1,1,112,0,0.662457," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{3}{8} \, {\left(A a + B a\right)} x + \frac{B a \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(A a + B a\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, A a + 5 \, B a\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a + B a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(6 \, A a + 5 \, B a\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"3/8*(A*a + B*a)*x + 1/80*B*a*sin(5*d*x + 5*c)/d + 1/32*(A*a + B*a)*sin(4*d*x + 4*c)/d + 1/48*(4*A*a + 5*B*a)*sin(3*d*x + 3*c)/d + 1/4*(A*a + B*a)*sin(2*d*x + 2*c)/d + 1/8*(6*A*a + 5*B*a)*sin(d*x + c)/d","A",0
2,1,89,0,0.909060," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A a + 3 \, B a\right)} x + \frac{B a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(A a + B a\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(A a + B a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{3 \, {\left(A a + B a\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/8*(4*A*a + 3*B*a)*x + 1/32*B*a*sin(4*d*x + 4*c)/d + 1/12*(A*a + B*a)*sin(3*d*x + 3*c)/d + 1/4*(A*a + B*a)*sin(2*d*x + 2*c)/d + 3/4*(A*a + B*a)*sin(d*x + c)/d","A",0
3,1,68,0,0.363310," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(A a + B a\right)} x + \frac{B a \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(A a + B a\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a + 3 \, B a\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/2*(A*a + B*a)*x + 1/12*B*a*sin(3*d*x + 3*c)/d + 1/4*(A*a + B*a)*sin(2*d*x + 2*c)/d + 1/4*(4*A*a + 3*B*a)*sin(d*x + c)/d","A",0
4,1,45,0,0.497034," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, A a + B a\right)} x + \frac{B a \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(A a + B a\right)} \sin\left(d x + c\right)}{d}"," ",0,"1/2*(2*A*a + B*a)*x + 1/4*B*a*sin(2*d*x + 2*c)/d + (A*a + B*a)*sin(d*x + c)/d","A",0
5,1,79,0,0.803546," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\frac{A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(A a + B a\right)} {\left(d x + c\right)} + \frac{2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(A*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - A*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (A*a + B*a)*(d*x + c) + 2*B*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
6,1,84,0,0.347798," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} B a + {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"((d*x + c)*B*a + (A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*A*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
7,1,124,0,0.467551," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(A a + 2 \, B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a + 2 \, B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((A*a + 2*B*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a + 2*B*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*a*tan(1/2*d*x + 1/2*c)^3 - 3*A*a*tan(1/2*d*x + 1/2*c) - 2*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
8,1,154,0,2.499989," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*A*a*tan(1/2*d*x + 1/2*c)^5 + 3*B*a*tan(1/2*d*x + 1/2*c)^5 - 4*A*a*tan(1/2*d*x + 1/2*c)^3 - 12*B*a*tan(1/2*d*x + 1/2*c)^3 + 9*A*a*tan(1/2*d*x + 1/2*c) + 9*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
9,1,188,0,1.685974," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a + 4 \, B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 49 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 28 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 52 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 39 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*B*a)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a + 4*B*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(9*A*a*tan(1/2*d*x + 1/2*c)^7 + 12*B*a*tan(1/2*d*x + 1/2*c)^7 - 49*A*a*tan(1/2*d*x + 1/2*c)^5 - 28*B*a*tan(1/2*d*x + 1/2*c)^5 + 31*A*a*tan(1/2*d*x + 1/2*c)^3 + 52*B*a*tan(1/2*d*x + 1/2*c)^3 - 39*A*a*tan(1/2*d*x + 1/2*c) - 36*B*a*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
10,1,166,0,0.413715," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B a^{2} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{1}{16} \, {\left(12 \, A a^{2} + 11 \, B a^{2}\right)} x + \frac{{\left(A a^{2} + 2 \, B a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(4 \, A a^{2} + 5 \, B a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(9 \, A a^{2} + 10 \, B a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(32 \, A a^{2} + 31 \, B a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(11 \, A a^{2} + 10 \, B a^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*B*a^2*sin(6*d*x + 6*c)/d + 1/16*(12*A*a^2 + 11*B*a^2)*x + 1/80*(A*a^2 + 2*B*a^2)*sin(5*d*x + 5*c)/d + 1/64*(4*A*a^2 + 5*B*a^2)*sin(4*d*x + 4*c)/d + 1/48*(9*A*a^2 + 10*B*a^2)*sin(3*d*x + 3*c)/d + 1/64*(32*A*a^2 + 31*B*a^2)*sin(2*d*x + 2*c)/d + 1/8*(11*A*a^2 + 10*B*a^2)*sin(d*x + c)/d","A",0
11,1,137,0,0.699798," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B a^{2} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(7 \, A a^{2} + 6 \, B a^{2}\right)} x + \frac{{\left(A a^{2} + 2 \, B a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(8 \, A a^{2} + 9 \, B a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a^{2} + B a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(12 \, A a^{2} + 11 \, B a^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*B*a^2*sin(5*d*x + 5*c)/d + 1/8*(7*A*a^2 + 6*B*a^2)*x + 1/32*(A*a^2 + 2*B*a^2)*sin(4*d*x + 4*c)/d + 1/48*(8*A*a^2 + 9*B*a^2)*sin(3*d*x + 3*c)/d + 1/2*(A*a^2 + B*a^2)*sin(2*d*x + 2*c)/d + 1/8*(12*A*a^2 + 11*B*a^2)*sin(d*x + c)/d","A",0
12,1,110,0,1.067389," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B a^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(8 \, A a^{2} + 7 \, B a^{2}\right)} x + \frac{{\left(A a^{2} + 2 \, B a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(A a^{2} + B a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(7 \, A a^{2} + 6 \, B a^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/32*B*a^2*sin(4*d*x + 4*c)/d + 1/8*(8*A*a^2 + 7*B*a^2)*x + 1/12*(A*a^2 + 2*B*a^2)*sin(3*d*x + 3*c)/d + 1/2*(A*a^2 + B*a^2)*sin(2*d*x + 2*c)/d + 1/4*(7*A*a^2 + 6*B*a^2)*sin(d*x + c)/d","A",0
13,1,85,0,0.327329," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B a^{2} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{1}{2} \, {\left(3 \, A a^{2} + 2 \, B a^{2}\right)} x + \frac{{\left(A a^{2} + 2 \, B a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(8 \, A a^{2} + 7 \, B a^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/12*B*a^2*sin(3*d*x + 3*c)/d + 1/2*(3*A*a^2 + 2*B*a^2)*x + 1/4*(A*a^2 + 2*B*a^2)*sin(2*d*x + 2*c)/d + 1/4*(8*A*a^2 + 7*B*a^2)*sin(d*x + c)/d","A",0
14,1,145,0,0.428945," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\frac{2 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(4 \, A a^{2} + 3 \, B a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (4*A*a^2 + 3*B*a^2)*(d*x + c) + 2*(2*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 2*A*a^2*tan(1/2*d*x + 1/2*c) + 5*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
15,1,155,0,1.056657," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(A a^{2} + 2 \, B a^{2}\right)} {\left(d x + c\right)} + {\left(2 \, A a^{2} + B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, A a^{2} + B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((A*a^2 + 2*B*a^2)*(d*x + c) + (2*A*a^2 + B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*A*a^2 + B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(A*a^2*tan(1/2*d*x + 1/2*c)^3 - B*a^2*tan(1/2*d*x + 1/2*c)^3 + A*a^2*tan(1/2*d*x + 1/2*c) + B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
16,1,154,0,0.498380," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} B a^{2} + {\left(3 \, A a^{2} + 4 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(3 \, A a^{2} + 4 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a^2 + (3*A*a^2 + 4*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (3*A*a^2 + 4*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 5*A*a^2*tan(1/2*d*x + 1/2*c) - 2*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
17,1,178,0,0.497864," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, A a^{2} + 3 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, A a^{2} + 3 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*A*a^2 + 3*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*A*a^2 + 3*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 9*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 16*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 18*A*a^2*tan(1/2*d*x + 1/2*c) + 15*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
18,1,212,0,0.869794," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(7 \, A a^{2} + 8 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(7 \, A a^{2} + 8 \, B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(21 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 77 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 88 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 83 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 136 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 75 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 72 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(7*A*a^2 + 8*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(7*A*a^2 + 8*B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(21*A*a^2*tan(1/2*d*x + 1/2*c)^7 + 24*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 77*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 88*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 83*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 136*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 75*A*a^2*tan(1/2*d*x + 1/2*c) - 72*B*a^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
19,1,166,0,0.357274," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B a^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{1}{16} \, {\left(26 \, A a^{3} + 23 \, B a^{3}\right)} x + \frac{{\left(A a^{3} + 3 \, B a^{3}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{3 \, {\left(2 \, A a^{3} + 3 \, B a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(17 \, A a^{3} + 19 \, B a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(64 \, A a^{3} + 63 \, B a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(23 \, A a^{3} + 21 \, B a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*B*a^3*sin(6*d*x + 6*c)/d + 1/16*(26*A*a^3 + 23*B*a^3)*x + 1/80*(A*a^3 + 3*B*a^3)*sin(5*d*x + 5*c)/d + 3/64*(2*A*a^3 + 3*B*a^3)*sin(4*d*x + 4*c)/d + 1/48*(17*A*a^3 + 19*B*a^3)*sin(3*d*x + 3*c)/d + 1/64*(64*A*a^3 + 63*B*a^3)*sin(2*d*x + 2*c)/d + 1/8*(23*A*a^3 + 21*B*a^3)*sin(d*x + c)/d","A",0
20,1,136,0,0.410273," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B a^{3} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(15 \, A a^{3} + 13 \, B a^{3}\right)} x + \frac{{\left(A a^{3} + 3 \, B a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(12 \, A a^{3} + 17 \, B a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a^{3} + B a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{d} + \frac{{\left(26 \, A a^{3} + 23 \, B a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*B*a^3*sin(5*d*x + 5*c)/d + 1/8*(15*A*a^3 + 13*B*a^3)*x + 1/32*(A*a^3 + 3*B*a^3)*sin(4*d*x + 4*c)/d + 1/48*(12*A*a^3 + 17*B*a^3)*sin(3*d*x + 3*c)/d + (A*a^3 + B*a^3)*sin(2*d*x + 2*c)/d + 1/8*(26*A*a^3 + 23*B*a^3)*sin(d*x + c)/d","A",0
21,1,112,0,0.357663," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B a^{3} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{5}{8} \, {\left(4 \, A a^{3} + 3 \, B a^{3}\right)} x + \frac{{\left(A a^{3} + 3 \, B a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(3 \, A a^{3} + 4 \, B a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(15 \, A a^{3} + 13 \, B a^{3}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/32*B*a^3*sin(4*d*x + 4*c)/d + 5/8*(4*A*a^3 + 3*B*a^3)*x + 1/12*(A*a^3 + 3*B*a^3)*sin(3*d*x + 3*c)/d + 1/4*(3*A*a^3 + 4*B*a^3)*sin(2*d*x + 2*c)/d + 1/4*(15*A*a^3 + 13*B*a^3)*sin(d*x + c)/d","A",0
22,1,180,0,0.452199," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\frac{6 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(7 \, A a^{3} + 5 \, B a^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(7*A*a^3 + 5*B*a^3)*(d*x + c) + 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 21*A*a^3*tan(1/2*d*x + 1/2*c) + 33*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
23,1,192,0,0.919282," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{4 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - {\left(6 \, A a^{3} + 7 \, B a^{3}\right)} {\left(d x + c\right)} - 2 \, {\left(3 \, A a^{3} + B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(3 \, A a^{3} + B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (6*A*a^3 + 7*B*a^3)*(d*x + c) - 2*(3*A*a^3 + B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(3*A*a^3 + B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(2*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 2*A*a^3*tan(1/2*d*x + 1/2*c) + 7*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
24,1,192,0,0.611774," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{\frac{4 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(A a^{3} + 3 \, B a^{3}\right)} {\left(d x + c\right)} + {\left(7 \, A a^{3} + 6 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(7 \, A a^{3} + 6 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(5 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*B*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(A*a^3 + 3*B*a^3)*(d*x + c) + (7*A*a^3 + 6*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (7*A*a^3 + 6*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(5*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 7*A*a^3*tan(1/2*d*x + 1/2*c) - 2*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
25,1,189,0,0.410881," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} B a^{3} + 3 \, {\left(5 \, A a^{3} + 7 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(5 \, A a^{3} + 7 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*B*a^3 + 3*(5*A*a^3 + 7*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(5*A*a^3 + 7*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 40*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 33*A*a^3*tan(1/2*d*x + 1/2*c) + 21*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
26,1,212,0,0.758553," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, A a^{3} + 4 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, A a^{3} + 4 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(45 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 60 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 165 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 220 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 219 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 292 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 147 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 132 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(15*(3*A*a^3 + 4*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*A*a^3 + 4*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(45*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 60*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 165*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 220*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 219*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 292*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 147*A*a^3*tan(1/2*d*x + 1/2*c) - 132*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
27,1,246,0,1.716507," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(13 \, A a^{3} + 15 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(13 \, A a^{3} + 15 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(195 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 225 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 910 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1050 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1664 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1920 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1330 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1830 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 765 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 735 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(13*A*a^3 + 15*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(13*A*a^3 + 15*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(195*A*a^3*tan(1/2*d*x + 1/2*c)^9 + 225*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 910*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 1050*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 1664*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1920*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 1330*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 1830*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 765*A*a^3*tan(1/2*d*x + 1/2*c) + 735*B*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
28,1,193,0,0.530924," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B a^{4} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{1}{16} \, {\left(49 \, A a^{4} + 44 \, B a^{4}\right)} x + \frac{{\left(A a^{4} + 4 \, B a^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(16 \, A a^{4} + 31 \, B a^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{5 \, {\left(3 \, A a^{4} + 4 \, B a^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(144 \, A a^{4} + 157 \, B a^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(127 \, A a^{4} + 124 \, B a^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(352 \, A a^{4} + 323 \, B a^{4}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/448*B*a^4*sin(7*d*x + 7*c)/d + 1/16*(49*A*a^4 + 44*B*a^4)*x + 1/192*(A*a^4 + 4*B*a^4)*sin(6*d*x + 6*c)/d + 1/320*(16*A*a^4 + 31*B*a^4)*sin(5*d*x + 5*c)/d + 5/64*(3*A*a^4 + 4*B*a^4)*sin(4*d*x + 4*c)/d + 1/192*(144*A*a^4 + 157*B*a^4)*sin(3*d*x + 3*c)/d + 1/64*(127*A*a^4 + 124*B*a^4)*sin(2*d*x + 2*c)/d + 1/64*(352*A*a^4 + 323*B*a^4)*sin(d*x + c)/d","A",0
29,1,166,0,0.997153," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B a^{4} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{7}{16} \, {\left(8 \, A a^{4} + 7 \, B a^{4}\right)} x + \frac{{\left(A a^{4} + 4 \, B a^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(8 \, A a^{4} + 15 \, B a^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(29 \, A a^{4} + 36 \, B a^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(128 \, A a^{4} + 127 \, B a^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(49 \, A a^{4} + 44 \, B a^{4}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*B*a^4*sin(6*d*x + 6*c)/d + 7/16*(8*A*a^4 + 7*B*a^4)*x + 1/80*(A*a^4 + 4*B*a^4)*sin(5*d*x + 5*c)/d + 1/64*(8*A*a^4 + 15*B*a^4)*sin(4*d*x + 4*c)/d + 1/48*(29*A*a^4 + 36*B*a^4)*sin(3*d*x + 3*c)/d + 1/64*(128*A*a^4 + 127*B*a^4)*sin(2*d*x + 2*c)/d + 1/8*(49*A*a^4 + 44*B*a^4)*sin(d*x + c)/d","A",0
30,1,139,0,1.390658," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B a^{4} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{7}{8} \, {\left(5 \, A a^{4} + 4 \, B a^{4}\right)} x + \frac{{\left(A a^{4} + 4 \, B a^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(16 \, A a^{4} + 29 \, B a^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(7 \, A a^{4} + 8 \, B a^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{7 \, {\left(8 \, A a^{4} + 7 \, B a^{4}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*B*a^4*sin(5*d*x + 5*c)/d + 7/8*(5*A*a^4 + 4*B*a^4)*x + 1/32*(A*a^4 + 4*B*a^4)*sin(4*d*x + 4*c)/d + 1/48*(16*A*a^4 + 29*B*a^4)*sin(3*d*x + 3*c)/d + 1/4*(7*A*a^4 + 8*B*a^4)*sin(2*d*x + 2*c)/d + 7/8*(8*A*a^4 + 7*B*a^4)*sin(d*x + c)/d","A",0
31,1,214,0,1.065023," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\frac{24 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(48 \, A a^{4} + 35 \, B a^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(120 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 424 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 520 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 511 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 216 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 279 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(48*A*a^4 + 35*B*a^4)*(d*x + c) + 2*(120*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 105*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 424*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 385*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 520*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 511*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 216*A*a^4*tan(1/2*d*x + 1/2*c) + 279*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
32,1,226,0,0.892518," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{12 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(13 \, A a^{4} + 12 \, B a^{4}\right)} {\left(d x + c\right)} - 6 \, {\left(4 \, A a^{4} + B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 6 \, {\left(4 \, A a^{4} + B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 76 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 54 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(12*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(13*A*a^4 + 12*B*a^4)*(d*x + c) - 6*(4*A*a^4 + B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 6*(4*A*a^4 + B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(21*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 30*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 48*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 76*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 27*A*a^4*tan(1/2*d*x + 1/2*c) + 54*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
33,1,230,0,1.941188," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(8 \, A a^{4} + 13 \, B a^{4}\right)} {\left(d x + c\right)} + {\left(13 \, A a^{4} + 8 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(13 \, A a^{4} + 8 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(5 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 11 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 11 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((8*A*a^4 + 13*B*a^4)*(d*x + c) + (13*A*a^4 + 8*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (13*A*a^4 + 8*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(5*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 5*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 7*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 7*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 11*A*a^4*tan(1/2*d*x + 1/2*c) - 11*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","A",0
34,1,227,0,0.494325," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{\frac{12 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 6 \, {\left(A a^{4} + 4 \, B a^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(12 \, A a^{4} + 13 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(12 \, A a^{4} + 13 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(30 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 76 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 54 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*B*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 6*(A*a^4 + 4*B*a^4)*(d*x + c) + 3*(12*A*a^4 + 13*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(12*A*a^4 + 13*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(30*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 21*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 76*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 48*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 54*A*a^4*tan(1/2*d*x + 1/2*c) + 27*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
35,1,223,0,0.676615," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} B a^{4} + 3 \, {\left(35 \, A a^{4} + 48 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(35 \, A a^{4} + 48 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 385 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 424 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 511 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 520 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 279 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 216 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)*B*a^4 + 3*(35*A*a^4 + 48*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(35*A*a^4 + 48*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(105*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 120*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 385*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 424*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 511*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 520*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 279*A*a^4*tan(1/2*d*x + 1/2*c) - 216*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
