*b^2 + 4*C*a^2*b^3 - B*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (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*C*a^5*b - 4*B*a^4*b^2 - 6*C*a^3*b^3 + 5*B*a^2*b^4 - B*b^6 + (4*C*a^4*b^2 - 3*B*a^3*b^3 - 2*C*a^2*b^4 + 3*B*a*b^5 - 2*C*b^6)*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*C*a^5 - 2*B*a^4*b + 4*C*a^3*b^2 - B*a^2*b^3 + (2*C*a^3*b^2 - 2*B*a^2*b^3 + 4*C*a*b^4 - B*b^5)*cos(d*x + c)^2 + 2*(2*C*a^4*b - 2*B*a^3*b^2 + 4*C*a^2*b^3 - B*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))) - (6*C*a^5*b - 4*B*a^4*b^2 - 6*C*a^3*b^3 + 5*B*a^2*b^4 - B*b^6 + (4*C*a^4*b^2 - 3*B*a^3*b^3 - 2*C*a^2*b^4 + 3*B*a*b^5 - 2*C*b^6)*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
1013,1,1305,0,1.154641," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, C a^{7} - 2 \, B a^{6} b + 7 \, C a^{5} b^{2} - 3 \, B a^{4} b^{3} + C a^{3} b^{4} + {\left(2 \, C a^{4} b^{3} - 2 \, B a^{3} b^{4} + 7 \, C a^{2} b^{5} - 3 \, B a b^{6} + C b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} + 7 \, C a^{3} b^{4} - 3 \, B a^{2} b^{5} + C a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{6} b - 2 \, B a^{5} b^{2} + 7 \, C a^{4} b^{3} - 3 \, B a^{3} b^{4} + C a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(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 \, C a^{7} b - 18 \, B a^{6} b^{2} - 19 \, C a^{5} b^{3} + 23 \, B a^{4} b^{4} - 4 \, C a^{3} b^{5} - 7 \, B a^{2} b^{6} - C a b^{7} + 2 \, B b^{8} + {\left(13 \, C a^{5} b^{3} - 11 \, B a^{4} b^{4} + 4 \, C a^{3} b^{5} + 7 \, B a^{2} b^{6} - 17 \, C a b^{7} + 4 \, B b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(11 \, C a^{6} b^{2} - 9 \, B a^{5} b^{3} - C a^{4} b^{4} + 8 \, B a^{3} b^{5} - 11 \, C a^{2} b^{6} + B a b^{7} + C b^{8}\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 \, C a^{7} - 2 \, B a^{6} b + 7 \, C a^{5} b^{2} - 3 \, B a^{4} b^{3} + C a^{3} b^{4} + {\left(2 \, C a^{4} b^{3} - 2 \, B a^{3} b^{4} + 7 \, C a^{2} b^{5} - 3 \, B a b^{6} + C b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, C a^{5} b^{2} - 2 \, B a^{4} b^{3} + 7 \, C a^{3} b^{4} - 3 \, B a^{2} b^{5} + C a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, C a^{6} b - 2 \, B a^{5} b^{2} + 7 \, C a^{4} b^{3} - 3 \, B a^{3} b^{4} + C a^{2} b^{5}\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 \, C a^{7} b - 18 \, B a^{6} b^{2} - 19 \, C a^{5} b^{3} + 23 \, B a^{4} b^{4} - 4 \, C a^{3} b^{5} - 7 \, B a^{2} b^{6} - C a b^{7} + 2 \, B b^{8} + {\left(13 \, C a^{5} b^{3} - 11 \, B a^{4} b^{4} + 4 \, C a^{3} b^{5} + 7 \, B a^{2} b^{6} - 17 \, C a b^{7} + 4 \, B b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(11 \, C a^{6} b^{2} - 9 \, B a^{5} b^{3} - C a^{4} b^{4} + 8 \, B a^{3} b^{5} - 11 \, C a^{2} b^{6} + B a b^{7} + C b^{8}\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*C*a^7 - 2*B*a^6*b + 7*C*a^5*b^2 - 3*B*a^4*b^3 + C*a^3*b^4 + (2*C*a^4*b^3 - 2*B*a^3*b^4 + 7*C*a^2*b^5 - 3*B*a*b^6 + C*b^7)*cos(d*x + c)^3 + 3*(2*C*a^5*b^2 - 2*B*a^4*b^3 + 7*C*a^3*b^4 - 3*B*a^2*b^5 + C*a*b^6)*cos(d*x + c)^2 + 3*(2*C*a^6*b - 2*B*a^5*b^2 + 7*C*a^4*b^3 - 3*B*a^3*b^4 + C*a^2*b^5)*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*C*a^7*b - 18*B*a^6*b^2 - 19*C*a^5*b^3 + 23*B*a^4*b^4 - 4*C*a^3*b^5 - 7*B*a^2*b^6 - C*a*b^7 + 2*B*b^8 + (13*C*a^5*b^3 - 11*B*a^4*b^4 + 4*C*a^3*b^5 + 7*B*a^2*b^6 - 17*C*a*b^7 + 4*B*b^8)*cos(d*x + c)^2 + 3*(11*C*a^6*b^2 - 9*B*a^5*b^3 - C*a^4*b^4 + 8*B*a^3*b^5 - 11*C*a^2*b^6 + B*a*b^7 + C*b^8)*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*C*a^7 - 2*B*a^6*b + 7*C*a^5*b^2 - 3*B*a^4*b^3 + C*a^3*b^4 + (2*C*a^4*b^3 - 2*B*a^3*b^4 + 7*C*a^2*b^5 - 3*B*a*b^6 + C*b^7)*cos(d*x + c)^3 + 3*(2*C*a^5*b^2 - 2*B*a^4*b^3 + 7*C*a^3*b^4 - 3*B*a^2*b^5 + C*a*b^6)*cos(d*x + c)^2 + 3*(2*C*a^6*b - 2*B*a^5*b^2 + 7*C*a^4*b^3 - 3*B*a^3*b^4 + C*a^2*b^5)*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*C*a^7*b - 18*B*a^6*b^2 - 19*C*a^5*b^3 + 23*B*a^4*b^4 - 4*C*a^3*b^5 - 7*B*a^2*b^6 - C*a*b^7 + 2*B*b^8 + (13*C*a^5*b^3 - 11*B*a^4*b^4 + 4*C*a^3*b^5 + 7*B*a^2*b^6 - 17*C*a*b^7 + 4*B*b^8)*cos(d*x + c)^2 + 3*(11*C*a^6*b^2 - 9*B*a^5*b^3 - C*a^4*b^4 + 8*B*a^3*b^5 - 11*C*a^2*b^6 + B*a*b^7 + C*b^8)*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
1014,0,0,0,1.116386," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
1015,0,0,0,0.681617," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
1016,0,0,0,0.774969," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a), x)","F",0
1017,0,0,0,2.233774," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right), x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
1018,0,0,0,4.876582," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
1019,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1020,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1021,0,0,0,1.187772," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{5} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^5 + (C*a + 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
1022,0,0,0,0.976685," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^4 + (C*a + 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
1023,0,0,0,1.913627," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1024,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1025,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1026,0,0,0,11.199224," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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)^{3}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + (C*a + 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, x)","F",0
1027,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1028,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1029,0,0,0,1.985176," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{6} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{5} + A a^{2} \cos\left(d x + c\right)^{2} + {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{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((C*b^2*cos(d*x + c)^6 + (2*C*a*b + B*b^2)*cos(d*x + c)^5 + A*a^2*cos(d*x + c)^2 + (C*a^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
1030,0,0,0,0.576878," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{5} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{4} + A a^{2} \cos\left(d x + c\right) + {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{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((C*b^2*cos(d*x + c)^5 + (2*C*a*b + B*b^2)*cos(d*x + c)^4 + A*a^2*cos(d*x + c) + (C*a^2 + 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
1031,0,0,0,0.612564," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1032,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1033,0,0,0,8.282139," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1034,0,0,0,9.713079," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1035,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1036,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1037,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1038,0,0,0,1.142083," ","integrate((a+b*cos(d*x+c))^(3/2)*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{3} - C a^{3} + B a^{2} b + {\left(C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(C a^{2} b - 2 \, B a b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^3 - C*a^3 + B*a^2*b + (C*a*b^2 + B*b^3)*cos(d*x + c)^2 - (C*a^2*b - 2*B*a*b^2)*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
1039,0,0,0,0.794471," ","integrate((a+b*cos(d*x+c))^(1/2)*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)*sqrt(b*cos(d*x + c) + a), x)","F",0
1040,0,0,0,1.091954," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + B*cos(d*x + c)^3 + A*cos(d*x + c)^2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1041,0,0,0,0.750276," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + B*cos(d*x + c)^2 + A*cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1042,0,0,0,0.710021," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sqrt(b*cos(d*x + c) + a), x)","F",0
1043,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1044,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1045,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1046,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1047,0,0,0,2.045887," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + 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
1048,0,0,0,1.115139," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
1049,0,0,0,1.161032," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
1050,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1051,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1052,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1053,0,0,0,1.586629," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{5} + 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((C*cos(d*x + c)^5 + 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
1054,0,0,0,1.052806," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{4} + 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((C*cos(d*x + c)^4 + 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
1055,0,0,0,0.924543," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
1056,0,0,0,0.673267," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{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((C*cos(d*x + c)^2 + 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
1057,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1058,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1059,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1060,0,0,0,1.236495," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{b^{4} \cos\left(d x + c\right)^{4} + 4 \, a b^{3} \cos\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} + 4 \, a^{3} b \cos\left(d x + c\right) + a^{4}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/(b^4*cos(d*x + c)^4 + 4*a*b^3*cos(d*x + c)^3 + 6*a^2*b^2*cos(d*x + c)^2 + 4*a^3*b*cos(d*x + c) + a^4), x)","F",0
1061,0,0,0,1.403212," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right) - C a + B b\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*b*cos(d*x + c) - C*a + B*b)*sqrt(b*cos(d*x + c) + a), x)","F",0
1062,0,0,0,1.080819," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right) - C a + B b}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*b*cos(d*x + c) - C*a + B*b)/sqrt(b*cos(d*x + c) + a), x)","F",0
1063,0,0,0,1.189519," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right) - C a + B b\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((C*b*cos(d*x + c) - C*a + B*b)*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
1064,0,0,0,0.652908," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right) - C a + B b\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((C*b*cos(d*x + c) - C*a + B*b)*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
1065,0,0,0,0.471477," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{4} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^4 + (C*a + 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
1066,0,0,0,0.503351," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1067,0,0,0,0.494389," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1068,0,0,0,0.490305," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1069,0,0,0,0.545614," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1070,0,0,0,0.475926," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1071,0,0,0,0.467937," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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{9}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + (C*a + B*b)*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))/cos(d*x + c)^(9/2), x)","F",0
1072,0,0,0,0.676367," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{5} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{4} + A a^{2} \cos\left(d x + c\right) + {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{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((C*b^2*cos(d*x + c)^5 + (2*C*a*b + B*b^2)*cos(d*x + c)^4 + A*a^2*cos(d*x + c) + (C*a^2 + 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
1073,0,0,0,0.537326," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1074,0,0,0,0.513802," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1075,0,0,0,0.512583," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1076,0,0,0,0.499046," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1077,0,0,0,0.652134," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1078,0,0,0,0.596436," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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{9}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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)^(9/2), x)","F",0
1079,0,0,0,0.526754," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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{11}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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)^(11/2), x)","F",0
1080,0,0,0,0.709327," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1081,0,0,0,0.636051," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1082,0,0,0,0.554444," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1083,0,0,0,0.521666," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1084,0,0,0,0.652695," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1085,0,0,0,0.763493," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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)^(9/2), x)","F",0
1086,0,0,0,0.630774," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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)^(11/2), x)","F",0
1087,0,0,0,0.575211," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1088,0,0,0,0.662664," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
1089,0,0,0,0.567768," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
1090,0,0,0,0.549084," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))/cos(d*x + c)^(5/2), x)","F",0
1091,0,0,0,0.547647," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))/cos(d*x + c)^(7/2), x)","F",0
1092,0,0,0,0.568937," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))/cos(d*x + c)^(9/2), x)","F",0
1093,0,0,0,0.613467," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))/cos(d*x + c)^(11/2), x)","F",0
1094,0,0,0,0.562913," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{13}{2}}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))/cos(d*x + c)^(13/2), x)","F",0
