1,1,131,0,0.460113," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{105 \, a c^{4} \cos\left(f x + e\right)^{5} \log\left(\sin\left(f x + e\right) + 1\right) - 105 \, a c^{4} \cos\left(f x + e\right)^{5} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(136 \, a c^{4} \cos\left(f x + e\right)^{4} + 15 \, a c^{4} \cos\left(f x + e\right)^{3} - 112 \, a c^{4} \cos\left(f x + e\right)^{2} + 90 \, a c^{4} \cos\left(f x + e\right) - 24 \, a c^{4}\right)} \sin\left(f x + e\right)}{240 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/240*(105*a*c^4*cos(f*x + e)^5*log(sin(f*x + e) + 1) - 105*a*c^4*cos(f*x + e)^5*log(-sin(f*x + e) + 1) - 2*(136*a*c^4*cos(f*x + e)^4 + 15*a*c^4*cos(f*x + e)^3 - 112*a*c^4*cos(f*x + e)^2 + 90*a*c^4*cos(f*x + e) - 24*a*c^4)*sin(f*x + e))/(f*cos(f*x + e)^5)","A",0
2,1,117,0,0.472880," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, a c^{3} \cos\left(f x + e\right)^{4} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, a c^{3} \cos\left(f x + e\right)^{4} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(16 \, a c^{3} \cos\left(f x + e\right)^{3} + 9 \, a c^{3} \cos\left(f x + e\right)^{2} - 16 \, a c^{3} \cos\left(f x + e\right) + 6 \, a c^{3}\right)} \sin\left(f x + e\right)}{48 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/48*(15*a*c^3*cos(f*x + e)^4*log(sin(f*x + e) + 1) - 15*a*c^3*cos(f*x + e)^4*log(-sin(f*x + e) + 1) - 2*(16*a*c^3*cos(f*x + e)^3 + 9*a*c^3*cos(f*x + e)^2 - 16*a*c^3*cos(f*x + e) + 6*a*c^3)*sin(f*x + e))/(f*cos(f*x + e)^4)","A",0
3,1,103,0,0.446383," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, a c^{2} \cos\left(f x + e\right)^{3} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, a c^{2} \cos\left(f x + e\right)^{3} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, a c^{2} \cos\left(f x + e\right)^{2} + 3 \, a c^{2} \cos\left(f x + e\right) - 2 \, a c^{2}\right)} \sin\left(f x + e\right)}{12 \, f \cos\left(f x + e\right)^{3}}"," ",0,"1/12*(3*a*c^2*cos(f*x + e)^3*log(sin(f*x + e) + 1) - 3*a*c^2*cos(f*x + e)^3*log(-sin(f*x + e) + 1) - 2*(2*a*c^2*cos(f*x + e)^2 + 3*a*c^2*cos(f*x + e) - 2*a*c^2)*sin(f*x + e))/(f*cos(f*x + e)^3)","A",0
4,1,67,0,0.445001," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{a c \cos\left(f x + e\right)^{2} \log\left(\sin\left(f x + e\right) + 1\right) - a c \cos\left(f x + e\right)^{2} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, a c \sin\left(f x + e\right)}{4 \, f \cos\left(f x + e\right)^{2}}"," ",0,"1/4*(a*c*cos(f*x + e)^2*log(sin(f*x + e) + 1) - a*c*cos(f*x + e)^2*log(-sin(f*x + e) + 1) - 2*a*c*sin(f*x + e))/(f*cos(f*x + e)^2)","A",0
5,1,66,0,0.443819," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{a \log\left(\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) - a \log\left(-\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) - 4 \, a \cos\left(f x + e\right) - 4 \, a}{2 \, c f \sin\left(f x + e\right)}"," ",0,"-1/2*(a*log(sin(f*x + e) + 1)*sin(f*x + e) - a*log(-sin(f*x + e) + 1)*sin(f*x + e) - 4*a*cos(f*x + e) - 4*a)/(c*f*sin(f*x + e))","A",0
6,1,51,0,0.428171," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{a \cos\left(f x + e\right)^{2} + 2 \, a \cos\left(f x + e\right) + a}{3 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"1/3*(a*cos(f*x + e)^2 + 2*a*cos(f*x + e) + a)/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))","A",0
7,1,78,0,0.438116," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{4 \, a \cos\left(f x + e\right)^{3} + 7 \, a \cos\left(f x + e\right)^{2} + 2 \, a \cos\left(f x + e\right) - a}{15 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/15*(4*a*cos(f*x + e)^3 + 7*a*cos(f*x + e)^2 + 2*a*cos(f*x + e) - a)/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))","A",0
8,1,104,0,0.436794," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{23 \, a \cos\left(f x + e\right)^{4} + 36 \, a \cos\left(f x + e\right)^{3} + 5 \, a \cos\left(f x + e\right)^{2} - 6 \, a \cos\left(f x + e\right) + 2 \, a}{105 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/105*(23*a*cos(f*x + e)^4 + 36*a*cos(f*x + e)^3 + 5*a*cos(f*x + e)^2 - 6*a*cos(f*x + e) + 2*a)/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))","A",0
9,1,128,0,0.422744," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{58 \, a \cos\left(f x + e\right)^{5} + 83 \, a \cos\left(f x + e\right)^{4} + 4 \, a \cos\left(f x + e\right)^{3} - 11 \, a \cos\left(f x + e\right)^{2} + 8 \, a \cos\left(f x + e\right) - 2 \, a}{315 \, {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} + 6 \, c^{5} f \cos\left(f x + e\right)^{2} - 4 \, c^{5} f \cos\left(f x + e\right) + c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/315*(58*a*cos(f*x + e)^5 + 83*a*cos(f*x + e)^4 + 4*a*cos(f*x + e)^3 - 11*a*cos(f*x + e)^2 + 8*a*cos(f*x + e) - 2*a)/((c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 + 6*c^5*f*cos(f*x + e)^2 - 4*c^5*f*cos(f*x + e) + c^5*f)*sin(f*x + e))","A",0
10,1,177,0,0.460274," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{315 \, a^{2} c^{5} \cos\left(f x + e\right)^{7} \log\left(\sin\left(f x + e\right) + 1\right) - 315 \, a^{2} c^{5} \cos\left(f x + e\right)^{7} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(368 \, a^{2} c^{5} \cos\left(f x + e\right)^{6} + 245 \, a^{2} c^{5} \cos\left(f x + e\right)^{5} - 656 \, a^{2} c^{5} \cos\left(f x + e\right)^{4} + 350 \, a^{2} c^{5} \cos\left(f x + e\right)^{3} + 208 \, a^{2} c^{5} \cos\left(f x + e\right)^{2} - 280 \, a^{2} c^{5} \cos\left(f x + e\right) + 80 \, a^{2} c^{5}\right)} \sin\left(f x + e\right)}{1120 \, f \cos\left(f x + e\right)^{7}}"," ",0,"1/1120*(315*a^2*c^5*cos(f*x + e)^7*log(sin(f*x + e) + 1) - 315*a^2*c^5*cos(f*x + e)^7*log(-sin(f*x + e) + 1) - 2*(368*a^2*c^5*cos(f*x + e)^6 + 245*a^2*c^5*cos(f*x + e)^5 - 656*a^2*c^5*cos(f*x + e)^4 + 350*a^2*c^5*cos(f*x + e)^3 + 208*a^2*c^5*cos(f*x + e)^2 - 280*a^2*c^5*cos(f*x + e) + 80*a^2*c^5)*sin(f*x + e))/(f*cos(f*x + e)^7)","A",0
11,1,161,0,0.488677," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{105 \, a^{2} c^{4} \cos\left(f x + e\right)^{6} \log\left(\sin\left(f x + e\right) + 1\right) - 105 \, a^{2} c^{4} \cos\left(f x + e\right)^{6} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(96 \, a^{2} c^{4} \cos\left(f x + e\right)^{5} + 135 \, a^{2} c^{4} \cos\left(f x + e\right)^{4} - 192 \, a^{2} c^{4} \cos\left(f x + e\right)^{3} + 10 \, a^{2} c^{4} \cos\left(f x + e\right)^{2} + 96 \, a^{2} c^{4} \cos\left(f x + e\right) - 40 \, a^{2} c^{4}\right)} \sin\left(f x + e\right)}{480 \, f \cos\left(f x + e\right)^{6}}"," ",0,"1/480*(105*a^2*c^4*cos(f*x + e)^6*log(sin(f*x + e) + 1) - 105*a^2*c^4*cos(f*x + e)^6*log(-sin(f*x + e) + 1) - 2*(96*a^2*c^4*cos(f*x + e)^5 + 135*a^2*c^4*cos(f*x + e)^4 - 192*a^2*c^4*cos(f*x + e)^3 + 10*a^2*c^4*cos(f*x + e)^2 + 96*a^2*c^4*cos(f*x + e) - 40*a^2*c^4)*sin(f*x + e))/(f*cos(f*x + e)^6)","A",0
12,1,145,0,0.476232," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, a^{2} c^{3} \cos\left(f x + e\right)^{5} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, a^{2} c^{3} \cos\left(f x + e\right)^{5} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(8 \, a^{2} c^{3} \cos\left(f x + e\right)^{4} + 25 \, a^{2} c^{3} \cos\left(f x + e\right)^{3} - 16 \, a^{2} c^{3} \cos\left(f x + e\right)^{2} - 10 \, a^{2} c^{3} \cos\left(f x + e\right) + 8 \, a^{2} c^{3}\right)} \sin\left(f x + e\right)}{80 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/80*(15*a^2*c^3*cos(f*x + e)^5*log(sin(f*x + e) + 1) - 15*a^2*c^3*cos(f*x + e)^5*log(-sin(f*x + e) + 1) - 2*(8*a^2*c^3*cos(f*x + e)^4 + 25*a^2*c^3*cos(f*x + e)^3 - 16*a^2*c^3*cos(f*x + e)^2 - 10*a^2*c^3*cos(f*x + e) + 8*a^2*c^3)*sin(f*x + e))/(f*cos(f*x + e)^5)","A",0
13,1,99,0,0.449903," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} c^{2} \cos\left(f x + e\right)^{4} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, a^{2} c^{2} \cos\left(f x + e\right)^{4} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(5 \, a^{2} c^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} c^{2}\right)} \sin\left(f x + e\right)}{16 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/16*(3*a^2*c^2*cos(f*x + e)^4*log(sin(f*x + e) + 1) - 3*a^2*c^2*cos(f*x + e)^4*log(-sin(f*x + e) + 1) - 2*(5*a^2*c^2*cos(f*x + e)^2 - 2*a^2*c^2)*sin(f*x + e))/(f*cos(f*x + e)^4)","A",0
14,1,103,0,0.463872," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, a^{2} c \cos\left(f x + e\right)^{3} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, a^{2} c \cos\left(f x + e\right)^{3} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, a^{2} c \cos\left(f x + e\right)^{2} - 3 \, a^{2} c \cos\left(f x + e\right) - 2 \, a^{2} c\right)} \sin\left(f x + e\right)}{12 \, f \cos\left(f x + e\right)^{3}}"," ",0,"1/12*(3*a^2*c*cos(f*x + e)^3*log(sin(f*x + e) + 1) - 3*a^2*c*cos(f*x + e)^3*log(-sin(f*x + e) + 1) + 2*(2*a^2*c*cos(f*x + e)^2 - 3*a^2*c*cos(f*x + e) - 2*a^2*c)*sin(f*x + e))/(f*cos(f*x + e)^3)","A",0
15,1,108,0,0.445336," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{3 \, a^{2} \cos\left(f x + e\right) \log\left(\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) - 3 \, a^{2} \cos\left(f x + e\right) \log\left(-\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) - 10 \, a^{2} \cos\left(f x + e\right)^{2} - 8 \, a^{2} \cos\left(f x + e\right) + 2 \, a^{2}}{2 \, c f \cos\left(f x + e\right) \sin\left(f x + e\right)}"," ",0,"-1/2*(3*a^2*cos(f*x + e)*log(sin(f*x + e) + 1)*sin(f*x + e) - 3*a^2*cos(f*x + e)*log(-sin(f*x + e) + 1)*sin(f*x + e) - 10*a^2*cos(f*x + e)^2 - 8*a^2*cos(f*x + e) + 2*a^2)/(c*f*cos(f*x + e)*sin(f*x + e))","A",0
16,1,128,0,0.470735," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","-\frac{8 \, a^{2} \cos\left(f x + e\right)^{2} - 8 \, a^{2} \cos\left(f x + e\right) - 3 \, {\left(a^{2} \cos\left(f x + e\right) - a^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) + 3 \, {\left(a^{2} \cos\left(f x + e\right) - a^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) - 16 \, a^{2}}{6 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"-1/6*(8*a^2*cos(f*x + e)^2 - 8*a^2*cos(f*x + e) - 3*(a^2*cos(f*x + e) - a^2)*log(sin(f*x + e) + 1)*sin(f*x + e) + 3*(a^2*cos(f*x + e) - a^2)*log(-sin(f*x + e) + 1)*sin(f*x + e) - 16*a^2)/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))","A",0
17,1,83,0,0.436908," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{a^{2} \cos\left(f x + e\right)^{3} + 3 \, a^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} \cos\left(f x + e\right) + a^{2}}{5 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/5*(a^2*cos(f*x + e)^3 + 3*a^2*cos(f*x + e)^2 + 3*a^2*cos(f*x + e) + a^2)/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))","B",0
18,1,114,0,0.466510," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{6 \, a^{2} \cos\left(f x + e\right)^{4} + 17 \, a^{2} \cos\left(f x + e\right)^{3} + 15 \, a^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} \cos\left(f x + e\right) - a^{2}}{35 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/35*(6*a^2*cos(f*x + e)^4 + 17*a^2*cos(f*x + e)^3 + 15*a^2*cos(f*x + e)^2 + 3*a^2*cos(f*x + e) - a^2)/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))","A",0
19,1,140,0,0.432264," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{47 \, a^{2} \cos\left(f x + e\right)^{5} + 127 \, a^{2} \cos\left(f x + e\right)^{4} + 101 \, a^{2} \cos\left(f x + e\right)^{3} + 11 \, a^{2} \cos\left(f x + e\right)^{2} - 8 \, a^{2} \cos\left(f x + e\right) + 2 \, a^{2}}{315 \, {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} + 6 \, c^{5} f \cos\left(f x + e\right)^{2} - 4 \, c^{5} f \cos\left(f x + e\right) + c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/315*(47*a^2*cos(f*x + e)^5 + 127*a^2*cos(f*x + e)^4 + 101*a^2*cos(f*x + e)^3 + 11*a^2*cos(f*x + e)^2 - 8*a^2*cos(f*x + e) + 2*a^2)/((c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 + 6*c^5*f*cos(f*x + e)^2 - 4*c^5*f*cos(f*x + e) + c^5*f)*sin(f*x + e))","A",0