36,1,246,0,0.458949," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{105 \, {\left(4 \, A a^{4} + 5 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(4 \, A a^{4} + 5 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(420 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 525 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1960 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2450 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3584 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4480 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3950 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1500 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1395 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(105*(4*A*a^4 + 5*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(4*A*a^4 + 5*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(420*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 525*B*a^4*tan(1/2*d*x + 1/2*c)^9 - 1960*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 2450*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 3584*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 4480*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 3160*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 3950*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 1500*A*a^4*tan(1/2*d*x + 1/2*c) + 1395*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
37,1,280,0,0.542602," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{105 \, {\left(7 \, A a^{4} + 8 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(7 \, A a^{4} + 8 \, B a^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(735 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 840 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 4165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4760 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 9702 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 11088 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 11802 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 13488 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7355 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9320 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3105 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3000 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(105*(7*A*a^4 + 8*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(7*A*a^4 + 8*B*a^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(735*A*a^4*tan(1/2*d*x + 1/2*c)^11 + 840*B*a^4*tan(1/2*d*x + 1/2*c)^11 - 4165*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 4760*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 9702*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 11088*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 11802*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 13488*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 7355*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 9320*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 3105*A*a^4*tan(1/2*d*x + 1/2*c) - 3000*B*a^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
38,1,181,0,0.850008," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{9 \, {\left(d x + c\right)} {\left(4 \, A - 5 \, B\right)}}{a} - \frac{24 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(60 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 75 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 124 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 115 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 100 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 109 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"-1/24*(9*(d*x + c)*(4*A - 5*B)/a - 24*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a - 2*(60*A*tan(1/2*d*x + 1/2*c)^7 - 75*B*tan(1/2*d*x + 1/2*c)^7 + 124*A*tan(1/2*d*x + 1/2*c)^5 - 115*B*tan(1/2*d*x + 1/2*c)^5 + 100*A*tan(1/2*d*x + 1/2*c)^3 - 109*B*tan(1/2*d*x + 1/2*c)^3 + 36*A*tan(1/2*d*x + 1/2*c) - 21*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
39,1,151,0,0.493294," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{9 \, {\left(d x + c\right)} {\left(A - B\right)}}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"1/6*(9*(d*x + c)*(A - B)/a - 6*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a - 2*(9*A*tan(1/2*d*x + 1/2*c)^5 - 15*B*tan(1/2*d*x + 1/2*c)^5 + 12*A*tan(1/2*d*x + 1/2*c)^3 - 16*B*tan(1/2*d*x + 1/2*c)^3 + 3*A*tan(1/2*d*x + 1/2*c) - 9*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
40,1,124,0,1.061338," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(d x + c\right)} {\left(2 \, A - 3 \, B\right)}}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} - \frac{2 \, {\left(2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"-1/2*((d*x + c)*(2*A - 3*B)/a - 2*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a - 2*(2*A*tan(1/2*d*x + 1/2*c)^3 - 3*B*tan(1/2*d*x + 1/2*c)^3 + 2*A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
41,1,78,0,0.911527," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} {\left(A - B\right)}}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a}}{d}"," ",0,"((d*x + c)*(A - B)/a - (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a + 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a))/d","A",0
42,1,43,0,0.736562," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(d x + c\right)} B}{a} + \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"((d*x + c)*B/a + (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a)/d","A",0
43,1,71,0,1.040300," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a}}{d}"," ",0,"(A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a)/d","A",0
44,1,110,0,0.349030," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a}}{d}"," ",0,"-((A - B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (A - B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - (A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a + 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
45,1,157,0,0.365946," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(3 \, A - 2 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{{\left(3 \, A - 2 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a}}{2 \, d}"," ",0,"1/2*((3*A - 2*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - (3*A - 2*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 2*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a + 2*(3*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 - A*tan(1/2*d*x + 1/2*c) + 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a))/d","A",0
46,1,182,0,0.395738," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{9 \, {\left(A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{9 \, {\left(A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} - \frac{6 \, {\left(A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a} + \frac{2 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(9*(A - B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - 9*(A - B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a - 6*(A*tan(1/2*d*x + 1/2*c) - B*tan(1/2*d*x + 1/2*c))/a + 2*(15*A*tan(1/2*d*x + 1/2*c)^5 - 9*B*tan(1/2*d*x + 1/2*c)^5 - 16*A*tan(1/2*d*x + 1/2*c)^3 + 12*B*tan(1/2*d*x + 1/2*c)^3 + 9*A*tan(1/2*d*x + 1/2*c) - 3*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
47,1,192,0,0.732916," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)} {\left(7 \, A - 10 \, B\right)}}{a^{2}} - \frac{2 \, {\left(15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*(7*A - 10*B)/a^2 - 2*(15*A*tan(1/2*d*x + 1/2*c)^5 - 30*B*tan(1/2*d*x + 1/2*c)^5 + 24*A*tan(1/2*d*x + 1/2*c)^3 - 40*B*tan(1/2*d*x + 1/2*c)^3 + 9*A*tan(1/2*d*x + 1/2*c) - 18*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 - 21*A*a^4*tan(1/2*d*x + 1/2*c) + 27*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
48,1,164,0,0.543773," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)} {\left(4 \, A - 7 \, B\right)}}{a^{2}} - \frac{6 \, {\left(2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(d*x + c)*(4*A - 7*B)/a^2 - 6*(2*A*tan(1/2*d*x + 1/2*c)^3 - 5*B*tan(1/2*d*x + 1/2*c)^3 + 2*A*tan(1/2*d*x + 1/2*c) - 3*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 - 15*A*a^4*tan(1/2*d*x + 1/2*c) + 21*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
49,1,119,0,1.603893," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} {\left(A - 2 \, B\right)}}{a^{2}} + \frac{12 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*(A - 2*B)/a^2 + 12*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) + (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 - 9*A*a^4*tan(1/2*d*x + 1/2*c) + 15*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
50,1,86,0,0.677422," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} B}{a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*B/a^2 - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^4*tan(1/2*d*x + 1/2*c) + 9*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
51,1,60,0,1.925256," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{6 \, a^{2} d}"," ",0,"1/6*(A*tan(1/2*d*x + 1/2*c)^3 - B*tan(1/2*d*x + 1/2*c)^3 + 3*A*tan(1/2*d*x + 1/2*c) + 3*B*tan(1/2*d*x + 1/2*c))/(a^2*d)","A",0
52,1,113,0,0.435268," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(6*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + 9*A*a^4*tan(1/2*d*x + 1/2*c) - 3*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
53,1,155,0,0.450042," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(2 \, A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, {\left(2 \, A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{12 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(2*A - B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 6*(2*A - B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 12*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^4*tan(1/2*d*x + 1/2*c) - 9*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
54,1,198,0,1.294828," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(7 \, A - 4 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(7 \, A - 4 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(7*A - 4*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(7*A - 4*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 6*(5*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 - 3*A*tan(1/2*d*x + 1/2*c) + 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + 21*A*a^4*tan(1/2*d*x + 1/2*c) - 15*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
55,1,226,0,0.971883," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(10 \, A - 7 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{3 \, {\left(10 \, A - 7 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(30 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{2}} - \frac{A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(3*(10*A - 7*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - 3*(10*A - 7*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 + 2*(30*A*tan(1/2*d*x + 1/2*c)^5 - 15*B*tan(1/2*d*x + 1/2*c)^5 - 40*A*tan(1/2*d*x + 1/2*c)^3 + 24*B*tan(1/2*d*x + 1/2*c)^3 + 18*A*tan(1/2*d*x + 1/2*c) - 9*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^2) - (A*a^4*tan(1/2*d*x + 1/2*c)^3 - B*a^4*tan(1/2*d*x + 1/2*c)^3 + 27*A*a^4*tan(1/2*d*x + 1/2*c) - 21*B*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
56,1,228,0,1.903939," ","integrate(cos(d*x+c)^5*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(d x + c\right)} {\left(13 \, A - 23 \, B\right)}}{a^{3}} - \frac{20 \, {\left(21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 51 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 76 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 40 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 50 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 735 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(d*x + c)*(13*A - 23*B)/a^3 - 20*(21*A*tan(1/2*d*x + 1/2*c)^5 - 51*B*tan(1/2*d*x + 1/2*c)^5 + 36*A*tan(1/2*d*x + 1/2*c)^3 - 76*B*tan(1/2*d*x + 1/2*c)^3 + 15*A*tan(1/2*d*x + 1/2*c) - 33*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 40*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 50*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*A*a^12*tan(1/2*d*x + 1/2*c) - 735*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
57,1,200,0,1.941074," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, {\left(d x + c\right)} {\left(6 \, A - 13 \, B\right)}}{a^{3}} - \frac{60 \, {\left(2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 465 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(30*(d*x + c)*(6*A - 13*B)/a^3 - 60*(2*A*tan(1/2*d*x + 1/2*c)^3 - 7*B*tan(1/2*d*x + 1/2*c)^3 + 2*A*tan(1/2*d*x + 1/2*c) - 5*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 30*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 40*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*A*a^12*tan(1/2*d*x + 1/2*c) - 465*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
58,1,155,0,0.358439," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} {\left(A - 3 \, B\right)}}{a^{3}} + \frac{120 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*(A - 3*B)/a^3 + 120*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) - 255*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
59,1,120,0,0.503827," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(d x + c\right)} B}{a^{3}} + \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*B/a^3 + (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 - 10*A*a^12*tan(1/2*d*x + 1/2*c)^3 + 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^12*tan(1/2*d*x + 1/2*c) - 105*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
60,1,75,0,1.900089," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"-1/60*(3*A*tan(1/2*d*x + 1/2*c)^5 - 3*B*tan(1/2*d*x + 1/2*c)^5 + 10*B*tan(1/2*d*x + 1/2*c)^3 - 15*A*tan(1/2*d*x + 1/2*c) - 15*B*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
61,1,75,0,0.448063," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, a^{3} d}"," ",0,"1/60*(3*A*tan(1/2*d*x + 1/2*c)^5 - 3*B*tan(1/2*d*x + 1/2*c)^5 + 10*A*tan(1/2*d*x + 1/2*c)^3 + 15*A*tan(1/2*d*x + 1/2*c) + 15*B*tan(1/2*d*x + 1/2*c))/(a^3*d)","A",0
62,1,148,0,4.309442," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(60*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 20*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 10*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 105*A*a^12*tan(1/2*d*x + 1/2*c) - 15*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
63,1,190,0,0.439650," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(3 \, A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, {\left(3 \, A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{120 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 255 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"-1/60*(60*(3*A - B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 60*(3*A - B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 120*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 30*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 20*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 255*A*a^12*tan(1/2*d*x + 1/2*c) - 105*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
64,1,233,0,2.213277," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{30 \, {\left(13 \, A - 6 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{30 \, {\left(13 \, A - 6 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} + \frac{60 \, {\left(7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}} - \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, A a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 255 \, B a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{60 \, d}"," ",0,"1/60*(30*(13*A - 6*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 30*(13*A - 6*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 + 60*(7*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 - 5*A*tan(1/2*d*x + 1/2*c) + 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3) - (3*A*a^12*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^12*tan(1/2*d*x + 1/2*c)^5 + 40*A*a^12*tan(1/2*d*x + 1/2*c)^3 - 30*B*a^12*tan(1/2*d*x + 1/2*c)^3 + 465*A*a^12*tan(1/2*d*x + 1/2*c) - 255*B*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
65,1,233,0,0.518777," ","integrate(cos(d*x+c)^5*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{420 \, {\left(d x + c\right)} {\left(8 \, A - 21 \, B\right)}}{a^{4}} - \frac{840 \, {\left(2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 147 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 189 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 805 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1365 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5145 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11655 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(420*(d*x + c)*(8*A - 21*B)/a^4 - 840*(2*A*tan(1/2*d*x + 1/2*c)^3 - 9*B*tan(1/2*d*x + 1/2*c)^3 + 2*A*tan(1/2*d*x + 1/2*c) - 7*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 - 147*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 189*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 805*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 1365*B*a^24*tan(1/2*d*x + 1/2*c)^3 - 5145*A*a^24*tan(1/2*d*x + 1/2*c) + 11655*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
66,1,188,0,0.790591," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(d x + c\right)} {\left(A - 4 \, B\right)}}{a^{4}} + \frac{1680 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 147 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 805 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5145 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*(d*x + c)*(A - 4*B)/a^4 + 1680*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^4) + (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 - 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 147*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 805*B*a^24*tan(1/2*d*x + 1/2*c)^3 - 1575*A*a^24*tan(1/2*d*x + 1/2*c) + 5145*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
67,1,155,0,0.400919," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(d x + c\right)} B}{a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 63 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 385 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1575 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*(d*x + c)*B/a^4 - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 - 63*A*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 385*B*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*A*a^24*tan(1/2*d*x + 1/2*c) + 1575*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
68,1,117,0,0.624282," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 - 15*B*tan(1/2*d*x + 1/2*c)^7 - 21*A*tan(1/2*d*x + 1/2*c)^5 + 63*B*tan(1/2*d*x + 1/2*c)^5 - 35*A*tan(1/2*d*x + 1/2*c)^3 - 105*B*tan(1/2*d*x + 1/2*c)^3 + 105*A*tan(1/2*d*x + 1/2*c) + 105*B*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
69,1,117,0,0.584733," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 21 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"-1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 - 15*B*tan(1/2*d*x + 1/2*c)^7 + 21*A*tan(1/2*d*x + 1/2*c)^5 + 21*B*tan(1/2*d*x + 1/2*c)^5 - 35*A*tan(1/2*d*x + 1/2*c)^3 + 35*B*tan(1/2*d*x + 1/2*c)^3 - 105*A*tan(1/2*d*x + 1/2*c) - 105*B*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
70,1,117,0,0.928267," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 63 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 21 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{840 \, a^{4} d}"," ",0,"1/840*(15*A*tan(1/2*d*x + 1/2*c)^7 - 15*B*tan(1/2*d*x + 1/2*c)^7 + 63*A*tan(1/2*d*x + 1/2*c)^5 - 21*B*tan(1/2*d*x + 1/2*c)^5 + 105*A*tan(1/2*d*x + 1/2*c)^3 + 35*B*tan(1/2*d*x + 1/2*c)^3 + 105*A*tan(1/2*d*x + 1/2*c) + 105*B*tan(1/2*d*x + 1/2*c))/(a^4*d)","A",0
71,1,182,0,0.971158," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{840 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{840 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1575 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(840*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 840*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 105*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 63*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 385*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 105*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 1575*A*a^24*tan(1/2*d*x + 1/2*c) - 105*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
72,1,224,0,0.411144," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{840 \, {\left(4 \, A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{840 \, {\left(4 \, A - B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{1680 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 147 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 805 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 385 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5145 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1575 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"-1/840*(840*(4*A - B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 840*(4*A - B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 1680*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 147*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 105*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 805*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 385*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 5145*A*a^24*tan(1/2*d*x + 1/2*c) - 1575*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
73,1,267,0,1.450737," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(21 \, A - 8 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{420 \, {\left(21 \, A - 8 \, B\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{840 \, {\left(9 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{4}} - \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 189 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 147 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1365 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 805 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11655 \, A a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5145 \, B a^{24} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{28}}}{840 \, d}"," ",0,"1/840*(420*(21*A - 8*B)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 420*(21*A - 8*B)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 840*(9*A*tan(1/2*d*x + 1/2*c)^3 - 2*B*tan(1/2*d*x + 1/2*c)^3 - 7*A*tan(1/2*d*x + 1/2*c) + 2*B*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^4) - (15*A*a^24*tan(1/2*d*x + 1/2*c)^7 - 15*B*a^24*tan(1/2*d*x + 1/2*c)^7 + 189*A*a^24*tan(1/2*d*x + 1/2*c)^5 - 147*B*a^24*tan(1/2*d*x + 1/2*c)^5 + 1365*A*a^24*tan(1/2*d*x + 1/2*c)^3 - 805*B*a^24*tan(1/2*d*x + 1/2*c)^3 + 11655*A*a^24*tan(1/2*d*x + 1/2*c) - 5145*B*a^24*tan(1/2*d*x + 1/2*c))/a^28)/d","A",0
74,1,194,0,0.527035," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{35 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{45 \, {\left(2 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{126 \, {\left(A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{210 \, {\left(3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{1890 \, {\left(A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(35*B*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 45*(2*A*sgn(cos(1/2*d*x + 1/2*c)) + B*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 126*(A*sgn(cos(1/2*d*x + 1/2*c)) + 2*B*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 210*(3*A*sgn(cos(1/2*d*x + 1/2*c)) + 2*B*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 1890*(A*sgn(cos(1/2*d*x + 1/2*c)) + B*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
75,1,165,0,1.444252," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{420} \, \sqrt{2} {\left(\frac{15 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{420 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{315 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{21 \, {\left(2 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{35 \, {\left(2 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/420*sqrt(2)*(15*B*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 420*A*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d + 315*B*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d + 21*(2*A*sgn(cos(1/2*d*x + 1/2*c)) + B*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 35*(2*A*sgn(cos(1/2*d*x + 1/2*c)) + 3*B*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d)*sqrt(a)","A",0
76,1,113,0,2.889360," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{30} \, \sqrt{2} {\left(\frac{3 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{5 \, {\left(2 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{30 \, {\left(A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/30*sqrt(2)*(3*B*sgn(cos(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)/d + 5*(2*A*sgn(cos(1/2*d*x + 1/2*c)) + B*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 30*(A*sgn(cos(1/2*d*x + 1/2*c)) + B*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
77,1,83,0,0.373286," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} {\left(\frac{B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{3 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/3*sqrt(2)*(B*sgn(cos(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)/d + 6*A*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d + 3*B*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