1095,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1096,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1097,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1098,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1099,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1100,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1101,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1102,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1103,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1104,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1105,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1106,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1107,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1108,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1109,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1110,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1111,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1112,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1113,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1114,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1115,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1116,0,0,0,124.913522," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1117,0,0,0,4.981252," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1118,0,0,0,60.753610," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1119,0,0,0,1.070602," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
1120,0,0,0,0.581223," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
1121,0,0,0,0.576720," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
1122,0,0,0,93.344446," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1123,0,0,0,76.728370," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1124,0,0,0,2.696243," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1125,0,0,0,1.243717," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1126,0,0,0,23.201429," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1127,0,0,0,0.578235," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1128,0,0,0,0.843522," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1129,0,0,0,6.717420," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1130,0,0,0,97.016531," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1131,0,0,0,2.866672," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1132,0,0,0,2.183060," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1133,0,0,0,50.283562," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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{7}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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)^(7/2), x)","F",0
1134,0,0,0,0.936496," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1135,0,0,0,0.500945," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1136,0,0,0,2.748757," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
1137,0,0,0,80.330694," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1138,0,0,0,1.224461," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
1139,0,0,0,0.800166," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
1140,0,0,0,0.452117," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
1141,0,0,0,0.454716," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{5} + a \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
1142,0,0,0,0.480778," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{6} + a \cos\left(d x + c\right)^{5}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)^6 + a*cos(d*x + c)^5), x)","F",0
1143,0,0,0,1.550688," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""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
1144,0,0,0,0.457044," ","integrate((a+a*cos(d*x+c)+2*b*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, b \cos\left(d x + c\right)^{2} + a \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((2*b*cos(d*x + c)^2 + a*cos(d*x + c) + a)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)^2 + a*cos(d*x + c)), x)","F",0
1145,0,0,0,75.908354," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
1146,0,0,0,1.285071," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
1147,0,0,0,0.860446," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
1148,0,0,0,0.485476," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
1149,0,0,0,0.502937," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
1150,0,0,0,0.537257," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{6} + 2 \, a b \cos\left(d x + c\right)^{5} + a^{2} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^6 + 2*a*b*cos(d*x + c)^5 + a^2*cos(d*x + c)^4), x)","F",0
1151,0,0,0,53.201347," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{3} + 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((C*cos(d*x + c)^3 + 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
1152,0,0,0,1.014944," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
1153,0,0,0,0.608424," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
1154,0,0,0,0.555010," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
1155,0,0,0,0.537695," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
1156,0,0,0,0.429292," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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)^m, x)","F",0
1157,0,0,0,0.426085," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + (C*a + B*b)*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*cos(d*x + c)^m, x)","F",0
1158,0,0,0,0.464185," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{m}}{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^m/(b*cos(d*x + c) + a), x)","F",0
1159,0,0,0,0.503681," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{m}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^m/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
1160,0,0,0,0.466346," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)*sec(d*x + c)^(9/2), x)","F",0
1161,0,0,0,0.421226," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)*sec(d*x + c)^(7/2), x)","F",0
1162,0,0,0,0.450105," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)*sec(d*x + c)^(5/2), x)","F",0
1163,0,0,0,1.219318," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)*sec(d*x + c)^(3/2), x)","F",0
1164,0,0,0,0.442143," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)*sqrt(sec(d*x + c)), x)","F",0
1165,0,0,0,0.427329," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)/sqrt(sec(d*x + c)), x)","F",0
1166,0,0,0,0.444782," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A a \cos\left(d x + c\right) + A a}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*a*cos(d*x + c) + A*a)/sec(d*x + c)^(3/2), x)","F",0
1167,0,0,0,0.423452," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)*sec(d*x + c)^(11/2), x)","F",0
1168,0,0,0,0.498637," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)*sec(d*x + c)^(9/2), x)","F",0
1169,0,0,0,0.517267," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A 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((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)*sec(d*x + c)^(7/2), x)","F",0
1170,0,0,0,0.534607," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A 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((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)*sec(d*x + c)^(5/2), x)","F",0
1171,0,0,0,0.494432," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A 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((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)*sec(d*x + c)^(3/2), x)","F",0
1172,0,0,0,0.449437," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)*sqrt(sec(d*x + c)), x)","F",0
1173,0,0,0,0.522537," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)/sqrt(sec(d*x + c)), x)","F",0
1174,0,0,0,0.451814," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + 2 \, C a^{2} \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, A a^{2} \cos\left(d x + c\right) + A a^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + 2*C*a^2*cos(d*x + c)^3 + (A + C)*a^2*cos(d*x + c)^2 + 2*A*a^2*cos(d*x + c) + A*a^2)/sec(d*x + c)^(3/2), x)","F",0
1175,0,0,0,0.425593," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sec\left(d x + c\right)^{\frac{13}{2}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(13/2), x)","F",0
1176,0,0,0,1.174394," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(11/2), x)","F",0
1177,0,0,0,0.612430," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A 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((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(9/2), x)","F",0
1178,0,0,0,0.449994," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A 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((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(7/2), x)","F",0
1179,0,0,0,0.467951," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A 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((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(5/2), x)","F",0
1180,0,0,0,0.446220," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A 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((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(3/2), x)","F",0
1181,0,0,0,0.453562," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)*sqrt(sec(d*x + c)), x)","F",0
1182,0,0,0,0.454159," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)/sqrt(sec(d*x + c)), x)","F",0
1183,0,0,0,0.437388," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + 3 \, C a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + C\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, A a^{3} \cos\left(d x + c\right) + A a^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + 3*C*a^3*cos(d*x + c)^4 + (A + 3*C)*a^3*cos(d*x + c)^3 + (3*A + C)*a^3*cos(d*x + c)^2 + 3*A*a^3*cos(d*x + c) + A*a^3)/sec(d*x + c)^(3/2), x)","F",0
1184,0,0,0,0.458077," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a), x)","F",0
1185,0,0,0,0.450194," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
1186,0,0,0,0.475630," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
1187,0,0,0,0.447582," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
1188,0,0,0,0.506460," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1189,0,0,0,0.446934," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1190,0,0,0,0.535486," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1191,0,0,0,0.443265," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{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((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
1192,0,0,0,0.526399," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1193,0,0,0,0.402464," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1194,0,0,0,0.436116," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1195,0,0,0,0.577364," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1196,0,0,0,0.421772," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1197,0,0,0,0.419303," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{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((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(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
1198,0,0,0,0.431224," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1199,0,0,0,0.448859," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1200,0,0,0,0.408100," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1201,0,0,0,0.470867," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1202,0,0,0,0.486627," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1203,0,0,0,0.453826," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1204,1,115,0,0.405766," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(16 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(16 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(16 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{2} + 40 \, A \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*(8*(16*A + 21*C)*cos(d*x + c)^4 + 4*(16*A + 21*C)*cos(d*x + c)^3 + 3*(16*A + 21*C)*cos(d*x + c)^2 + 40*A*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
1205,1,97,0,0.466913," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(24 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(24 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 18 \, A \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*(2*(24*A + 35*C)*cos(d*x + c)^3 + (24*A + 35*C)*cos(d*x + c)^2 + 18*A*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
1206,1,80,0,0.496362," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(8 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{2} + 4 \, A \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*((8*A + 15*C)*cos(d*x + c)^2 + 4*A*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
1207,1,120,0,0.548457," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, {\left(C \cos\left(d x + c\right)^{2} + C \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(2 \, A \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)}}\right)}}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"-2/3*(3*(C*cos(d*x + c)^2 + C*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))) - (2*A*cos(d*x + c) + 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
1208,1,102,0,0.497766," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(C \cos\left(d x + c\right) + C\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(C \cos\left(d x + c\right) + 2 \, 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,"-((C*cos(d*x + c) + C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (C*cos(d*x + c) + 2*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
1209,1,122,0,0.542687," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(8 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 3 \, C\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 \, C \cos\left(d x + c\right)^{2} + 3 \, C \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*(((8*A + 3*C)*cos(d*x + c) + 8*A + 3*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (2*C*cos(d*x + c)^2 + 3*C*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
1210,1,140,0,0.540767," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(8 \, A + 5 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 5 \, C\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 \, C \cos\left(d x + c\right)^{3} + 10 \, C \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 5 \, C\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*((8*A + 5*C)*cos(d*x + c) + 8*A + 5*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*C*cos(d*x + c)^3 + 10*C*cos(d*x + c)^2 + 3*(8*A + 5*C)*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
1211,1,157,0,0.622998," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(48 \, A + 35 \, C\right)} \cos\left(d x + c\right) + 48 \, A + 35 \, C\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 \, C \cos\left(d x + c\right)^{4} + 56 \, C \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(48 \, A + 35 \, C\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)}}}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/192*(3*((48*A + 35*C)*cos(d*x + c) + 48*A + 35*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (48*C*cos(d*x + c)^4 + 56*C*cos(d*x + c)^3 + 2*(48*A + 35*C)*cos(d*x + c)^2 + 3*(48*A + 35*C)*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