20,1,168,0,0.453454," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^6,x, algorithm=""fricas"")","\frac{152 \, a^{2} \cos\left(f x + e\right)^{6} + 395 \, a^{2} \cos\left(f x + e\right)^{5} + 289 \, a^{2} \cos\left(f x + e\right)^{4} + 15 \, a^{2} \cos\left(f x + e\right)^{3} - 19 \, a^{2} \cos\left(f x + e\right)^{2} + 10 \, a^{2} \cos\left(f x + e\right) - 2 \, a^{2}}{1155 \, {\left(c^{6} f \cos\left(f x + e\right)^{5} - 5 \, c^{6} f \cos\left(f x + e\right)^{4} + 10 \, c^{6} f \cos\left(f x + e\right)^{3} - 10 \, c^{6} f \cos\left(f x + e\right)^{2} + 5 \, c^{6} f \cos\left(f x + e\right) - c^{6} f\right)} \sin\left(f x + e\right)}"," ",0,"1/1155*(152*a^2*cos(f*x + e)^6 + 395*a^2*cos(f*x + e)^5 + 289*a^2*cos(f*x + e)^4 + 15*a^2*cos(f*x + e)^3 - 19*a^2*cos(f*x + e)^2 + 10*a^2*cos(f*x + e) - 2*a^2)/((c^6*f*cos(f*x + e)^5 - 5*c^6*f*cos(f*x + e)^4 + 10*c^6*f*cos(f*x + e)^3 - 10*c^6*f*cos(f*x + e)^2 + 5*c^6*f*cos(f*x + e) - c^6*f)*sin(f*x + e))","A",0
21,1,209,0,0.521729," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^6,x, algorithm=""fricas"")","\frac{3465 \, a^{3} c^{6} \cos\left(f x + e\right)^{9} \log\left(\sin\left(f x + e\right) + 1\right) - 3465 \, a^{3} c^{6} \cos\left(f x + e\right)^{9} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(3712 \, a^{3} c^{6} \cos\left(f x + e\right)^{8} + 4599 \, a^{3} c^{6} \cos\left(f x + e\right)^{7} - 10240 \, a^{3} c^{6} \cos\left(f x + e\right)^{6} + 3066 \, a^{3} c^{6} \cos\left(f x + e\right)^{5} + 8448 \, a^{3} c^{6} \cos\left(f x + e\right)^{4} - 7224 \, a^{3} c^{6} \cos\left(f x + e\right)^{3} - 1024 \, a^{3} c^{6} \cos\left(f x + e\right)^{2} + 3024 \, a^{3} c^{6} \cos\left(f x + e\right) - 896 \, a^{3} c^{6}\right)} \sin\left(f x + e\right)}{16128 \, f \cos\left(f x + e\right)^{9}}"," ",0,"1/16128*(3465*a^3*c^6*cos(f*x + e)^9*log(sin(f*x + e) + 1) - 3465*a^3*c^6*cos(f*x + e)^9*log(-sin(f*x + e) + 1) - 2*(3712*a^3*c^6*cos(f*x + e)^8 + 4599*a^3*c^6*cos(f*x + e)^7 - 10240*a^3*c^6*cos(f*x + e)^6 + 3066*a^3*c^6*cos(f*x + e)^5 + 8448*a^3*c^6*cos(f*x + e)^4 - 7224*a^3*c^6*cos(f*x + e)^3 - 1024*a^3*c^6*cos(f*x + e)^2 + 3024*a^3*c^6*cos(f*x + e) - 896*a^3*c^6)*sin(f*x + e))/(f*cos(f*x + e)^9)","A",0
22,1,193,0,0.499603," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{315 \, a^{3} c^{5} \cos\left(f x + e\right)^{8} \log\left(\sin\left(f x + e\right) + 1\right) - 315 \, a^{3} c^{5} \cos\left(f x + e\right)^{8} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(256 \, a^{3} c^{5} \cos\left(f x + e\right)^{7} + 581 \, a^{3} c^{5} \cos\left(f x + e\right)^{6} - 768 \, a^{3} c^{5} \cos\left(f x + e\right)^{5} - 210 \, a^{3} c^{5} \cos\left(f x + e\right)^{4} + 768 \, a^{3} c^{5} \cos\left(f x + e\right)^{3} - 168 \, a^{3} c^{5} \cos\left(f x + e\right)^{2} - 256 \, a^{3} c^{5} \cos\left(f x + e\right) + 112 \, a^{3} c^{5}\right)} \sin\left(f x + e\right)}{1792 \, f \cos\left(f x + e\right)^{8}}"," ",0,"1/1792*(315*a^3*c^5*cos(f*x + e)^8*log(sin(f*x + e) + 1) - 315*a^3*c^5*cos(f*x + e)^8*log(-sin(f*x + e) + 1) - 2*(256*a^3*c^5*cos(f*x + e)^7 + 581*a^3*c^5*cos(f*x + e)^6 - 768*a^3*c^5*cos(f*x + e)^5 - 210*a^3*c^5*cos(f*x + e)^4 + 768*a^3*c^5*cos(f*x + e)^3 - 168*a^3*c^5*cos(f*x + e)^2 - 256*a^3*c^5*cos(f*x + e) + 112*a^3*c^5)*sin(f*x + e))/(f*cos(f*x + e)^8)","A",0
23,1,177,0,0.509656," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{105 \, a^{3} c^{4} \cos\left(f x + e\right)^{7} \log\left(\sin\left(f x + e\right) + 1\right) - 105 \, a^{3} c^{4} \cos\left(f x + e\right)^{7} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(48 \, a^{3} c^{4} \cos\left(f x + e\right)^{6} + 231 \, a^{3} c^{4} \cos\left(f x + e\right)^{5} - 144 \, a^{3} c^{4} \cos\left(f x + e\right)^{4} - 182 \, a^{3} c^{4} \cos\left(f x + e\right)^{3} + 144 \, a^{3} c^{4} \cos\left(f x + e\right)^{2} + 56 \, a^{3} c^{4} \cos\left(f x + e\right) - 48 \, a^{3} c^{4}\right)} \sin\left(f x + e\right)}{672 \, f \cos\left(f x + e\right)^{7}}"," ",0,"1/672*(105*a^3*c^4*cos(f*x + e)^7*log(sin(f*x + e) + 1) - 105*a^3*c^4*cos(f*x + e)^7*log(-sin(f*x + e) + 1) - 2*(48*a^3*c^4*cos(f*x + e)^6 + 231*a^3*c^4*cos(f*x + e)^5 - 144*a^3*c^4*cos(f*x + e)^4 - 182*a^3*c^4*cos(f*x + e)^3 + 144*a^3*c^4*cos(f*x + e)^2 + 56*a^3*c^4*cos(f*x + e) - 48*a^3*c^4)*sin(f*x + e))/(f*cos(f*x + e)^7)","A",0
24,1,115,0,0.475430," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, a^{3} c^{3} \cos\left(f x + e\right)^{6} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, a^{3} c^{3} \cos\left(f x + e\right)^{6} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(33 \, a^{3} c^{3} \cos\left(f x + e\right)^{4} - 26 \, a^{3} c^{3} \cos\left(f x + e\right)^{2} + 8 \, a^{3} c^{3}\right)} \sin\left(f x + e\right)}{96 \, f \cos\left(f x + e\right)^{6}}"," ",0,"1/96*(15*a^3*c^3*cos(f*x + e)^6*log(sin(f*x + e) + 1) - 15*a^3*c^3*cos(f*x + e)^6*log(-sin(f*x + e) + 1) - 2*(33*a^3*c^3*cos(f*x + e)^4 - 26*a^3*c^3*cos(f*x + e)^2 + 8*a^3*c^3)*sin(f*x + e))/(f*cos(f*x + e)^6)","A",0
25,1,145,0,0.490175," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{15 \, a^{3} c^{2} \cos\left(f x + e\right)^{5} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, a^{3} c^{2} \cos\left(f x + e\right)^{5} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(8 \, a^{3} c^{2} \cos\left(f x + e\right)^{4} - 25 \, a^{3} c^{2} \cos\left(f x + e\right)^{3} - 16 \, a^{3} c^{2} \cos\left(f x + e\right)^{2} + 10 \, a^{3} c^{2} \cos\left(f x + e\right) + 8 \, a^{3} c^{2}\right)} \sin\left(f x + e\right)}{80 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/80*(15*a^3*c^2*cos(f*x + e)^5*log(sin(f*x + e) + 1) - 15*a^3*c^2*cos(f*x + e)^5*log(-sin(f*x + e) + 1) + 2*(8*a^3*c^2*cos(f*x + e)^4 - 25*a^3*c^2*cos(f*x + e)^3 - 16*a^3*c^2*cos(f*x + e)^2 + 10*a^3*c^2*cos(f*x + e) + 8*a^3*c^2)*sin(f*x + e))/(f*cos(f*x + e)^5)","A",0
26,1,117,0,0.486637," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{15 \, a^{3} c \cos\left(f x + e\right)^{4} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, a^{3} c \cos\left(f x + e\right)^{4} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(16 \, a^{3} c \cos\left(f x + e\right)^{3} - 9 \, a^{3} c \cos\left(f x + e\right)^{2} - 16 \, a^{3} c \cos\left(f x + e\right) - 6 \, a^{3} c\right)} \sin\left(f x + e\right)}{48 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/48*(15*a^3*c*cos(f*x + e)^4*log(sin(f*x + e) + 1) - 15*a^3*c*cos(f*x + e)^4*log(-sin(f*x + e) + 1) + 2*(16*a^3*c*cos(f*x + e)^3 - 9*a^3*c*cos(f*x + e)^2 - 16*a^3*c*cos(f*x + e) - 6*a^3*c)*sin(f*x + e))/(f*cos(f*x + e)^4)","A",0
27,1,125,0,0.486879," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{15 \, a^{3} \cos\left(f x + e\right)^{2} \log\left(\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) - 15 \, a^{3} \cos\left(f x + e\right)^{2} \log\left(-\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) - 48 \, a^{3} \cos\left(f x + e\right)^{3} - 34 \, a^{3} \cos\left(f x + e\right)^{2} + 16 \, a^{3} \cos\left(f x + e\right) + 2 \, a^{3}}{4 \, c f \cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}"," ",0,"-1/4*(15*a^3*cos(f*x + e)^2*log(sin(f*x + e) + 1)*sin(f*x + e) - 15*a^3*cos(f*x + e)^2*log(-sin(f*x + e) + 1)*sin(f*x + e) - 48*a^3*cos(f*x + e)^3 - 34*a^3*cos(f*x + e)^2 + 16*a^3*cos(f*x + e) + 2*a^3)/(c*f*cos(f*x + e)^2*sin(f*x + e))","A",0
28,1,165,0,0.487988," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","-\frac{46 \, a^{3} \cos\left(f x + e\right)^{3} - 22 \, a^{3} \cos\left(f x + e\right)^{2} - 62 \, a^{3} \cos\left(f x + e\right) + 6 \, a^{3} - 15 \, {\left(a^{3} \cos\left(f x + e\right)^{2} - a^{3} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) + 15 \, {\left(a^{3} \cos\left(f x + e\right)^{2} - a^{3} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right)}{6 \, {\left(c^{2} f \cos\left(f x + e\right)^{2} - c^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}"," ",0,"-1/6*(46*a^3*cos(f*x + e)^3 - 22*a^3*cos(f*x + e)^2 - 62*a^3*cos(f*x + e) + 6*a^3 - 15*(a^3*cos(f*x + e)^2 - a^3*cos(f*x + e))*log(sin(f*x + e) + 1)*sin(f*x + e) + 15*(a^3*cos(f*x + e)^2 - a^3*cos(f*x + e))*log(-sin(f*x + e) + 1)*sin(f*x + e))/((c^2*f*cos(f*x + e)^2 - c^2*f*cos(f*x + e))*sin(f*x + e))","A",0
29,1,176,0,0.487548," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{52 \, a^{3} \cos\left(f x + e\right)^{3} - 44 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} \cos\left(f x + e\right) + 92 \, a^{3} - 15 \, {\left(a^{3} \cos\left(f x + e\right)^{2} - 2 \, a^{3} \cos\left(f x + e\right) + a^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) + 15 \, {\left(a^{3} \cos\left(f x + e\right)^{2} - 2 \, a^{3} \cos\left(f x + e\right) + a^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right)}{30 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/30*(52*a^3*cos(f*x + e)^3 - 44*a^3*cos(f*x + e)^2 - 4*a^3*cos(f*x + e) + 92*a^3 - 15*(a^3*cos(f*x + e)^2 - 2*a^3*cos(f*x + e) + a^3)*log(sin(f*x + e) + 1)*sin(f*x + e) + 15*(a^3*cos(f*x + e)^2 - 2*a^3*cos(f*x + e) + a^3)*log(-sin(f*x + e) + 1)*sin(f*x + e))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))","A",0
30,1,111,0,0.453984," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{a^{3} \cos\left(f x + e\right)^{4} + 4 \, a^{3} \cos\left(f x + e\right)^{3} + 6 \, a^{3} \cos\left(f x + e\right)^{2} + 4 \, a^{3} \cos\left(f x + e\right) + a^{3}}{7 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/7*(a^3*cos(f*x + e)^4 + 4*a^3*cos(f*x + e)^3 + 6*a^3*cos(f*x + e)^2 + 4*a^3*cos(f*x + e) + a^3)/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))","B",0
31,1,140,0,0.451528," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{8 \, a^{3} \cos\left(f x + e\right)^{5} + 31 \, a^{3} \cos\left(f x + e\right)^{4} + 44 \, a^{3} \cos\left(f x + e\right)^{3} + 26 \, a^{3} \cos\left(f x + e\right)^{2} + 4 \, a^{3} \cos\left(f x + e\right) - a^{3}}{63 \, {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} + 6 \, c^{5} f \cos\left(f x + e\right)^{2} - 4 \, c^{5} f \cos\left(f x + e\right) + c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/63*(8*a^3*cos(f*x + e)^5 + 31*a^3*cos(f*x + e)^4 + 44*a^3*cos(f*x + e)^3 + 26*a^3*cos(f*x + e)^2 + 4*a^3*cos(f*x + e) - a^3)/((c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 + 6*c^5*f*cos(f*x + e)^2 - 4*c^5*f*cos(f*x + e) + c^5*f)*sin(f*x + e))","A",0
32,1,168,0,0.500233," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^6,x, algorithm=""fricas"")","\frac{79 \, a^{3} \cos\left(f x + e\right)^{6} + 298 \, a^{3} \cos\left(f x + e\right)^{5} + 404 \, a^{3} \cos\left(f x + e\right)^{4} + 216 \, a^{3} \cos\left(f x + e\right)^{3} + 19 \, a^{3} \cos\left(f x + e\right)^{2} - 10 \, a^{3} \cos\left(f x + e\right) + 2 \, a^{3}}{693 \, {\left(c^{6} f \cos\left(f x + e\right)^{5} - 5 \, c^{6} f \cos\left(f x + e\right)^{4} + 10 \, c^{6} f \cos\left(f x + e\right)^{3} - 10 \, c^{6} f \cos\left(f x + e\right)^{2} + 5 \, c^{6} f \cos\left(f x + e\right) - c^{6} f\right)} \sin\left(f x + e\right)}"," ",0,"1/693*(79*a^3*cos(f*x + e)^6 + 298*a^3*cos(f*x + e)^5 + 404*a^3*cos(f*x + e)^4 + 216*a^3*cos(f*x + e)^3 + 19*a^3*cos(f*x + e)^2 - 10*a^3*cos(f*x + e) + 2*a^3)/((c^6*f*cos(f*x + e)^5 - 5*c^6*f*cos(f*x + e)^4 + 10*c^6*f*cos(f*x + e)^3 - 10*c^6*f*cos(f*x + e)^2 + 5*c^6*f*cos(f*x + e) - c^6*f)*sin(f*x + e))","A",0