78,1,1884,0,15.588845," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{a} {\left(\frac{\sqrt{2} {\left(A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} + 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 20 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} - 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} - A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) + 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} - A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) - 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) + A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \log\left(\frac{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} + \frac{\sqrt{2} {\left(A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 20 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} - 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} + A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} + 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) - 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 60 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} - A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 18 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) + 15 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \log\left(\frac{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{4} \, d x + c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{4} \, d x + c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} - \frac{8 \, {\left(B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 6 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} + 15 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 20 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} - B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, B \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{4} \, d x + c\right)^{2} + 1\right)}}\right)}}{2 \, d}"," ",0,"1/2*sqrt(2)*sqrt(a)*(sqrt(2)*(A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 + 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 - 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 + 20*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 - 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 - A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^6 + 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^5 - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) + 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 - 60*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 + 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^4 - A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^3 - 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) - 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c) - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) + A*sgn(cos(1/2*d*x + 1/2*c)))*log(abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 - 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 - 2*tan(1/4*d*x + c) + 6*tan(1/2*c) + 2)/abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 + 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 - 2*tan(1/4*d*x + c) + 6*tan(1/2*c) + 2))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) + sqrt(2)*(A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 + 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 - 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 - 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 - 20*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 + 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 - 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 + A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^6 + 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^5 + 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) - 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 + 60*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 - 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^4 - A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^3 + 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)^2 - 18*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) + 15*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 3*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/2*c) - 6*A*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) - A*sgn(cos(1/2*d*x + 1/2*c)))*log(abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 - 6*tan(1/4*d*x + c)*tan(1/2*c)^2 + 2*tan(1/2*c)^3 - 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 + 2*tan(1/4*d*x + c) - 6*tan(1/2*c) + 2)/abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 - 6*tan(1/4*d*x + c)*tan(1/2*c)^2 + 2*tan(1/2*c)^3 + 2*sqrt(2)*(tan(1/2*c)^2 + 1)^(3/2) + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 + 2*tan(1/4*d*x + c) - 6*tan(1/2*c) + 2))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) - 8*(B*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^6 - 15*B*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^4 + 6*B*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^5 + 15*B*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^2 - 20*B*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^3 - B*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x + c) + 6*B*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/4*d*x + c)^2 + 1)))/d","B",0
79,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,1,250,0,2.995551," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{55440} \, \sqrt{2} {\left(\frac{315 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{385 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{495 \, {\left(6 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{693 \, {\left(12 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 13 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{2310 \, {\left(10 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 9 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{6930 \, {\left(12 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 11 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/55440*sqrt(2)*(315*B*a*sgn(cos(1/2*d*x + 1/2*c))*sin(11/2*d*x + 11/2*c)/d + 385*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(9/2*d*x + 9/2*c)/d + 495*(6*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 7*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 693*(12*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 13*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 2310*(10*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 9*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 6930*(12*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 11*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
83,1,245,0,1.842486," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{35 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{45 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{378 \, {\left(A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{1050 \, {\left(A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{630 \, {\left(3 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 4 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{1260 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(35*B*a*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 45*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 378*(A*a*sgn(cos(1/2*d*x + 1/2*c)) + B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 1050*(A*a*sgn(cos(1/2*d*x + 1/2*c)) + B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 630*(3*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 4*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 1260*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
84,1,164,0,0.495952," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{420} \, \sqrt{2} {\left(\frac{15 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{21 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{35 \, {\left(6 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{105 \, {\left(8 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/420*sqrt(2)*(15*B*a*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 21*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 35*(6*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 5*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 105*(8*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 7*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
85,1,161,0,0.539995," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{30} \, \sqrt{2} {\left(\frac{3 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{5 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{30 \, {\left(2 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{30 \, {\left(A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/30*sqrt(2)*(3*B*a*sgn(cos(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)/d + 5*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + 3*B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 30*(2*A*a*sgn(cos(1/2*d*x + 1/2*c)) + B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 30*(A*a*sgn(cos(1/2*d*x + 1/2*c)) + B*a*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
86,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,1,319,0,0.928030," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{55440} \, \sqrt{2} {\left(\frac{315 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{385 \, {\left(2 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{495 \, {\left(10 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 13 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{693 \, {\left(24 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 25 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{2310 \, {\left(20 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 19 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{6930 \, {\left(14 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 15 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{27720 \, {\left(3 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/55440*sqrt(2)*(315*B*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(11/2*d*x + 11/2*c)/d + 385*(2*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 5*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(9/2*d*x + 9/2*c)/d + 495*(10*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 13*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 693*(24*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 25*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 2310*(20*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 19*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 6930*(14*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 15*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 27720*(3*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 2*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
92,1,225,0,0.860857," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{35 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{45 \, {\left(2 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{126 \, {\left(5 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{210 \, {\left(11 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 10 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{630 \, {\left(15 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 13 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(35*B*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(9/2*d*x + 9/2*c)/d + 45*(2*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 5*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(7/2*d*x + 7/2*c)/d + 126*(5*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 6*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 210*(11*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 10*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 630*(15*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 13*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
93,1,225,0,1.390044," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{420} \, \sqrt{2} {\left(\frac{15 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{21 \, {\left(2 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{35 \, {\left(10 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 11 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{105 \, {\left(8 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 7 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{420 \, {\left(3 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/420*sqrt(2)*(15*B*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 21*(2*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 5*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(5/2*d*x + 5/2*c)/d + 35*(10*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 11*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(3/2*d*x + 3/2*c)/d + 105*(8*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 7*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d + 420*(3*A*a^2*sgn(cos(1/2*d*x + 1/2*c)) + 2*B*a^2*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
94,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,1,181,0,1.841779," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{105 \, \sqrt{2} {\left(A - B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} + \frac{2 \, {\left(105 \, \sqrt{2} A a^{3} + {\left({\left(\sqrt{2} {\left(119 \, A a^{3} - 92 \, B a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, \sqrt{2} {\left(37 \, A a^{3} - 16 \, B a^{3}\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, \sqrt{2} {\left(7 \, A a^{3} - 4 \, B a^{3}\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}}{105 \, d}"," ",0,"1/105*(105*sqrt(2)*(A - B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) + 2*(105*sqrt(2)*A*a^3 + ((sqrt(2)*(119*A*a^3 - 92*B*a^3)*tan(1/2*d*x + 1/2*c)^2 + 7*sqrt(2)*(37*A*a^3 - 16*B*a^3))*tan(1/2*d*x + 1/2*c)^2 + 35*sqrt(2)*(7*A*a^3 - 4*B*a^3))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","A",0
101,1,158,0,1.975259," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(\sqrt{2} A - \sqrt{2} B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} - \frac{2 \, {\left(15 \, \sqrt{2} B a^{2} - {\left(10 \, \sqrt{2} A a^{2} - 20 \, \sqrt{2} B a^{2} + {\left(10 \, \sqrt{2} A a^{2} - 17 \, \sqrt{2} B a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}}{15 \, d}"," ",0,"-1/15*(15*(sqrt(2)*A - sqrt(2)*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) - 2*(15*sqrt(2)*B*a^2 - (10*sqrt(2)*A*a^2 - 20*sqrt(2)*B*a^2 + (10*sqrt(2)*A*a^2 - 17*sqrt(2)*B*a^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","A",0
102,1,113,0,1.557651," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, \sqrt{2} {\left(A - B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}} + \frac{2 \, {\left(\sqrt{2} {\left(3 \, A a - 2 \, B a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, \sqrt{2} A a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}}}{3 \, d}"," ",0,"1/3*(3*sqrt(2)*(A - B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a) + 2*(sqrt(2)*(3*A*a - 2*B*a)*tan(1/2*d*x + 1/2*c)^2 + 3*sqrt(2)*A*a)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2))/d","A",0
103,1,88,0,2.922052," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{{\left(\sqrt{2} A - \sqrt{2} B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a}}}{d}"," ",0,"(2*sqrt(2)*B*tan(1/2*d*x + 1/2*c)/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - (sqrt(2)*A - sqrt(2)*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/sqrt(a))/d","A",0
104,1,168,0,2.079978," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(A \sqrt{a} - B \sqrt{a}\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{a} + \frac{2 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{a}} - \frac{2 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{a}}}{2 \, d}"," ",0,"1/2*(sqrt(2)*(A*sqrt(a) - B*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a + 2*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/sqrt(a) - 2*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/sqrt(a))/d","B",0
105,1,321,0,3.890754," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} {\left(A \sqrt{a} - B \sqrt{a}\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{a} + \frac{{\left(A \sqrt{a} - 2 \, B \sqrt{a}\right)} \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a} - \frac{{\left(A \sqrt{a} - 2 \, B \sqrt{a}\right)} \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a} - \frac{4 \, \sqrt{2} {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{a} - A a^{\frac{3}{2}}\right)}}{{\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}}}{2 \, d}"," ",0,"-1/2*(sqrt(2)*(A*sqrt(a) - B*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a + (A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a - (A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a - 4*sqrt(2)*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(a) - A*a^(3/2))/((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2))/d","B",0
106,1,535,0,3.635197," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{4 \, \sqrt{2} {\left(A \sqrt{a} - B \sqrt{a}\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{a} + \frac{{\left(7 \, A \sqrt{a} - 4 \, B \sqrt{a}\right)} \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a} - \frac{{\left(7 \, A \sqrt{a} - 4 \, B \sqrt{a}\right)} \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a} - \frac{4 \, \sqrt{2} {\left(17 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} A \sqrt{a} - 12 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} B \sqrt{a} - 57 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} A a^{\frac{3}{2}} + 76 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} B a^{\frac{3}{2}} + 19 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A a^{\frac{5}{2}} - 36 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} B a^{\frac{5}{2}} - 3 \, A a^{\frac{7}{2}} + 4 \, B a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)}^{2}}}{8 \, d}"," ",0,"1/8*(4*sqrt(2)*(A*sqrt(a) - B*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a + (7*A*sqrt(a) - 4*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a - (7*A*sqrt(a) - 4*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a - 4*sqrt(2)*(17*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*A*sqrt(a) - 12*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*B*sqrt(a) - 57*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*A*a^(3/2) + 76*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*B*a^(3/2) + 19*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*a^(5/2) - 36*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*B*a^(5/2) - 3*A*a^(7/2) + 4*B*a^(7/2))/((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)^2)/d","B",0
107,1,254,0,2.398582," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{105 \, {\left(15 \, \sqrt{2} A - 19 \, \sqrt{2} B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}} + \frac{{\left({\left({\left({\left(\frac{105 \, {\left(\sqrt{2} A a^{5} - \sqrt{2} B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} + \frac{4 \, {\left(693 \, \sqrt{2} A a^{5} - 877 \, \sqrt{2} B a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{14 \, {\left(453 \, \sqrt{2} A a^{5} - 517 \, \sqrt{2} B a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{140 \, {\left(39 \, \sqrt{2} A a^{5} - 47 \, \sqrt{2} B a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{1785 \, {\left(\sqrt{2} A a^{5} - \sqrt{2} B a^{5}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}}{420 \, d}"," ",0,"1/420*(105*(15*sqrt(2)*A - 19*sqrt(2)*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2) + ((((105*(sqrt(2)*A*a^5 - sqrt(2)*B*a^5)*tan(1/2*d*x + 1/2*c)^2/a^3 + 4*(693*sqrt(2)*A*a^5 - 877*sqrt(2)*B*a^5)/a^3)*tan(1/2*d*x + 1/2*c)^2 + 14*(453*sqrt(2)*A*a^5 - 517*sqrt(2)*B*a^5)/a^3)*tan(1/2*d*x + 1/2*c)^2 + 140*(39*sqrt(2)*A*a^5 - 47*sqrt(2)*B*a^5)/a^3)*tan(1/2*d*x + 1/2*c)^2 + 1785*(sqrt(2)*A*a^5 - sqrt(2)*B*a^5)/a^3)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","A",0
108,1,202,0,3.099517," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{15 \, \sqrt{2} {\left(11 \, A - 15 \, B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}} + \frac{{\left({\left({\left(\frac{15 \, \sqrt{2} {\left(A a^{3} - B a^{3}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2}} + \frac{\sqrt{2} {\left(245 \, A a^{3} - 381 \, B a^{3}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{5 \, \sqrt{2} {\left(73 \, A a^{3} - 105 \, B a^{3}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{15 \, \sqrt{2} {\left(9 \, A a^{3} - 17 \, B a^{3}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}}{60 \, d}"," ",0,"-1/60*(15*sqrt(2)*(11*A - 15*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2) + (((15*sqrt(2)*(A*a^3 - B*a^3)*tan(1/2*d*x + 1/2*c)^2/a^2 + sqrt(2)*(245*A*a^3 - 381*B*a^3)/a^2)*tan(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*(73*A*a^3 - 105*B*a^3)/a^2)*tan(1/2*d*x + 1/2*c)^2 + 15*sqrt(2)*(9*A*a^3 - 17*B*a^3)/a^2)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","A",0
109,1,168,0,1.930850," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(7 \, \sqrt{2} A - 11 \, \sqrt{2} B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}} + \frac{{\left({\left(\frac{3 \, {\left(\sqrt{2} A a - \sqrt{2} B a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a} + \frac{2 \, {\left(15 \, \sqrt{2} A a - 23 \, \sqrt{2} B a\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{27 \, {\left(\sqrt{2} A a - \sqrt{2} B a\right)}}{a}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}}}{12 \, d}"," ",0,"1/12*(3*(7*sqrt(2)*A - 11*sqrt(2)*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2) + ((3*(sqrt(2)*A*a - sqrt(2)*B*a)*tan(1/2*d*x + 1/2*c)^2/a + 2*(15*sqrt(2)*A*a - 23*sqrt(2)*B*a)/a)*tan(1/2*d*x + 1/2*c)^2 + 27*(sqrt(2)*A*a - sqrt(2)*B*a)/a)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2))/d","A",0
110,1,131,0,1.703457," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(\frac{\sqrt{2} {\left(A a^{2} - B a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} + \frac{\sqrt{2} {\left(A a^{2} - 9 \, B a^{2}\right)}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{\sqrt{2} {\left(3 \, A - 7 \, B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}}}{4 \, d}"," ",0,"-1/4*((sqrt(2)*(A*a^2 - B*a^2)*tan(1/2*d*x + 1/2*c)^2/a^3 + sqrt(2)*(A*a^2 - 9*B*a^2)/a^3)*tan(1/2*d*x + 1/2*c)/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(2)*(3*A - 7*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2))/d","A",0
111,1,101,0,1.302402," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(\sqrt{2} A + 3 \, \sqrt{2} B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}}} - \frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\sqrt{2} A a - \sqrt{2} B a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}}}{4 \, d}"," ",0,"-1/4*((sqrt(2)*A + 3*sqrt(2)*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(3/2) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(sqrt(2)*A*a - sqrt(2)*B*a)*tan(1/2*d*x + 1/2*c)/a^3)/d","A",0
112,1,214,0,2.863629," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} {\left(5 \, A \sqrt{a} - B \sqrt{a}\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{a^{2}} + \frac{8 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{\frac{3}{2}}} - \frac{8 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{\frac{3}{2}}} - \frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\sqrt{2} A a - \sqrt{2} B a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}}}{8 \, d}"," ",0,"1/8*(sqrt(2)*(5*A*sqrt(a) - B*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a^2 + 8*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^(3/2) - 8*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^(3/2) - 2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(sqrt(2)*A*a - sqrt(2)*B*a)*tan(1/2*d*x + 1/2*c)/a^3)/d","B",0
113,1,373,0,3.226807," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} {\left(9 \, A \sqrt{a} - 5 \, B \sqrt{a}\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{a^{2}} + \frac{4 \, {\left(3 \, A \sqrt{a} - 2 \, B \sqrt{a}\right)} \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{2}} - \frac{4 \, {\left(3 \, A \sqrt{a} - 2 \, B \sqrt{a}\right)} \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{2}} - \frac{16 \, \sqrt{2} {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{a} - A a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} a} - \frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\sqrt{2} A a - \sqrt{2} B a\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}}}{8 \, d}"," ",0,"-1/8*(sqrt(2)*(9*A*sqrt(a) - 5*B*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a^2 + 4*(3*A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^2 - 4*(3*A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^2 - 16*sqrt(2)*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(a) - A*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*a) - 2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(sqrt(2)*A*a - sqrt(2)*B*a)*tan(1/2*d*x + 1/2*c)/a^3)/d","B",0
114,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2))]Discontinuities at zeroes of cos((d*t_nostep+c)/2) were not checkedEvaluation time: 0.69Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[23574053482485268906770432,0]:[1,0,-2]%%},[16]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0]%%%} / %%%{%%%{%%{[604462909807314587353088,0]:[1,0,-2]%%},[16]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
115,1,257,0,2.685309," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(163 \, \sqrt{2} A - 283 \, \sqrt{2} B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}} - \frac{{\left({\left({\left(15 \, {\left(\frac{2 \, {\left(\sqrt{2} A a^{2} - \sqrt{2} B a^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{2}} - \frac{21 \, \sqrt{2} A a^{2} - 29 \, \sqrt{2} B a^{2}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{3685 \, \sqrt{2} A a^{2} - 6733 \, \sqrt{2} B a^{2}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{5 \, {\left(1133 \, \sqrt{2} A a^{2} - 1973 \, \sqrt{2} B a^{2}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{15 \, {\left(155 \, \sqrt{2} A a^{2} - 291 \, \sqrt{2} B a^{2}\right)}}{a^{2}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}}{480 \, d}"," ",0,"-1/480*(15*(163*sqrt(2)*A - 283*sqrt(2)*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2) - (((15*(2*(sqrt(2)*A*a^2 - sqrt(2)*B*a^2)*tan(1/2*d*x + 1/2*c)^2/a^2 - (21*sqrt(2)*A*a^2 - 29*sqrt(2)*B*a^2)/a^2)*tan(1/2*d*x + 1/2*c)^2 - (3685*sqrt(2)*A*a^2 - 6733*sqrt(2)*B*a^2)/a^2)*tan(1/2*d*x + 1/2*c)^2 - 5*(1133*sqrt(2)*A*a^2 - 1973*sqrt(2)*B*a^2)/a^2)*tan(1/2*d*x + 1/2*c)^2 - 15*(155*sqrt(2)*A*a^2 - 291*sqrt(2)*B*a^2)/a^2)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","A",0