1212,1,138,0,0.416104," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(112 \, A + 143 \, C\right)} a \cos\left(d x + c\right)^{5} + 4 \, {\left(112 \, A + 143 \, C\right)} a \cos\left(d x + c\right)^{4} + 3 \, {\left(112 \, A + 143 \, C\right)} a \cos\left(d x + c\right)^{3} + 5 \, {\left(56 \, A + 33 \, C\right)} a \cos\left(d x + c\right)^{2} + 245 \, A a \cos\left(d x + c\right) + 105 \, A a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{1155 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/1155*(8*(112*A + 143*C)*a*cos(d*x + c)^5 + 4*(112*A + 143*C)*a*cos(d*x + c)^4 + 3*(112*A + 143*C)*a*cos(d*x + c)^3 + 5*(56*A + 33*C)*a*cos(d*x + c)^2 + 245*A*a*cos(d*x + c) + 105*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
1213,1,119,0,0.481978," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(136 \, A + 189 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(136 \, A + 189 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(34 \, A + 21 \, C\right)} a \cos\left(d x + c\right)^{2} + 85 \, A 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*(2*(136*A + 189*C)*a*cos(d*x + c)^4 + (136*A + 189*C)*a*cos(d*x + c)^3 + 3*(34*A + 21*C)*a*cos(d*x + c)^2 + 85*A*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
1214,1,100,0,0.465055," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(104 \, A + 175 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(52 \, A + 35 \, C\right)} a \cos\left(d x + c\right)^{2} + 39 \, A 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*((104*A + 175*C)*a*cos(d*x + c)^3 + (52*A + 35*C)*a*cos(d*x + c)^2 + 39*A*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
1215,1,146,0,0.477521," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, {\left(C a \cos\left(d x + c\right)^{3} + C 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) - \frac{{\left({\left(6 \, A + 5 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, A 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)}}{5 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-2/5*(5*(C*a*cos(d*x + c)^3 + C*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))) - ((6*A + 5*C)*a*cos(d*x + c)^2 + 3*A*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)^3 + d*cos(d*x + c)^2)","A",0
1216,1,138,0,0.443398," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{9 \, {\left(C a \cos\left(d x + c\right)^{2} + C a \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\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 \, C a \cos\left(d x + c\right)^{2} + 10 \, A 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)}}}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(9*(C*a*cos(d*x + c)^2 + C*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))) - (3*C*a*cos(d*x + c)^2 + 10*A*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)^2 + d*cos(d*x + c))","A",0
1217,1,132,0,0.601434," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left({\left(8 \, A + 7 \, C\right)} a \cos\left(d x + c\right) + {\left(8 \, A + 7 \, C\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 \, C a \cos\left(d x + c\right)^{2} + 7 \, C 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)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/4*(((8*A + 7*C)*a*cos(d*x + c) + (8*A + 7*C)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (2*C*a*cos(d*x + c)^2 + 7*C*a*cos(d*x + c) + 8*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
1218,1,147,0,0.791619," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(24 \, A + 11 \, C\right)} a \cos\left(d x + c\right) + {\left(24 \, A + 11 \, C\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 \, C a \cos\left(d x + c\right)^{3} + 22 \, C a \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 11 \, C\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*((24*A + 11*C)*a*cos(d*x + c) + (24*A + 11*C)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*C*a*cos(d*x + c)^3 + 22*C*a*cos(d*x + c)^2 + 3*(8*A + 11*C)*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
1219,1,163,0,0.577142," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(112 \, A + 75 \, C\right)} a \cos\left(d x + c\right) + {\left(112 \, A + 75 \, C\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(16 \, C a \cos\left(d x + c\right)^{4} + 40 \, C a \cos\left(d x + c\right)^{3} + 2 \, {\left(16 \, A + 25 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(112 \, A + 75 \, C\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)}}}{64 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/64*(((112*A + 75*C)*a*cos(d*x + c) + (112*A + 75*C)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (16*C*a*cos(d*x + c)^4 + 40*C*a*cos(d*x + c)^3 + 2*(16*A + 25*C)*a*cos(d*x + c)^2 + (112*A + 75*C)*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
1220,1,183,0,0.603813," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right) + {\left(176 \, A + 133 \, C\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(384 \, C a \cos\left(d x + c\right)^{5} + 912 \, C a \cos\left(d x + c\right)^{4} + 8 \, {\left(80 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{3} + 10 \, {\left(176 \, A + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(176 \, A + 133 \, C\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)}}}{1920 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/1920*(15*((176*A + 133*C)*a*cos(d*x + c) + (176*A + 133*C)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (384*C*a*cos(d*x + c)^5 + 912*C*a*cos(d*x + c)^4 + 8*(80*A + 133*C)*a*cos(d*x + c)^3 + 10*(176*A + 133*C)*a*cos(d*x + c)^2 + 15*(176*A + 133*C)*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
1221,1,170,0,0.502551," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(15/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(8368 \, A + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + 4 \, {\left(8368 \, A + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 3 \, {\left(8368 \, A + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(2092 \, A + 1859 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 35 \, {\left(523 \, A + 143 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 11970 \, A 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*(8*(8368*A + 10439*C)*a^2*cos(d*x + c)^6 + 4*(8368*A + 10439*C)*a^2*cos(d*x + c)^5 + 3*(8368*A + 10439*C)*a^2*cos(d*x + c)^4 + 10*(2092*A + 1859*C)*a^2*cos(d*x + c)^3 + 35*(523*A + 143*C)*a^2*cos(d*x + c)^2 + 11970*A*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
1222,1,148,0,0.474326," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(568 \, A + 759 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(568 \, A + 759 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 6 \, {\left(71 \, A + 66 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(355 \, A + 99 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 224 \, A a^{2} \cos\left(d x + c\right) + 63 \, A a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{693 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/693*(2*(568*A + 759*C)*a^2*cos(d*x + c)^5 + (568*A + 759*C)*a^2*cos(d*x + c)^4 + 6*(71*A + 66*C)*a^2*cos(d*x + c)^3 + (355*A + 99*C)*a^2*cos(d*x + c)^2 + 224*A*a^2*cos(d*x + c) + 63*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
1223,1,129,0,0.417082," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(584 \, A + 903 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 2 \, {\left(146 \, A + 147 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(73 \, A + 21 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 130 \, A 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*((584*A + 903*C)*a^2*cos(d*x + c)^4 + 2*(146*A + 147*C)*a^2*cos(d*x + c)^3 + 3*(73*A + 21*C)*a^2*cos(d*x + c)^2 + 130*A*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
1224,1,177,0,0.479641," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(21 \, {\left(C a^{2} \cos\left(d x + c\right)^{4} + C 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) - \frac{{\left(2 \, {\left(23 \, A + 28 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(23 \, A + 7 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 12 \, A 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)}}{21 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-2/21*(21*(C*a^2*cos(d*x + c)^4 + C*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))) - (2*(23*A + 28*C)*a^2*cos(d*x + c)^3 + (23*A + 7*C)*a^2*cos(d*x + c)^2 + 12*A*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)^4 + d*cos(d*x + c)^3)","A",0
1225,1,172,0,0.463079," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{75 \, {\left(C a^{2} \cos\left(d x + c\right)^{3} + C 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(15 \, C a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(43 \, A + 15 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 28 \, A a^{2} \cos\left(d x + c\right) + 6 \, 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)}}}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/15*(75*(C*a^2*cos(d*x + c)^3 + C*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))) - (15*C*a^2*cos(d*x + c)^3 + 2*(43*A + 15*C)*a^2*cos(d*x + c)^2 + 28*A*a^2*cos(d*x + c) + 6*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
1226,1,174,0,0.512433," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(8 \, A + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 19 \, C\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\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(6 \, C a^{2} \cos\left(d x + c\right)^{3} + 33 \, C a^{2} \cos\left(d x + c\right)^{2} + 64 \, A 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)}}}{12 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"-1/12*(3*((8*A + 19*C)*a^2*cos(d*x + c)^2 + (8*A + 19*C)*a^2*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (6*C*a^2*cos(d*x + c)^3 + 33*C*a^2*cos(d*x + c)^2 + 64*A*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)^2 + d*cos(d*x + c))","A",0
1227,1,163,0,0.547972," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(8 \, A + 5 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(8 \, A + 5 \, C\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 \, C a^{2} \cos\left(d x + c\right)^{3} + 34 \, C a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 25 \, C\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)}{\sqrt{\cos\left(d x + c\right)}}}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/24*(15*((8*A + 5*C)*a^2*cos(d*x + c) + (8*A + 5*C)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*C*a^2*cos(d*x + c)^3 + 34*C*a^2*cos(d*x + c)^2 + 3*(8*A + 25*C)*a^2*cos(d*x + c) + 48*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
1228,1,177,0,0.590929," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(304 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(304 \, A + 163 \, C\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 \, C a^{2} \cos\left(d x + c\right)^{4} + 184 \, C a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(176 \, A + 163 \, C\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*((304*A + 163*C)*a^2*cos(d*x + c) + (304*A + 163*C)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (48*C*a^2*cos(d*x + c)^4 + 184*C*a^2*cos(d*x + c)^3 + 2*(48*A + 163*C)*a^2*cos(d*x + c)^2 + 3*(176*A + 163*C)*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
1229,1,197,0,0.572903," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(400 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(400 \, A + 283 \, C\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 \, C a^{2} \cos\left(d x + c\right)^{5} + 1392 \, C a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(80 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(272 \, A + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(400 \, A + 283 \, C\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*((400*A + 283*C)*a^2*cos(d*x + c) + (400*A + 283*C)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (384*C*a^2*cos(d*x + c)^5 + 1392*C*a^2*cos(d*x + c)^4 + 8*(80*A + 283*C)*a^2*cos(d*x + c)^3 + 10*(272*A + 283*C)*a^2*cos(d*x + c)^2 + 15*(400*A + 283*C)*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
1230,1,217,0,0.623025," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(1304 \, A + 1015 \, C\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(256 \, C a^{2} \cos\left(d x + c\right)^{6} + 896 \, C a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(8 \, A + 29 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(184 \, A + 203 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(1304 \, A + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(1304 \, A + 1015 \, C\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)}}}{1536 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/1536*(3*((1304*A + 1015*C)*a^2*cos(d*x + c) + (1304*A + 1015*C)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (256*C*a^2*cos(d*x + c)^6 + 896*C*a^2*cos(d*x + c)^5 + 48*(8*A + 29*C)*a^2*cos(d*x + c)^4 + 8*(184*A + 203*C)*a^2*cos(d*x + c)^3 + 2*(1304*A + 1015*C)*a^2*cos(d*x + c)^2 + 3*(1304*A + 1015*C)*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
1231,1,190,0,0.717458," ","integrate((A+C*cos(d*x+c)^2)*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 + C\right)} a \cos\left(d x + c\right)^{5} + {\left(A + C\right)} a \cos\left(d x + c\right)^{4}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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 + 273 \, C\right)} \cos\left(d x + c\right)^{4} - {\left(29 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 21 \, C\right)} \cos\left(d x + c\right)^{2} - 5 \, A \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 + C)*a*cos(d*x + c)^5 + (A + C)*a*cos(d*x + c)^4)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*((257*A + 273*C)*cos(d*x + c)^4 - (29*A + 21*C)*cos(d*x + c)^3 + 3*(19*A + 21*C)*cos(d*x + c)^2 - 5*A*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
1232,1,173,0,0.460004," ","integrate((A+C*cos(d*x+c)^2)*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 + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A + C\right)} a \cos\left(d x + c\right)^{3}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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 + 35 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(31 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, A \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 + C)*a*cos(d*x + c)^4 + (A + C)*a*cos(d*x + c)^3)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*((43*A + 35*C)*cos(d*x + c)^3 - (31*A + 35*C)*cos(d*x + c)^2 + 3*A*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