33,1,194,0,0.459059," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^7,x, algorithm=""fricas"")","\frac{310 \, a^{3} \cos\left(f x + e\right)^{7} + 1143 \, a^{3} \cos\left(f x + e\right)^{6} + 1492 \, a^{3} \cos\left(f x + e\right)^{5} + 736 \, a^{3} \cos\left(f x + e\right)^{4} + 34 \, a^{3} \cos\left(f x + e\right)^{3} - 29 \, a^{3} \cos\left(f x + e\right)^{2} + 12 \, a^{3} \cos\left(f x + e\right) - 2 \, a^{3}}{3003 \, {\left(c^{7} f \cos\left(f x + e\right)^{6} - 6 \, c^{7} f \cos\left(f x + e\right)^{5} + 15 \, c^{7} f \cos\left(f x + e\right)^{4} - 20 \, c^{7} f \cos\left(f x + e\right)^{3} + 15 \, c^{7} f \cos\left(f x + e\right)^{2} - 6 \, c^{7} f \cos\left(f x + e\right) + c^{7} f\right)} \sin\left(f x + e\right)}"," ",0,"1/3003*(310*a^3*cos(f*x + e)^7 + 1143*a^3*cos(f*x + e)^6 + 1492*a^3*cos(f*x + e)^5 + 736*a^3*cos(f*x + e)^4 + 34*a^3*cos(f*x + e)^3 - 29*a^3*cos(f*x + e)^2 + 12*a^3*cos(f*x + e) - 2*a^3)/((c^7*f*cos(f*x + e)^6 - 6*c^7*f*cos(f*x + e)^5 + 15*c^7*f*cos(f*x + e)^4 - 20*c^7*f*cos(f*x + e)^3 + 15*c^7*f*cos(f*x + e)^2 - 6*c^7*f*cos(f*x + e) + c^7*f)*sin(f*x + e))","A",0
34,1,153,0,0.519083," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^4/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{105 \, {\left(c^{4} \cos\left(f x + e\right)^{4} + c^{4} \cos\left(f x + e\right)^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 105 \, {\left(c^{4} \cos\left(f x + e\right)^{4} + c^{4} \cos\left(f x + e\right)^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(166 \, c^{4} \cos\left(f x + e\right)^{3} + 55 \, c^{4} \cos\left(f x + e\right)^{2} - 13 \, c^{4} \cos\left(f x + e\right) + 2 \, c^{4}\right)} \sin\left(f x + e\right)}{12 \, {\left(a f \cos\left(f x + e\right)^{4} + a f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"-1/12*(105*(c^4*cos(f*x + e)^4 + c^4*cos(f*x + e)^3)*log(sin(f*x + e) + 1) - 105*(c^4*cos(f*x + e)^4 + c^4*cos(f*x + e)^3)*log(-sin(f*x + e) + 1) - 2*(166*c^4*cos(f*x + e)^3 + 55*c^4*cos(f*x + e)^2 - 13*c^4*cos(f*x + e) + 2*c^4)*sin(f*x + e))/(a*f*cos(f*x + e)^4 + a*f*cos(f*x + e)^3)","A",0
35,1,140,0,0.458981," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^3/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{15 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + c^{3} \cos\left(f x + e\right)^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + c^{3} \cos\left(f x + e\right)^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(24 \, c^{3} \cos\left(f x + e\right)^{2} + 7 \, c^{3} \cos\left(f x + e\right) - c^{3}\right)} \sin\left(f x + e\right)}{4 \, {\left(a f \cos\left(f x + e\right)^{3} + a f \cos\left(f x + e\right)^{2}\right)}}"," ",0,"-1/4*(15*(c^3*cos(f*x + e)^3 + c^3*cos(f*x + e)^2)*log(sin(f*x + e) + 1) - 15*(c^3*cos(f*x + e)^3 + c^3*cos(f*x + e)^2)*log(-sin(f*x + e) + 1) - 2*(24*c^3*cos(f*x + e)^2 + 7*c^3*cos(f*x + e) - c^3)*sin(f*x + e))/(a*f*cos(f*x + e)^3 + a*f*cos(f*x + e)^2)","A",0
36,1,119,0,0.491108," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^2/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{3 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + c^{2} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + c^{2} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(5 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left(a f \cos\left(f x + e\right)^{2} + a f \cos\left(f x + e\right)\right)}}"," ",0,"-1/2*(3*(c^2*cos(f*x + e)^2 + c^2*cos(f*x + e))*log(sin(f*x + e) + 1) - 3*(c^2*cos(f*x + e)^2 + c^2*cos(f*x + e))*log(-sin(f*x + e) + 1) - 2*(5*c^2*cos(f*x + e) + c^2)*sin(f*x + e))/(a*f*cos(f*x + e)^2 + a*f*cos(f*x + e))","A",0
37,1,70,0,0.454860," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(c \cos\left(f x + e\right) + c\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(c \cos\left(f x + e\right) + c\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 4 \, c \sin\left(f x + e\right)}{2 \, {\left(a f \cos\left(f x + e\right) + a f\right)}}"," ",0,"-1/2*((c*cos(f*x + e) + c)*log(sin(f*x + e) + 1) - (c*cos(f*x + e) + c)*log(-sin(f*x + e) + 1) - 4*c*sin(f*x + e))/(a*f*cos(f*x + e) + a*f)","A",0
38,1,18,0,0.442270," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{1}{a c f \sin\left(f x + e\right)}"," ",0,"1/(a*c*f*sin(f*x + e))","A",0
39,1,50,0,0.430614," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 2}{3 \, {\left(a c^{2} f \cos\left(f x + e\right) - a c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"1/3*(cos(f*x + e)^2 + 2*cos(f*x + e) - 2)/((a*c^2*f*cos(f*x + e) - a*c^2*f)*sin(f*x + e))","A",0
40,1,74,0,0.442323," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, \cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - 4 \, \cos\left(f x + e\right) + 2}{5 \, {\left(a c^{3} f \cos\left(f x + e\right)^{2} - 2 \, a c^{3} f \cos\left(f x + e\right) + a c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/5*(2*cos(f*x + e)^3 + cos(f*x + e)^2 - 4*cos(f*x + e) + 2)/((a*c^3*f*cos(f*x + e)^2 - 2*a*c^3*f*cos(f*x + e) + a*c^3*f)*sin(f*x + e))","A",0
41,1,102,0,0.438951," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{13 \, \cos\left(f x + e\right)^{4} - 4 \, \cos\left(f x + e\right)^{3} - 20 \, \cos\left(f x + e\right)^{2} + 24 \, \cos\left(f x + e\right) - 8}{35 \, {\left(a c^{4} f \cos\left(f x + e\right)^{3} - 3 \, a c^{4} f \cos\left(f x + e\right)^{2} + 3 \, a c^{4} f \cos\left(f x + e\right) - a c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/35*(13*cos(f*x + e)^4 - 4*cos(f*x + e)^3 - 20*cos(f*x + e)^2 + 24*cos(f*x + e) - 8)/((a*c^4*f*cos(f*x + e)^3 - 3*a*c^4*f*cos(f*x + e)^2 + 3*a*c^4*f*cos(f*x + e) - a*c^4*f)*sin(f*x + e))","A",0
42,1,210,0,0.472209," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{315 \, {\left(c^{5} \cos\left(f x + e\right)^{5} + 2 \, c^{5} \cos\left(f x + e\right)^{4} + c^{5} \cos\left(f x + e\right)^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 315 \, {\left(c^{5} \cos\left(f x + e\right)^{5} + 2 \, c^{5} \cos\left(f x + e\right)^{4} + c^{5} \cos\left(f x + e\right)^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(494 \, c^{5} \cos\left(f x + e\right)^{4} + 679 \, c^{5} \cos\left(f x + e\right)^{3} + 102 \, c^{5} \cos\left(f x + e\right)^{2} - 17 \, c^{5} \cos\left(f x + e\right) + 2 \, c^{5}\right)} \sin\left(f x + e\right)}{12 \, {\left(a^{2} f \cos\left(f x + e\right)^{5} + 2 \, a^{2} f \cos\left(f x + e\right)^{4} + a^{2} f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"1/12*(315*(c^5*cos(f*x + e)^5 + 2*c^5*cos(f*x + e)^4 + c^5*cos(f*x + e)^3)*log(sin(f*x + e) + 1) - 315*(c^5*cos(f*x + e)^5 + 2*c^5*cos(f*x + e)^4 + c^5*cos(f*x + e)^3)*log(-sin(f*x + e) + 1) - 2*(494*c^5*cos(f*x + e)^4 + 679*c^5*cos(f*x + e)^3 + 102*c^5*cos(f*x + e)^2 - 17*c^5*cos(f*x + e) + 2*c^5)*sin(f*x + e))/(a^2*f*cos(f*x + e)^5 + 2*a^2*f*cos(f*x + e)^4 + a^2*f*cos(f*x + e)^3)","A",0
43,1,197,0,0.464236," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{105 \, {\left(c^{4} \cos\left(f x + e\right)^{4} + 2 \, c^{4} \cos\left(f x + e\right)^{3} + c^{4} \cos\left(f x + e\right)^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 105 \, {\left(c^{4} \cos\left(f x + e\right)^{4} + 2 \, c^{4} \cos\left(f x + e\right)^{3} + c^{4} \cos\left(f x + e\right)^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(164 \, c^{4} \cos\left(f x + e\right)^{3} + 229 \, c^{4} \cos\left(f x + e\right)^{2} + 30 \, c^{4} \cos\left(f x + e\right) - 3 \, c^{4}\right)} \sin\left(f x + e\right)}{12 \, {\left(a^{2} f \cos\left(f x + e\right)^{4} + 2 \, a^{2} f \cos\left(f x + e\right)^{3} + a^{2} f \cos\left(f x + e\right)^{2}\right)}}"," ",0,"1/12*(105*(c^4*cos(f*x + e)^4 + 2*c^4*cos(f*x + e)^3 + c^4*cos(f*x + e)^2)*log(sin(f*x + e) + 1) - 105*(c^4*cos(f*x + e)^4 + 2*c^4*cos(f*x + e)^3 + c^4*cos(f*x + e)^2)*log(-sin(f*x + e) + 1) - 2*(164*c^4*cos(f*x + e)^3 + 229*c^4*cos(f*x + e)^2 + 30*c^4*cos(f*x + e) - 3*c^4)*sin(f*x + e))/(a^2*f*cos(f*x + e)^4 + 2*a^2*f*cos(f*x + e)^3 + a^2*f*cos(f*x + e)^2)","A",0
44,1,178,0,0.492244," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{15 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + 2 \, c^{3} \cos\left(f x + e\right)^{2} + c^{3} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + 2 \, c^{3} \cos\left(f x + e\right)^{2} + c^{3} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(23 \, c^{3} \cos\left(f x + e\right)^{2} + 34 \, c^{3} \cos\left(f x + e\right) + 3 \, c^{3}\right)} \sin\left(f x + e\right)}{6 \, {\left(a^{2} f \cos\left(f x + e\right)^{3} + 2 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \cos\left(f x + e\right)\right)}}"," ",0,"1/6*(15*(c^3*cos(f*x + e)^3 + 2*c^3*cos(f*x + e)^2 + c^3*cos(f*x + e))*log(sin(f*x + e) + 1) - 15*(c^3*cos(f*x + e)^3 + 2*c^3*cos(f*x + e)^2 + c^3*cos(f*x + e))*log(-sin(f*x + e) + 1) - 2*(23*c^3*cos(f*x + e)^2 + 34*c^3*cos(f*x + e) + 3*c^3)*sin(f*x + e))/(a^2*f*cos(f*x + e)^3 + 2*a^2*f*cos(f*x + e)^2 + a^2*f*cos(f*x + e))","A",0
45,1,138,0,0.627425," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 8 \, {\left(c^{2} \cos\left(f x + e\right) + 2 \, c^{2}\right)} \sin\left(f x + e\right)}{6 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}"," ",0,"1/6*(3*(c^2*cos(f*x + e)^2 + 2*c^2*cos(f*x + e) + c^2)*log(sin(f*x + e) + 1) - 3*(c^2*cos(f*x + e)^2 + 2*c^2*cos(f*x + e) + c^2)*log(-sin(f*x + e) + 1) - 8*(c^2*cos(f*x + e) + 2*c^2)*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)","A",0
46,1,53,0,0.447736," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(c \cos\left(f x + e\right) - c\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}"," ",0,"1/3*(c*cos(f*x + e) - c)*sin(f*x + e)/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)","A",0
47,1,49,0,0.469944," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 2}{3 \, {\left(a^{2} c f \cos\left(f x + e\right) + a^{2} c f\right)} \sin\left(f x + e\right)}"," ",0,"-1/3*(cos(f*x + e)^2 - 2*cos(f*x + e) - 2)/((a^2*c*f*cos(f*x + e) + a^2*c*f)*sin(f*x + e))","A",0
48,1,50,0,0.447500," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, \cos\left(f x + e\right)^{2} - 2}{3 \, {\left(a^{2} c^{2} f \cos\left(f x + e\right)^{2} - a^{2} c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"1/3*(3*cos(f*x + e)^2 - 2)/((a^2*c^2*f*cos(f*x + e)^2 - a^2*c^2*f)*sin(f*x + e))","A",0
49,1,109,0,0.446730," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{3 \, \cos\left(f x + e\right)^{4} + 12 \, \cos\left(f x + e\right)^{3} - 12 \, \cos\left(f x + e\right)^{2} - 8 \, \cos\left(f x + e\right) + 8}{15 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} - a^{2} c^{3} f \cos\left(f x + e\right)^{2} - a^{2} c^{3} f \cos\left(f x + e\right) + a^{2} c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/15*(3*cos(f*x + e)^4 + 12*cos(f*x + e)^3 - 12*cos(f*x + e)^2 - 8*cos(f*x + e) + 8)/((a^2*c^3*f*cos(f*x + e)^3 - a^2*c^3*f*cos(f*x + e)^2 - a^2*c^3*f*cos(f*x + e) + a^2*c^3*f)*sin(f*x + e))","A",0
50,1,120,0,0.452758," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{6 \, \cos\left(f x + e\right)^{5} + 9 \, \cos\left(f x + e\right)^{4} - 24 \, \cos\left(f x + e\right)^{3} + 4 \, \cos\left(f x + e\right)^{2} + 16 \, \cos\left(f x + e\right) - 8}{21 \, {\left(a^{2} c^{4} f \cos\left(f x + e\right)^{4} - 2 \, a^{2} c^{4} f \cos\left(f x + e\right)^{3} + 2 \, a^{2} c^{4} f \cos\left(f x + e\right) - a^{2} c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/21*(6*cos(f*x + e)^5 + 9*cos(f*x + e)^4 - 24*cos(f*x + e)^3 + 4*cos(f*x + e)^2 + 16*cos(f*x + e) - 8)/((a^2*c^4*f*cos(f*x + e)^4 - 2*a^2*c^4*f*cos(f*x + e)^3 + 2*a^2*c^4*f*cos(f*x + e) - a^2*c^4*f)*sin(f*x + e))","A",0
51,1,163,0,0.461094," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{19 \, \cos\left(f x + e\right)^{6} + 6 \, \cos\left(f x + e\right)^{5} - 66 \, \cos\left(f x + e\right)^{4} + 56 \, \cos\left(f x + e\right)^{3} + 24 \, \cos\left(f x + e\right)^{2} - 48 \, \cos\left(f x + e\right) + 16}{63 \, {\left(a^{2} c^{5} f \cos\left(f x + e\right)^{5} - 3 \, a^{2} c^{5} f \cos\left(f x + e\right)^{4} + 2 \, a^{2} c^{5} f \cos\left(f x + e\right)^{3} + 2 \, a^{2} c^{5} f \cos\left(f x + e\right)^{2} - 3 \, a^{2} c^{5} f \cos\left(f x + e\right) + a^{2} c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/63*(19*cos(f*x + e)^6 + 6*cos(f*x + e)^5 - 66*cos(f*x + e)^4 + 56*cos(f*x + e)^3 + 24*cos(f*x + e)^2 - 48*cos(f*x + e) + 16)/((a^2*c^5*f*cos(f*x + e)^5 - 3*a^2*c^5*f*cos(f*x + e)^4 + 2*a^2*c^5*f*cos(f*x + e)^3 + 2*a^2*c^5*f*cos(f*x + e)^2 - 3*a^2*c^5*f*cos(f*x + e) + a^2*c^5*f)*sin(f*x + e))","A",0