116,1,204,0,4.721481," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(3 \, {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{6}} - \frac{\sqrt{2} {\left(15 \, A a^{5} - 23 \, B a^{5}\right)}}{a^{6}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{4 \, \sqrt{2} {\left(75 \, A a^{5} - 167 \, B a^{5}\right)}}{a^{6}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{3 \, \sqrt{2} {\left(83 \, A a^{5} - 155 \, B a^{5}\right)}}{a^{6}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}} - \frac{3 \, \sqrt{2} {\left(75 \, A - 163 \, B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{96 \, d}"," ",0,"-1/96*(((3*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*d*x + 1/2*c)^2/a^6 - sqrt(2)*(15*A*a^5 - 23*B*a^5)/a^6)*tan(1/2*d*x + 1/2*c)^2 - 4*sqrt(2)*(75*A*a^5 - 167*B*a^5)/a^6)*tan(1/2*d*x + 1/2*c)^2 - 3*sqrt(2)*(83*A*a^5 - 155*B*a^5)/a^6)*tan(1/2*d*x + 1/2*c)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) - 3*sqrt(2)*(75*A - 163*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
117,1,181,0,2.605998," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(\frac{2 \, {\left(\sqrt{2} A a^{6} - \sqrt{2} B a^{6}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} - \frac{9 \, \sqrt{2} A a^{6} - 17 \, \sqrt{2} B a^{6}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{11 \, \sqrt{2} A a^{6} - 83 \, \sqrt{2} B a^{6}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{{\left(19 \, \sqrt{2} A - 75 \, \sqrt{2} B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{32 \, d}"," ",0,"1/32*(((2*(sqrt(2)*A*a^6 - sqrt(2)*B*a^6)*tan(1/2*d*x + 1/2*c)^2/a^8 - (9*sqrt(2)*A*a^6 - 17*sqrt(2)*B*a^6)/a^8)*tan(1/2*d*x + 1/2*c)^2 - (11*sqrt(2)*A*a^6 - 83*sqrt(2)*B*a^6)/a^8)*tan(1/2*d*x + 1/2*c)/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - (19*sqrt(2)*A - 75*sqrt(2)*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
118,1,134,0,1.306364," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} - \frac{\sqrt{2} {\left(3 \, A a^{5} - 11 \, B a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{\sqrt{2} {\left(5 \, A + 19 \, B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{32 \, d}"," ",0,"-1/32*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*d*x + 1/2*c)^2/a^8 - sqrt(2)*(3*A*a^5 - 11*B*a^5)/a^8)*tan(1/2*d*x + 1/2*c) + sqrt(2)*(5*A + 19*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
119,1,134,0,3.839847," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{\sqrt{2} {\left(5 \, A a^{5} + 3 \, B a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{\sqrt{2} {\left(3 \, A + 5 \, B\right)} \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}}}}{32 \, d}"," ",0,"1/32*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*d*x + 1/2*c)^2/a^8 + sqrt(2)*(5*A*a^5 + 3*B*a^5)/a^8)*tan(1/2*d*x + 1/2*c) - sqrt(2)*(3*A + 5*B)*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/a^(5/2))/d","A",0
120,1,250,0,3.502167," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{\sqrt{2} {\left(13 \, A a^{5} - 5 \, B a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{\sqrt{2} {\left(43 \, A \sqrt{a} - 3 \, B \sqrt{a}\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{a^{3}} - \frac{64 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{\frac{5}{2}}} + \frac{64 \, A \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{\frac{5}{2}}}}{64 \, d}"," ",0,"-1/64*(2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*d*x + 1/2*c)^2/a^8 + sqrt(2)*(13*A*a^5 - 5*B*a^5)/a^8)*tan(1/2*d*x + 1/2*c) - sqrt(2)*(43*A*sqrt(a) - 3*B*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a^3 - 64*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^(5/2) + 64*A*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^(5/2))/d","A",0
121,1,409,0,3.949402," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{8}} + \frac{\sqrt{2} {\left(21 \, A a^{5} - 13 \, B a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{\sqrt{2} {\left(115 \, A \sqrt{a} - 43 \, B \sqrt{a}\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2}\right)}{a^{3}} - \frac{32 \, {\left(5 \, A \sqrt{a} - 2 \, B \sqrt{a}\right)} \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{3}} + \frac{32 \, {\left(5 \, A \sqrt{a} - 2 \, B \sqrt{a}\right)} \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{3}} + \frac{128 \, \sqrt{2} {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} A \sqrt{a} - A a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} - 6 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a + a^{2}\right)} a^{2}}}{64 \, d}"," ",0,"1/64*(2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*d*x + 1/2*c)^2/a^8 + sqrt(2)*(21*A*a^5 - 13*B*a^5)/a^8)*tan(1/2*d*x + 1/2*c) - sqrt(2)*(115*A*sqrt(a) - 43*B*sqrt(a))*log((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2)/a^3 - 32*(5*A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^3 + 32*(5*A*sqrt(a) - 2*B*sqrt(a))*log(abs((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^3 + 128*sqrt(2)*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*A*sqrt(a) - A*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4 - 6*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a + a^2)*a^2))/d","B",0
122,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2))]Discontinuities at zeroes of cos((d*t_nostep+c)/2) were not checkedEvaluation time: 1.15Unable to divide, perhaps due to rounding error%%%{%%{[%%%{%%{[663535861056963827345930584064,0]:[1,0,-2]%%},[16]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0]%%%} / %%%{%%%{%%{[9903520314283042199192993792,0]:[1,0,-2]%%},[16]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
123,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
124,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
126,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
127,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
128,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
129,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
130,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
131,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
132,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
133,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
134,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
135,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
136,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
137,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
138,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
139,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
140,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
141,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
142,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
143,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
145,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
146,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
147,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
148,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
149,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
150,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
151,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^2, x)","F",0
152,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^2, x)","F",0
153,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^2, x)","F",0
154,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
155,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
156,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
157,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
158,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(9/2)/(a*cos(d*x + c) + a)^3, x)","F",0
159,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^3, x)","F",0
160,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^3, x)","F",0
161,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^3, x)","F",0
162,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^3, x)","F",0
163,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
164,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
165,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
166,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
167,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
168,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
175,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
176,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
183,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
184,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(a*cos(d*x + c) + a), x)","F",0
192,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(a*cos(d*x + c) + a), x)","F",0
193,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
194,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
195,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
196,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
197,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
198,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
199,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
200,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
201,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
202,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
203,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
204,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
205,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
206,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
207,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
208,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^(7/2), x)","F",0
209,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(7/2), x)","F",0
210,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(7/2), x)","F",0
211,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(7/2), x)","F",0
212,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(7/2)*sqrt(cos(d*x + c))), x)","F",0
213,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(7/2)*cos(d*x + c)^(3/2)), x)","F",0
214,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(7/2)*cos(d*x + c)^(5/2)), x)","F",0
215,1,89,0,0.413339," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A a + 3 \, B b\right)} x + \frac{B b \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(B a + A b\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(A a + B b\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{3 \, {\left(B a + A b\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/8*(4*A*a + 3*B*b)*x + 1/32*B*b*sin(4*d*x + 4*c)/d + 1/12*(B*a + A*b)*sin(3*d*x + 3*c)/d + 1/4*(A*a + B*b)*sin(2*d*x + 2*c)/d + 3/4*(B*a + A*b)*sin(d*x + c)/d","A",0
216,1,68,0,0.312865," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(B a + A b\right)} x + \frac{B b \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(B a + A b\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a + 3 \, B b\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/2*(B*a + A*b)*x + 1/12*B*b*sin(3*d*x + 3*c)/d + 1/4*(B*a + A*b)*sin(2*d*x + 2*c)/d + 1/4*(4*A*a + 3*B*b)*sin(d*x + c)/d","A",0
217,1,45,0,0.302726," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, A a + B b\right)} x + \frac{B b \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(B a + A b\right)} \sin\left(d x + c\right)}{d}"," ",0,"1/2*(2*A*a + B*b)*x + 1/4*B*b*sin(2*d*x + 2*c)/d + (B*a + A*b)*sin(d*x + c)/d","A",0
218,1,79,0,0.668528," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\frac{A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - A a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(B a + A b\right)} {\left(d x + c\right)} + \frac{2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"(A*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - A*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (B*a + A*b)*(d*x + c) + 2*B*b*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
219,1,84,0,0.431293," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} B b + {\left(B a + A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a + A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"((d*x + c)*B*b + (B*a + A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a + A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*A*a*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
220,1,151,0,0.459322," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(A a + 2 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a + 2 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((A*a + 2*B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a + 2*B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 - 2*A*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) + 2*B*a*tan(1/2*d*x + 1/2*c) + 2*A*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
221,1,210,0,0.407462," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(B a + A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(B a + A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a + A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a + A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a*tan(1/2*d*x + 1/2*c)^5 - 3*B*a*tan(1/2*d*x + 1/2*c)^5 - 3*A*b*tan(1/2*d*x + 1/2*c)^5 + 6*B*b*tan(1/2*d*x + 1/2*c)^5 - 4*A*a*tan(1/2*d*x + 1/2*c)^3 - 12*B*b*tan(1/2*d*x + 1/2*c)^3 + 6*A*a*tan(1/2*d*x + 1/2*c) + 3*B*a*tan(1/2*d*x + 1/2*c) + 3*A*b*tan(1/2*d*x + 1/2*c) + 6*B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
222,1,304,0,0.512493," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a + 4 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a + 4 \, B b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a + 4*B*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a + 4*B*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a*tan(1/2*d*x + 1/2*c)^7 - 24*B*a*tan(1/2*d*x + 1/2*c)^7 - 24*A*b*tan(1/2*d*x + 1/2*c)^7 + 12*B*b*tan(1/2*d*x + 1/2*c)^7 + 9*A*a*tan(1/2*d*x + 1/2*c)^5 + 40*B*a*tan(1/2*d*x + 1/2*c)^5 + 40*A*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*b*tan(1/2*d*x + 1/2*c)^5 + 9*A*a*tan(1/2*d*x + 1/2*c)^3 - 40*B*a*tan(1/2*d*x + 1/2*c)^3 - 40*A*b*tan(1/2*d*x + 1/2*c)^3 - 12*B*b*tan(1/2*d*x + 1/2*c)^3 + 15*A*a*tan(1/2*d*x + 1/2*c) + 24*B*a*tan(1/2*d*x + 1/2*c) + 24*A*b*tan(1/2*d*x + 1/2*c) + 12*B*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
223,1,156,0,0.404325," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B b^{2} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(4 \, A a^{2} + 6 \, B a b + 3 \, A b^{2}\right)} x + \frac{{\left(2 \, B a b + A b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(4 \, B a^{2} + 8 \, A a b + 5 \, B b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(A a^{2} + 2 \, B a b + A b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(6 \, B a^{2} + 12 \, A a b + 5 \, B b^{2}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*B*b^2*sin(5*d*x + 5*c)/d + 1/8*(4*A*a^2 + 6*B*a*b + 3*A*b^2)*x + 1/32*(2*B*a*b + A*b^2)*sin(4*d*x + 4*c)/d + 1/48*(4*B*a^2 + 8*A*a*b + 5*B*b^2)*sin(3*d*x + 3*c)/d + 1/4*(A*a^2 + 2*B*a*b + A*b^2)*sin(2*d*x + 2*c)/d + 1/8*(6*B*a^2 + 12*A*a*b + 5*B*b^2)*sin(d*x + c)/d","A",0
224,1,124,0,0.376434," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B b^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(4 \, B a^{2} + 8 \, A a b + 3 \, B b^{2}\right)} x + \frac{{\left(2 \, B a b + A b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(B a^{2} + 2 \, A a b + B b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, A a^{2} + 6 \, B a b + 3 \, A b^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/32*B*b^2*sin(4*d*x + 4*c)/d + 1/8*(4*B*a^2 + 8*A*a*b + 3*B*b^2)*x + 1/12*(2*B*a*b + A*b^2)*sin(3*d*x + 3*c)/d + 1/4*(B*a^2 + 2*A*a*b + B*b^2)*sin(2*d*x + 2*c)/d + 1/4*(4*A*a^2 + 6*B*a*b + 3*A*b^2)*sin(d*x + c)/d","A",0
225,1,93,0,0.469415," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B b^{2} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{1}{2} \, {\left(2 \, A a^{2} + 2 \, B a b + A b^{2}\right)} x + \frac{{\left(2 \, B a b + A b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, B a^{2} + 8 \, A a b + 3 \, B b^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/12*B*b^2*sin(3*d*x + 3*c)/d + 1/2*(2*A*a^2 + 2*B*a*b + A*b^2)*x + 1/4*(2*B*a*b + A*b^2)*sin(2*d*x + 2*c)/d + 1/4*(4*B*a^2 + 8*A*a*b + 3*B*b^2)*sin(d*x + c)/d","A",0
226,1,178,0,0.450199," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\frac{2 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 2 \, A a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + {\left(2 \, B a^{2} + 4 \, A a b + B b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(4 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 2*A*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (2*B*a^2 + 4*A*a*b + B*b^2)*(d*x + c) + 2*(4*B*a*b*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^2*tan(1/2*d*x + 1/2*c)^3 - B*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*B*a*b*tan(1/2*d*x + 1/2*c) + 2*A*b^2*tan(1/2*d*x + 1/2*c) + B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
227,1,152,0,0.728284," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(2 \, B a b + A b^{2}\right)} {\left(d x + c\right)} + {\left(B a^{2} + 2 \, A a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(B a^{2} + 2 \, A a b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"((2*B*a*b + A*b^2)*(d*x + c) + (B*a^2 + 2*A*a*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (B*a^2 + 2*A*a*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(A*a^2*tan(1/2*d*x + 1/2*c)^3 - B*b^2*tan(1/2*d*x + 1/2*c)^3 + A*a^2*tan(1/2*d*x + 1/2*c) + B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","B",0
228,1,190,0,0.517322," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{2 \, {\left(d x + c\right)} B b^{2} + {\left(A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*b^2 + (A*a^2 + 4*B*a*b + 2*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a^2 + 4*B*a*b + 2*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a^2*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 4*A*a*b*tan(1/2*d*x + 1/2*c)^3 + A*a^2*tan(1/2*d*x + 1/2*c) + 2*B*a^2*tan(1/2*d*x + 1/2*c) + 4*A*a*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
229,1,294,0,0.819525," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{3 \, {\left(B a^{2} + 2 \, A a b + 2 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(B a^{2} + 2 \, A a b + 2 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a^2 + 2*A*a*b + 2*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a^2 + 2*A*a*b + 2*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) + 6*A*a*b*tan(1/2*d*x + 1/2*c) + 12*B*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
230,1,478,0,0.545572," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a^{2} + 8 \, B a b + 4 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a^{2} + 8 \, B a b + 4 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^2 + 8*B*a*b + 4*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a^2 + 8*B*a*b + 4*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*A*a*b*tan(1/2*d*x + 1/2*c)^7 + 24*B*a*b*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*B*b^2*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 40*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 80*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*A*a*b*tan(1/2*d*x + 1/2*c)^3 - 24*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^2*tan(1/2*d*x + 1/2*c) + 24*B*a^2*tan(1/2*d*x + 1/2*c) + 48*A*a*b*tan(1/2*d*x + 1/2*c) + 24*B*a*b*tan(1/2*d*x + 1/2*c) + 12*A*b^2*tan(1/2*d*x + 1/2*c) + 24*B*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
231,1,230,0,0.465940," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B b^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{1}{16} \, {\left(8 \, A a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2} + 5 \, B b^{3}\right)} x + \frac{{\left(3 \, B a b^{2} + A b^{3}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{3 \, {\left(2 \, B a^{2} b + 2 \, A a b^{2} + B b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(4 \, B a^{3} + 12 \, A a^{2} b + 15 \, B a b^{2} + 5 \, A b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(16 \, A a^{3} + 48 \, B a^{2} b + 48 \, A a b^{2} + 15 \, B b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(6 \, B a^{3} + 18 \, A a^{2} b + 15 \, B a b^{2} + 5 \, A b^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*B*b^3*sin(6*d*x + 6*c)/d + 1/16*(8*A*a^3 + 18*B*a^2*b + 18*A*a*b^2 + 5*B*b^3)*x + 1/80*(3*B*a*b^2 + A*b^3)*sin(5*d*x + 5*c)/d + 3/64*(2*B*a^2*b + 2*A*a*b^2 + B*b^3)*sin(4*d*x + 4*c)/d + 1/48*(4*B*a^3 + 12*A*a^2*b + 15*B*a*b^2 + 5*A*b^3)*sin(3*d*x + 3*c)/d + 1/64*(16*A*a^3 + 48*B*a^2*b + 48*A*a*b^2 + 15*B*b^3)*sin(2*d*x + 2*c)/d + 1/8*(6*B*a^3 + 18*A*a^2*b + 15*B*a*b^2 + 5*A*b^3)*sin(d*x + c)/d","A",0
232,1,188,0,0.511908," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B b^{3} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(4 \, B a^{3} + 12 \, A a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} x + \frac{{\left(3 \, B a b^{2} + A b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(12 \, B a^{2} b + 12 \, A a b^{2} + 5 \, B b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(B a^{3} + 3 \, A a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(8 \, A a^{3} + 18 \, B a^{2} b + 18 \, A a b^{2} + 5 \, B b^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*B*b^3*sin(5*d*x + 5*c)/d + 1/8*(4*B*a^3 + 12*A*a^2*b + 9*B*a*b^2 + 3*A*b^3)*x + 1/32*(3*B*a*b^2 + A*b^3)*sin(4*d*x + 4*c)/d + 1/48*(12*B*a^2*b + 12*A*a*b^2 + 5*B*b^3)*sin(3*d*x + 3*c)/d + 1/4*(B*a^3 + 3*A*a^2*b + 3*B*a*b^2 + A*b^3)*sin(2*d*x + 2*c)/d + 1/8*(8*A*a^3 + 18*B*a^2*b + 18*A*a*b^2 + 5*B*b^3)*sin(d*x + c)/d","A",0
233,1,148,0,0.591394," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B b^{3} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(8 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 3 \, B b^{3}\right)} x + \frac{{\left(3 \, B a b^{2} + A b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{{\left(3 \, B a^{2} b + 3 \, A a b^{2} + B b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(4 \, B a^{3} + 12 \, A a^{2} b + 9 \, B a b^{2} + 3 \, A b^{3}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/32*B*b^3*sin(4*d*x + 4*c)/d + 1/8*(8*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 3*B*b^3)*x + 1/12*(3*B*a*b^2 + A*b^3)*sin(3*d*x + 3*c)/d + 1/4*(3*B*a^2*b + 3*A*a*b^2 + B*b^3)*sin(2*d*x + 2*c)/d + 1/4*(4*B*a^3 + 12*A*a^2*b + 9*B*a*b^2 + 3*A*b^3)*sin(d*x + c)/d","A",0
234,1,314,0,0.647535," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\frac{6 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 6 \, A a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(2 \, B a^{3} + 6 \, A a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 6*A*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(2*B*a^3 + 6*A*a^2*b + 3*B*a*b^2 + A*b^3)*(d*x + c) + 2*(18*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 9*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*B*b^3*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 18*B*a^2*b*tan(1/2*d*x + 1/2*c) + 18*A*a*b^2*tan(1/2*d*x + 1/2*c) + 9*B*a*b^2*tan(1/2*d*x + 1/2*c) + 3*A*b^3*tan(1/2*d*x + 1/2*c) + 6*B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
235,1,234,0,1.291642," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{4 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - {\left(6 \, B a^{2} b + 6 \, A a b^{2} + B b^{3}\right)} {\left(d x + c\right)} - 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(4*A*a^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (6*B*a^2*b + 6*A*a*b^2 + B*b^3)*(d*x + c) - 2*(B*a^3 + 3*A*a^2*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 2*(B*a^3 + 3*A*a^2*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^3*tan(1/2*d*x + 1/2*c)^3 - B*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*B*a*b^2*tan(1/2*d*x + 1/2*c) + 2*A*b^3*tan(1/2*d*x + 1/2*c) + B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
236,1,239,0,0.569157," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{\frac{4 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} {\left(d x + c\right)} + {\left(A a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a^{3} + 6 \, B a^{2} b + 6 \, A a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*B*b^3*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(3*B*a*b^2 + A*b^3)*(d*x + c) + (A*a^3 + 6*B*a^2*b + 6*A*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a^3 + 6*B*a^2*b + 6*A*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 6*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 + A*a^3*tan(1/2*d*x + 1/2*c) + 2*B*a^3*tan(1/2*d*x + 1/2*c) + 6*A*a^2*b*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
237,1,336,0,0.440701," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} B b^{3} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(B a^{3} + 3 \, A a^{2} b + 6 \, B a b^{2} + 2 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*B*b^3 + 3*(B*a^3 + 3*A*a^2*b + 6*B*a*b^2 + 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a^3 + 3*A*a^2*b + 6*B*a*b^2 + 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^3*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^3*tan(1/2*d*x + 1/2*c) + 3*B*a^3*tan(1/2*d*x + 1/2*c) + 9*A*a^2*b*tan(1/2*d*x + 1/2*c) + 18*B*a^2*b*tan(1/2*d*x + 1/2*c) + 18*A*a*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
238,1,586,0,0.693468," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{3 \, {\left(3 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 8 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a^{3} + 12 \, B a^{2} b + 12 \, A a b^{2} + 8 \, B b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 216 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 216 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(3*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 8*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a^3 + 12*B*a^2*b + 12*A*a*b^2 + 8*B*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a^3*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^3*tan(1/2*d*x + 1/2*c)^7 - 72*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 - 24*A*b^3*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 40*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 120*A*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 216*B*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 72*A*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 120*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 216*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 72*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^3*tan(1/2*d*x + 1/2*c) + 24*B*a^3*tan(1/2*d*x + 1/2*c) + 72*A*a^2*b*tan(1/2*d*x + 1/2*c) + 36*B*a^2*b*tan(1/2*d*x + 1/2*c) + 36*A*a*b^2*tan(1/2*d*x + 1/2*c) + 72*B*a*b^2*tan(1/2*d*x + 1/2*c) + 24*A*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