1233,1,156,0,0.466110," ","integrate((A+C*cos(d*x+c)^2)*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 + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A + C\right)} a \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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 + 15 \, C\right)} \cos\left(d x + c\right)^{2} - A \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 + C)*a*cos(d*x + c)^3 + (A + C)*a*cos(d*x + c)^2)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*((13*A + 15*C)*cos(d*x + c)^2 - A*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
1234,1,135,0,0.482988," ","integrate((A+C*cos(d*x+c)^2)*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 + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A + C\right)} a \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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(A \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 + C)*a*cos(d*x + c)^2 + (A + C)*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*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
1235,1,156,0,1.785770," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(C \cos\left(d x + c\right) + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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,"-(2*(C*cos(d*x + c) + 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 + C)*a*cos(d*x + c) + (A + C)*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
1236,1,153,0,2.312341," ","integrate((A+C*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} C \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left(C \cos\left(d x + c\right) + C\right)} \sqrt{a} \arctan\left(\frac{\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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)*C*sqrt(cos(d*x + c))*sin(d*x + c) + (C*cos(d*x + c) + 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 + C)*a*cos(d*x + c) + (A + C)*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
1237,1,186,0,3.963494," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(8 \, A + 7 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 7 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A + C\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 \, C \cos\left(d x + c\right)^{2} - C \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*(((8*A + 7*C)*cos(d*x + c) + 8*A + 7*C)*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 + C)*a*cos(d*x + c) + (A + C)*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*C*cos(d*x + c)^2 - C*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
1238,1,203,0,4.195222," ","integrate((A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(8 \, A + 9 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 9 \, C\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{24 \, \sqrt{2} {\left({\left(A + C\right)} a \cos\left(d x + c\right) + {\left(A + C\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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(8 \, C \cos\left(d x + c\right)^{3} - 2 \, C \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 7 \, C\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(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/24*(3*((8*A + 9*C)*cos(d*x + c) + 8*A + 9*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 24*sqrt(2)*((A + C)*a*cos(d*x + c) + (A + C)*a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + (8*C*cos(d*x + c)^3 - 2*C*cos(d*x + c)^2 + 3*(8*A + 7*C)*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
1239,1,231,0,0.566250," ","integrate((A+C*cos(d*x+c)^2)*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 + 11 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(19 \, A + 11 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(19 \, A + 11 \, C\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 + 665 \, C\right)} \cos\left(d x + c\right)^{4} + 12 \, {\left(67 \, A + 35 \, C\right)} \cos\left(d x + c\right)^{3} - 28 \, {\left(7 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 36 \, A \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 + 11*C)*cos(d*x + c)^5 + 2*(19*A + 11*C)*cos(d*x + c)^4 + (19*A + 11*C)*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 + 665*C)*cos(d*x + c)^4 + 12*(67*A + 35*C)*cos(d*x + c)^3 - 28*(7*A + 5*C)*cos(d*x + c)^2 + 36*A*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
1240,1,214,0,0.510432," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{5 \, \sqrt{2} {\left({\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(15 \, A + 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(15 \, A + 7 \, C\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(49 \, A + 25 \, C\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(9 \, A + 5 \, C\right)} \cos\left(d x + c\right)^{2} - 4 \, A \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)}}}{20 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/20*(5*sqrt(2)*((15*A + 7*C)*cos(d*x + c)^4 + 2*(15*A + 7*C)*cos(d*x + c)^3 + (15*A + 7*C)*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*((49*A + 25*C)*cos(d*x + c)^3 + 4*(9*A + 5*C)*cos(d*x + c)^2 - 4*A*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)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)","A",0
1241,1,193,0,0.462776," ","integrate((A+C*cos(d*x+c)^2)*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 + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, A + 3 \, C\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 + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 12 \, A \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 + 3*C)*cos(d*x + c)^3 + 2*(11*A + 3*C)*cos(d*x + c)^2 + (11*A + 3*C)*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 + 3*C)*cos(d*x + c)^2 + 12*A*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
1242,1,161,0,0.480996," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(7 \, A - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - C\right)} \cos\left(d x + c\right) + 7 \, A - C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 + C\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 - C)*cos(d*x + c)^2 + 2*(7*A - C)*cos(d*x + c) + 7*A - 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*((5*A + C)*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
1243,1,207,0,5.924654," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 5 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 + C\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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)*((3*A - 5*C)*cos(d*x + c)^2 + 2*(3*A - 5*C)*cos(d*x + c) + 3*A - 5*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*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 + C)*sqrt(cos(d*x + c))*sin(d*x + c) + 8*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*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
1244,1,222,0,5.377831," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(A + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A + 9 \, C\right)} \cos\left(d x + c\right) + A + 9 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 12 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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 \, C \cos\left(d x + c\right)^{2} + {\left(A + 3 \, C\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)*((A + 9*C)*cos(d*x + c)^2 + 2*(A + 9*C)*cos(d*x + c) + A + 9*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 12*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(2*C*cos(d*x + c)^2 + (A + 3*C)*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
1245,1,258,0,10.668903," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(5 \, A + 13 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A + 13 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 13 \, C\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) - {\left({\left(8 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A + 19 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 19 \, C\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 \, C \cos\left(d x + c\right)^{3} - 3 \, C \cos\left(d x + c\right)^{2} - {\left(2 \, A + 7 \, C\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 + 13*C)*cos(d*x + c)^2 + 2*(5*A + 13*C)*cos(d*x + c) + 5*A + 13*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - ((8*A + 19*C)*cos(d*x + c)^2 + 2*(8*A + 19*C)*cos(d*x + c) + 8*A + 19*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + (2*C*cos(d*x + c)^3 - 3*C*cos(d*x + c)^2 - (2*A + 7*C)*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
1246,1,262,0,0.509361," ","integrate((A+C*cos(d*x+c)^2)*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 + 75 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(283 \, A + 75 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(283 \, A + 75 \, C\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 + 735 \, C\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(911 \, A + 255 \, C\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(49 \, A + 15 \, C\right)} \cos\left(d x + c\right)^{2} - 160 \, A \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 + 75*C)*cos(d*x + c)^5 + 3*(283*A + 75*C)*cos(d*x + c)^4 + 3*(283*A + 75*C)*cos(d*x + c)^3 + (283*A + 75*C)*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 + 735*C)*cos(d*x + c)^4 + 5*(911*A + 255*C)*cos(d*x + c)^3 + 32*(49*A + 15*C)*cos(d*x + c)^2 - 160*A*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
1247,1,240,0,0.555958," ","integrate((A+C*cos(d*x+c)^2)*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 + 19 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(163 \, A + 19 \, C\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 + 27 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(503 \, A + 39 \, C\right)} \cos\left(d x + c\right)^{2} + 160 \, A \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 + 19*C)*cos(d*x + c)^4 + 3*(163*A + 19*C)*cos(d*x + c)^3 + 3*(163*A + 19*C)*cos(d*x + c)^2 + (163*A + 19*C)*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 + 27*C)*cos(d*x + c)^3 + (503*A + 39*C)*cos(d*x + c)^2 + 160*A*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
1248,1,208,0,0.534039," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{5 \, \sqrt{2} {\left({\left(15 \, A - C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(15 \, A - C\right)} \cos\left(d x + c\right) + 15 \, A - C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 + C\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(17 \, A + C\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*(5*sqrt(2)*((15*A - C)*cos(d*x + c)^3 + 3*(15*A - C)*cos(d*x + c)^2 + 3*(15*A - C)*cos(d*x + c) + 15*A - C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((49*A + C)*cos(d*x + c)^2 + 5*(17*A + C)*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
1249,1,207,0,0.539055," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 3 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 - 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(13 \, A - 3 \, C\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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 3*C)*cos(d*x + c)^2 + 3*(19*A + 3*C)*cos(d*x + c) + 19*A + 3*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((9*A - 7*C)*cos(d*x + c)^2 + (13*A - 3*C)*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
1250,1,275,0,11.409263," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 43 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \sqrt{a} \arctan\left(\frac{\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 - 15 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A - 11 \, C\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 - 43*C)*cos(d*x + c)^3 + 3*(5*A - 43*C)*cos(d*x + c)^2 + 3*(5*A - 43*C)*cos(d*x + c) + 5*A - 43*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 64*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*((A - 15*C)*cos(d*x + c)^2 + (5*A - 11*C)*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
1251,1,288,0,11.329343," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A + 115 \, C\right)} \cos\left(d x + c\right) + 3 \, A + 115 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 160 \, {\left(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \sqrt{a} \arctan\left(\frac{\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 \, C \cos\left(d x + c\right)^{3} + {\left(7 \, A + 55 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A + 35 \, C\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 + 115*C)*cos(d*x + c)^3 + 3*(3*A + 115*C)*cos(d*x + c)^2 + 3*(3*A + 115*C)*cos(d*x + c) + 3*A + 115*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 160*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(16*C*cos(d*x + c)^3 + (7*A + 55*C)*cos(d*x + c)^2 + (3*A + 35*C)*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
1252,1,324,0,19.743117," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(43 \, A + 219 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(43 \, A + 219 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(43 \, A + 219 \, C\right)} \cos\left(d x + c\right) + 43 \, A + 219 \, C\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) - 8 \, {\left({\left(8 \, A + 39 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, A + 39 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 39 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 39 \, C\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(8 \, C \cos\left(d x + c\right)^{4} - 20 \, C \cos\left(d x + c\right)^{3} - 5 \, {\left(3 \, A + 19 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(11 \, A + 63 \, C\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 + 219*C)*cos(d*x + c)^3 + 3*(43*A + 219*C)*cos(d*x + c)^2 + 3*(43*A + 219*C)*cos(d*x + c) + 43*A + 219*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 8*((8*A + 39*C)*cos(d*x + c)^3 + 3*(8*A + 39*C)*cos(d*x + c)^2 + 3*(8*A + 39*C)*cos(d*x + c) + 8*A + 39*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(8*C*cos(d*x + c)^4 - 20*C*cos(d*x + c)^3 - 5*(3*A + 19*C)*cos(d*x + c)^2 - (11*A + 63*C)*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
1253,0,0,0,0.426129," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(9/2), x)","F",0
1254,0,0,0,0.444619," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(7/2), x)","F",0
1255,0,0,0,0.585122," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(5/2), x)","F",0
1256,0,0,0,0.449945," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(3/2), x)","F",0
1257,0,0,0,0.692698," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
1258,0,0,0,0.601110," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
1259,0,0,0,0.479010," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c))/sec(d*x + c)^(3/2), x)","F",0
1260,0,0,0,0.518567," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2), x)","F",0
1261,0,0,0,0.614464," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2), x)","F",0
1262,0,0,0,0.427621," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2), x)","F",0