52,1,263,0,0.483946," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^6/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","-\frac{3465 \, {\left(c^{6} \cos\left(f x + e\right)^{6} + 3 \, c^{6} \cos\left(f x + e\right)^{5} + 3 \, c^{6} \cos\left(f x + e\right)^{4} + c^{6} \cos\left(f x + e\right)^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3465 \, {\left(c^{6} \cos\left(f x + e\right)^{6} + 3 \, c^{6} \cos\left(f x + e\right)^{5} + 3 \, c^{6} \cos\left(f x + e\right)^{4} + c^{6} \cos\left(f x + e\right)^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(5446 \, c^{6} \cos\left(f x + e\right)^{5} + 12843 \, c^{6} \cos\left(f x + e\right)^{4} + 8711 \, c^{6} \cos\left(f x + e\right)^{3} + 815 \, c^{6} \cos\left(f x + e\right)^{2} - 105 \, c^{6} \cos\left(f x + e\right) + 10 \, c^{6}\right)} \sin\left(f x + e\right)}{60 \, {\left(a^{3} f \cos\left(f x + e\right)^{6} + 3 \, a^{3} f \cos\left(f x + e\right)^{5} + 3 \, a^{3} f \cos\left(f x + e\right)^{4} + a^{3} f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"-1/60*(3465*(c^6*cos(f*x + e)^6 + 3*c^6*cos(f*x + e)^5 + 3*c^6*cos(f*x + e)^4 + c^6*cos(f*x + e)^3)*log(sin(f*x + e) + 1) - 3465*(c^6*cos(f*x + e)^6 + 3*c^6*cos(f*x + e)^5 + 3*c^6*cos(f*x + e)^4 + c^6*cos(f*x + e)^3)*log(-sin(f*x + e) + 1) - 2*(5446*c^6*cos(f*x + e)^5 + 12843*c^6*cos(f*x + e)^4 + 8711*c^6*cos(f*x + e)^3 + 815*c^6*cos(f*x + e)^2 - 105*c^6*cos(f*x + e) + 10*c^6)*sin(f*x + e))/(a^3*f*cos(f*x + e)^6 + 3*a^3*f*cos(f*x + e)^5 + 3*a^3*f*cos(f*x + e)^4 + a^3*f*cos(f*x + e)^3)","A",0
53,1,250,0,0.473026," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","-\frac{315 \, {\left(c^{5} \cos\left(f x + e\right)^{5} + 3 \, c^{5} \cos\left(f x + e\right)^{4} + 3 \, c^{5} \cos\left(f x + e\right)^{3} + c^{5} \cos\left(f x + e\right)^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 315 \, {\left(c^{5} \cos\left(f x + e\right)^{5} + 3 \, c^{5} \cos\left(f x + e\right)^{4} + 3 \, c^{5} \cos\left(f x + e\right)^{3} + c^{5} \cos\left(f x + e\right)^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(496 \, c^{5} \cos\left(f x + e\right)^{4} + 1163 \, c^{5} \cos\left(f x + e\right)^{3} + 801 \, c^{5} \cos\left(f x + e\right)^{2} + 65 \, c^{5} \cos\left(f x + e\right) - 5 \, c^{5}\right)} \sin\left(f x + e\right)}{20 \, {\left(a^{3} f \cos\left(f x + e\right)^{5} + 3 \, a^{3} f \cos\left(f x + e\right)^{4} + 3 \, a^{3} f \cos\left(f x + e\right)^{3} + a^{3} f \cos\left(f x + e\right)^{2}\right)}}"," ",0,"-1/20*(315*(c^5*cos(f*x + e)^5 + 3*c^5*cos(f*x + e)^4 + 3*c^5*cos(f*x + e)^3 + c^5*cos(f*x + e)^2)*log(sin(f*x + e) + 1) - 315*(c^5*cos(f*x + e)^5 + 3*c^5*cos(f*x + e)^4 + 3*c^5*cos(f*x + e)^3 + c^5*cos(f*x + e)^2)*log(-sin(f*x + e) + 1) - 2*(496*c^5*cos(f*x + e)^4 + 1163*c^5*cos(f*x + e)^3 + 801*c^5*cos(f*x + e)^2 + 65*c^5*cos(f*x + e) - 5*c^5)*sin(f*x + e))/(a^3*f*cos(f*x + e)^5 + 3*a^3*f*cos(f*x + e)^4 + 3*a^3*f*cos(f*x + e)^3 + a^3*f*cos(f*x + e)^2)","A",0
54,1,231,0,0.482249," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","-\frac{105 \, {\left(c^{4} \cos\left(f x + e\right)^{4} + 3 \, c^{4} \cos\left(f x + e\right)^{3} + 3 \, c^{4} \cos\left(f x + e\right)^{2} + c^{4} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 105 \, {\left(c^{4} \cos\left(f x + e\right)^{4} + 3 \, c^{4} \cos\left(f x + e\right)^{3} + 3 \, c^{4} \cos\left(f x + e\right)^{2} + c^{4} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(167 \, c^{4} \cos\left(f x + e\right)^{3} + 381 \, c^{4} \cos\left(f x + e\right)^{2} + 277 \, c^{4} \cos\left(f x + e\right) + 15 \, c^{4}\right)} \sin\left(f x + e\right)}{30 \, {\left(a^{3} f \cos\left(f x + e\right)^{4} + 3 \, a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + a^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"-1/30*(105*(c^4*cos(f*x + e)^4 + 3*c^4*cos(f*x + e)^3 + 3*c^4*cos(f*x + e)^2 + c^4*cos(f*x + e))*log(sin(f*x + e) + 1) - 105*(c^4*cos(f*x + e)^4 + 3*c^4*cos(f*x + e)^3 + 3*c^4*cos(f*x + e)^2 + c^4*cos(f*x + e))*log(-sin(f*x + e) + 1) - 2*(167*c^4*cos(f*x + e)^3 + 381*c^4*cos(f*x + e)^2 + 277*c^4*cos(f*x + e) + 15*c^4)*sin(f*x + e))/(a^3*f*cos(f*x + e)^4 + 3*a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + a^3*f*cos(f*x + e))","A",0
55,1,192,0,0.482742," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + 3 \, c^{3} \cos\left(f x + e\right)^{2} + 3 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + 3 \, c^{3} \cos\left(f x + e\right)^{2} + 3 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 4 \, {\left(13 \, c^{3} \cos\left(f x + e\right)^{2} + 24 \, c^{3} \cos\left(f x + e\right) + 23 \, c^{3}\right)} \sin\left(f x + e\right)}{30 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"-1/30*(15*(c^3*cos(f*x + e)^3 + 3*c^3*cos(f*x + e)^2 + 3*c^3*cos(f*x + e) + c^3)*log(sin(f*x + e) + 1) - 15*(c^3*cos(f*x + e)^3 + 3*c^3*cos(f*x + e)^2 + 3*c^3*cos(f*x + e) + c^3)*log(-sin(f*x + e) + 1) - 4*(13*c^3*cos(f*x + e)^2 + 24*c^3*cos(f*x + e) + 23*c^3)*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","A",0
56,1,82,0,0.420603," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(c^{2} \cos\left(f x + e\right)^{2} - 2 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sin\left(f x + e\right)}{5 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"1/5*(c^2*cos(f*x + e)^2 - 2*c^2*cos(f*x + e) + c^2)*sin(f*x + e)/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","B",0
57,1,79,0,0.433722," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(4 \, c \cos\left(f x + e\right)^{2} - 3 \, c \cos\left(f x + e\right) - c\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"1/15*(4*c*cos(f*x + e)^2 - 3*c*cos(f*x + e) - c)*sin(f*x + e)/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","A",0
58,1,76,0,0.470771," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - 4 \, \cos\left(f x + e\right) - 2}{5 \, {\left(a^{3} c f \cos\left(f x + e\right)^{2} + 2 \, a^{3} c f \cos\left(f x + e\right) + a^{3} c f\right)} \sin\left(f x + e\right)}"," ",0,"-1/5*(2*cos(f*x + e)^3 - cos(f*x + e)^2 - 4*cos(f*x + e) - 2)/((a^3*c*f*cos(f*x + e)^2 + 2*a^3*c*f*cos(f*x + e) + a^3*c*f)*sin(f*x + e))","A",0
59,1,109,0,0.439202," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(f x + e\right)^{4} - 12 \, \cos\left(f x + e\right)^{3} - 12 \, \cos\left(f x + e\right)^{2} + 8 \, \cos\left(f x + e\right) + 8}{15 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} + a^{3} c^{2} f \cos\left(f x + e\right)^{2} - a^{3} c^{2} f \cos\left(f x + e\right) - a^{3} c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"-1/15*(3*cos(f*x + e)^4 - 12*cos(f*x + e)^3 - 12*cos(f*x + e)^2 + 8*cos(f*x + e) + 8)/((a^3*c^2*f*cos(f*x + e)^3 + a^3*c^2*f*cos(f*x + e)^2 - a^3*c^2*f*cos(f*x + e) - a^3*c^2*f)*sin(f*x + e))","A",0
60,1,76,0,0.433211," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, \cos\left(f x + e\right)^{4} - 20 \, \cos\left(f x + e\right)^{2} + 8}{15 \, {\left(a^{3} c^{3} f \cos\left(f x + e\right)^{4} - 2 \, a^{3} c^{3} f \cos\left(f x + e\right)^{2} + a^{3} c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/15*(15*cos(f*x + e)^4 - 20*cos(f*x + e)^2 + 8)/((a^3*c^3*f*cos(f*x + e)^4 - 2*a^3*c^3*f*cos(f*x + e)^2 + a^3*c^3*f)*sin(f*x + e))","A",0
61,1,163,0,0.424074," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{5 \, \cos\left(f x + e\right)^{6} + 30 \, \cos\left(f x + e\right)^{5} - 30 \, \cos\left(f x + e\right)^{4} - 40 \, \cos\left(f x + e\right)^{3} + 40 \, \cos\left(f x + e\right)^{2} + 16 \, \cos\left(f x + e\right) - 16}{35 \, {\left(a^{3} c^{4} f \cos\left(f x + e\right)^{5} - a^{3} c^{4} f \cos\left(f x + e\right)^{4} - 2 \, a^{3} c^{4} f \cos\left(f x + e\right)^{3} + 2 \, a^{3} c^{4} f \cos\left(f x + e\right)^{2} + a^{3} c^{4} f \cos\left(f x + e\right) - a^{3} c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/35*(5*cos(f*x + e)^6 + 30*cos(f*x + e)^5 - 30*cos(f*x + e)^4 - 40*cos(f*x + e)^3 + 40*cos(f*x + e)^2 + 16*cos(f*x + e) - 16)/((a^3*c^4*f*cos(f*x + e)^5 - a^3*c^4*f*cos(f*x + e)^4 - 2*a^3*c^4*f*cos(f*x + e)^3 + 2*a^3*c^4*f*cos(f*x + e)^2 + a^3*c^4*f*cos(f*x + e) - a^3*c^4*f)*sin(f*x + e))","A",0
62,1,190,0,0.453734," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{10 \, \cos\left(f x + e\right)^{7} + 25 \, \cos\left(f x + e\right)^{6} - 60 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{4} + 80 \, \cos\left(f x + e\right)^{3} - 24 \, \cos\left(f x + e\right)^{2} - 32 \, \cos\left(f x + e\right) + 16}{45 \, {\left(a^{3} c^{5} f \cos\left(f x + e\right)^{6} - 2 \, a^{3} c^{5} f \cos\left(f x + e\right)^{5} - a^{3} c^{5} f \cos\left(f x + e\right)^{4} + 4 \, a^{3} c^{5} f \cos\left(f x + e\right)^{3} - a^{3} c^{5} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} c^{5} f \cos\left(f x + e\right) + a^{3} c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/45*(10*cos(f*x + e)^7 + 25*cos(f*x + e)^6 - 60*cos(f*x + e)^5 - 10*cos(f*x + e)^4 + 80*cos(f*x + e)^3 - 24*cos(f*x + e)^2 - 32*cos(f*x + e) + 16)/((a^3*c^5*f*cos(f*x + e)^6 - 2*a^3*c^5*f*cos(f*x + e)^5 - a^3*c^5*f*cos(f*x + e)^4 + 4*a^3*c^5*f*cos(f*x + e)^3 - a^3*c^5*f*cos(f*x + e)^2 - 2*a^3*c^5*f*cos(f*x + e) + a^3*c^5*f)*sin(f*x + e))","A",0
63,1,217,0,0.449512," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^6,x, algorithm=""fricas"")","\frac{125 \, \cos\left(f x + e\right)^{8} + 120 \, \cos\left(f x + e\right)^{7} - 680 \, \cos\left(f x + e\right)^{6} + 400 \, \cos\left(f x + e\right)^{5} + 720 \, \cos\left(f x + e\right)^{4} - 832 \, \cos\left(f x + e\right)^{3} - 64 \, \cos\left(f x + e\right)^{2} + 384 \, \cos\left(f x + e\right) - 128}{495 \, {\left(a^{3} c^{6} f \cos\left(f x + e\right)^{7} - 3 \, a^{3} c^{6} f \cos\left(f x + e\right)^{6} + a^{3} c^{6} f \cos\left(f x + e\right)^{5} + 5 \, a^{3} c^{6} f \cos\left(f x + e\right)^{4} - 5 \, a^{3} c^{6} f \cos\left(f x + e\right)^{3} - a^{3} c^{6} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} c^{6} f \cos\left(f x + e\right) - a^{3} c^{6} f\right)} \sin\left(f x + e\right)}"," ",0,"1/495*(125*cos(f*x + e)^8 + 120*cos(f*x + e)^7 - 680*cos(f*x + e)^6 + 400*cos(f*x + e)^5 + 720*cos(f*x + e)^4 - 832*cos(f*x + e)^3 - 64*cos(f*x + e)^2 + 384*cos(f*x + e) - 128)/((a^3*c^6*f*cos(f*x + e)^7 - 3*a^3*c^6*f*cos(f*x + e)^6 + a^3*c^6*f*cos(f*x + e)^5 + 5*a^3*c^6*f*cos(f*x + e)^4 - 5*a^3*c^6*f*cos(f*x + e)^3 - a^3*c^6*f*cos(f*x + e)^2 + 3*a^3*c^6*f*cos(f*x + e) - a^3*c^6*f)*sin(f*x + e))","A",0
64,1,119,0,0.455577," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(319 \, a c^{3} \cos\left(f x + e\right)^{5} + 317 \, a c^{3} \cos\left(f x + e\right)^{4} - 158 \, a c^{3} \cos\left(f x + e\right)^{3} - 26 \, a c^{3} \cos\left(f x + e\right)^{2} + 95 \, a c^{3} \cos\left(f x + e\right) - 35 \, a c^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{315 \, f \cos\left(f x + e\right)^{4} \sin\left(f x + e\right)}"," ",0,"2/315*(319*a*c^3*cos(f*x + e)^5 + 317*a*c^3*cos(f*x + e)^4 - 158*a*c^3*cos(f*x + e)^3 - 26*a*c^3*cos(f*x + e)^2 + 95*a*c^3*cos(f*x + e) - 35*a*c^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^4*sin(f*x + e))","A",0
65,1,105,0,0.448472," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(71 \, a c^{2} \cos\left(f x + e\right)^{4} + 88 \, a c^{2} \cos\left(f x + e\right)^{3} - 22 \, a c^{2} \cos\left(f x + e\right)^{2} - 24 \, a c^{2} \cos\left(f x + e\right) + 15 \, a c^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{105 \, f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right)}"," ",0,"2/105*(71*a*c^2*cos(f*x + e)^4 + 88*a*c^2*cos(f*x + e)^3 - 22*a*c^2*cos(f*x + e)^2 - 24*a*c^2*cos(f*x + e) + 15*a*c^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^3*sin(f*x + e))","A",0