239,1,722,0,0.886799," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, B a^{3} + 9 \, A a^{2} b + 12 \, B a b^{2} + 4 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1200 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 90 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 960 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 225 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 180 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a^3 + 9*A*a^2*b + 12*B*a*b^2 + 4*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*B*a^3 + 9*A*a^2*b + 12*B*a*b^2 + 4*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*a^3*tan(1/2*d*x + 1/2*c)^9 - 75*B*a^3*tan(1/2*d*x + 1/2*c)^9 - 225*A*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*B*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 360*A*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 180*B*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 60*A*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*B*b^3*tan(1/2*d*x + 1/2*c)^9 - 160*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 30*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*B*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 120*A*b^3*tan(1/2*d*x + 1/2*c)^7 - 480*B*b^3*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 1200*B*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1200*A*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 720*B*b^3*tan(1/2*d*x + 1/2*c)^5 - 160*A*a^3*tan(1/2*d*x + 1/2*c)^3 - 30*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 90*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 960*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 360*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*A*b^3*tan(1/2*d*x + 1/2*c)^3 - 480*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^3*tan(1/2*d*x + 1/2*c) + 75*B*a^3*tan(1/2*d*x + 1/2*c) + 225*A*a^2*b*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b*tan(1/2*d*x + 1/2*c) + 360*A*a*b^2*tan(1/2*d*x + 1/2*c) + 180*B*a*b^2*tan(1/2*d*x + 1/2*c) + 60*A*b^3*tan(1/2*d*x + 1/2*c) + 120*B*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
240,1,313,0,0.520365," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B b^{4} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{1}{16} \, {\left(8 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 20 \, B a b^{3} + 5 \, A b^{4}\right)} x + \frac{{\left(4 \, B a b^{3} + A b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 7 \, B b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(8 \, B a^{3} b + 12 \, A a^{2} b^{2} + 12 \, B a b^{3} + 3 \, A b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(16 \, B a^{4} + 64 \, A a^{3} b + 120 \, B a^{2} b^{2} + 80 \, A a b^{3} + 21 \, B b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(16 \, A a^{4} + 64 \, B a^{3} b + 96 \, A a^{2} b^{2} + 60 \, B a b^{3} + 15 \, A b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(48 \, B a^{4} + 192 \, A a^{3} b + 240 \, B a^{2} b^{2} + 160 \, A a b^{3} + 35 \, B b^{4}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/448*B*b^4*sin(7*d*x + 7*c)/d + 1/16*(8*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 20*B*a*b^3 + 5*A*b^4)*x + 1/192*(4*B*a*b^3 + A*b^4)*sin(6*d*x + 6*c)/d + 1/320*(24*B*a^2*b^2 + 16*A*a*b^3 + 7*B*b^4)*sin(5*d*x + 5*c)/d + 1/64*(8*B*a^3*b + 12*A*a^2*b^2 + 12*B*a*b^3 + 3*A*b^4)*sin(4*d*x + 4*c)/d + 1/192*(16*B*a^4 + 64*A*a^3*b + 120*B*a^2*b^2 + 80*A*a*b^3 + 21*B*b^4)*sin(3*d*x + 3*c)/d + 1/64*(16*A*a^4 + 64*B*a^3*b + 96*A*a^2*b^2 + 60*B*a*b^3 + 15*A*b^4)*sin(2*d*x + 2*c)/d + 1/64*(48*B*a^4 + 192*A*a^3*b + 240*B*a^2*b^2 + 160*A*a*b^3 + 35*B*b^4)*sin(d*x + c)/d","A",0
241,1,263,0,0.470787," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B b^{4} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{1}{16} \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} x + \frac{{\left(4 \, B a b^{3} + A b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{{\left(12 \, B a^{2} b^{2} + 8 \, A a b^{3} + 3 \, B b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 20 \, B a b^{3} + 5 \, A b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(16 \, B a^{4} + 64 \, A a^{3} b + 96 \, B a^{2} b^{2} + 64 \, A a b^{3} + 15 \, B b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(8 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 20 \, B a b^{3} + 5 \, A b^{4}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/192*B*b^4*sin(6*d*x + 6*c)/d + 1/16*(8*B*a^4 + 32*A*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*x + 1/80*(4*B*a*b^3 + A*b^4)*sin(5*d*x + 5*c)/d + 1/64*(12*B*a^2*b^2 + 8*A*a*b^3 + 3*B*b^4)*sin(4*d*x + 4*c)/d + 1/48*(16*B*a^3*b + 24*A*a^2*b^2 + 20*B*a*b^3 + 5*A*b^4)*sin(3*d*x + 3*c)/d + 1/64*(16*B*a^4 + 64*A*a^3*b + 96*B*a^2*b^2 + 64*A*a*b^3 + 15*B*b^4)*sin(2*d*x + 2*c)/d + 1/8*(8*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 20*B*a*b^3 + 5*A*b^4)*sin(d*x + c)/d","A",0
242,1,212,0,0.506842," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\frac{B b^{4} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{1}{8} \, {\left(8 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 12 \, B a b^{3} + 3 \, A b^{4}\right)} x + \frac{{\left(4 \, B a b^{3} + A b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 5 \, B b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{{\left(4 \, B a^{3} b + 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{{\left(8 \, B a^{4} + 32 \, A a^{3} b + 36 \, B a^{2} b^{2} + 24 \, A a b^{3} + 5 \, B b^{4}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/80*B*b^4*sin(5*d*x + 5*c)/d + 1/8*(8*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 12*B*a*b^3 + 3*A*b^4)*x + 1/32*(4*B*a*b^3 + A*b^4)*sin(4*d*x + 4*c)/d + 1/48*(24*B*a^2*b^2 + 16*A*a*b^3 + 5*B*b^4)*sin(3*d*x + 3*c)/d + 1/4*(4*B*a^3*b + 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*sin(2*d*x + 2*c)/d + 1/8*(8*B*a^4 + 32*A*a^3*b + 36*B*a^2*b^2 + 24*A*a*b^3 + 5*B*b^4)*sin(d*x + c)/d","A",0
243,1,603,0,0.640755," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\frac{24 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 24 \, A a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 3 \, {\left(8 \, B a^{4} + 32 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 3 \, B b^{4}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(96 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 144 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 288 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 432 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 432 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 96 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 144 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 24*A*a^4*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 3*(8*B*a^4 + 32*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 3*B*b^4)*(d*x + c) + 2*(96*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 144*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 72*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 48*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 96*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 24*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 15*B*b^4*tan(1/2*d*x + 1/2*c)^7 + 288*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 432*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 72*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 48*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 160*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 40*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 9*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 288*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 432*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 72*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 48*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 160*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 40*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 9*B*b^4*tan(1/2*d*x + 1/2*c)^3 + 96*B*a^3*b*tan(1/2*d*x + 1/2*c) + 144*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 72*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 48*A*a*b^3*tan(1/2*d*x + 1/2*c) + 96*B*a*b^3*tan(1/2*d*x + 1/2*c) + 24*A*b^4*tan(1/2*d*x + 1/2*c) + 15*B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
244,1,371,0,1.231858," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{12 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, {\left(8 \, B a^{3} b + 12 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)} - 6 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 6 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(36 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(12*A*a^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 1) - 3*(8*B*a^3*b + 12*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*(d*x + c) - 6*(B*a^4 + 4*A*a^3*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) + 6*(B*a^4 + 4*A*a^3*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(36*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 24*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 3*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 72*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 48*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*B*b^4*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 24*A*a*b^3*tan(1/2*d*x + 1/2*c) + 12*B*a*b^3*tan(1/2*d*x + 1/2*c) + 3*A*b^4*tan(1/2*d*x + 1/2*c) + 6*B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
245,1,526,0,0.689084," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\frac{{\left(12 \, B a^{2} b^{2} + 8 \, A a b^{3} + B b^{4}\right)} {\left(d x + c\right)} + {\left(A a^{4} + 8 \, B a^{3} b + 12 \, A a^{2} b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(A a^{4} + 8 \, B a^{3} b + 12 \, A a^{2} b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((12*B*a^2*b^2 + 8*A*a*b^3 + B*b^4)*(d*x + c) + (A*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (A*a^4 + 8*B*a^3*b + 12*A*a^2*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(A*a^4*tan(1/2*d*x + 1/2*c)^7 - 2*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 8*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 8*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 2*A*b^4*tan(1/2*d*x + 1/2*c)^7 - B*b^4*tan(1/2*d*x + 1/2*c)^7 + 3*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 2*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 8*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 8*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 2*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^4*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^4*tan(1/2*d*x + 1/2*c)^3 + 8*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 8*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 3*B*b^4*tan(1/2*d*x + 1/2*c)^3 + A*a^4*tan(1/2*d*x + 1/2*c) + 2*B*a^4*tan(1/2*d*x + 1/2*c) + 8*A*a^3*b*tan(1/2*d*x + 1/2*c) + 8*B*a*b^3*tan(1/2*d*x + 1/2*c) + 2*A*b^4*tan(1/2*d*x + 1/2*c) + B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^4 - 1)^2)/d","B",0
246,1,387,0,0.679960," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\frac{\frac{12 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(B a^{4} + 4 \, A a^{3} b + 12 \, B a^{2} b^{2} + 8 \, A a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*B*b^4*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 1) + 6*(4*B*a*b^3 + A*b^4)*(d*x + c) + 3*(B*a^4 + 4*A*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(B*a^4 + 4*A*a^3*b + 12*B*a^2*b^2 + 8*A*a*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(6*A*a^4*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^4*tan(1/2*d*x + 1/2*c)^5 - 12*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 24*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^4*tan(1/2*d*x + 1/2*c) + 3*B*a^4*tan(1/2*d*x + 1/2*c) + 12*A*a^3*b*tan(1/2*d*x + 1/2*c) + 24*B*a^3*b*tan(1/2*d*x + 1/2*c) + 36*A*a^2*b^2*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
247,1,635,0,0.694157," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\frac{24 \, {\left(d x + c\right)} B b^{4} + 3 \, {\left(3 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(3 \, A a^{4} + 16 \, B a^{3} b + 24 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 24 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 432 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 288 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 144 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)*B*b^4 + 3*(3*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(3*A*a^4 + 16*B*a^3*b + 24*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(15*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 24*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 96*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 96*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 40*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 40*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 160*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 48*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 432*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 288*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*A*a^4*tan(1/2*d*x + 1/2*c) + 24*B*a^4*tan(1/2*d*x + 1/2*c) + 96*A*a^3*b*tan(1/2*d*x + 1/2*c) + 48*B*a^3*b*tan(1/2*d*x + 1/2*c) + 72*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 144*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 96*A*a*b^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
248,1,850,0,0.544045," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""giac"")","\frac{15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 8 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(3 \, B a^{4} + 12 \, A a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 8 \, B b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(120 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 300 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 120 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1280 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1920 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1920 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 480 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 464 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2880 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 720 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 160 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1280 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1920 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 720 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1920 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 300 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 720 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 360 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(3*B*a^4 + 12*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 8*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(3*B*a^4 + 12*A*a^3*b + 24*B*a^2*b^2 + 16*A*a*b^3 + 8*B*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(120*A*a^4*tan(1/2*d*x + 1/2*c)^9 - 75*B*a^4*tan(1/2*d*x + 1/2*c)^9 - 300*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 480*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 - 240*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 480*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^9 - 160*A*a^4*tan(1/2*d*x + 1/2*c)^7 + 30*B*a^4*tan(1/2*d*x + 1/2*c)^7 + 120*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 1280*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 1920*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 + 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 1920*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 - 480*A*b^4*tan(1/2*d*x + 1/2*c)^7 + 464*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 1600*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 2400*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 2880*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 720*A*b^4*tan(1/2*d*x + 1/2*c)^5 - 160*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 30*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 120*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1280*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1920*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 720*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 480*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 1920*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 480*A*b^4*tan(1/2*d*x + 1/2*c)^3 + 120*A*a^4*tan(1/2*d*x + 1/2*c) + 75*B*a^4*tan(1/2*d*x + 1/2*c) + 300*A*a^3*b*tan(1/2*d*x + 1/2*c) + 480*B*a^3*b*tan(1/2*d*x + 1/2*c) + 720*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 360*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 240*A*a*b^3*tan(1/2*d*x + 1/2*c) + 480*B*a*b^3*tan(1/2*d*x + 1/2*c) + 120*A*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
249,1,1186,0,0.932391," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^7,x, algorithm=""giac"")","\frac{15 \, {\left(5 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(5 \, A a^{4} + 24 \, B a^{3} b + 36 \, A a^{2} b^{2} + 32 \, B a b^{3} + 8 \, A b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1440 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 240 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 560 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 840 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5280 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1440 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1248 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8640 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2400 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1248 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4992 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 360 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8640 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5760 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 960 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 560 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 840 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1260 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5280 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3520 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1440 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 360 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1200 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 165 \, A a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 600 \, B a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 900 \, A a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1440 \, B a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 960 \, A a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, B b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(5*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(5*A*a^4 + 24*B*a^3*b + 36*A*a^2*b^2 + 32*B*a*b^3 + 8*A*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(165*A*a^4*tan(1/2*d*x + 1/2*c)^11 - 240*B*a^4*tan(1/2*d*x + 1/2*c)^11 - 960*A*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 600*B*a^3*b*tan(1/2*d*x + 1/2*c)^11 + 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 1440*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^11 - 960*A*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 480*B*a*b^3*tan(1/2*d*x + 1/2*c)^11 + 120*A*b^4*tan(1/2*d*x + 1/2*c)^11 - 240*B*b^4*tan(1/2*d*x + 1/2*c)^11 + 25*A*a^4*tan(1/2*d*x + 1/2*c)^9 + 560*B*a^4*tan(1/2*d*x + 1/2*c)^9 + 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 840*B*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 5280*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^9 + 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 1440*B*a*b^3*tan(1/2*d*x + 1/2*c)^9 - 360*A*b^4*tan(1/2*d*x + 1/2*c)^9 + 1200*B*b^4*tan(1/2*d*x + 1/2*c)^9 + 450*A*a^4*tan(1/2*d*x + 1/2*c)^7 - 1248*B*a^4*tan(1/2*d*x + 1/2*c)^7 - 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 240*B*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 8640*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^7 - 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 960*B*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 240*A*b^4*tan(1/2*d*x + 1/2*c)^7 - 2400*B*b^4*tan(1/2*d*x + 1/2*c)^7 + 450*A*a^4*tan(1/2*d*x + 1/2*c)^5 + 1248*B*a^4*tan(1/2*d*x + 1/2*c)^5 + 4992*A*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 240*B*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 360*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 8640*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 + 5760*A*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 960*B*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 240*A*b^4*tan(1/2*d*x + 1/2*c)^5 + 2400*B*b^4*tan(1/2*d*x + 1/2*c)^5 + 25*A*a^4*tan(1/2*d*x + 1/2*c)^3 - 560*B*a^4*tan(1/2*d*x + 1/2*c)^3 - 2240*A*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 840*B*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 1260*A*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 5280*B*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 3520*A*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 1440*B*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 360*A*b^4*tan(1/2*d*x + 1/2*c)^3 - 1200*B*b^4*tan(1/2*d*x + 1/2*c)^3 + 165*A*a^4*tan(1/2*d*x + 1/2*c) + 240*B*a^4*tan(1/2*d*x + 1/2*c) + 960*A*a^3*b*tan(1/2*d*x + 1/2*c) + 600*B*a^3*b*tan(1/2*d*x + 1/2*c) + 900*A*a^2*b^2*tan(1/2*d*x + 1/2*c) + 1440*B*a^2*b^2*tan(1/2*d*x + 1/2*c) + 960*A*a*b^3*tan(1/2*d*x + 1/2*c) + 480*B*a*b^3*tan(1/2*d*x + 1/2*c) + 120*A*b^4*tan(1/2*d*x + 1/2*c) + 240*B*b^4*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
250,1,360,0,0.488359," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, B a^{3} - 2 \, A a^{2} b + B a b^{2} - A b^{3}\right)} {\left(d x + c\right)}}{b^{4}} + \frac{12 \, {\left(B a^{4} - A a^{3} b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} - \frac{2 \, {\left(6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*B*a^3 - 2*A*a^2*b + B*a*b^2 - A*b^3)*(d*x + c)/b^4 + 12*(B*a^4 - A*a^3*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) - 2*(6*B*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b*tan(1/2*d*x + 1/2*c)^5 + 3*B*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*A*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*B*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^2*tan(1/2*d*x + 1/2*c)^3 - 12*A*a*b*tan(1/2*d*x + 1/2*c)^3 + 4*B*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^2*tan(1/2*d*x + 1/2*c) - 6*A*a*b*tan(1/2*d*x + 1/2*c) - 3*B*a*b*tan(1/2*d*x + 1/2*c) + 3*A*b^2*tan(1/2*d*x + 1/2*c) + 6*B*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^3))/d","B",0
251,1,227,0,0.492428," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, B a^{2} - 2 \, A a b + B b^{2}\right)} {\left(d x + c\right)}}{b^{3}} + \frac{4 \, {\left(B a^{3} - A a^{2} b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{3}} - \frac{2 \, {\left(2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*((2*B*a^2 - 2*A*a*b + B*b^2)*(d*x + c)/b^3 + 4*(B*a^3 - A*a^2*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^3) - 2*(2*B*a*tan(1/2*d*x + 1/2*c)^3 - 2*A*b*tan(1/2*d*x + 1/2*c)^3 + B*b*tan(1/2*d*x + 1/2*c)^3 + 2*B*a*tan(1/2*d*x + 1/2*c) - 2*A*b*tan(1/2*d*x + 1/2*c) - B*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^2))/d","A",0
252,1,142,0,0.448795," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(B a - A b\right)} {\left(d x + c\right)}}{b^{2}} - \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b} + \frac{2 \, {\left(B a^{2} - A a b\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{2}}}{d}"," ",0,"-((B*a - A*b)*(d*x + c)/b^2 - 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b) + 2*(B*a^2 - A*a*b)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^2))/d","A",0
253,1,296,0,0.660826," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(\sqrt{a^{2} - b^{2}} B {\left(2 \, a - b\right)} {\left| a - b \right|} - \sqrt{a^{2} - b^{2}} A b {\left| a - b \right|} - \sqrt{a^{2} - b^{2}} A {\left| a - b \right|} {\left| b \right|} + \sqrt{a^{2} - b^{2}} B {\left| a - b \right|} {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} + \frac{{\left(2 \, B a - A b - B b + A {\left| b \right|} - B {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{b^{2} - a {\left| b \right|}}}{d}"," ",0,"-((sqrt(a^2 - b^2)*B*(2*a - b)*abs(a - b) - sqrt(a^2 - b^2)*A*b*abs(a - b) - sqrt(a^2 - b^2)*A*abs(a - b)*abs(b) + sqrt(a^2 - b^2)*B*abs(a - b)*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) + (2*B*a - A*b - B*b + A*abs(b) - B*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/(b^2 - a*abs(b)))/d","B",0
254,1,127,0,0.467316," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(B a - A b\right)}}{\sqrt{a^{2} - b^{2}} a}}{d}"," ",0,"(A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a + 2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*(B*a - A*b)/(sqrt(a^2 - b^2)*a))/d","A",0