1263,0,0,0,0.490366," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c)), x)","F",0
1264,0,0,0,0.597974," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sqrt(sec(d*x + c)), x)","F",0
1265,0,0,0,0.455951," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sec(d*x + c)^(3/2), x)","F",0
1266,0,0,0,1.483291," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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{9}{2}}, x\right)"," ",0,"integral((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sec(d*x + c)^(9/2), x)","F",0
1267,0,0,0,1.711956," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sec(d*x + c)^(7/2), x)","F",0
1268,0,0,0,0.993187," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sec(d*x + c)^(5/2), x)","F",0
1269,0,0,0,0.560511," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sec(d*x + c)^(3/2), x)","F",0
1270,0,0,0,0.557626," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)*sqrt(sec(d*x + c)), x)","F",0
1271,0,0,0,0.452023," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/sqrt(sec(d*x + c)), x)","F",0
1272,0,0,0,0.465399," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a \cos\left(d x + c\right)^{3} + {\left(B + C\right)} 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((C*a*cos(d*x + c)^3 + (B + C)*a*cos(d*x + c)^2 + (A + B)*a*cos(d*x + c) + A*a)/sec(d*x + c)^(3/2), x)","F",0
1273,0,0,0,0.437078," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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{11}{2}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)*sec(d*x + c)^(11/2), x)","F",0
1274,0,0,0,0.492800," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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{9}{2}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*a^2*cos(d*x + c)^2 + (2*A + B)*a^2*cos(d*x + c) + A*a^2)*sec(d*x + c)^(9/2), x)","F",0
1275,0,0,0,0.624589," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
1276,0,0,0,0.536633," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
1277,0,0,0,0.592058," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
1278,0,0,0,1.440320," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
1279,0,0,0,0.508304," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
1280,0,0,0,1.636115," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{2} \cos\left(d x + c\right)^{4} + {\left(B + 2 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(A + 2 \, B + C\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}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a^2*cos(d*x + c)^4 + (B + 2*C)*a^2*cos(d*x + c)^3 + (A + 2*B + C)*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
1281,0,0,0,0.721711," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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{13}{2}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(13/2), x)","F",0
1282,0,0,0,0.470415," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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{11}{2}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*a^3*cos(d*x + c)^2 + (3*A + B)*a^3*cos(d*x + c) + A*a^3)*sec(d*x + c)^(11/2), x)","F",0
1283,0,0,0,0.544757," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
1284,0,0,0,0.637546," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
1285,0,0,0,0.474989," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
1286,0,0,0,0.521236," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
1287,0,0,0,0.565684," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
1288,0,0,0,0.618774," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
1289,0,0,0,0.617296," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C a^{3} \cos\left(d x + c\right)^{5} + {\left(B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{4} + {\left(A + 3 \, B + 3 \, C\right)} a^{3} \cos\left(d x + c\right)^{3} + {\left(3 \, A + 3 \, B + C\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}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*a^3*cos(d*x + c)^5 + (B + 3*C)*a^3*cos(d*x + c)^4 + (A + 3*B + 3*C)*a^3*cos(d*x + c)^3 + (3*A + 3*B + C)*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
1290,0,0,0,0.776012," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a), x)","F",0
1291,0,0,0,0.516679," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
1292,0,0,0,0.484054," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
1293,0,0,0,0.603133," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
1294,0,0,0,0.449534," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1295,0,0,0,0.434633," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1296,0,0,0,0.520803," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1297,0,0,0,0.502113," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
1298,0,0,0,0.684827," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
1299,0,0,0,0.558919," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
1300,0,0,0,0.451562," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1301,0,0,0,0.495399," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1302,0,0,0,0.698074," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1303,0,0,0,0.535604," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a^{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((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(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
1304,0,0,0,0.488981," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a^{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((C*cos(d*x + c)^2 + 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
1305,0,0,0,0.532511," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a^{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((C*cos(d*x + c)^2 + 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
1306,0,0,0,0.474803," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1307,0,0,0,0.422695," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1308,0,0,0,0.472934," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1309,0,0,0,0.550280," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1310,1,130,0,0.403741," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(16 \, A + 18 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(16 \, A + 18 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(16 \, A + 18 \, B + 21 \, C\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*(8*(16*A + 18*B + 21*C)*cos(d*x + c)^4 + 4*(16*A + 18*B + 21*C)*cos(d*x + c)^3 + 3*(16*A + 18*B + 21*C)*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
1311,1,109,0,0.400721," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(24 \, A + 28 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(24 \, A + 28 \, B + 35 \, C\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*(2*(24*A + 28*B + 35*C)*cos(d*x + c)^3 + (24*A + 28*B + 35*C)*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
1312,1,88,0,0.398370," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(8 \, A + 10 \, B + 15 \, C\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*((8*A + 10*B + 15*C)*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
1313,1,125,0,0.445113," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, {\left(C \cos\left(d x + c\right)^{2} + C \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(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)}{\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*(C*cos(d*x + c)^2 + C*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))) - ((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)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
1314,1,109,0,0.484488," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(2 \, B + C\right)} \cos\left(d x + c\right) + 2 \, B + C\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(C \cos\left(d x + c\right) + 2 \, 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*B + C)*cos(d*x + c) + 2*B + C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (C*cos(d*x + c) + 2*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
1315,1,133,0,0.760259," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(8 \, A + 4 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 4 \, B + 3 \, C\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 \, C \cos\left(d x + c\right)^{2} + {\left(4 \, B + 3 \, C\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*(((8*A + 4*B + 3*C)*cos(d*x + c) + 8*A + 4*B + 3*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (2*C*cos(d*x + c)^2 + (4*B + 3*C)*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
1316,1,155,0,0.731355," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(8 \, A + 6 \, B + 5 \, C\right)} \cos\left(d x + c\right) + 8 \, A + 6 \, B + 5 \, C\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 \, C \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, B + 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 6 \, B + 5 \, C\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*((8*A + 6*B + 5*C)*cos(d*x + c) + 8*A + 6*B + 5*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*C*cos(d*x + c)^3 + 2*(6*B + 5*C)*cos(d*x + c)^2 + 3*(8*A + 6*B + 5*C)*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
1317,1,175,0,1.162638," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right) + 48 \, A + 40 \, B + 35 \, C\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 \, C \cos\left(d x + c\right)^{4} + 8 \, {\left(8 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 40 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(48 \, A + 40 \, B + 35 \, C\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)}}}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/192*(3*((48*A + 40*B + 35*C)*cos(d*x + c) + 48*A + 40*B + 35*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (48*C*cos(d*x + c)^4 + 8*(8*B + 7*C)*cos(d*x + c)^3 + 2*(48*A + 40*B + 35*C)*cos(d*x + c)^2 + 3*(48*A + 40*B + 35*C)*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
1318,1,156,0,0.743253," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(336 \, A + 374 \, B + 429 \, C\right)} a \cos\left(d x + c\right)^{5} + 4 \, {\left(336 \, A + 374 \, B + 429 \, C\right)} a \cos\left(d x + c\right)^{4} + 3 \, {\left(336 \, A + 374 \, B + 429 \, C\right)} a \cos\left(d x + c\right)^{3} + 5 \, {\left(168 \, A + 187 \, B + 99 \, C\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*(8*(336*A + 374*B + 429*C)*a*cos(d*x + c)^5 + 4*(336*A + 374*B + 429*C)*a*cos(d*x + c)^4 + 3*(336*A + 374*B + 429*C)*a*cos(d*x + c)^3 + 5*(168*A + 187*B + 99*C)*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
1319,1,134,0,0.669444," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(136 \, A + 156 \, B + 189 \, C\right)} a \cos\left(d x + c\right)^{4} + {\left(136 \, A + 156 \, B + 189 \, C\right)} a \cos\left(d x + c\right)^{3} + 3 \, {\left(34 \, A + 39 \, B + 21 \, C\right)} a \cos\left(d x + c\right)^{2} + 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*(2*(136*A + 156*B + 189*C)*a*cos(d*x + c)^4 + (136*A + 156*B + 189*C)*a*cos(d*x + c)^3 + 3*(34*A + 39*B + 21*C)*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
1320,1,112,0,0.459998," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(104 \, A + 126 \, B + 175 \, C\right)} a \cos\left(d x + c\right)^{3} + {\left(52 \, A + 63 \, B + 35 \, C\right)} a \cos\left(d x + c\right)^{2} + 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*((104*A + 126*B + 175*C)*a*cos(d*x + c)^3 + (52*A + 63*B + 35*C)*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
1321,1,155,0,0.811611," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, {\left(C a \cos\left(d x + c\right)^{3} + C 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) - \frac{{\left({\left(18 \, A + 25 \, B + 15 \, C\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)}{\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*(C*a*cos(d*x + c)^3 + C*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))) - ((18*A + 25*B + 15*C)*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)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
1322,1,156,0,0.772061," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(2 \, B + 3 \, C\right)} a \cos\left(d x + c\right)^{2} + {\left(2 \, B + 3 \, C\right)} a \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\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 \, C a \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A + 3 \, 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)}{\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*B + 3*C)*a*cos(d*x + c)^2 + (2*B + 3*C)*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))) - (3*C*a*cos(d*x + c)^2 + 2*(5*A + 3*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)^2 + d*cos(d*x + c))","A",0
1323,1,143,0,1.073071," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left({\left(8 \, A + 12 \, B + 7 \, C\right)} a \cos\left(d x + c\right) + {\left(8 \, A + 12 \, B + 7 \, C\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 \, C a \cos\left(d x + c\right)^{2} + {\left(4 \, B + 7 \, C\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)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/4*(((8*A + 12*B + 7*C)*a*cos(d*x + c) + (8*A + 12*B + 7*C)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (2*C*a*cos(d*x + c)^2 + (4*B + 7*C)*a*cos(d*x + c) + 8*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
1324,1,162,0,1.107155," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(24 \, A + 14 \, B + 11 \, C\right)} a \cos\left(d x + c\right) + {\left(24 \, A + 14 \, B + 11 \, C\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 \, C a \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, B + 11 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 14 \, B + 11 \, C\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*((24*A + 14*B + 11*C)*a*cos(d*x + c) + (24*A + 14*B + 11*C)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*C*a*cos(d*x + c)^3 + 2*(6*B + 11*C)*a*cos(d*x + c)^2 + 3*(8*A + 14*B + 11*C)*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
1325,1,183,0,1.124650," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(112 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right) + {\left(112 \, A + 88 \, B + 75 \, C\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 \, C a \cos\left(d x + c\right)^{4} + 8 \, {\left(8 \, B + 15 \, C\right)} a \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 88 \, B + 75 \, C\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(112 \, A + 88 \, B + 75 \, C\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*((112*A + 88*B + 75*C)*a*cos(d*x + c) + (112*A + 88*B + 75*C)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (48*C*a*cos(d*x + c)^4 + 8*(8*B + 15*C)*a*cos(d*x + c)^3 + 2*(48*A + 88*B + 75*C)*a*cos(d*x + c)^2 + 3*(112*A + 88*B + 75*C)*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