66,1,82,0,0.425911," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, a c \cos\left(f x + e\right)^{3} + 11 \, a c \cos\left(f x + e\right)^{2} + a c \cos\left(f x + e\right) - 3 \, a c\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{15 \, f \cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}"," ",0,"2/15*(7*a*c*cos(f*x + e)^3 + 11*a*c*cos(f*x + e)^2 + a*c*cos(f*x + e) - 3*a*c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^2*sin(f*x + e))","A",0
67,1,65,0,0.458034," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a \cos\left(f x + e\right)^{2} + 2 \, a \cos\left(f x + e\right) + a\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3 \, f \cos\left(f x + e\right) \sin\left(f x + e\right)}"," ",0,"2/3*(a*cos(f*x + e)^2 + 2*a*cos(f*x + e) + a)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)*sin(f*x + e))","A",0
68,1,272,0,0.521658," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a c \sqrt{-\frac{1}{c}} \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{c}} - {\left(3 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + a\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{c f \sin\left(f x + e\right)}, \frac{2 \, {\left(\sqrt{2} a \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - {\left(a \cos\left(f x + e\right) + a\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}\right)}}{c f \sin\left(f x + e\right)}\right]"," ",0,"[(sqrt(2)*a*c*sqrt(-1/c)*log(-(2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sqrt(-1/c) - (3*cos(f*x + e) + 1)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) - 2*(a*cos(f*x + e) + a)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/(c*f*sin(f*x + e)), 2*(sqrt(2)*a*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - (a*cos(f*x + e) + a)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/(c*f*sin(f*x + e))]","A",0
69,1,342,0,0.534733," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(a c \cos\left(f x + e\right) - a c\right)} \sqrt{-\frac{1}{c}} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{c}} + {\left(3 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{4 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}, -\frac{\frac{\sqrt{2} {\left(a c \cos\left(f x + e\right) - a c\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right)}{\sqrt{c}} - 2 \, {\left(a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{2 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/4*(sqrt(2)*(a*c*cos(f*x + e) - a*c)*sqrt(-1/c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sqrt(-1/c) + (3*cos(f*x + e) + 1)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(a*cos(f*x + e)^2 + a*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e)), -1/2*(sqrt(2)*(a*c*cos(f*x + e) - a*c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e)/sqrt(c) - 2*(a*cos(f*x + e)^2 + a*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))]","B",0
70,1,405,0,0.513550," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a\right)} \sqrt{-c} \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} - {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 4 \, {\left(3 \, a \cos\left(f x + e\right)^{3} + 4 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{32 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}, -\frac{\sqrt{2} {\left(a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(3 \, a \cos\left(f x + e\right)^{3} + 4 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{16 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/32*(sqrt(2)*(a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)*sqrt(-c)*log(-(2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) - (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) - 4*(3*a*cos(f*x + e)^3 + 4*a*cos(f*x + e)^2 + a*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e)), -1/16*(sqrt(2)*(a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*(3*a*cos(f*x + e)^3 + 4*a*cos(f*x + e)^2 + a*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))]","A",0
71,1,147,0,0.453221," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(533 \, a^{2} c^{3} \cos\left(f x + e\right)^{6} + 844 \, a^{2} c^{3} \cos\left(f x + e\right)^{5} - 211 \, a^{2} c^{3} \cos\left(f x + e\right)^{4} - 472 \, a^{2} c^{3} \cos\left(f x + e\right)^{3} + 295 \, a^{2} c^{3} \cos\left(f x + e\right)^{2} + 140 \, a^{2} c^{3} \cos\left(f x + e\right) - 105 \, a^{2} c^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{1155 \, f \cos\left(f x + e\right)^{5} \sin\left(f x + e\right)}"," ",0,"2/1155*(533*a^2*c^3*cos(f*x + e)^6 + 844*a^2*c^3*cos(f*x + e)^5 - 211*a^2*c^3*cos(f*x + e)^4 - 472*a^2*c^3*cos(f*x + e)^3 + 295*a^2*c^3*cos(f*x + e)^2 + 140*a^2*c^3*cos(f*x + e) - 105*a^2*c^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^5*sin(f*x + e))","A",0
72,1,131,0,0.435637," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(107 \, a^{2} c^{2} \cos\left(f x + e\right)^{5} + 211 \, a^{2} c^{2} \cos\left(f x + e\right)^{4} + 26 \, a^{2} c^{2} \cos\left(f x + e\right)^{3} - 118 \, a^{2} c^{2} \cos\left(f x + e\right)^{2} - 5 \, a^{2} c^{2} \cos\left(f x + e\right) + 35 \, a^{2} c^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{315 \, f \cos\left(f x + e\right)^{4} \sin\left(f x + e\right)}"," ",0,"2/315*(107*a^2*c^2*cos(f*x + e)^5 + 211*a^2*c^2*cos(f*x + e)^4 + 26*a^2*c^2*cos(f*x + e)^3 - 118*a^2*c^2*cos(f*x + e)^2 - 5*a^2*c^2*cos(f*x + e) + 35*a^2*c^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^4*sin(f*x + e))","A",0
73,1,105,0,0.441525," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(9 \, a^{2} c \cos\left(f x + e\right)^{4} + 22 \, a^{2} c \cos\left(f x + e\right)^{3} + 12 \, a^{2} c \cos\left(f x + e\right)^{2} - 6 \, a^{2} c \cos\left(f x + e\right) - 5 \, a^{2} c\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{35 \, f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right)}"," ",0,"2/35*(9*a^2*c*cos(f*x + e)^4 + 22*a^2*c*cos(f*x + e)^3 + 12*a^2*c*cos(f*x + e)^2 - 6*a^2*c*cos(f*x + e) - 5*a^2*c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^3*sin(f*x + e))","A",0
74,1,84,0,0.445960," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} \cos\left(f x + e\right)^{3} + 3 \, a^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{5 \, f \cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}"," ",0,"2/5*(a^2*cos(f*x + e)^3 + 3*a^2*cos(f*x + e)^2 + 3*a^2*cos(f*x + e) + a^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^2*sin(f*x + e))","B",0
75,1,343,0,0.532690," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, \sqrt{2} a^{2} c \sqrt{-\frac{1}{c}} \cos\left(f x + e\right) \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{c}} - {\left(3 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - {\left(7 \, a^{2} \cos\left(f x + e\right)^{2} + 8 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}\right)}}{3 \, c f \cos\left(f x + e\right) \sin\left(f x + e\right)}, \frac{2 \, {\left(6 \, \sqrt{2} a^{2} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(7 \, a^{2} \cos\left(f x + e\right)^{2} + 8 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}\right)}}{3 \, c f \cos\left(f x + e\right) \sin\left(f x + e\right)}\right]"," ",0,"[2/3*(3*sqrt(2)*a^2*c*sqrt(-1/c)*cos(f*x + e)*log(-(2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sqrt(-1/c) - (3*cos(f*x + e) + 1)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) - (7*a^2*cos(f*x + e)^2 + 8*a^2*cos(f*x + e) + a^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/(c*f*cos(f*x + e)*sin(f*x + e)), 2/3*(6*sqrt(2)*a^2*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*cos(f*x + e)*sin(f*x + e) - (7*a^2*cos(f*x + e)^2 + 8*a^2*cos(f*x + e) + a^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/(c*f*cos(f*x + e)*sin(f*x + e))]","A",0
76,1,372,0,0.518069," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(a^{2} c \cos\left(f x + e\right) - a^{2} c\right)} \sqrt{-\frac{1}{c}} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{c}} + {\left(3 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(2 \, a^{2} \cos\left(f x + e\right)^{2} + a^{2} \cos\left(f x + e\right) - a^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{2 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}, -\frac{\frac{3 \, \sqrt{2} {\left(a^{2} c \cos\left(f x + e\right) - a^{2} c\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right)}{\sqrt{c}} - 2 \, {\left(2 \, a^{2} \cos\left(f x + e\right)^{2} + a^{2} \cos\left(f x + e\right) - a^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{{\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/2*(3*sqrt(2)*(a^2*c*cos(f*x + e) - a^2*c)*sqrt(-1/c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sqrt(-1/c) + (3*cos(f*x + e) + 1)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(2*a^2*cos(f*x + e)^2 + a^2*cos(f*x + e) - a^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e)), -(3*sqrt(2)*(a^2*c*cos(f*x + e) - a^2*c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e)/sqrt(c) - 2*(2*a^2*cos(f*x + e)^2 + a^2*cos(f*x + e) - a^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))]","A",0
77,1,429,0,0.557302," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left(a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{-c} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(a^{2} \cos\left(f x + e\right)^{3} - 4 \, a^{2} \cos\left(f x + e\right)^{2} - 5 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{16 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}, \frac{3 \, \sqrt{2} {\left(a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(a^{2} \cos\left(f x + e\right)^{3} - 4 \, a^{2} \cos\left(f x + e\right)^{2} - 5 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{8 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/16*(3*sqrt(2)*(a^2*cos(f*x + e)^2 - 2*a^2*cos(f*x + e) + a^2)*sqrt(-c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(a^2*cos(f*x + e)^3 - 4*a^2*cos(f*x + e)^2 - 5*a^2*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e)), 1/8*(3*sqrt(2)*(a^2*cos(f*x + e)^2 - 2*a^2*cos(f*x + e) + a^2)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*(a^2*cos(f*x + e)^3 - 4*a^2*cos(f*x + e)^2 - 5*a^2*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))]","A",0
78,1,517,0,0.582242," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left(a^{2} \cos\left(f x + e\right)^{3} - 3 \, a^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} \cos\left(f x + e\right) - a^{2}\right)} \sqrt{-c} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 4 \, {\left(7 \, a^{2} \cos\left(f x + e\right)^{4} + 29 \, a^{2} \cos\left(f x + e\right)^{3} + 25 \, a^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{192 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}, \frac{3 \, \sqrt{2} {\left(a^{2} \cos\left(f x + e\right)^{3} - 3 \, a^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} \cos\left(f x + e\right) - a^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 2 \, {\left(7 \, a^{2} \cos\left(f x + e\right)^{4} + 29 \, a^{2} \cos\left(f x + e\right)^{3} + 25 \, a^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{96 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/192*(3*sqrt(2)*(a^2*cos(f*x + e)^3 - 3*a^2*cos(f*x + e)^2 + 3*a^2*cos(f*x + e) - a^2)*sqrt(-c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) - 4*(7*a^2*cos(f*x + e)^4 + 29*a^2*cos(f*x + e)^3 + 25*a^2*cos(f*x + e)^2 + 3*a^2*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e)), 1/96*(3*sqrt(2)*(a^2*cos(f*x + e)^3 - 3*a^2*cos(f*x + e)^2 + 3*a^2*cos(f*x + e) - a^2)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) + 2*(7*a^2*cos(f*x + e)^4 + 29*a^2*cos(f*x + e)^3 + 25*a^2*cos(f*x + e)^2 + 3*a^2*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))]","A",0