255,1,175,0,0.965671," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(B a - A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{{\left(B a - A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a} + \frac{2 \, {\left(B a b - A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{2}}}{d}"," ",0,"((B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - (B*a - A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a) + 2*(B*a*b - A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^2))/d","A",0
256,1,269,0,0.772448," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(A a^{2} - 2 \, B a b + 2 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{{\left(A a^{2} - 2 \, B a b + 2 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{4 \, {\left(B a b^{2} - A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3}} + \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*((A*a^2 - 2*B*a*b + 2*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (A*a^2 - 2*B*a*b + 2*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - 4*(B*a*b^2 - A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3) + 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 2*A*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) + 2*B*a*tan(1/2*d*x + 1/2*c) - 2*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2))/d","B",0
257,1,412,0,0.615717," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(B a^{3} - A a^{2} b + 2 \, B a b^{2} - 2 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3 \, {\left(B a^{3} - A a^{2} b + 2 \, B a b^{2} - 2 \, A b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} + \frac{12 \, {\left(B a b^{3} - A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4}} - \frac{2 \, {\left(6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"1/6*(3*(B*a^3 - A*a^2*b + 2*B*a*b^2 - 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3*(B*a^3 - A*a^2*b + 2*B*a*b^2 - 2*A*b^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 + 12*(B*a*b^3 - A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4) - 2*(6*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^2*tan(1/2*d*x + 1/2*c)^5 - 4*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 12*B*a*b*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) - 3*A*a*b*tan(1/2*d*x + 1/2*c) - 6*B*a*b*tan(1/2*d*x + 1/2*c) + 6*A*b^2*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^3))/d","B",0
258,1,338,0,0.830670," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(3 \, B a^{5} - 2 \, A a^{4} b - 4 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{4 \, {\left(B a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} + \frac{{\left(6 \, B a^{2} - 4 \, A a b + B b^{2}\right)} {\left(d x + c\right)}}{b^{4}} - \frac{2 \, {\left(4 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{3}}}{2 \, d}"," ",0,"1/2*(4*(3*B*a^5 - 2*A*a^4*b - 4*B*a^3*b^2 + 3*A*a^2*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - 4*(B*a^4*tan(1/2*d*x + 1/2*c) - A*a^3*b*tan(1/2*d*x + 1/2*c))/((a^2*b^3 - b^5)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) + (6*B*a^2 - 4*A*a*b + B*b^2)*(d*x + c)/b^4 - 2*(4*B*a*tan(1/2*d*x + 1/2*c)^3 - 2*A*b*tan(1/2*d*x + 1/2*c)^3 + B*b*tan(1/2*d*x + 1/2*c)^3 + 4*B*a*tan(1/2*d*x + 1/2*c) - 2*A*b*tan(1/2*d*x + 1/2*c) - B*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^3))/d","A",0
259,1,1116,0,3.218781," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{{\left(4 \, B a^{6} b^{2} - 2 \, A a^{5} b^{3} - 2 \, B a^{5} b^{3} + A a^{4} b^{4} - 9 \, B a^{4} b^{4} + 5 \, A a^{3} b^{5} + 4 \, B a^{3} b^{5} - 2 \, A a^{2} b^{6} + 5 \, B a^{2} b^{6} - 3 \, A a b^{7} - 2 \, B a b^{7} + A b^{8} + 2 \, B a^{3} {\left| -a^{2} b^{3} + b^{5} \right|} - A a^{2} b {\left| -a^{2} b^{3} + b^{5} \right|} - B a^{2} b {\left| -a^{2} b^{3} + b^{5} \right|} + A a b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} - 2 \, B a b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} + A b^{3} {\left| -a^{2} b^{3} + b^{5} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a^{3} b^{2} - 2 \, a b^{4} + \sqrt{-4 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)}^{2}}}{a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}}}}\right)\right)}}{a^{3} b^{2} {\left| -a^{2} b^{3} + b^{5} \right|} - a b^{4} {\left| -a^{2} b^{3} + b^{5} \right|} + {\left(a^{2} b^{3} - b^{5}\right)}^{2}} + \frac{{\left({\left(a^{2} b - a b^{2} - b^{3}\right)} \sqrt{a^{2} - b^{2}} A {\left| -a^{2} b^{3} + b^{5} \right|} {\left| -a + b \right|} - {\left(2 \, a^{3} - a^{2} b - 2 \, a b^{2}\right)} \sqrt{a^{2} - b^{2}} B {\left| -a^{2} b^{3} + b^{5} \right|} {\left| -a + b \right|} - {\left(2 \, a^{5} b^{3} - a^{4} b^{4} - 5 \, a^{3} b^{5} + 2 \, a^{2} b^{6} + 3 \, a b^{7} - b^{8}\right)} \sqrt{a^{2} - b^{2}} A {\left| -a + b \right|} + {\left(4 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 9 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + 5 \, a^{2} b^{6} - 2 \, a b^{7}\right)} \sqrt{a^{2} - b^{2}} B {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a^{3} b^{2} - 2 \, a b^{4} - \sqrt{-4 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)}^{2}}}{a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} - {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} {\left| -a^{2} b^{3} + b^{5} \right|}} + \frac{2 \, {\left(2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} {\left(a^{2} b^{2} - b^{4}\right)}}}{d}"," ",0,"((4*B*a^6*b^2 - 2*A*a^5*b^3 - 2*B*a^5*b^3 + A*a^4*b^4 - 9*B*a^4*b^4 + 5*A*a^3*b^5 + 4*B*a^3*b^5 - 2*A*a^2*b^6 + 5*B*a^2*b^6 - 3*A*a*b^7 - 2*B*a*b^7 + A*b^8 + 2*B*a^3*abs(-a^2*b^3 + b^5) - A*a^2*b*abs(-a^2*b^3 + b^5) - B*a^2*b*abs(-a^2*b^3 + b^5) + A*a*b^2*abs(-a^2*b^3 + b^5) - 2*B*a*b^2*abs(-a^2*b^3 + b^5) + A*b^3*abs(-a^2*b^3 + b^5))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a^3*b^2 - 2*a*b^4 + sqrt(-4*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5) + 4*(a^3*b^2 - a*b^4)^2))/(a^3*b^2 - a^2*b^3 - a*b^4 + b^5))))/(a^3*b^2*abs(-a^2*b^3 + b^5) - a*b^4*abs(-a^2*b^3 + b^5) + (a^2*b^3 - b^5)^2) + ((a^2*b - a*b^2 - b^3)*sqrt(a^2 - b^2)*A*abs(-a^2*b^3 + b^5)*abs(-a + b) - (2*a^3 - a^2*b - 2*a*b^2)*sqrt(a^2 - b^2)*B*abs(-a^2*b^3 + b^5)*abs(-a + b) - (2*a^5*b^3 - a^4*b^4 - 5*a^3*b^5 + 2*a^2*b^6 + 3*a*b^7 - b^8)*sqrt(a^2 - b^2)*A*abs(-a + b) + (4*a^6*b^2 - 2*a^5*b^3 - 9*a^4*b^4 + 4*a^3*b^5 + 5*a^2*b^6 - 2*a*b^7)*sqrt(a^2 - b^2)*B*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a^3*b^2 - 2*a*b^4 - sqrt(-4*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5) + 4*(a^3*b^2 - a*b^4)^2))/(a^3*b^2 - a^2*b^3 - a*b^4 + b^5))))/((a^2*b^3 - b^5)^2*(a^2 - 2*a*b + b^2) - (a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*abs(-a^2*b^3 + b^5)) + 2*(2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + B*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^3*tan(1/2*d*x + 1/2*c) - A*a^2*b*tan(1/2*d*x + 1/2*c) + B*a^2*b*tan(1/2*d*x + 1/2*c) - B*a*b^2*tan(1/2*d*x + 1/2*c) - B*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)*(a^2*b^2 - b^4)))/d","B",0
260,1,199,0,0.440124," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a^{3} - 2 \, B a b^{2} + A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{{\left(d x + c\right)} B}{b^{2}} - \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{2} b - b^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}}}{d}"," ",0,"(2*(B*a^3 - 2*B*a*b^2 + A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^2*b^2 - b^4)*sqrt(a^2 - b^2)) + (d*x + c)*B/b^2 - 2*(B*a^2*tan(1/2*d*x + 1/2*c) - A*a*b*tan(1/2*d*x + 1/2*c))/((a^2*b - b^3)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)))/d","A",0
261,1,159,0,0.413741," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(A a - B b\right)}}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} - \frac{B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)} {\left(a^{2} - b^{2}\right)}}\right)}}{d}"," ",0,"-2*((pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*(A*a - B*b)/(a^2 - b^2)^(3/2) - (B*a*tan(1/2*d*x + 1/2*c) - A*b*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)*(a^2 - b^2)))/d","A",0
262,1,223,0,1.488820," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a^{3} - 2 \, A a^{2} b + A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(B a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}}}{d}"," ",0,"(2*(B*a^3 - 2*A*a^2*b + A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - a^2*b^2)*sqrt(a^2 - b^2)) + A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 2*(B*a*b*tan(1/2*d*x + 1/2*c) - A*b^2*tan(1/2*d*x + 1/2*c))/((a^3 - a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)))/d","A",0
263,1,404,0,0.800118," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2} - B a b^{3} + 2 \, A b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)} {\left(a^{4} - a^{2} b^{2}\right)}} + \frac{{\left(B a - 2 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{{\left(B a - 2 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}}}{d}"," ",0,"(2*(2*B*a^3*b - 3*A*a^2*b^2 - B*a*b^3 + 2*A*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^5 - a^3*b^2)*sqrt(a^2 - b^2)) - 2*(A*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - A*a*b^2*tan(1/2*d*x + 1/2*c)^3 - B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^3*tan(1/2*d*x + 1/2*c)^3 + A*a^3*tan(1/2*d*x + 1/2*c) + A*a^2*b*tan(1/2*d*x + 1/2*c) - A*a*b^2*tan(1/2*d*x + 1/2*c) + B*a*b^2*tan(1/2*d*x + 1/2*c) - 2*A*b^3*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)*(a^4 - a^2*b^2)) + (B*a - 2*A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (B*a - 2*A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3)/d","B",0
264,1,378,0,1.230919," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(3 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3} - 2 \, B a b^{4} + 3 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{4 \, {\left(B a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}} - \frac{{\left(A a^{2} - 4 \, B a b + 6 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} + \frac{{\left(A a^{2} - 4 \, B a b + 6 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{2 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}}}{2 \, d}"," ",0,"-1/2*(4*(3*B*a^3*b^2 - 4*A*a^2*b^3 - 2*B*a*b^4 + 3*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - a^4*b^2)*sqrt(a^2 - b^2)) + 4*(B*a*b^3*tan(1/2*d*x + 1/2*c) - A*b^4*tan(1/2*d*x + 1/2*c))/((a^5 - a^3*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)) - (A*a^2 - 4*B*a*b + 6*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 + (A*a^2 - 4*B*a*b + 6*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - 2*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 4*A*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) + 2*B*a*tan(1/2*d*x + 1/2*c) - 4*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3))/d","A",0
265,1,2712,0,2.316764," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(3 \, {\left(2 \, a^{5} b - a^{4} b^{2} - 4 \, a^{3} b^{3} + 2 \, a^{2} b^{4} + 2 \, a b^{5}\right)} \sqrt{a^{2} - b^{2}} A {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} {\left| -a + b \right|} - {\left(12 \, a^{6} - 6 \, a^{5} b - 23 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} - a b^{5} + b^{6}\right)} \sqrt{a^{2} - b^{2}} B {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} {\left| -a + b \right|} + 3 \, {\left(4 \, a^{10} b^{5} - 2 \, a^{9} b^{6} - 17 \, a^{8} b^{7} + 8 \, a^{7} b^{8} + 28 \, a^{6} b^{9} - 12 \, a^{5} b^{10} - 21 \, a^{4} b^{11} + 8 \, a^{3} b^{12} + 6 \, a^{2} b^{13} - 2 \, a b^{14}\right)} \sqrt{a^{2} - b^{2}} A {\left| -a + b \right|} - {\left(24 \, a^{11} b^{4} - 12 \, a^{10} b^{5} - 100 \, a^{9} b^{6} + 47 \, a^{8} b^{7} + 158 \, a^{7} b^{8} - 68 \, a^{6} b^{9} - 111 \, a^{5} b^{10} + 42 \, a^{4} b^{11} + 28 \, a^{3} b^{12} - 8 \, a^{2} b^{13} + a b^{14} - b^{15}\right)} \sqrt{a^{2} - b^{2}} B {\left| -a + b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{4 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 4 \, a b^{8} + \sqrt{-16 \, {\left(a^{5} b^{4} + a^{4} b^{5} - 2 \, a^{3} b^{6} - 2 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} {\left(a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} + 16 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)}^{2}}}{a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}}}}\right)\right)}}{{\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)}^{2} {\left(a^{2} - 2 \, a b + b^{2}\right)} + {\left(a^{7} b^{4} - 2 \, a^{6} b^{5} - a^{5} b^{6} + 4 \, a^{4} b^{7} - a^{3} b^{8} - 2 \, a^{2} b^{9} + a b^{10}\right)} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|}} + \frac{{\left(24 \, B a^{11} b^{4} - 12 \, A a^{10} b^{5} - 12 \, B a^{10} b^{5} + 6 \, A a^{9} b^{6} - 100 \, B a^{9} b^{6} + 51 \, A a^{8} b^{7} + 47 \, B a^{8} b^{7} - 24 \, A a^{7} b^{8} + 158 \, B a^{7} b^{8} - 84 \, A a^{6} b^{9} - 68 \, B a^{6} b^{9} + 36 \, A a^{5} b^{10} - 111 \, B a^{5} b^{10} + 63 \, A a^{4} b^{11} + 42 \, B a^{4} b^{11} - 24 \, A a^{3} b^{12} + 28 \, B a^{3} b^{12} - 18 \, A a^{2} b^{13} - 8 \, B a^{2} b^{13} + 6 \, A a b^{14} + B a b^{14} - B b^{15} - 12 \, B a^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, A a^{5} b {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, B a^{5} b {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 3 \, A a^{4} b^{2} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 23 \, B a^{4} b^{2} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 12 \, A a^{3} b^{3} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 10 \, B a^{3} b^{3} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, A a^{2} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 10 \, B a^{2} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + 6 \, A a b^{5} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + B a b^{5} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - B b^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{4 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 4 \, a b^{8} - \sqrt{-16 \, {\left(a^{5} b^{4} + a^{4} b^{5} - 2 \, a^{3} b^{6} - 2 \, a^{2} b^{7} + a b^{8} + b^{9}\right)} {\left(a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}\right)} + 16 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)}^{2}}}{a^{5} b^{4} - a^{4} b^{5} - 2 \, a^{3} b^{6} + 2 \, a^{2} b^{7} + a b^{8} - b^{9}}}}\right)\right)}}{a^{5} b^{4} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - 2 \, a^{3} b^{6} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} + a b^{8} {\left| a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9} \right|} - {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)}^{2}} - \frac{2 \, {\left(12 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 36 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 67 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 35 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 29 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 26 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 17 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 33 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{2 \, d}"," ",0,"1/2*((3*(2*a^5*b - a^4*b^2 - 4*a^3*b^3 + 2*a^2*b^4 + 2*a*b^5)*sqrt(a^2 - b^2)*A*abs(a^4*b^5 - 2*a^2*b^7 + b^9)*abs(-a + b) - (12*a^6 - 6*a^5*b - 23*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 - a*b^5 + b^6)*sqrt(a^2 - b^2)*B*abs(a^4*b^5 - 2*a^2*b^7 + b^9)*abs(-a + b) + 3*(4*a^10*b^5 - 2*a^9*b^6 - 17*a^8*b^7 + 8*a^7*b^8 + 28*a^6*b^9 - 12*a^5*b^10 - 21*a^4*b^11 + 8*a^3*b^12 + 6*a^2*b^13 - 2*a*b^14)*sqrt(a^2 - b^2)*A*abs(-a + b) - (24*a^11*b^4 - 12*a^10*b^5 - 100*a^9*b^6 + 47*a^8*b^7 + 158*a^7*b^8 - 68*a^6*b^9 - 111*a^5*b^10 + 42*a^4*b^11 + 28*a^3*b^12 - 8*a^2*b^13 + a*b^14 - b^15)*sqrt(a^2 - b^2)*B*abs(-a + b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*tan(1/2*d*x + 1/2*c)/sqrt((4*a^5*b^4 - 8*a^3*b^6 + 4*a*b^8 + sqrt(-16*(a^5*b^4 + a^4*b^5 - 2*a^3*b^6 - 2*a^2*b^7 + a*b^8 + b^9)*(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9) + 16*(a^5*b^4 - 2*a^3*b^6 + a*b^8)^2))/(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9))))/((a^4*b^5 - 2*a^2*b^7 + b^9)^2*(a^2 - 2*a*b + b^2) + (a^7*b^4 - 2*a^6*b^5 - a^5*b^6 + 4*a^4*b^7 - a^3*b^8 - 2*a^2*b^9 + a*b^10)*abs(a^4*b^5 - 2*a^2*b^7 + b^9)) + (24*B*a^11*b^4 - 12*A*a^10*b^5 - 12*B*a^10*b^5 + 6*A*a^9*b^6 - 100*B*a^9*b^6 + 51*A*a^8*b^7 + 47*B*a^8*b^7 - 24*A*a^7*b^8 + 158*B*a^7*b^8 - 84*A*a^6*b^9 - 68*B*a^6*b^9 + 36*A*a^5*b^10 - 111*B*a^5*b^10 + 63*A*a^4*b^11 + 42*B*a^4*b^11 - 24*A*a^3*b^12 + 28*B*a^3*b^12 - 18*A*a^2*b^13 - 8*B*a^2*b^13 + 6*A*a*b^14 + B*a*b^14 - B*b^15 - 12*B*a^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*A*a^5*b*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*B*a^5*b*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 3*A*a^4*b^2*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 23*B*a^4*b^2*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 12*A*a^3*b^3*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 10*B*a^3*b^3*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*A*a^2*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 10*B*a^2*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + 6*A*a*b^5*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + B*a*b^5*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - B*b^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*tan(1/2*d*x + 1/2*c)/sqrt((4*a^5*b^4 - 8*a^3*b^6 + 4*a*b^8 - sqrt(-16*(a^5*b^4 + a^4*b^5 - 2*a^3*b^6 - 2*a^2*b^7 + a*b^8 + b^9)*(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9) + 16*(a^5*b^4 - 2*a^3*b^6 + a*b^8)^2))/(a^5*b^4 - a^4*b^5 - 2*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9))))/(a^5*b^4*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - 2*a^3*b^6*abs(a^4*b^5 - 2*a^2*b^7 + b^9) + a*b^8*abs(a^4*b^5 - 2*a^2*b^7 + b^9) - (a^4*b^5 - 2*a^2*b^7 + b^9)^2) - 2*(12*B*a^7*tan(1/2*d*x + 1/2*c)^7 - 6*A*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 17*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 9*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 16*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 2*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 2*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 13*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 4*A*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^7 - 2*A*b^7*tan(1/2*d*x + 1/2*c)^7 + B*b^7*tan(1/2*d*x + 1/2*c)^7 + 36*B*a^7*tan(1/2*d*x + 1/2*c)^5 - 18*A*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 9*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 67*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 35*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 29*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 16*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 26*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 10*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 5*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 4*A*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 2*A*b^7*tan(1/2*d*x + 1/2*c)^5 - 3*B*b^7*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^7*tan(1/2*d*x + 1/2*c)^3 - 18*A*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 18*B*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 9*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 67*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 35*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 16*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 26*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 10*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 5*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*A*a*b^6*tan(1/2*d*x + 1/2*c)^3 - 4*B*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 2*A*b^7*tan(1/2*d*x + 1/2*c)^3 + 3*B*b^7*tan(1/2*d*x + 1/2*c)^3 + 12*B*a^7*tan(1/2*d*x + 1/2*c) - 6*A*a^6*b*tan(1/2*d*x + 1/2*c) + 18*B*a^6*b*tan(1/2*d*x + 1/2*c) - 9*A*a^5*b^2*tan(1/2*d*x + 1/2*c) - 17*B*a^5*b^2*tan(1/2*d*x + 1/2*c) + 9*A*a^4*b^3*tan(1/2*d*x + 1/2*c) - 33*B*a^4*b^3*tan(1/2*d*x + 1/2*c) + 16*A*a^3*b^4*tan(1/2*d*x + 1/2*c) - 2*B*a^3*b^4*tan(1/2*d*x + 1/2*c) + 2*A*a^2*b^5*tan(1/2*d*x + 1/2*c) + 13*B*a^2*b^5*tan(1/2*d*x + 1/2*c) - 4*A*a*b^6*tan(1/2*d*x + 1/2*c) + 4*B*a*b^6*tan(1/2*d*x + 1/2*c) - 2*A*b^7*tan(1/2*d*x + 1/2*c) - B*b^7*tan(1/2*d*x + 1/2*c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*a*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
266,1,543,0,1.176639," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, B a^{6} - 2 \, A a^{5} b - 15 \, B a^{4} b^{2} + 5 \, A a^{3} b^{3} + 12 \, B a^{2} b^{4} - 6 \, A a b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} - b^{2}}} - \frac{4 \, B a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} + \frac{{\left(3 \, B a - A b\right)} {\left(d x + c\right)}}{b^{4}} - \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b^{3}}}{d}"," ",0,"-((6*B*a^6 - 2*A*a^5*b - 15*B*a^4*b^2 + 5*A*a^3*b^3 + 12*B*a^2*b^4 - 6*A*a*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(a^2 - b^2)) - (4*B*a^6*tan(1/2*d*x + 1/2*c)^3 - 2*A*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 5*B*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 7*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 6*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*B*a^6*tan(1/2*d*x + 1/2*c) - 2*A*a^5*b*tan(1/2*d*x + 1/2*c) + 5*B*a^5*b*tan(1/2*d*x + 1/2*c) - 3*A*a^4*b^2*tan(1/2*d*x + 1/2*c) - 7*B*a^4*b^2*tan(1/2*d*x + 1/2*c) + 5*A*a^3*b^3*tan(1/2*d*x + 1/2*c) - 8*B*a^3*b^3*tan(1/2*d*x + 1/2*c) + 6*A*a^2*b^4*tan(1/2*d*x + 1/2*c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) + (3*B*a - A*b)*(d*x + c)/b^4 - 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b^3))/d","B",0
267,1,455,0,1.211826," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, B a^{5} - 5 \, B a^{3} b^{2} - A a^{2} b^{3} + 6 \, B a b^{4} - 2 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{a^{2} - b^{2}}} - \frac{{\left(d x + c\right)} B}{b^{3}} + \frac{2 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"-((2*B*a^5 - 5*B*a^3*b^2 - A*a^2*b^3 + 6*B*a*b^4 - 2*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(a^2 - b^2)) - (d*x + c)*B/b^3 + (2*B*a^5*tan(1/2*d*x + 1/2*c)^3 - 3*B*a^4*b*tan(1/2*d*x + 1/2*c)^3 + A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 3*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 4*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^5*tan(1/2*d*x + 1/2*c) + 3*B*a^4*b*tan(1/2*d*x + 1/2*c) - A*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 3*A*a^2*b^3*tan(1/2*d*x + 1/2*c) - 6*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 4*A*a*b^4*tan(1/2*d*x + 1/2*c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
268,1,391,0,0.705515," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(B a^{2} - 3 \, A a b + 2 \, B b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"((B*a^2 - 3*A*a*b + 2*B*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (2*A*a^3*tan(1/2*d*x + 1/2*c)^3 - B*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 4*B*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 2*A*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*A*a^3*tan(1/2*d*x + 1/2*c) + B*a^3*tan(1/2*d*x + 1/2*c) + A*a^2*b*tan(1/2*d*x + 1/2*c) - 3*B*a^2*b*tan(1/2*d*x + 1/2*c) + A*a*b^2*tan(1/2*d*x + 1/2*c) - 4*B*a*b^2*tan(1/2*d*x + 1/2*c) + 2*A*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
269,1,390,0,0.786425," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, A a^{2} - 3 \, B a b + A b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + B a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"((2*A*a^2 - 3*B*a*b + A*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (2*B*a^3*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^2*b*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*A*a*b^2*tan(1/2*d*x + 1/2*c)^3 + B*a*b^2*tan(1/2*d*x + 1/2*c)^3 + A*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*B*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^3*tan(1/2*d*x + 1/2*c) - 4*A*a^2*b*tan(1/2*d*x + 1/2*c) + B*a^2*b*tan(1/2*d*x + 1/2*c) - 3*A*a*b^2*tan(1/2*d*x + 1/2*c) + B*a*b^2*tan(1/2*d*x + 1/2*c) + A*b^3*tan(1/2*d*x + 1/2*c) + 2*B*b^3*tan(1/2*d*x + 1/2*c))/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
270,1,481,0,1.766487," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, B a^{5} - 6 \, A a^{4} b + B a^{3} b^{2} + 5 \, A a^{2} b^{3} - 2 \, A b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{4 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}}}{d}"," ",0,"((2*B*a^5 - 6*A*a^4*b + B*a^3*b^2 + 5*A*a^2*b^3 - 2*A*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(a^2 - b^2)) + A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - (4*B*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 2*A*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*B*a^4*b*tan(1/2*d*x + 1/2*c) - 6*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 3*B*a^3*b^2*tan(1/2*d*x + 1/2*c) - 5*A*a^2*b^3*tan(1/2*d*x + 1/2*c) - B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 3*A*a*b^4*tan(1/2*d*x + 1/2*c) + 2*A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2))/d","B",0
271,1,574,0,6.993849," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(6 \, B a^{5} b - 12 \, A a^{4} b^{2} - 5 \, B a^{3} b^{3} + 15 \, A a^{2} b^{4} + 2 \, B a b^{5} - 6 \, A b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{6 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, A a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, B a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, A a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, A a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, A b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{2}} + \frac{{\left(B a - 3 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{{\left(B a - 3 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{2 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{3}}}{d}"," ",0,"((6*B*a^5*b - 12*A*a^4*b^2 - 5*B*a^3*b^3 + 15*A*a^2*b^4 + 2*B*a*b^5 - 6*A*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(a^2 - b^2)) + (6*B*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 - 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 3*B*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 + 5*A*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 2*B*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*A*b^6*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^4*b^2*tan(1/2*d*x + 1/2*c) - 8*A*a^3*b^3*tan(1/2*d*x + 1/2*c) + 5*B*a^3*b^3*tan(1/2*d*x + 1/2*c) - 7*A*a^2*b^4*tan(1/2*d*x + 1/2*c) - 3*B*a^2*b^4*tan(1/2*d*x + 1/2*c) + 5*A*a*b^5*tan(1/2*d*x + 1/2*c) - 2*B*a*b^5*tan(1/2*d*x + 1/2*c) + 4*A*b^6*tan(1/2*d*x + 1/2*c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^2) + (B*a - 3*A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - (B*a - 3*A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - 2*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^3))/d","B",0