1326,1,204,0,0.981665," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right) + {\left(176 \, A + 150 \, B + 133 \, C\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(384 \, C a \cos\left(d x + c\right)^{5} + 48 \, {\left(10 \, B + 19 \, C\right)} a \cos\left(d x + c\right)^{4} + 8 \, {\left(80 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{3} + 10 \, {\left(176 \, A + 150 \, B + 133 \, C\right)} a \cos\left(d x + c\right)^{2} + 15 \, {\left(176 \, A + 150 \, B + 133 \, C\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)}}}{1920 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/1920*(15*((176*A + 150*B + 133*C)*a*cos(d*x + c) + (176*A + 150*B + 133*C)*a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (384*C*a*cos(d*x + c)^5 + 48*(10*B + 19*C)*a*cos(d*x + c)^4 + 8*(80*A + 150*B + 133*C)*a*cos(d*x + c)^3 + 10*(176*A + 150*B + 133*C)*a*cos(d*x + c)^2 + 15*(176*A + 150*B + 133*C)*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
1327,1,191,0,0.510824," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(15/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{6} + 4 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 3 \, {\left(8368 \, A + 9230 \, B + 10439 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 5 \, {\left(4184 \, A + 4615 \, B + 3718 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 35 \, {\left(523 \, A + 416 \, B + 143 \, C\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*(8*(8368*A + 9230*B + 10439*C)*a^2*cos(d*x + c)^6 + 4*(8368*A + 9230*B + 10439*C)*a^2*cos(d*x + c)^5 + 3*(8368*A + 9230*B + 10439*C)*a^2*cos(d*x + c)^4 + 5*(4184*A + 4615*B + 3718*C)*a^2*cos(d*x + c)^3 + 35*(523*A + 416*B + 143*C)*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
1328,1,167,0,0.471815," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(2840 \, A + 3212 \, B + 3795 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + {\left(2840 \, A + 3212 \, B + 3795 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(710 \, A + 803 \, B + 660 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 5 \, {\left(355 \, A + 286 \, B + 99 \, C\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*(2*(2840*A + 3212*B + 3795*C)*a^2*cos(d*x + c)^5 + (2840*A + 3212*B + 3795*C)*a^2*cos(d*x + c)^4 + 3*(710*A + 803*B + 660*C)*a^2*cos(d*x + c)^3 + 5*(355*A + 286*B + 99*C)*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
1329,1,143,0,0.954085," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(584 \, A + 690 \, B + 903 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + {\left(292 \, A + 345 \, B + 294 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(73 \, A + 60 \, B + 21 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 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*((584*A + 690*B + 903*C)*a^2*cos(d*x + c)^4 + (292*A + 345*B + 294*C)*a^2*cos(d*x + c)^3 + 3*(73*A + 60*B + 21*C)*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
1330,1,188,0,0.509484," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(105 \, {\left(C a^{2} \cos\left(d x + c\right)^{4} + C 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) - \frac{{\left({\left(230 \, A + 301 \, B + 280 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(115 \, A + 98 \, B + 35 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 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)}{\sqrt{\cos\left(d x + c\right)}}\right)}}{105 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-2/105*(105*(C*a^2*cos(d*x + c)^4 + C*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))) - ((230*A + 301*B + 280*C)*a^2*cos(d*x + c)^3 + (115*A + 98*B + 35*C)*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)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
1331,1,193,0,0.677192," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(2 \, B + 5 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + {\left(2 \, B + 5 \, C\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) - \frac{{\left(15 \, C a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(43 \, A + 40 \, B + 15 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(14 \, A + 5 \, B\right)} a^{2} \cos\left(d x + c\right) + 6 \, 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)}}}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/15*(15*((2*B + 5*C)*a^2*cos(d*x + c)^3 + (2*B + 5*C)*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))) - (15*C*a^2*cos(d*x + c)^3 + 2*(43*A + 40*B + 15*C)*a^2*cos(d*x + c)^2 + 2*(14*A + 5*B)*a^2*cos(d*x + c) + 6*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
1332,1,192,0,1.621634," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(8 \, A + 20 \, B + 19 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(8 \, A + 20 \, B + 19 \, C\right)} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\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(6 \, C a^{2} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, B + 11 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, A + 3 \, 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)}}}{12 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"-1/12*(3*((8*A + 20*B + 19*C)*a^2*cos(d*x + c)^2 + (8*A + 20*B + 19*C)*a^2*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (6*C*a^2*cos(d*x + c)^3 + 3*(4*B + 11*C)*a^2*cos(d*x + c)^2 + 8*(8*A + 3*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)^2 + d*cos(d*x + c))","A",0
1333,1,178,0,0.773888," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(40 \, A + 38 \, B + 25 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(40 \, A + 38 \, B + 25 \, C\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 \, C a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, B + 17 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A + 22 \, B + 25 \, C\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)}{\sqrt{\cos\left(d x + c\right)}}}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/24*(3*((40*A + 38*B + 25*C)*a^2*cos(d*x + c) + (40*A + 38*B + 25*C)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*C*a^2*cos(d*x + c)^3 + 2*(6*B + 17*C)*a^2*cos(d*x + c)^2 + 3*(8*A + 22*B + 25*C)*a^2*cos(d*x + c) + 48*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
1334,1,195,0,1.020922," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(304 \, A + 200 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(304 \, A + 200 \, B + 163 \, C\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 \, C a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(8 \, B + 23 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 2 \, {\left(48 \, A + 136 \, B + 163 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 3 \, {\left(176 \, A + 200 \, B + 163 \, C\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*((304*A + 200*B + 163*C)*a^2*cos(d*x + c) + (304*A + 200*B + 163*C)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (48*C*a^2*cos(d*x + c)^4 + 8*(8*B + 23*C)*a^2*cos(d*x + c)^3 + 2*(48*A + 136*B + 163*C)*a^2*cos(d*x + c)^2 + 3*(176*A + 200*B + 163*C)*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
1335,1,218,0,1.020400," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(400 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(400 \, A + 326 \, B + 283 \, C\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 \, C a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(10 \, B + 29 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(80 \, A + 230 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(272 \, A + 326 \, B + 283 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(400 \, A + 326 \, B + 283 \, C\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*((400*A + 326*B + 283*C)*a^2*cos(d*x + c) + (400*A + 326*B + 283*C)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (384*C*a^2*cos(d*x + c)^5 + 48*(10*B + 29*C)*a^2*cos(d*x + c)^4 + 8*(80*A + 230*B + 283*C)*a^2*cos(d*x + c)^3 + 10*(272*A + 326*B + 283*C)*a^2*cos(d*x + c)^2 + 15*(400*A + 326*B + 283*C)*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
1336,1,241,0,1.581271," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{15 \, {\left({\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right) + {\left(1304 \, A + 1132 \, B + 1015 \, C\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(1280 \, C a^{2} \cos\left(d x + c\right)^{6} + 128 \, {\left(12 \, B + 35 \, C\right)} a^{2} \cos\left(d x + c\right)^{5} + 48 \, {\left(40 \, A + 116 \, B + 145 \, C\right)} a^{2} \cos\left(d x + c\right)^{4} + 8 \, {\left(920 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{3} + 10 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\right)} a^{2} \cos\left(d x + c\right)^{2} + 15 \, {\left(1304 \, A + 1132 \, B + 1015 \, C\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)}}}{7680 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/7680*(15*((1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c) + (1304*A + 1132*B + 1015*C)*a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (1280*C*a^2*cos(d*x + c)^6 + 128*(12*B + 35*C)*a^2*cos(d*x + c)^5 + 48*(40*A + 116*B + 145*C)*a^2*cos(d*x + c)^4 + 8*(920*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^3 + 10*(1304*A + 1132*B + 1015*C)*a^2*cos(d*x + c)^2 + 15*(1304*A + 1132*B + 1015*C)*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
1337,1,209,0,0.514963," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\frac{315 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{5} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{4}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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 + 273 \, C\right)} \cos\left(d x + c\right)^{4} - {\left(29 \, A - 93 \, B + 21 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A - 3 \, B + 21 \, C\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 + C)*a*cos(d*x + c)^5 + (A - B + C)*a*cos(d*x + c)^4)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*((257*A - 129*B + 273*C)*cos(d*x + c)^4 - (29*A - 93*B + 21*C)*cos(d*x + c)^3 + 3*(19*A - 3*B + 21*C)*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
1338,1,189,0,0.573224," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\frac{105 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{4} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{3}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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 + 35 \, C\right)} \cos\left(d x + c\right)^{3} - {\left(31 \, A - 7 \, B + 35 \, C\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 + C)*a*cos(d*x + c)^4 + (A - B + C)*a*cos(d*x + c)^3)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*((43*A - 91*B + 35*C)*cos(d*x + c)^3 - (31*A - 7*B + 35*C)*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
1339,1,169,0,0.558313," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\frac{15 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{3} + {\left(A - B + C\right)} a \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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 + 15 \, C\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 + C)*a*cos(d*x + c)^3 + (A - B + C)*a*cos(d*x + c)^2)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*((13*A - 5*B + 15*C)*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
1340,1,145,0,0.926101," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\frac{3 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right)^{2} + {\left(A - B + C\right)} a \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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 + C)*a*cos(d*x + c)^2 + (A - B + C)*a*cos(d*x + c))*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*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
1341,1,162,0,8.509613," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(C \cos\left(d x + c\right) + C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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,"-(2*(C*cos(d*x + c) + 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 + C)*a*cos(d*x + c) + (A - B + C)*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
1342,1,171,0,10.960141," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} C \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left({\left(2 \, B - C\right)} \cos\left(d x + c\right) + 2 \, B - C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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)*C*sqrt(cos(d*x + c))*sin(d*x + c) - ((2*B - C)*cos(d*x + c) + 2*B - 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 + C)*a*cos(d*x + c) + (A - B + C)*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
1343,1,203,0,30.600577," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(8 \, A - 4 \, B + 7 \, C\right)} \cos\left(d x + c\right) + 8 \, A - 4 \, B + 7 \, C\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 + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\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 \, C \cos\left(d x + c\right)^{2} + {\left(4 \, B - C\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*(((8*A - 4*B + 7*C)*cos(d*x + c) + 8*A - 4*B + 7*C)*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 + C)*a*cos(d*x + c) + (A - B + C)*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*C*cos(d*x + c)^2 + (4*B - C)*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
1344,1,224,0,31.076748," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(8 \, A - 14 \, B + 9 \, C\right)} \cos\left(d x + c\right) + 8 \, A - 14 \, B + 9 \, C\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{24 \, \sqrt{2} {\left({\left(A - B + C\right)} a \cos\left(d x + c\right) + {\left(A - B + C\right)} a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{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(8 \, C \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, B - C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, A - 2 \, B + 7 \, C\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(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/24*(3*((8*A - 14*B + 9*C)*cos(d*x + c) + 8*A - 14*B + 9*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 24*sqrt(2)*((A - B + C)*a*cos(d*x + c) + (A - B + C)*a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + (8*C*cos(d*x + c)^3 + 2*(6*B - C)*cos(d*x + c)^2 + 3*(8*A - 2*B + 7*C)*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
1345,1,208,0,24.978000," ","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
1346,1,255,0,0.579975," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{2} {\left({\left(19 \, A - 15 \, B + 11 \, C\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(19 \, A - 15 \, B + 11 \, C\right)} \cos\left(d x + c\right)^{4} + {\left(19 \, A - 15 \, B + 11 \, C\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 + 665 \, C\right)} \cos\left(d x + c\right)^{4} + 12 \, {\left(67 \, A - 63 \, B + 35 \, C\right)} \cos\left(d x + c\right)^{3} - 28 \, {\left(7 \, A - 3 \, B + 5 \, C\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 + 11*C)*cos(d*x + c)^5 + 2*(19*A - 15*B + 11*C)*cos(d*x + c)^4 + (19*A - 15*B + 11*C)*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 + 665*C)*cos(d*x + c)^4 + 12*(67*A - 63*B + 35*C)*cos(d*x + c)^3 - 28*(7*A - 3*B + 5*C)*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