79,1,163,0,0.472274," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(835 \, a^{3} c^{3} \cos\left(f x + e\right)^{7} + 1919 \, a^{3} c^{3} \cos\left(f x + e\right)^{6} + 271 \, a^{3} c^{3} \cos\left(f x + e\right)^{5} - 1637 \, a^{3} c^{3} \cos\left(f x + e\right)^{4} - 103 \, a^{3} c^{3} \cos\left(f x + e\right)^{3} + 973 \, a^{3} c^{3} \cos\left(f x + e\right)^{2} + 21 \, a^{3} c^{3} \cos\left(f x + e\right) - 231 \, a^{3} c^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3003 \, f \cos\left(f x + e\right)^{6} \sin\left(f x + e\right)}"," ",0,"2/3003*(835*a^3*c^3*cos(f*x + e)^7 + 1919*a^3*c^3*cos(f*x + e)^6 + 271*a^3*c^3*cos(f*x + e)^5 - 1637*a^3*c^3*cos(f*x + e)^4 - 103*a^3*c^3*cos(f*x + e)^3 + 973*a^3*c^3*cos(f*x + e)^2 + 21*a^3*c^3*cos(f*x + e) - 231*a^3*c^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^6*sin(f*x + e))","A",0
80,1,147,0,0.430453," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(151 \, a^{3} c^{2} \cos\left(f x + e\right)^{6} + 422 \, a^{3} c^{2} \cos\left(f x + e\right)^{5} + 241 \, a^{3} c^{2} \cos\left(f x + e\right)^{4} - 236 \, a^{3} c^{2} \cos\left(f x + e\right)^{3} - 199 \, a^{3} c^{2} \cos\left(f x + e\right)^{2} + 70 \, a^{3} c^{2} \cos\left(f x + e\right) + 63 \, a^{3} c^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{693 \, f \cos\left(f x + e\right)^{5} \sin\left(f x + e\right)}"," ",0,"2/693*(151*a^3*c^2*cos(f*x + e)^6 + 422*a^3*c^2*cos(f*x + e)^5 + 241*a^3*c^2*cos(f*x + e)^4 - 236*a^3*c^2*cos(f*x + e)^3 - 199*a^3*c^2*cos(f*x + e)^2 + 70*a^3*c^2*cos(f*x + e) + 63*a^3*c^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^5*sin(f*x + e))","A",0
81,1,119,0,0.432048," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(11 \, a^{3} c \cos\left(f x + e\right)^{5} + 37 \, a^{3} c \cos\left(f x + e\right)^{4} + 38 \, a^{3} c \cos\left(f x + e\right)^{3} + 2 \, a^{3} c \cos\left(f x + e\right)^{2} - 17 \, a^{3} c \cos\left(f x + e\right) - 7 \, a^{3} c\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{63 \, f \cos\left(f x + e\right)^{4} \sin\left(f x + e\right)}"," ",0,"2/63*(11*a^3*c*cos(f*x + e)^5 + 37*a^3*c*cos(f*x + e)^4 + 38*a^3*c*cos(f*x + e)^3 + 2*a^3*c*cos(f*x + e)^2 - 17*a^3*c*cos(f*x + e) - 7*a^3*c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^4*sin(f*x + e))","A",0
82,1,97,0,0.422921," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} \cos\left(f x + e\right)^{4} + 4 \, a^{3} \cos\left(f x + e\right)^{3} + 6 \, a^{3} \cos\left(f x + e\right)^{2} + 4 \, a^{3} \cos\left(f x + e\right) + a^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{7 \, f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right)}"," ",0,"2/7*(a^3*cos(f*x + e)^4 + 4*a^3*cos(f*x + e)^3 + 6*a^3*cos(f*x + e)^2 + 4*a^3*cos(f*x + e) + a^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^3*sin(f*x + e))","B",0
83,1,377,0,0.511733," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(30 \, \sqrt{2} a^{3} c \sqrt{-\frac{1}{c}} \cos\left(f x + e\right)^{2} \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{c}} - {\left(3 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - {\left(73 \, a^{3} \cos\left(f x + e\right)^{3} + 89 \, a^{3} \cos\left(f x + e\right)^{2} + 19 \, a^{3} \cos\left(f x + e\right) + 3 \, a^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}\right)}}{15 \, c f \cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}, \frac{2 \, {\left(60 \, \sqrt{2} a^{3} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - {\left(73 \, a^{3} \cos\left(f x + e\right)^{3} + 89 \, a^{3} \cos\left(f x + e\right)^{2} + 19 \, a^{3} \cos\left(f x + e\right) + 3 \, a^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}\right)}}{15 \, c f \cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}\right]"," ",0,"[2/15*(30*sqrt(2)*a^3*c*sqrt(-1/c)*cos(f*x + e)^2*log(-(2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sqrt(-1/c) - (3*cos(f*x + e) + 1)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) - (73*a^3*cos(f*x + e)^3 + 89*a^3*cos(f*x + e)^2 + 19*a^3*cos(f*x + e) + 3*a^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/(c*f*cos(f*x + e)^2*sin(f*x + e)), 2/15*(60*sqrt(2)*a^3*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*cos(f*x + e)^2*sin(f*x + e) - (73*a^3*cos(f*x + e)^3 + 89*a^3*cos(f*x + e)^2 + 19*a^3*cos(f*x + e) + 3*a^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/(c*f*cos(f*x + e)^2*sin(f*x + e))]","A",0
84,1,432,0,0.539945," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left(a^{3} c \cos\left(f x + e\right)^{2} - a^{3} c \cos\left(f x + e\right)\right)} \sqrt{-\frac{1}{c}} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{c}} + {\left(3 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 2 \, {\left(19 \, a^{3} \cos\left(f x + e\right)^{3} + 7 \, a^{3} \cos\left(f x + e\right)^{2} - 13 \, a^{3} \cos\left(f x + e\right) - a^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3 \, {\left(c^{2} f \cos\left(f x + e\right)^{2} - c^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}, -\frac{2 \, {\left(\frac{15 \, \sqrt{2} {\left(a^{3} c \cos\left(f x + e\right)^{2} - a^{3} c \cos\left(f x + e\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right)}{\sqrt{c}} - {\left(19 \, a^{3} \cos\left(f x + e\right)^{3} + 7 \, a^{3} \cos\left(f x + e\right)^{2} - 13 \, a^{3} \cos\left(f x + e\right) - a^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}\right)}}{3 \, {\left(c^{2} f \cos\left(f x + e\right)^{2} - c^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/3*(15*sqrt(2)*(a^3*c*cos(f*x + e)^2 - a^3*c*cos(f*x + e))*sqrt(-1/c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sqrt(-1/c) + (3*cos(f*x + e) + 1)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 2*(19*a^3*cos(f*x + e)^3 + 7*a^3*cos(f*x + e)^2 - 13*a^3*cos(f*x + e) - a^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^2*f*cos(f*x + e)^2 - c^2*f*cos(f*x + e))*sin(f*x + e)), -2/3*(15*sqrt(2)*(a^3*c*cos(f*x + e)^2 - a^3*c*cos(f*x + e))*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e)/sqrt(c) - (19*a^3*cos(f*x + e)^3 + 7*a^3*cos(f*x + e)^2 - 13*a^3*cos(f*x + e) - a^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^2*f*cos(f*x + e)^2 - c^2*f*cos(f*x + e))*sin(f*x + e))]","A",0
85,1,441,0,0.581310," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left(a^{3} \cos\left(f x + e\right)^{2} - 2 \, a^{3} \cos\left(f x + e\right) + a^{3}\right)} \sqrt{-c} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(9 \, a^{3} \cos\left(f x + e\right)^{3} - 8 \, a^{3} \cos\left(f x + e\right)^{2} - 13 \, a^{3} \cos\left(f x + e\right) + 4 \, a^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{8 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}, \frac{15 \, \sqrt{2} {\left(a^{3} \cos\left(f x + e\right)^{2} - 2 \, a^{3} \cos\left(f x + e\right) + a^{3}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(9 \, a^{3} \cos\left(f x + e\right)^{3} - 8 \, a^{3} \cos\left(f x + e\right)^{2} - 13 \, a^{3} \cos\left(f x + e\right) + 4 \, a^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{4 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/8*(15*sqrt(2)*(a^3*cos(f*x + e)^2 - 2*a^3*cos(f*x + e) + a^3)*sqrt(-c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(9*a^3*cos(f*x + e)^3 - 8*a^3*cos(f*x + e)^2 - 13*a^3*cos(f*x + e) + 4*a^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e)), 1/4*(15*sqrt(2)*(a^3*cos(f*x + e)^2 - 2*a^3*cos(f*x + e) + a^3)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*(9*a^3*cos(f*x + e)^3 - 8*a^3*cos(f*x + e)^2 - 13*a^3*cos(f*x + e) + 4*a^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))]","A",0
86,1,88,0,0.444524," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, {\left(91 \, c^{3} \cos\left(f x + e\right)^{3} + 43 \, c^{3} \cos\left(f x + e\right)^{2} - 7 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{5 \, a f \cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}"," ",0,"-2/5*(91*c^3*cos(f*x + e)^3 + 43*c^3*cos(f*x + e)^2 - 7*c^3*cos(f*x + e) + c^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*f*cos(f*x + e)^2*sin(f*x + e))","A",0
87,1,77,0,0.430304," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, {\left(23 \, c^{2} \cos\left(f x + e\right)^{2} + 10 \, c^{2} \cos\left(f x + e\right) - c^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3 \, a f \cos\left(f x + e\right) \sin\left(f x + e\right)}"," ",0,"-2/3*(23*c^2*cos(f*x + e)^2 + 10*c^2*cos(f*x + e) - c^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*f*cos(f*x + e)*sin(f*x + e))","A",0
88,1,50,0,0.427937," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{a f \sin\left(f x + e\right)}"," ",0,"-2*(3*c*cos(f*x + e) + c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*f*sin(f*x + e))","A",0
89,1,45,0,0.440850," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a f \sin\left(f x + e\right)}"," ",0,"-2*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(a*f*sin(f*x + e))","A",0
90,1,269,0,0.512358," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} c \sqrt{-\frac{1}{c}} \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{c}} - {\left(3 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 4 \, \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{4 \, a c f \sin\left(f x + e\right)}, \frac{\sqrt{2} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{2 \, a c f \sin\left(f x + e\right)}\right]"," ",0,"[1/4*(sqrt(2)*c*sqrt(-1/c)*log(-(2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sqrt(-1/c) - (3*cos(f*x + e) + 1)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) - 4*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e))/(a*c*f*sin(f*x + e)), 1/2*(sqrt(2)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e))/(a*c*f*sin(f*x + e))]","A",0
91,1,329,0,0.511932," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} \sqrt{-c} {\left(\cos\left(f x + e\right) - 1\right)} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(\cos\left(f x + e\right)^{2} - 3 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{16 \, {\left(a c^{2} f \cos\left(f x + e\right) - a c^{2} f\right)} \sin\left(f x + e\right)}, \frac{3 \, \sqrt{2} \sqrt{c} {\left(\cos\left(f x + e\right) - 1\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(\cos\left(f x + e\right)^{2} - 3 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{8 \, {\left(a c^{2} f \cos\left(f x + e\right) - a c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/16*(3*sqrt(2)*sqrt(-c)*(cos(f*x + e) - 1)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(cos(f*x + e)^2 - 3*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a*c^2*f*cos(f*x + e) - a*c^2*f)*sin(f*x + e)), 1/8*(3*sqrt(2)*sqrt(c)*(cos(f*x + e) - 1)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*(cos(f*x + e)^2 - 3*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a*c^2*f*cos(f*x + e) - a*c^2*f)*sin(f*x + e))]","A",0
92,1,401,0,0.552136," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{-c} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 4 \, {\left(3 \, \cos\left(f x + e\right)^{3} + 20 \, \cos\left(f x + e\right)^{2} - 15 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{128 \, {\left(a c^{3} f \cos\left(f x + e\right)^{2} - 2 \, a c^{3} f \cos\left(f x + e\right) + a c^{3} f\right)} \sin\left(f x + e\right)}, \frac{15 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 2 \, {\left(3 \, \cos\left(f x + e\right)^{3} + 20 \, \cos\left(f x + e\right)^{2} - 15 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{64 \, {\left(a c^{3} f \cos\left(f x + e\right)^{2} - 2 \, a c^{3} f \cos\left(f x + e\right) + a c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/128*(15*sqrt(2)*(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sqrt(-c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) - 4*(3*cos(f*x + e)^3 + 20*cos(f*x + e)^2 - 15*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a*c^3*f*cos(f*x + e)^2 - 2*a*c^3*f*cos(f*x + e) + a*c^3*f)*sin(f*x + e)), 1/64*(15*sqrt(2)*(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) + 2*(3*cos(f*x + e)^3 + 20*cos(f*x + e)^2 - 15*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a*c^3*f*cos(f*x + e)^2 - 2*a*c^3*f*cos(f*x + e) + a*c^3*f)*sin(f*x + e))]","A",0