272,1,1395,0,1.920610," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(12 \, B a^{5} b^{2} - 20 \, A a^{4} b^{3} - 15 \, B a^{3} b^{4} + 29 \, A a^{2} b^{5} + 6 \, B a b^{6} - 12 \, A b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 10 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 26 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 29 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 67 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, A a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 13 \, A a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 \, B a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 33 \, A a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17 \, A a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, B a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, A b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a - b\right)}^{2}} - \frac{{\left(A a^{2} - 6 \, B a b + 12 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} + \frac{{\left(A a^{2} - 6 \, B a b + 12 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}}}{2 \, d}"," ",0,"-1/2*(2*(12*B*a^5*b^2 - 20*A*a^4*b^3 - 15*B*a^3*b^4 + 29*A*a^2*b^5 + 6*B*a*b^6 - 12*A*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^9 - 2*a^7*b^2 + a^5*b^4)*sqrt(a^2 - b^2)) - 2*(A*a^7*tan(1/2*d*x + 1/2*c)^7 - 2*B*a^7*tan(1/2*d*x + 1/2*c)^7 + 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 2*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 - 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 + 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^7 - 6*B*a*b^6*tan(1/2*d*x + 1/2*c)^7 + 12*A*b^7*tan(1/2*d*x + 1/2*c)^7 + 3*A*a^7*tan(1/2*d*x + 1/2*c)^5 - 2*B*a^7*tan(1/2*d*x + 1/2*c)^5 + 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 10*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 - 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 - 35*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 - 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^5 + 18*B*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 36*A*b^7*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^7*tan(1/2*d*x + 1/2*c)^3 + 2*B*a^7*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 5*A*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 10*B*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 + 26*A*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 29*A*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 35*B*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 67*A*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 18*A*a*b^6*tan(1/2*d*x + 1/2*c)^3 - 18*B*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^7*tan(1/2*d*x + 1/2*c)^3 + A*a^7*tan(1/2*d*x + 1/2*c) + 2*B*a^7*tan(1/2*d*x + 1/2*c) - 4*A*a^6*b*tan(1/2*d*x + 1/2*c) + 4*B*a^6*b*tan(1/2*d*x + 1/2*c) - 13*A*a^5*b^2*tan(1/2*d*x + 1/2*c) - 2*B*a^5*b^2*tan(1/2*d*x + 1/2*c) + 2*A*a^4*b^3*tan(1/2*d*x + 1/2*c) - 16*B*a^4*b^3*tan(1/2*d*x + 1/2*c) + 33*A*a^3*b^4*tan(1/2*d*x + 1/2*c) - 9*B*a^3*b^4*tan(1/2*d*x + 1/2*c) + 17*A*a^2*b^5*tan(1/2*d*x + 1/2*c) + 9*B*a^2*b^5*tan(1/2*d*x + 1/2*c) - 18*A*a*b^6*tan(1/2*d*x + 1/2*c) + 6*B*a*b^6*tan(1/2*d*x + 1/2*c) - 12*A*b^7*tan(1/2*d*x + 1/2*c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 - b*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^2 - a - b)^2) - (A*a^2 - 6*B*a*b + 12*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 + (A*a^2 - 6*B*a*b + 12*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5)/d","B",0
273,1,966,0,3.431040," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, B a^{8} - 2 \, A a^{7} b - 28 \, B a^{6} b^{2} + 7 \, A a^{5} b^{3} + 35 \, B a^{4} b^{4} - 8 \, A a^{3} b^{5} - 20 \, B a^{2} b^{6} + 8 \, A a b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} \sqrt{a^{2} - b^{2}}} - \frac{18 \, B a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, B a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, A a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 152 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 236 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, B a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, A a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}} + \frac{3 \, {\left(4 \, B a - A b\right)} {\left(d x + c\right)}}{b^{5}} - \frac{6 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b^{4}}}{3 \, d}"," ",0,"-1/3*(3*(8*B*a^8 - 2*A*a^7*b - 28*B*a^6*b^2 + 7*A*a^5*b^3 + 35*B*a^4*b^4 - 8*A*a^3*b^5 - 20*B*a^2*b^6 + 8*A*a*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*sqrt(a^2 - b^2)) - (18*B*a^9*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^8*b*tan(1/2*d*x + 1/2*c)^5 - 42*B*a^8*b*tan(1/2*d*x + 1/2*c)^5 + 15*A*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 - 24*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 117*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 45*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 24*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 105*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 60*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 60*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 36*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^9*tan(1/2*d*x + 1/2*c)^3 - 12*A*a^8*b*tan(1/2*d*x + 1/2*c)^3 - 152*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 + 56*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 + 236*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 - 116*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 - 120*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 72*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 + 18*B*a^9*tan(1/2*d*x + 1/2*c) - 6*A*a^8*b*tan(1/2*d*x + 1/2*c) + 42*B*a^8*b*tan(1/2*d*x + 1/2*c) - 15*A*a^7*b^2*tan(1/2*d*x + 1/2*c) - 24*B*a^7*b^2*tan(1/2*d*x + 1/2*c) + 6*A*a^6*b^3*tan(1/2*d*x + 1/2*c) - 117*B*a^6*b^3*tan(1/2*d*x + 1/2*c) + 45*A*a^5*b^4*tan(1/2*d*x + 1/2*c) - 24*B*a^5*b^4*tan(1/2*d*x + 1/2*c) + 6*A*a^4*b^5*tan(1/2*d*x + 1/2*c) + 105*B*a^4*b^5*tan(1/2*d*x + 1/2*c) - 60*A*a^3*b^6*tan(1/2*d*x + 1/2*c) + 60*B*a^3*b^6*tan(1/2*d*x + 1/2*c) - 36*A*a^2*b^7*tan(1/2*d*x + 1/2*c))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) + 3*(4*B*a - A*b)*(d*x + c)/b^5 - 6*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b^4))/d","B",0
274,1,813,0,2.192288," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, B a^{7} - 7 \, B a^{5} b^{2} + 8 \, B a^{3} b^{4} + 3 \, A a^{2} b^{5} - 8 \, B a b^{6} + 2 \, A b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, {\left(d x + c\right)} B}{b^{4}} - \frac{6 \, B a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, B a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, B a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(2*B*a^7 - 7*B*a^5*b^2 + 8*B*a^3*b^4 + 3*A*a^2*b^5 - 8*B*a*b^6 + 2*A*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*sqrt(a^2 - b^2)) + 3*(d*x + c)*B/b^4 - (6*B*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*B*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 45*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 60*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 27*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 - 18*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^8*tan(1/2*d*x + 1/2*c)^3 - 56*B*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 - 4*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^3 + 116*B*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 32*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^3 - 72*B*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 36*A*a*b^7*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^8*tan(1/2*d*x + 1/2*c) + 15*B*a^7*b*tan(1/2*d*x + 1/2*c) - 6*B*a^6*b^2*tan(1/2*d*x + 1/2*c) - 6*A*a^5*b^3*tan(1/2*d*x + 1/2*c) - 45*B*a^5*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a^4*b^4*tan(1/2*d*x + 1/2*c) - 6*B*a^4*b^4*tan(1/2*d*x + 1/2*c) - 6*A*a^3*b^5*tan(1/2*d*x + 1/2*c) + 60*B*a^3*b^5*tan(1/2*d*x + 1/2*c) - 27*A*a^2*b^6*tan(1/2*d*x + 1/2*c) + 36*B*a^2*b^6*tan(1/2*d*x + 1/2*c) - 18*A*a*b^7*tan(1/2*d*x + 1/2*c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
275,1,689,0,1.030547," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(A a^{3} - 3 \, B a^{2} b + 4 \, A a b^{2} - 2 \, B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(A*a^3 - 3*B*a^2*b + 4*A*a*b^2 - 2*B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + (3*A*a^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^5*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 3*B*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 18*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*A*b^5*tan(1/2*d*x + 1/2*c)^5 - 4*B*a^5*tan(1/2*d*x + 1/2*c)^3 + 28*A*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 32*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 16*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 36*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 12*A*b^5*tan(1/2*d*x + 1/2*c)^3 - 3*A*a^5*tan(1/2*d*x + 1/2*c) - 6*B*a^5*tan(1/2*d*x + 1/2*c) + 12*A*a^4*b*tan(1/2*d*x + 1/2*c) - 3*B*a^4*b*tan(1/2*d*x + 1/2*c) + 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - 6*B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 12*A*a^2*b^3*tan(1/2*d*x + 1/2*c) - 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 6*A*a*b^4*tan(1/2*d*x + 1/2*c) - 18*B*a*b^4*tan(1/2*d*x + 1/2*c) + 6*A*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
276,1,722,0,1.891751," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(B a^{3} - 4 \, A a^{2} b + 4 \, B a b^{2} - A b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(B*a^3 - 4*A*a^2*b + 4*B*a*b^2 - A*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - (6*A*a^5*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^5*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 27*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 12*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 12*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 3*A*b^5*tan(1/2*d*x + 1/2*c)^5 - 6*B*b^5*tan(1/2*d*x + 1/2*c)^5 + 12*A*a^5*tan(1/2*d*x + 1/2*c)^3 - 28*B*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 16*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 28*A*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 12*B*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^5*tan(1/2*d*x + 1/2*c) + 3*B*a^5*tan(1/2*d*x + 1/2*c) + 6*A*a^4*b*tan(1/2*d*x + 1/2*c) - 12*B*a^4*b*tan(1/2*d*x + 1/2*c) + 12*A*a^3*b^2*tan(1/2*d*x + 1/2*c) - 27*B*a^3*b^2*tan(1/2*d*x + 1/2*c) + 27*A*a^2*b^3*tan(1/2*d*x + 1/2*c) - 12*B*a^2*b^3*tan(1/2*d*x + 1/2*c) + 12*A*a*b^4*tan(1/2*d*x + 1/2*c) - 6*B*a*b^4*tan(1/2*d*x + 1/2*c) - 3*A*b^5*tan(1/2*d*x + 1/2*c) - 6*B*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
277,1,691,0,1.217357," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, A a^{3} - 4 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, B a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, B b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(2*A*a^3 - 4*B*a^2*b + 3*A*a*b^2 - B*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - (6*B*a^5*tan(1/2*d*x + 1/2*c)^5 - 18*A*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*A*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 12*B*a*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*A*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*B*b^5*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^5*tan(1/2*d*x + 1/2*c)^3 - 36*A*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 16*B*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 32*A*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 - 28*B*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*A*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*B*a^5*tan(1/2*d*x + 1/2*c) - 18*A*a^4*b*tan(1/2*d*x + 1/2*c) + 6*B*a^4*b*tan(1/2*d*x + 1/2*c) - 27*A*a^3*b^2*tan(1/2*d*x + 1/2*c) + 12*B*a^3*b^2*tan(1/2*d*x + 1/2*c) - 6*A*a^2*b^3*tan(1/2*d*x + 1/2*c) + 27*B*a^2*b^3*tan(1/2*d*x + 1/2*c) - 3*A*a*b^4*tan(1/2*d*x + 1/2*c) + 12*B*a*b^4*tan(1/2*d*x + 1/2*c) - 6*A*b^5*tan(1/2*d*x + 1/2*c) - 3*B*b^5*tan(1/2*d*x + 1/2*c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
278,1,837,0,2.401030," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, B a^{7} - 8 \, A a^{6} b + 3 \, B a^{5} b^{2} + 8 \, A a^{4} b^{3} - 7 \, A a^{2} b^{5} + 2 \, A b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3 \, A \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{4}} - \frac{18 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 116 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, B a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, A a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, B a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, A a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 45 \, A a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, A a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, A a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, A b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(2*B*a^7 - 8*A*a^6*b + 3*B*a^5*b^2 + 8*A*a^4*b^3 - 7*A*a^2*b^5 + 2*A*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*sqrt(a^2 - b^2)) + 3*A*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3*A*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^4 - (18*B*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*B*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 + 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 - 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 + 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 15*A*a*b^7*tan(1/2*d*x + 1/2*c)^5 - 6*A*b^8*tan(1/2*d*x + 1/2*c)^5 + 36*B*a^7*b*tan(1/2*d*x + 1/2*c)^3 - 72*A*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 - 32*B*a^5*b^3*tan(1/2*d*x + 1/2*c)^3 + 116*A*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 4*B*a^3*b^5*tan(1/2*d*x + 1/2*c)^3 - 56*A*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 12*A*b^8*tan(1/2*d*x + 1/2*c)^3 + 18*B*a^7*b*tan(1/2*d*x + 1/2*c) - 36*A*a^6*b^2*tan(1/2*d*x + 1/2*c) + 27*B*a^6*b^2*tan(1/2*d*x + 1/2*c) - 60*A*a^5*b^3*tan(1/2*d*x + 1/2*c) + 6*B*a^5*b^3*tan(1/2*d*x + 1/2*c) + 6*A*a^4*b^4*tan(1/2*d*x + 1/2*c) + 3*B*a^4*b^4*tan(1/2*d*x + 1/2*c) + 45*A*a^3*b^5*tan(1/2*d*x + 1/2*c) + 6*B*a^3*b^5*tan(1/2*d*x + 1/2*c) + 6*A*a^2*b^6*tan(1/2*d*x + 1/2*c) - 15*A*a*b^7*tan(1/2*d*x + 1/2*c) - 6*A*b^8*tan(1/2*d*x + 1/2*c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3))/d","B",0
279,1,996,0,6.388247," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, B a^{7} b - 20 \, A a^{6} b^{2} - 8 \, B a^{5} b^{3} + 35 \, A a^{4} b^{4} + 7 \, B a^{3} b^{5} - 28 \, A a^{2} b^{6} - 2 \, B a b^{7} + 8 \, A b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{36 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 116 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 236 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 152 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, B a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, A a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60 \, B a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, A a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, B a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 117 \, A a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, B a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, A a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 42 \, A a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, B a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, A b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}} + \frac{3 \, {\left(B a - 4 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{5}} - \frac{3 \, {\left(B a - 4 \, A b\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{5}} - \frac{6 \, A \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{4}}}{3 \, d}"," ",0,"1/3*(3*(8*B*a^7*b - 20*A*a^6*b^2 - 8*B*a^5*b^3 + 35*A*a^4*b^4 + 7*B*a^3*b^5 - 28*A*a^2*b^6 - 2*B*a*b^7 + 8*A*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*sqrt(a^2 - b^2)) + (36*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^5 - 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 - 60*B*a^6*b^3*tan(1/2*d*x + 1/2*c)^5 + 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^5 + 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 + 45*B*a^4*b^5*tan(1/2*d*x + 1/2*c)^5 - 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 - 6*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^5 + 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 - 15*B*a^2*b^7*tan(1/2*d*x + 1/2*c)^5 + 42*A*a*b^8*tan(1/2*d*x + 1/2*c)^5 + 6*B*a*b^8*tan(1/2*d*x + 1/2*c)^5 - 18*A*b^9*tan(1/2*d*x + 1/2*c)^5 + 72*B*a^7*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*A*a^6*b^3*tan(1/2*d*x + 1/2*c)^3 - 116*B*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 + 236*A*a^4*b^5*tan(1/2*d*x + 1/2*c)^3 + 56*B*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 - 152*A*a^2*b^7*tan(1/2*d*x + 1/2*c)^3 - 12*B*a*b^8*tan(1/2*d*x + 1/2*c)^3 + 36*A*b^9*tan(1/2*d*x + 1/2*c)^3 + 36*B*a^7*b^2*tan(1/2*d*x + 1/2*c) - 60*A*a^6*b^3*tan(1/2*d*x + 1/2*c) + 60*B*a^6*b^3*tan(1/2*d*x + 1/2*c) - 105*A*a^5*b^4*tan(1/2*d*x + 1/2*c) - 6*B*a^5*b^4*tan(1/2*d*x + 1/2*c) + 24*A*a^4*b^5*tan(1/2*d*x + 1/2*c) - 45*B*a^4*b^5*tan(1/2*d*x + 1/2*c) + 117*A*a^3*b^6*tan(1/2*d*x + 1/2*c) - 6*B*a^3*b^6*tan(1/2*d*x + 1/2*c) + 24*A*a^2*b^7*tan(1/2*d*x + 1/2*c) + 15*B*a^2*b^7*tan(1/2*d*x + 1/2*c) - 42*A*a*b^8*tan(1/2*d*x + 1/2*c) + 6*B*a*b^8*tan(1/2*d*x + 1/2*c) - 18*A*b^9*tan(1/2*d*x + 1/2*c))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) + 3*(B*a - 4*A*b)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^5 - 3*(B*a - 4*A*b)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^5 - 6*A*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^4))/d","B",0
280,1,1090,0,1.829703," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(20 \, B a^{7} b^{2} - 40 \, A a^{6} b^{3} - 35 \, B a^{5} b^{4} + 84 \, A a^{4} b^{5} + 28 \, B a^{3} b^{6} - 69 \, A a^{2} b^{7} - 8 \, B a b^{8} + 20 \, A b^{9}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(60 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, B a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 117 \, B a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 42 \, B a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 120 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 180 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 236 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 392 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 284 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, B a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 90 \, A a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, B a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 162 \, A a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, A a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 117 \, B a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 213 \, A a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, A a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42 \, B a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 81 \, A a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, B a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 36 \, A b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a + b\right)}^{3}} - \frac{3 \, {\left(A a^{2} - 8 \, B a b + 20 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{6}} + \frac{3 \, {\left(A a^{2} - 8 \, B a b + 20 \, A b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{6}} - \frac{6 \, {\left(A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, A b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{5}}}{6 \, d}"," ",0,"-1/6*(6*(20*B*a^7*b^2 - 40*A*a^6*b^3 - 35*B*a^5*b^4 + 84*A*a^4*b^5 + 28*B*a^3*b^6 - 69*A*a^2*b^7 - 8*B*a*b^8 + 20*A*b^9)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))/((a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*sqrt(a^2 - b^2)) + 2*(60*B*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 - 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 - 105*B*a^6*b^4*tan(1/2*d*x + 1/2*c)^5 + 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 - 24*B*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 + 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 + 117*B*a^4*b^6*tan(1/2*d*x + 1/2*c)^5 - 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 24*B*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 + 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 - 42*B*a^2*b^8*tan(1/2*d*x + 1/2*c)^5 + 81*A*a*b^9*tan(1/2*d*x + 1/2*c)^5 + 18*B*a*b^9*tan(1/2*d*x + 1/2*c)^5 - 36*A*b^10*tan(1/2*d*x + 1/2*c)^5 + 120*B*a^7*b^3*tan(1/2*d*x + 1/2*c)^3 - 180*A*a^6*b^4*tan(1/2*d*x + 1/2*c)^3 - 236*B*a^5*b^5*tan(1/2*d*x + 1/2*c)^3 + 392*A*a^4*b^6*tan(1/2*d*x + 1/2*c)^3 + 152*B*a^3*b^7*tan(1/2*d*x + 1/2*c)^3 - 284*A*a^2*b^8*tan(1/2*d*x + 1/2*c)^3 - 36*B*a*b^9*tan(1/2*d*x + 1/2*c)^3 + 72*A*b^10*tan(1/2*d*x + 1/2*c)^3 + 60*B*a^7*b^3*tan(1/2*d*x + 1/2*c) - 90*A*a^6*b^4*tan(1/2*d*x + 1/2*c) + 105*B*a^6*b^4*tan(1/2*d*x + 1/2*c) - 162*A*a^5*b^5*tan(1/2*d*x + 1/2*c) - 24*B*a^5*b^5*tan(1/2*d*x + 1/2*c) + 48*A*a^4*b^6*tan(1/2*d*x + 1/2*c) - 117*B*a^4*b^6*tan(1/2*d*x + 1/2*c) + 213*A*a^3*b^7*tan(1/2*d*x + 1/2*c) - 24*B*a^3*b^7*tan(1/2*d*x + 1/2*c) + 48*A*a^2*b^8*tan(1/2*d*x + 1/2*c) + 42*B*a^2*b^8*tan(1/2*d*x + 1/2*c) - 81*A*a*b^9*tan(1/2*d*x + 1/2*c) + 18*B*a*b^9*tan(1/2*d*x + 1/2*c) - 36*A*b^10*tan(1/2*d*x + 1/2*c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c)^2 + a + b)^3) - 3*(A*a^2 - 8*B*a*b + 20*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^6 + 3*(A*a^2 - 8*B*a*b + 20*A*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^6 - 6*(A*a*tan(1/2*d*x + 1/2*c)^3 - 2*B*a*tan(1/2*d*x + 1/2*c)^3 + 8*A*b*tan(1/2*d*x + 1/2*c)^3 + A*a*tan(1/2*d*x + 1/2*c) + 2*B*a*tan(1/2*d*x + 1/2*c) - 8*A*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^5))/d","B",0
281,1,25,0,0.421191," ","integrate(cos(d*x+c)^3*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","-\frac{B \sin\left(d x + c\right)^{3} - 3 \, B \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(B*sin(d*x + c)^3 - 3*B*sin(d*x + c))/d","A",0
282,1,33,0,0.374735," ","integrate(cos(d*x+c)^2*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} B + \frac{B \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*((d*x + c)*B + B*tan(d*x + c)/(tan(d*x + c)^2 + 1))/d","A",0
283,1,11,0,0.348926," ","integrate(cos(d*x+c)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{B \sin\left(d x + c\right)}{d}"," ",0,"B*sin(d*x + c)/d","A",0
284,1,10,0,0.333836," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} B}{d}"," ",0,"(d*x + c)*B/d","C",0
285,1,47,0,0.448610," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{B \log\left({\left| \frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) + 2 \right|}\right) - B \log\left({\left| \frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) - 2 \right|}\right)}{4 \, d}"," ",0,"1/4*(B*log(abs(1/sin(d*x + c) + sin(d*x + c) + 2)) - B*log(abs(1/sin(d*x + c) + sin(d*x + c) - 2)))/d","B",0
286,1,11,0,0.418607," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{B \tan\left(d x + c\right)}{d}"," ",0,"B*tan(d*x + c)/d","A",0
287,1,52,0,0.587172," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{B \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - B \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, B \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*(B*log(abs(sin(d*x + c) + 1)) - B*log(abs(sin(d*x + c) - 1)) - 2*B*sin(d*x + c)/(sin(d*x + c)^2 - 1))/d","A",0
288,1,25,0,0.573515," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\frac{B \tan\left(d x + c\right)^{3} + 3 \, B \tan\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(B*tan(d*x + c)^3 + 3*B*tan(d*x + c))/d","A",0
289,1,185,0,0.424641," ","integrate(cos(d*x+c)^3*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} B a^{3}}{\sqrt{a^{2} - b^{2}} b^{3}} - \frac{{\left(2 \, B a^{2} + B b^{2}\right)} {\left(d x + c\right)}}{b^{3}} + \frac{2 \, {\left(2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"-1/2*(4*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*B*a^3/(sqrt(a^2 - b^2)*b^3) - (2*B*a^2 + B*b^2)*(d*x + c)/b^3 + 2*(2*B*a*tan(1/2*d*x + 1/2*c)^3 + B*b*tan(1/2*d*x + 1/2*c)^3 + 2*B*a*tan(1/2*d*x + 1/2*c) - B*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^2))/d","A",0
290,1,128,0,0.459509," ","integrate(cos(d*x+c)^2*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} B a^{2}}{\sqrt{a^{2} - b^{2}} b^{2}} - \frac{{\left(d x + c\right)} B a}{b^{2}} + \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b}}{d}"," ",0,"(2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*B*a^2/(sqrt(a^2 - b^2)*b^2) - (d*x + c)*B*a/b^2 + 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 + 1)*b))/d","A",0
291,1,245,0,0.647453," ","integrate(cos(d*x+c)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{{\left(\sqrt{a^{2} - b^{2}} B {\left(2 \, a - b\right)} {\left| a - b \right|} + \sqrt{a^{2} - b^{2}} B {\left| a - b \right|} {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} + \frac{{\left(2 \, B a - B b - B {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{b^{2} - a {\left| b \right|}}}{d}"," ",0,"-((sqrt(a^2 - b^2)*B*(2*a - b)*abs(a - b) + sqrt(a^2 - b^2)*B*abs(a - b)*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) + (2*B*a - B*b - B*abs(b))*(pi*floor(1/2*(d*x + c)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*d*x + 1/2*c)/sqrt((2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/(b^2 - a*abs(b)))/d","B",0