1347,1,235,0,0.526399," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(15 \, A - 11 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(15 \, A - 11 \, B + 7 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(15 \, A - 11 \, B + 7 \, C\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 + 75 \, C\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(9 \, A - 5 \, B + 5 \, C\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 + 7*C)*cos(d*x + c)^4 + 2*(15*A - 11*B + 7*C)*cos(d*x + c)^3 + (15*A - 11*B + 7*C)*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 + 75*C)*cos(d*x + c)^3 + 12*(9*A - 5*B + 5*C)*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
1348,1,209,0,0.602314," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(11 \, A - 7 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(11 \, A - 7 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, A - 7 \, B + 3 \, C\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 + 3 \, C\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 + 3*C)*cos(d*x + c)^3 + 2*(11*A - 7*B + 3*C)*cos(d*x + c)^2 + (11*A - 7*B + 3*C)*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 + 3*C)*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
1349,1,173,0,1.183648," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(7 \, A - 3 \, B - C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, A - 3 \, B - C\right)} \cos\left(d x + c\right) + 7 \, A - 3 \, B - C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 + C\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 - C)*cos(d*x + c)^2 + 2*(7*A - 3*B - C)*cos(d*x + c) + 7*A - 3*B - C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((5*A - B + C)*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
1350,1,213,0,28.398499," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A + B - 5 \, C\right)} \cos\left(d x + c\right) + 3 \, A + B - 5 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 + C\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, {\left(C \cos\left(d x + c\right)^{2} + 2 \, C \cos\left(d x + c\right) + C\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)*((3*A + B - 5*C)*cos(d*x + c)^2 + 2*(3*A + B - 5*C)*cos(d*x + c) + 3*A + B - 5*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*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 + C)*sqrt(cos(d*x + c))*sin(d*x + c) + 8*(C*cos(d*x + c)^2 + 2*C*cos(d*x + c) + C)*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
1351,1,251,0,39.884079," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - 5 \, B + 9 \, C\right)} \cos\left(d x + c\right) + A - 5 \, B + 9 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, B - 3 \, C\right)} \cos\left(d x + c\right) + 2 \, B - 3 \, C\right)} \sqrt{a} \arctan\left(\frac{\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 \, C \cos\left(d x + c\right)^{2} + {\left(A - B + 3 \, C\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)*((A - 5*B + 9*C)*cos(d*x + c)^2 + 2*(A - 5*B + 9*C)*cos(d*x + c) + A - 5*B + 9*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 4*((2*B - 3*C)*cos(d*x + c)^2 + 2*(2*B - 3*C)*cos(d*x + c) + 2*B - 3*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(2*C*cos(d*x + c)^2 + (A - B + 3*C)*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
1352,1,284,0,79.375619," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - 9 \, B + 13 \, C\right)} \cos\left(d x + c\right) + 5 \, A - 9 \, B + 13 \, C\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) - {\left({\left(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A - 12 \, B + 19 \, C\right)} \cos\left(d x + c\right) + 8 \, A - 12 \, B + 19 \, C\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 \, C \cos\left(d x + c\right)^{3} + {\left(4 \, B - 3 \, C\right)} \cos\left(d x + c\right)^{2} - {\left(2 \, A - 6 \, B + 7 \, C\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 + 13*C)*cos(d*x + c)^2 + 2*(5*A - 9*B + 13*C)*cos(d*x + c) + 5*A - 9*B + 13*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - ((8*A - 12*B + 19*C)*cos(d*x + c)^2 + 2*(8*A - 12*B + 19*C)*cos(d*x + c) + 8*A - 12*B + 19*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + (2*C*cos(d*x + c)^3 + (4*B - 3*C)*cos(d*x + c)^2 - (2*A - 6*B + 7*C)*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
1353,1,287,0,0.509807," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right)^{5} + 3 \, {\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(283 \, A - 163 \, B + 75 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(283 \, A - 163 \, B + 75 \, C\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 + 735 \, C\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(911 \, A - 503 \, B + 255 \, C\right)} \cos\left(d x + c\right)^{3} + 32 \, {\left(49 \, A - 25 \, B + 15 \, C\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 + 75*C)*cos(d*x + c)^5 + 3*(283*A - 163*B + 75*C)*cos(d*x + c)^4 + 3*(283*A - 163*B + 75*C)*cos(d*x + c)^3 + (283*A - 163*B + 75*C)*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 + 735*C)*cos(d*x + c)^4 + 5*(911*A - 503*B + 255*C)*cos(d*x + c)^3 + 32*(49*A - 25*B + 15*C)*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
1354,1,264,0,0.728065," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(163 \, A - 75 \, B + 19 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(163 \, A - 75 \, B + 19 \, C\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 + 27 \, C\right)} \cos\left(d x + c\right)^{3} + {\left(503 \, A - 255 \, B + 39 \, C\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 + 19*C)*cos(d*x + c)^4 + 3*(163*A - 75*B + 19*C)*cos(d*x + c)^3 + 3*(163*A - 75*B + 19*C)*cos(d*x + c)^2 + (163*A - 75*B + 19*C)*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 + 27*C)*cos(d*x + c)^3 + (503*A - 255*B + 39*C)*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
1355,1,226,0,0.560130," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(75 \, A - 19 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 75 \, A - 19 \, B - 5 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 + C\right)} \cos\left(d x + c\right)^{2} + {\left(85 \, A - 13 \, B + 5 \, C\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 - 5*C)*cos(d*x + c)^3 + 3*(75*A - 19*B - 5*C)*cos(d*x + c)^2 + 3*(75*A - 19*B - 5*C)*cos(d*x + c) + 75*A - 19*B - 5*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((49*A - 9*B + C)*cos(d*x + c)^2 + (85*A - 13*B + 5*C)*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
1356,1,225,0,0.684441," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(19 \, A + 5 \, B + 3 \, C\right)} \cos\left(d x + c\right) + 19 \, A + 5 \, B + 3 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 - 7 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(13 \, A - 5 \, B - 3 \, C\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 + 3*C)*cos(d*x + c)^3 + 3*(19*A + 5*B + 3*C)*cos(d*x + c)^2 + 3*(19*A + 5*B + 3*C)*cos(d*x + c) + 19*A + 5*B + 3*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*((9*A - B - 7*C)*cos(d*x + c)^2 + (13*A - 5*B - 3*C)*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
1357,1,293,0,64.224513," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(5 \, A + 3 \, B - 43 \, C\right)} \cos\left(d x + c\right) + 5 \, A + 3 \, B - 43 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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(C \cos\left(d x + c\right)^{3} + 3 \, C \cos\left(d x + c\right)^{2} + 3 \, C \cos\left(d x + c\right) + C\right)} \sqrt{a} \arctan\left(\frac{\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 - 15 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, A + 3 \, B - 11 \, C\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 - 43*C)*cos(d*x + c)^3 + 3*(5*A + 3*B - 43*C)*cos(d*x + c)^2 + 3*(5*A + 3*B - 43*C)*cos(d*x + c) + 5*A + 3*B - 43*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 64*(C*cos(d*x + c)^3 + 3*C*cos(d*x + c)^2 + 3*C*cos(d*x + c) + C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*((A + 7*B - 15*C)*cos(d*x + c)^2 + (5*A + 3*B - 11*C)*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
1358,1,329,0,84.238079," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, A - 43 \, B + 115 \, C\right)} \cos\left(d x + c\right) + 3 \, A - 43 \, B + 115 \, C\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \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 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, B - 5 \, C\right)} \cos\left(d x + c\right) + 2 \, B - 5 \, C\right)} \sqrt{a} \arctan\left(\frac{\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 \, C \cos\left(d x + c\right)^{3} + {\left(7 \, A - 15 \, B + 55 \, C\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, A - 11 \, B + 35 \, C\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 + 115*C)*cos(d*x + c)^3 + 3*(3*A - 43*B + 115*C)*cos(d*x + c)^2 + 3*(3*A - 43*B + 115*C)*cos(d*x + c) + 3*A - 43*B + 115*C)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 32*((2*B - 5*C)*cos(d*x + c)^3 + 3*(2*B - 5*C)*cos(d*x + c)^2 + 3*(2*B - 5*C)*cos(d*x + c) + 2*B - 5*C)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(16*C*cos(d*x + c)^3 + (7*A - 15*B + 55*C)*cos(d*x + c)^2 + (3*A - 11*B + 35*C)*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
1359,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1360,0,0,0,1.831589," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sec(d*x + c)^(9/2), x)","F",0
1361,0,0,0,1.603561," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sec(d*x + c)^(7/2), x)","F",0
1362,0,0,0,0.559190," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sec(d*x + c)^(5/2), x)","F",0
1363,0,0,0,1.584613," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sec(d*x + c)^(3/2), x)","F",0
1364,0,0,0,0.654502," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(sec(d*x + c)), x)","F",0
1365,0,0,0,0.553164," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)/sqrt(sec(d*x + c)), x)","F",0
1366,0,0,0,0.594759," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)/sec(d*x + c)^(3/2), x)","F",0
1367,0,0,0,0.670405," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(11/2), x)","F",0
1368,0,0,0,0.785826," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(9/2), x)","F",0
1369,0,0,0,1.407573," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(7/2), x)","F",0
1370,0,0,0,1.720978," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(5/2), x)","F",0
1371,0,0,0,0.669340," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(3/2), x)","F",0
1372,0,0,0,0.632063," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
1373,0,0,0,0.486369," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)/sqrt(sec(d*x + c)), x)","F",0
1374,0,0,0,0.719580," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)/sec(d*x + c)^(3/2), x)","F",0
1375,0,0,0,0.547659," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(11/2), x)","F",0
1376,0,0,0,1.187955," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(9/2), x)","F",0
1377,0,0,0,2.678466," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(7/2), x)","F",0
1378,0,0,0,0.691039," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(5/2), x)","F",0
1379,0,0,0,0.970520," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(3/2), x)","F",0
1380,0,0,0,0.640907," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
1381,0,0,0,1.239579," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)/sqrt(sec(d*x + c)), x)","F",0
1382,0,0,0,0.871922," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + 3 \, C a b^{2} \cos\left(d x + c\right)^{4} + 3 \, A a^{2} b \cos\left(d x + c\right) + A a^{3} + {\left(3 \, C a^{2} b + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + 3*C*a*b^2*cos(d*x + c)^4 + 3*A*a^2*b*cos(d*x + c) + A*a^3 + (3*C*a^2*b + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*A*a*b^2)*cos(d*x + c)^2)/sec(d*x + c)^(3/2), x)","F",0
1383,0,0,0,0.940655," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{13}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(13/2), x)","F",0
1384,0,0,0,0.840302," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(11/2), x)","F",0
1385,0,0,0,0.770320," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(9/2), x)","F",0
1386,0,0,0,0.622340," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(7/2), x)","F",0
1387,0,0,0,0.998427," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(5/2), x)","F",0
1388,0,0,0,0.689832," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)*sec(d*x + c)^(3/2), x)","F",0
1389,0,0,0,1.268751," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
1390,0,0,0,0.901367," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + 4 \, C a b^{3} \cos\left(d x + c\right)^{5} + 4 \, A a^{3} b \cos\left(d x + c\right) + A a^{4} + {\left(6 \, C a^{2} b^{2} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(C a^{3} b + A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + 4*C*a*b^3*cos(d*x + c)^5 + 4*A*a^3*b*cos(d*x + c) + A*a^4 + (6*C*a^2*b^2 + A*b^4)*cos(d*x + c)^4 + 4*(C*a^3*b + A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 6*A*a^2*b^2)*cos(d*x + c)^2)/sqrt(sec(d*x + c)), x)","F",0
1391,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1392,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1393,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1394,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1395,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1396,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1397,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1398,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1399,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1400,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1401,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1402,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1403,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1404,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1405,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1406,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1407,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1408,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1409,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1410,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1411,0,0,0,0.916430," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(11/2), x)","F",0