93,1,103,0,0.429640," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(45 \, c^{3} \cos\left(f x + e\right)^{3} + 69 \, c^{3} \cos\left(f x + e\right)^{2} + 15 \, c^{3} \cos\left(f x + e\right) - c^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}"," ",0,"2/3*(45*c^3*cos(f*x + e)^3 + 69*c^3*cos(f*x + e)^2 + 15*c^3*cos(f*x + e) - c^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((a^2*f*cos(f*x + e)^2 + a^2*f*cos(f*x + e))*sin(f*x + e))","A",0
94,1,82,0,0.451364," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(11 \, c^{2} \cos\left(f x + e\right)^{2} + 18 \, c^{2} \cos\left(f x + e\right) + 3 \, c^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3 \, {\left(a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"2/3*(11*c^2*cos(f*x + e)^2 + 18*c^2*cos(f*x + e) + 3*c^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((a^2*f*cos(f*x + e) + a^2*f)*sin(f*x + e))","A",0
95,1,72,0,0.448608," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(c \cos\left(f x + e\right)^{2} + 3 \, c \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3 \, {\left(a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"2/3*(c*cos(f*x + e)^2 + 3*c*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((a^2*f*cos(f*x + e) + a^2*f)*sin(f*x + e))","A",0
96,1,60,0,0.495223," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2}}{3 \, {\left(a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"-2/3*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2/((a^2*f*cos(f*x + e) + a^2*f)*sin(f*x + e))","A",0
97,1,331,0,0.534752," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} \sqrt{-c} {\left(\cos\left(f x + e\right) + 1\right)} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(5 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{24 \, {\left(a^{2} c f \cos\left(f x + e\right) + a^{2} c f\right)} \sin\left(f x + e\right)}, \frac{3 \, \sqrt{2} \sqrt{c} {\left(\cos\left(f x + e\right) + 1\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(5 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{12 \, {\left(a^{2} c f \cos\left(f x + e\right) + a^{2} c f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/24*(3*sqrt(2)*sqrt(-c)*(cos(f*x + e) + 1)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(5*cos(f*x + e)^2 + 3*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^2*c*f*cos(f*x + e) + a^2*c*f)*sin(f*x + e)), 1/12*(3*sqrt(2)*sqrt(c)*(cos(f*x + e) + 1)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*(5*cos(f*x + e)^2 + 3*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^2*c*f*cos(f*x + e) + a^2*c*f)*sin(f*x + e))]","A",0
98,1,369,0,0.533087," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-c} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(13 \, \cos\left(f x + e\right)^{3} - 10 \, \cos\left(f x + e\right)^{2} - 15 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{96 \, {\left(a^{2} c^{2} f \cos\left(f x + e\right)^{2} - a^{2} c^{2} f\right)} \sin\left(f x + e\right)}, \frac{15 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(13 \, \cos\left(f x + e\right)^{3} - 10 \, \cos\left(f x + e\right)^{2} - 15 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{48 \, {\left(a^{2} c^{2} f \cos\left(f x + e\right)^{2} - a^{2} c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/96*(15*sqrt(2)*(cos(f*x + e)^2 - 1)*sqrt(-c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(13*cos(f*x + e)^3 - 10*cos(f*x + e)^2 - 15*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^2*c^2*f*cos(f*x + e)^2 - a^2*c^2*f)*sin(f*x + e)), 1/48*(15*sqrt(2)*(cos(f*x + e)^2 - 1)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*(13*cos(f*x + e)^3 - 10*cos(f*x + e)^2 - 15*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^2*c^2*f*cos(f*x + e)^2 - a^2*c^2*f)*sin(f*x + e))]","A",0
99,1,487,0,0.572290," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) + 1\right)} \sqrt{-c} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(43 \, \cos\left(f x + e\right)^{4} - 161 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)^{2} + 105 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{768 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} - a^{2} c^{3} f \cos\left(f x + e\right)^{2} - a^{2} c^{3} f \cos\left(f x + e\right) + a^{2} c^{3} f\right)} \sin\left(f x + e\right)}, \frac{105 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) + 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(43 \, \cos\left(f x + e\right)^{4} - 161 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)^{2} + 105 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{384 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} - a^{2} c^{3} f \cos\left(f x + e\right)^{2} - a^{2} c^{3} f \cos\left(f x + e\right) + a^{2} c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/768*(105*sqrt(2)*(cos(f*x + e)^3 - cos(f*x + e)^2 - cos(f*x + e) + 1)*sqrt(-c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(43*cos(f*x + e)^4 - 161*cos(f*x + e)^3 - 35*cos(f*x + e)^2 + 105*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^2*c^3*f*cos(f*x + e)^3 - a^2*c^3*f*cos(f*x + e)^2 - a^2*c^3*f*cos(f*x + e) + a^2*c^3*f)*sin(f*x + e)), 1/384*(105*sqrt(2)*(cos(f*x + e)^3 - cos(f*x + e)^2 - cos(f*x + e) + 1)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*(43*cos(f*x + e)^4 - 161*cos(f*x + e)^3 - 35*cos(f*x + e)^2 + 105*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^2*c^3*f*cos(f*x + e)^3 - a^2*c^3*f*cos(f*x + e)^2 - a^2*c^3*f*cos(f*x + e) + a^2*c^3*f)*sin(f*x + e))]","A",0
100,1,109,0,0.429675," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(23 \, c^{3} \cos\left(f x + e\right)^{3} + 55 \, c^{3} \cos\left(f x + e\right)^{2} + 45 \, c^{3} \cos\left(f x + e\right) + 5 \, c^{3}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{5 \, {\left(a^{3} f \cos\left(f x + e\right)^{2} + 2 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"-2/5*(23*c^3*cos(f*x + e)^3 + 55*c^3*cos(f*x + e)^2 + 45*c^3*cos(f*x + e) + 5*c^3)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((a^3*f*cos(f*x + e)^2 + 2*a^3*f*cos(f*x + e) + a^3*f)*sin(f*x + e))","A",0
101,1,104,0,0.446273," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(7 \, c^{2} \cos\left(f x + e\right)^{3} + 10 \, c^{2} \cos\left(f x + e\right)^{2} + 15 \, c^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{2} + 2 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"-2/15*(7*c^2*cos(f*x + e)^3 + 10*c^2*cos(f*x + e)^2 + 15*c^2*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((a^3*f*cos(f*x + e)^2 + 2*a^3*f*cos(f*x + e) + a^3*f)*sin(f*x + e))","A",0
102,1,88,0,0.451728," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(c \cos\left(f x + e\right)^{3} - 5 \, c \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{2} + 2 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"-2/15*(c*cos(f*x + e)^3 - 5*c*cos(f*x + e)^2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((a^3*f*cos(f*x + e)^2 + 2*a^3*f*cos(f*x + e) + a^3*f)*sin(f*x + e))","A",0
103,1,74,0,0.445756," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{3}}{5 \, {\left(a^{3} f \cos\left(f x + e\right)^{2} + 2 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"-2/5*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^3/((a^3*f*cos(f*x + e)^2 + 2*a^3*f*cos(f*x + e) + a^3*f)*sin(f*x + e))","A",0
104,1,401,0,0.538422," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{-c} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(37 \, \cos\left(f x + e\right)^{3} + 40 \, \cos\left(f x + e\right)^{2} + 15 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{240 \, {\left(a^{3} c f \cos\left(f x + e\right)^{2} + 2 \, a^{3} c f \cos\left(f x + e\right) + a^{3} c f\right)} \sin\left(f x + e\right)}, \frac{15 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(37 \, \cos\left(f x + e\right)^{3} + 40 \, \cos\left(f x + e\right)^{2} + 15 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{120 \, {\left(a^{3} c f \cos\left(f x + e\right)^{2} + 2 \, a^{3} c f \cos\left(f x + e\right) + a^{3} c f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/240*(15*sqrt(2)*(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)*sqrt(-c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(37*cos(f*x + e)^3 + 40*cos(f*x + e)^2 + 15*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c*f*cos(f*x + e)^2 + 2*a^3*c*f*cos(f*x + e) + a^3*c*f)*sin(f*x + e)), 1/120*(15*sqrt(2)*(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*(37*cos(f*x + e)^3 + 40*cos(f*x + e)^2 + 15*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c*f*cos(f*x + e)^2 + 2*a^3*c*f*cos(f*x + e) + a^3*c*f)*sin(f*x + e))]","A",0
105,1,483,0,0.533215," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) - 1\right)} \sqrt{-c} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(139 \, \cos\left(f x + e\right)^{4} + 21 \, \cos\left(f x + e\right)^{3} - 175 \, \cos\left(f x + e\right)^{2} - 105 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{960 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} + a^{3} c^{2} f \cos\left(f x + e\right)^{2} - a^{3} c^{2} f \cos\left(f x + e\right) - a^{3} c^{2} f\right)} \sin\left(f x + e\right)}, \frac{105 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(139 \, \cos\left(f x + e\right)^{4} + 21 \, \cos\left(f x + e\right)^{3} - 175 \, \cos\left(f x + e\right)^{2} - 105 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{480 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} + a^{3} c^{2} f \cos\left(f x + e\right)^{2} - a^{3} c^{2} f \cos\left(f x + e\right) - a^{3} c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/960*(105*sqrt(2)*(cos(f*x + e)^3 + cos(f*x + e)^2 - cos(f*x + e) - 1)*sqrt(-c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(139*cos(f*x + e)^4 + 21*cos(f*x + e)^3 - 175*cos(f*x + e)^2 - 105*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c^2*f*cos(f*x + e)^3 + a^3*c^2*f*cos(f*x + e)^2 - a^3*c^2*f*cos(f*x + e) - a^3*c^2*f)*sin(f*x + e)), 1/480*(105*sqrt(2)*(cos(f*x + e)^3 + cos(f*x + e)^2 - cos(f*x + e) - 1)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*(139*cos(f*x + e)^4 + 21*cos(f*x + e)^3 - 175*cos(f*x + e)^2 - 105*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c^2*f*cos(f*x + e)^3 + a^3*c^2*f*cos(f*x + e)^2 - a^3*c^2*f*cos(f*x + e) - a^3*c^2*f)*sin(f*x + e))]","A",0
106,1,461,0,0.615824," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-c} \log\left(\frac{2 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-c} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right) - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 4 \, {\left(257 \, \cos\left(f x + e\right)^{5} - 354 \, \cos\left(f x + e\right)^{4} - 588 \, \cos\left(f x + e\right)^{3} + 210 \, \cos\left(f x + e\right)^{2} + 315 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{2560 \, {\left(a^{3} c^{3} f \cos\left(f x + e\right)^{4} - 2 \, a^{3} c^{3} f \cos\left(f x + e\right)^{2} + a^{3} c^{3} f\right)} \sin\left(f x + e\right)}, \frac{315 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{c} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(257 \, \cos\left(f x + e\right)^{5} - 354 \, \cos\left(f x + e\right)^{4} - 588 \, \cos\left(f x + e\right)^{3} + 210 \, \cos\left(f x + e\right)^{2} + 315 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{1280 \, {\left(a^{3} c^{3} f \cos\left(f x + e\right)^{4} - 2 \, a^{3} c^{3} f \cos\left(f x + e\right)^{2} + a^{3} c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/2560*(315*sqrt(2)*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-c)*log((2*sqrt(2)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-c)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (3*c*cos(f*x + e) + c)*sin(f*x + e))/((cos(f*x + e) - 1)*sin(f*x + e)))*sin(f*x + e) + 4*(257*cos(f*x + e)^5 - 354*cos(f*x + e)^4 - 588*cos(f*x + e)^3 + 210*cos(f*x + e)^2 + 315*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c^3*f*cos(f*x + e)^4 - 2*a^3*c^3*f*cos(f*x + e)^2 + a^3*c^3*f)*sin(f*x + e)), 1/1280*(315*sqrt(2)*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(c)*arctan(sqrt(2)*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/(sqrt(c)*sin(f*x + e)))*sin(f*x + e) - 2*(257*cos(f*x + e)^5 - 354*cos(f*x + e)^4 - 588*cos(f*x + e)^3 + 210*cos(f*x + e)^2 + 315*cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c^3*f*cos(f*x + e)^4 - 2*a^3*c^3*f*cos(f*x + e)^2 + a^3*c^3*f)*sin(f*x + e))]","A",0