292,1,78,0,0.521541," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} B}{\sqrt{a^{2} - b^{2}} d}"," ",0,"2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*B/(sqrt(a^2 - b^2)*d)","A",0
293,1,122,0,0.501484," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} B b}{\sqrt{a^{2} - b^{2}} a} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a} + \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a}}{d}"," ",0,"-(2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*B*b/(sqrt(a^2 - b^2)*a) - B*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a + B*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a)/d","A",0
294,1,155,0,0.791002," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} B b^{2}}{\sqrt{a^{2} - b^{2}} a^{2}} - \frac{B b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{2}} + \frac{B b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{2}} - \frac{2 \, B \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a}}{d}"," ",0,"(2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*B*b^2/(sqrt(a^2 - b^2)*a^2) - B*b*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^2 + B*b*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^2 - 2*B*tan(1/2*d*x + 1/2*c)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
295,1,221,0,0.745690," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} B b^{3}}{\sqrt{a^{2} - b^{2}} a^{3}} - \frac{{\left(B a^{2} + 2 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} + \frac{{\left(B a^{2} + 2 \, B b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{a^{3}} - \frac{2 \, {\left(B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, B b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"-1/2*(4*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*d*x + 1/2*c) - b*tan(1/2*d*x + 1/2*c))/sqrt(a^2 - b^2)))*B*b^3/(sqrt(a^2 - b^2)*a^3) - (B*a^2 + 2*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 + (B*a^2 + 2*B*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/a^3 - 2*(B*a*tan(1/2*d*x + 1/2*c)^3 + 2*B*b*tan(1/2*d*x + 1/2*c)^3 + B*a*tan(1/2*d*x + 1/2*c) - 2*B*b*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2))/d","B",0
296,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
297,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*cos(d*x + c), x)","F",0
299,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a), x)","F",0
300,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
301,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
302,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
303,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
304,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
305,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2), x)","F",0
307,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
308,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
309,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
310,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
311,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
312,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
315,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
316,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
317,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
318,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^5, x)","F",0
319,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
320,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
321,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
322,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/sqrt(b*cos(d*x + c) + a), x)","F",0
323,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
324,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
325,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
326,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^3/(b*cos(d*x + c) + a)^(3/2), x)","F",0
327,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
328,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
329,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
330,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
331,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
332,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^3/(b*cos(d*x + c) + a)^(3/2), x)","F",0
333,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{4}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^4/(b*cos(d*x + c) + a)^(5/2), x)","F",0
334,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^3/(b*cos(d*x + c) + a)^(5/2), x)","F",0
335,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
336,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
337,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
338,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
339,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
340,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^3/(b*cos(d*x + c) + a)^(5/2), x)","F",0
341,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
342,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*sec(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
343,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
344,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*sec(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
345,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
346,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
347,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
348,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
349,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
350,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
351,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
352,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
353,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
354,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
355,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
356,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
357,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
358,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
359,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
360,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
361,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
362,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
363,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
364,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
365,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
366,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
367,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
368,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
369,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
370,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
371,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
372,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
373,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
374,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
375,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
376,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
377,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^3, x)","F",0
378,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^3, x)","F",0
379,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^3, x)","F",0
380,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c))), x)","F",0
381,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2)), x)","F",0
382,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*cos(d*x + c)^(5/2)), x)","F",0
383,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
384,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
385,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
386,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
387,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
388,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
389,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
390,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
391,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
392,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
393,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
394,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
395,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\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)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
397,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
398,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
399,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
400,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
401,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
402,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
404,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
405,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
406,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(5/2), x)","F",0
407,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(7/2), x)","F",0
408,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(9/2), x)","F",0
409,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
414,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(3/2*b*B/a+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
421,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
422,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
423,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
424,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
425,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
427,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
428,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
431,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
432,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
433,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
434,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
435,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
438,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
439,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
440,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
441,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(2+3*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) + 1}{\sqrt{3 \, \cos\left(d x + c\right) + 2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((cos(d*x + c) + 1)/(sqrt(3*cos(d*x + c) + 2)*cos(d*x + c)^(3/2)), x)","F",0
442,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-2+3*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) + 1}{\sqrt{3 \, \cos\left(d x + c\right) - 2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((cos(d*x + c) + 1)/(sqrt(3*cos(d*x + c) - 2)*cos(d*x + c)^(3/2)), x)","F",0
443,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(2-3*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) + 1}{\sqrt{-3 \, \cos\left(d x + c\right) + 2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((cos(d*x + c) + 1)/(sqrt(-3*cos(d*x + c) + 2)*cos(d*x + c)^(3/2)), x)","F",0
444,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-2-3*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) + 1}{\sqrt{-3 \, \cos\left(d x + c\right) - 2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((cos(d*x + c) + 1)/(sqrt(-3*cos(d*x + c) - 2)*cos(d*x + c)^(3/2)), x)","F",0
445,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(3+2*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) + 1}{\sqrt{2 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((cos(d*x + c) + 1)/(sqrt(2*cos(d*x + c) + 3)*cos(d*x + c)^(3/2)), x)","F",0
446,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(3-2*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) + 1}{\sqrt{-2 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((cos(d*x + c) + 1)/(sqrt(-2*cos(d*x + c) + 3)*cos(d*x + c)^(3/2)), x)","F",0
447,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-3+2*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) + 1}{\sqrt{2 \, \cos\left(d x + c\right) - 3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((cos(d*x + c) + 1)/(sqrt(2*cos(d*x + c) - 3)*cos(d*x + c)^(3/2)), x)","F",0
448,0,0,0,0.000000," ","integrate((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-3-2*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) + 1}{\sqrt{-2 \, \cos\left(d x + c\right) - 3} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((cos(d*x + c) + 1)/(sqrt(-2*cos(d*x + c) - 3)*cos(d*x + c)^(3/2)), x)","F",0
449,0,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^n*(A+B*cos(f*x+e)),x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{n} \left(c \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^n*(c*cos(f*x + e))^m, x)","F",0
450,0,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^4*(A+B*cos(f*x+e)),x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{4} \left(c \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^4*(c*cos(f*x + e))^m, x)","F",0
451,0,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^3*(A+B*cos(f*x+e)),x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{3} \left(c \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^3*(c*cos(f*x + e))^m, x)","F",0
452,0,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^2*(A+B*cos(f*x+e)),x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{2} \left(c \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^2*(c*cos(f*x + e))^m, x)","F",0
453,0,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))*(A+B*cos(f*x+e)),x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)} \left(c \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)*(c*cos(f*x + e))^m, x)","F",0
454,-2,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Evaluation time: 0.74Unable to divide, perhaps due to rounding error%%%{-1,[0,1,0,0]%%%} / %%%{1,[0,0,1,0]%%%}+%%%{-1,[0,0,0,1]%%%} Error: Bad Argument Value","F(-2)",0
455,-1,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^(3/2)*(A+B*cos(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,0,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(A+B*cos(f*x+e))*(a+b*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} \sqrt{b \cos\left(f x + e\right) + a} \left(c \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*sqrt(b*cos(f*x + e) + a)*(c*cos(f*x + e))^m, x)","F",0
457,0,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(f x + e\right) + A\right)} \left(c \cos\left(f x + e\right)\right)^{m}}{\sqrt{b \cos\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(c*cos(f*x + e))^m/sqrt(b*cos(f*x + e) + a), x)","F",0
458,0,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(f x + e\right) + A\right)} \left(c \cos\left(f x + e\right)\right)^{m}}{{\left(b \cos\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(c*cos(f*x + e))^m/(b*cos(f*x + e) + a)^(3/2), x)","F",0
459,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
460,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
461,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
462,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
463,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
464,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
465,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
466,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
467,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
468,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
469,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
470,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
471,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
472,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
473,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
474,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
475,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
476,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
477,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
478,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
479,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
480,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
481,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
482,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^2, x)","F",0
483,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
484,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
485,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
486,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
487,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^3, x)","F",0
488,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^3, x)","F",0
489,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
490,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
491,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
492,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2)), x)","F",0
493,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(11/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(15/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
512,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
513,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
514,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
520,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(11/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/sqrt(a*cos(d*x + c) + a), x)","F",0
523,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(a*cos(d*x + c) + a), x)","F",0
525,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(a*cos(d*x + c) + a), x)","F",0
526,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
527,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{a \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
528,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(sec(d*x + c))/sqrt(a*cos(d*x + c) + a), x)","F",0
529,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(9/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
530,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
531,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
532,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
533,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
534,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
535,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
536,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
537,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
538,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
539,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
540,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
541,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
542,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
543,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(7/2), x)","F",0
544,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(7/2), x)","F",0
545,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(7/2), x)","F",0
546,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(7/2)*sqrt(sec(d*x + c))), x)","F",0
547,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(7/2)*sec(d*x + c)^(3/2)), x)","F",0
548,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(7/2)*sec(d*x + c)^(5/2)), x)","F",0
549,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
551,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
552,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
553,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
554,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
555,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
556,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
557,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
558,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
559,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
560,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
561,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
562,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
563,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
564,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
565,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
566,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
567,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
568,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
569,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
570,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
571,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
572,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
573,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
574,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
575,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
576,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
577,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
578,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^3, x)","F",0
579,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^3, x)","F",0
580,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
581,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
582,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
583,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2)), x)","F",0
584,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
585,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
586,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \sqrt{\sec\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
587,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
588,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
589,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
590,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\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)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
595,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
596,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
602,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
604,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
605,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
608,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
612,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
613,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
614,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
615,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
616,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
617,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
618,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
619,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
620,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
621,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
622,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
623,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
626,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
632,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B b \cos\left(d x + c\right) + B a\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
633,-1,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{B b \cos\left(d x + c\right) + B a}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
635,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))^n*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{n} \left(c \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^n*(c*sec(f*x + e))^m, x)","F",0
636,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))^4*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{4} \left(c \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^4*(c*sec(f*x + e))^m, x)","F",0
637,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))^3*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{3} \left(c \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^3*(c*sec(f*x + e))^m, x)","F",0
638,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))^2*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{2} \left(c \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^2*(c*sec(f*x + e))^m, x)","F",0
639,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)} \left(c \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)*(c*sec(f*x + e))^m, x)","F",0
640,-2,0,0,0.000000," ","integrate((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to divide, perhaps due to rounding error%%%{-1,[0,1,0,0]%%%} / %%%{1,[0,0,1,0]%%%}+%%%{-1,[0,0,0,1]%%%} Error: Bad Argument Value","F(-2)",0
641,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))^(3/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} {\left(b \cos\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(c \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(b*cos(f*x + e) + a)^(3/2)*(c*sec(f*x + e))^m, x)","F",0
642,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))^(1/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x, algorithm=""giac"")","\int {\left(B \cos\left(f x + e\right) + A\right)} \sqrt{b \cos\left(f x + e\right) + a} \left(c \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*sqrt(b*cos(f*x + e) + a)*(c*sec(f*x + e))^m, x)","F",0
643,0,0,0,0.000000," ","integrate((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(f x + e\right) + A\right)} \left(c \sec\left(f x + e\right)\right)^{m}}{\sqrt{b \cos\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(c*sec(f*x + e))^m/sqrt(b*cos(f*x + e) + a), x)","F",0
644,0,0,0,0.000000," ","integrate((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B \cos\left(f x + e\right) + A\right)} \left(c \sec\left(f x + e\right)\right)^{m}}{{\left(b \cos\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(f*x + e) + A)*(c*sec(f*x + e))^m/(b*cos(f*x + e) + a)^(3/2), x)","F",0