1412,0,0,0,0.892716," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1413,0,0,0,0.942568," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1414,0,0,0,44.535684," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1415,0,0,0,1.358664," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1416,0,0,0,6.994282," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1417,0,0,0,103.006255," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1418,0,0,0,2.494486," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1419,0,0,0,1.916503," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(11/2), x)","F",0
1420,0,0,0,2.461954," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1421,0,0,0,41.514734," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1422,0,0,0,1.226831," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1423,0,0,0,3.010120," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1424,0,0,0,99.349508," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1425,0,0,0,144.445028," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + C a \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right) + A a\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + C*a*cos(d*x + c)^2 + A*b*cos(d*x + c) + A*a)*sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1426,0,0,0,1.397598," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{13}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(13/2), x)","F",0
1427,0,0,0,1.443563," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(11/2), x)","F",0
1428,0,0,0,50.995829," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1429,0,0,0,2.337785," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1430,0,0,0,3.312515," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1431,0,0,0,3.044301," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1432,0,0,0,4.719712," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1433,0,0,0,4.759651," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + 2 \, C a b \cos\left(d x + c\right)^{3} + 2 \, A a b \cos\left(d x + c\right) + A a^{2} + {\left(C a^{2} + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + 2*C*a*b*cos(d*x + c)^3 + 2*A*a*b*cos(d*x + c) + A*a^2 + (C*a^2 + A*b^2)*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1434,0,0,0,0.469844," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(9/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1435,0,0,0,0.447342," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1436,0,0,0,1.509178," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1437,0,0,0,2.115763," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1438,0,0,0,53.222170," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1439,0,0,0,5.147756," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1440,0,0,0,0.948236," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{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((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
1441,0,0,0,1.516155," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\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((C*cos(d*x + c)^2 + 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
1442,0,0,0,1.889200," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\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((C*cos(d*x + c)^2 + 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
1443,0,0,0,49.273351," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + 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
1444,0,0,0,1.774031," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1445,0,0,0,125.287639," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1446,0,0,0,1.100144," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\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((C*cos(d*x + c)^2 + 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
1447,0,0,0,1.344893," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\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((C*cos(d*x + c)^2 + 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
1448,0,0,0,0.852071," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{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((C*cos(d*x + c)^2 + 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
1449,0,0,0,49.184030," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1450,0,0,0,54.519703," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + 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((C*cos(d*x + c)^2 + 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
1451,0,0,0,1.309098," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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{9}{2}}, x\right)"," ",0,"integral((C*b*cos(d*x + c)^3 + (C*a + B*b)*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sec(d*x + c)^(9/2), x)","F",0
1452,0,0,0,1.826715," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1453,0,0,0,0.885734," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1454,0,0,0,1.590863," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1455,0,0,0,0.832985," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1456,0,0,0,0.896199," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1457,0,0,0,1.010047," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1458,0,0,0,0.516299," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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{11}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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)^(11/2), x)","F",0
1459,0,0,0,1.677120," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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{9}{2}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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)^(9/2), x)","F",0
1460,0,0,0,1.468267," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1461,0,0,0,0.839237," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1462,0,0,0,3.039502," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1463,0,0,0,1.750972," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1464,0,0,0,3.028621," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1465,0,0,0,1.692758," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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)}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1466,0,0,0,2.096095," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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)^(11/2), x)","F",0
1467,0,0,0,1.615573," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1468,0,0,0,1.051172," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1469,0,0,0,0.997369," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1470,0,0,0,3.257457," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1471,0,0,0,1.269539," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1472,0,0,0,0.882209," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\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((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1473,0,0,0,1.076013," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{3} \cos\left(d x + c\right)^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} \cos\left(d x + c\right)^{4} + A a^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} \cos\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*b^3*cos(d*x + c)^5 + (3*C*a*b^2 + B*b^3)*cos(d*x + c)^4 + A*a^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*cos(d*x + c)^3 + (C*a^3 + 3*B*a^2*b + 3*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
1474,0,0,0,0.860342," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{13}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sec(d*x + c)^(13/2), x)","F",0
1475,0,0,0,1.128356," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sec(d*x + c)^(11/2), x)","F",0
1476,0,0,0,2.679587," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sec(d*x + c)^(9/2), x)","F",0
1477,0,0,0,1.751405," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sec(d*x + c)^(7/2), x)","F",0
1478,0,0,0,2.048380," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sec(d*x + c)^(5/2), x)","F",0
1479,0,0,0,1.937325," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sec(d*x + c)^(3/2), x)","F",0
1480,0,0,0,0.632337," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
1481,0,0,0,1.031295," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C b^{4} \cos\left(d x + c\right)^{6} + {\left(4 \, C a b^{3} + B b^{4}\right)} \cos\left(d x + c\right)^{5} + A a^{4} + {\left(6 \, C a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, C a^{3} b + 3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(C a^{4} + 4 \, B a^{3} b + 6 \, A a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(B a^{4} + 4 \, A a^{3} b\right)} \cos\left(d x + c\right)}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*b^4*cos(d*x + c)^6 + (4*C*a*b^3 + B*b^4)*cos(d*x + c)^5 + A*a^4 + (6*C*a^2*b^2 + 4*B*a*b^3 + A*b^4)*cos(d*x + c)^4 + 2*(2*C*a^3*b + 3*B*a^2*b^2 + 2*A*a*b^3)*cos(d*x + c)^3 + (C*a^4 + 4*B*a^3*b + 6*A*a^2*b^2)*cos(d*x + c)^2 + (B*a^4 + 4*A*a^3*b)*cos(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
1482,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1483,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1484,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1485,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1486,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1487,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1488,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1489,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1490,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1491,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1492,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1493,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1494,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1495,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1496,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1497,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1498,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1499,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1500,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1501,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1502,0,0,0,1.642761," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(11/2), x)","F",0
1503,0,0,0,1.670981," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1504,0,0,0,0.640989," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1505,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1506,0,0,0,83.415579," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1507,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1508,0,0,0,126.270795," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1509,0,0,0,87.808868," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1510,0,0,0,0.540823," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1511,0,0,0,0.529239," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1512,0,0,0,26.115737," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1513,0,0,0,1.381450," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1514,0,0,0,2.271986," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1515,0,0,0,84.713407," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1516,0,0,0,6.514169," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b \cos\left(d x + c\right)^{3} + {\left(C a + B b\right)} \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((C*b*cos(d*x + c)^3 + (C*a + 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
1517,0,0,0,0.724262," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1518,0,0,0,0.678849," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1519,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1520,0,0,0,99.711154," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1521,0,0,0,5.228343," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1522,0,0,0,5.130591," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1523,0,0,0,11.791848," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1524,0,0,0,9.046058," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C b^{2} \cos\left(d x + c\right)^{4} + {\left(2 \, C a b + B b^{2}\right)} \cos\left(d x + c\right)^{3} + A a^{2} + {\left(C a^{2} + 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((C*b^2*cos(d*x + c)^4 + (2*C*a*b + B*b^2)*cos(d*x + c)^3 + A*a^2 + (C*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
1525,0,0,0,0.849406," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(9/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1526,0,0,0,0.811874," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1527,0,0,0,0.900851," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1528,0,0,0,1.221769," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1529,0,0,0,1.290140," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1530,0,0,0,95.040787," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1531,0,0,0,3.747840," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1532,0,0,0,1.967557," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""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
1533,0,0,0,0.836772," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{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((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
1534,0,0,0,0.559558," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \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((C*cos(d*x + c)^2 + 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
1535,0,0,0,0.574171," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \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((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
1536,0,0,0,2.211205," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\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((C*cos(d*x + c)^2 + 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
1537,0,0,0,1.936392," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{{\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((C*cos(d*x + c)^2 + 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
1538,0,0,0,121.133056," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{{\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((C*cos(d*x + c)^2 + 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
1539,0,0,0,1.034454," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \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((C*cos(d*x + c)^2 + 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
1540,0,0,0,0.792422," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \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((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)/(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
1541,0,0,0,0.844861," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\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((C*cos(d*x + c)^2 + 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