107,1,93,0,0.426699," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, c^{2} \cos\left(f x + e\right)^{2} - 3 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3 \, f \cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}"," ",0,"1/3*(3*c^2*cos(f*x + e)^2 - 3*c^2*cos(f*x + e) + c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^2*sin(f*x + e))","B",0
108,1,78,0,0.422399," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, c \cos\left(f x + e\right) - c\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{2 \, f \cos\left(f x + e\right) \sin\left(f x + e\right)}"," ",0,"1/2*(2*c*cos(f*x + e) - c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)*sin(f*x + e))","B",0
109,1,56,0,0.450921," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)*(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{f \sin\left(f x + e\right)}"," ",0,"sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*sin(f*x + e))","A",0
110,0,0,0,0.554909," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c} \sec\left(f x + e\right)}{c \sec\left(f x + e\right) - c}, x\right)"," ",0,"integral(-sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)*sec(f*x + e)/(c*sec(f*x + e) - c), x)","F",0
111,1,79,0,0.462234," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))","B",0
112,1,106,0,0.437407," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{2 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/2*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))","B",0
113,1,112,0,0.472285," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(10 \, a c^{3} \cos\left(f x + e\right)^{4} - 10 \, a c^{3} \cos\left(f x + e\right)^{3} + 5 \, a c^{3} \cos\left(f x + e\right) - 2 \, a c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{10 \, f \cos\left(f x + e\right)^{4} \sin\left(f x + e\right)}"," ",0,"1/10*(10*a*c^3*cos(f*x + e)^4 - 10*a*c^3*cos(f*x + e)^3 + 5*a*c^3*cos(f*x + e) - 2*a*c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^4*sin(f*x + e))","A",0
114,1,112,0,0.449360," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(12 \, a c^{2} \cos\left(f x + e\right)^{3} - 6 \, a c^{2} \cos\left(f x + e\right)^{2} - 4 \, a c^{2} \cos\left(f x + e\right) + 3 \, a c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{12 \, f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right)}"," ",0,"1/12*(12*a*c^2*cos(f*x + e)^3 - 6*a*c^2*cos(f*x + e)^2 - 4*a*c^2*cos(f*x + e) + 3*a*c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^3*sin(f*x + e))","A",0
115,1,82,0,0.431788," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a c \cos\left(f x + e\right)^{2} - a c\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3 \, f \cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}"," ",0,"1/3*(3*a*c*cos(f*x + e)^2 - a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^2*sin(f*x + e))","A",0
116,1,76,0,0.429952," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a \cos\left(f x + e\right) + a\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{2 \, f \cos\left(f x + e\right) \sin\left(f x + e\right)}"," ",0,"1/2*(2*a*cos(f*x + e) + a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)*sin(f*x + e))","B",0
117,0,0,0,0.672491," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sec\left(f x + e\right)^{2} + a \sec\left(f x + e\right)\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c \sec\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(a*sec(f*x + e)^2 + a*sec(f*x + e))*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c*sec(f*x + e) - c), x)","F",0
118,0,0,0,0.857119," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(f x + e\right)^{2} + a \sec\left(f x + e\right)\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{2} \sec\left(f x + e\right)^{2} - 2 \, c^{2} \sec\left(f x + e\right) + c^{2}}, x\right)"," ",0,"integral((a*sec(f*x + e)^2 + a*sec(f*x + e))*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c^2*sec(f*x + e)^2 - 2*c^2*sec(f*x + e) + c^2), x)","F",0
119,1,95,0,0.442140," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{a \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2}}{{\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"a*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))","B",0
120,1,133,0,0.418869," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(6 \, a \cos\left(f x + e\right)^{3} - 3 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{6 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/6*(6*a*cos(f*x + e)^3 - 3*a*cos(f*x + e)^2 + a*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))","A",0
121,1,158,0,0.454294," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{{\left(6 \, a \cos\left(f x + e\right)^{4} - 6 \, a \cos\left(f x + e\right)^{3} + 4 \, a \cos\left(f x + e\right)^{2} - a \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{6 \, {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} + 6 \, c^{5} f \cos\left(f x + e\right)^{2} - 4 \, c^{5} f \cos\left(f x + e\right) + c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/6*(6*a*cos(f*x + e)^4 - 6*a*cos(f*x + e)^3 + 4*a*cos(f*x + e)^2 - a*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 + 6*c^5*f*cos(f*x + e)^2 - 4*c^5*f*cos(f*x + e) + c^5*f)*sin(f*x + e))","A",0
122,1,184,0,0.427526," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(11/2),x, algorithm=""fricas"")","\frac{{\left(20 \, a \cos\left(f x + e\right)^{5} - 30 \, a \cos\left(f x + e\right)^{4} + 30 \, a \cos\left(f x + e\right)^{3} - 15 \, a \cos\left(f x + e\right)^{2} + 3 \, a \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{20 \, {\left(c^{6} f \cos\left(f x + e\right)^{5} - 5 \, c^{6} f \cos\left(f x + e\right)^{4} + 10 \, c^{6} f \cos\left(f x + e\right)^{3} - 10 \, c^{6} f \cos\left(f x + e\right)^{2} + 5 \, c^{6} f \cos\left(f x + e\right) - c^{6} f\right)} \sin\left(f x + e\right)}"," ",0,"1/20*(20*a*cos(f*x + e)^5 - 30*a*cos(f*x + e)^4 + 30*a*cos(f*x + e)^3 - 15*a*cos(f*x + e)^2 + 3*a*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((c^6*f*cos(f*x + e)^5 - 5*c^6*f*cos(f*x + e)^4 + 10*c^6*f*cos(f*x + e)^3 - 10*c^6*f*cos(f*x + e)^2 + 5*c^6*f*cos(f*x + e) - c^6*f)*sin(f*x + e))","B",0
123,1,152,0,0.475805," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(30 \, a^{2} c^{3} \cos\left(f x + e\right)^{5} - 15 \, a^{2} c^{3} \cos\left(f x + e\right)^{4} - 20 \, a^{2} c^{3} \cos\left(f x + e\right)^{3} + 15 \, a^{2} c^{3} \cos\left(f x + e\right)^{2} + 6 \, a^{2} c^{3} \cos\left(f x + e\right) - 5 \, a^{2} c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{30 \, f \cos\left(f x + e\right)^{5} \sin\left(f x + e\right)}"," ",0,"1/30*(30*a^2*c^3*cos(f*x + e)^5 - 15*a^2*c^3*cos(f*x + e)^4 - 20*a^2*c^3*cos(f*x + e)^3 + 15*a^2*c^3*cos(f*x + e)^2 + 6*a^2*c^3*cos(f*x + e) - 5*a^2*c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^5*sin(f*x + e))","A",0
124,1,106,0,0.464368," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, a^{2} c^{2} \cos\left(f x + e\right)^{4} - 10 \, a^{2} c^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{15 \, f \cos\left(f x + e\right)^{4} \sin\left(f x + e\right)}"," ",0,"1/15*(15*a^2*c^2*cos(f*x + e)^4 - 10*a^2*c^2*cos(f*x + e)^2 + 3*a^2*c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^4*sin(f*x + e))","A",0
125,1,112,0,0.437037," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(12 \, a^{2} c \cos\left(f x + e\right)^{3} + 6 \, a^{2} c \cos\left(f x + e\right)^{2} - 4 \, a^{2} c \cos\left(f x + e\right) - 3 \, a^{2} c\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{12 \, f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right)}"," ",0,"1/12*(12*a^2*c*cos(f*x + e)^3 + 6*a^2*c*cos(f*x + e)^2 - 4*a^2*c*cos(f*x + e) - 3*a^2*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^3*sin(f*x + e))","A",0
126,1,93,0,0.444264," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3 \, f \cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}"," ",0,"1/3*(3*a^2*cos(f*x + e)^2 + 3*a^2*cos(f*x + e) + a^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(f*cos(f*x + e)^2*sin(f*x + e))","B",0
127,0,0,0,0.770424," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \sec\left(f x + e\right)^{3} + 2 \, a^{2} \sec\left(f x + e\right)^{2} + a^{2} \sec\left(f x + e\right)\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c \sec\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(a^2*sec(f*x + e)^3 + 2*a^2*sec(f*x + e)^2 + a^2*sec(f*x + e))*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c*sec(f*x + e) - c), x)","F",0
128,0,0,0,0.969971," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} \sec\left(f x + e\right)^{3} + 2 \, a^{2} \sec\left(f x + e\right)^{2} + a^{2} \sec\left(f x + e\right)\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{2} \sec\left(f x + e\right)^{2} - 2 \, c^{2} \sec\left(f x + e\right) + c^{2}}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^3 + 2*a^2*sec(f*x + e)^2 + a^2*sec(f*x + e))*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c^2*sec(f*x + e)^2 - 2*c^2*sec(f*x + e) + c^2), x)","F",0
129,0,0,0,1.279164," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \sec\left(f x + e\right)^{3} + 2 \, a^{2} \sec\left(f x + e\right)^{2} + a^{2} \sec\left(f x + e\right)\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{3} \sec\left(f x + e\right)^{3} - 3 \, c^{3} \sec\left(f x + e\right)^{2} + 3 \, c^{3} \sec\left(f x + e\right) - c^{3}}, x\right)"," ",0,"integral(-(a^2*sec(f*x + e)^3 + 2*a^2*sec(f*x + e)^2 + a^2*sec(f*x + e))*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c^3*sec(f*x + e)^3 - 3*c^3*sec(f*x + e)^2 + 3*c^3*sec(f*x + e) - c^3), x)","F",0
130,1,126,0,0.440745," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} \cos\left(f x + e\right)^{3} + a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{3 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/3*(3*a^2*cos(f*x + e)^3 + a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))","B",0
131,1,166,0,0.447295," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{{\left(6 \, a^{2} \cos\left(f x + e\right)^{4} - 3 \, a^{2} \cos\left(f x + e\right)^{3} + 4 \, a^{2} \cos\left(f x + e\right)^{2} - a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{6 \, {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} + 6 \, c^{5} f \cos\left(f x + e\right)^{2} - 4 \, c^{5} f \cos\left(f x + e\right) + c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/6*(6*a^2*cos(f*x + e)^4 - 3*a^2*cos(f*x + e)^3 + 4*a^2*cos(f*x + e)^2 - a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 + 6*c^5*f*cos(f*x + e)^2 - 4*c^5*f*cos(f*x + e) + c^5*f)*sin(f*x + e))","B",0
132,1,194,0,0.436246," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(11/2),x, algorithm=""fricas"")","\frac{{\left(15 \, a^{2} \cos\left(f x + e\right)^{5} - 15 \, a^{2} \cos\left(f x + e\right)^{4} + 20 \, a^{2} \cos\left(f x + e\right)^{3} - 10 \, a^{2} \cos\left(f x + e\right)^{2} + 2 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{15 \, {\left(c^{6} f \cos\left(f x + e\right)^{5} - 5 \, c^{6} f \cos\left(f x + e\right)^{4} + 10 \, c^{6} f \cos\left(f x + e\right)^{3} - 10 \, c^{6} f \cos\left(f x + e\right)^{2} + 5 \, c^{6} f \cos\left(f x + e\right) - c^{6} f\right)} \sin\left(f x + e\right)}"," ",0,"1/15*(15*a^2*cos(f*x + e)^5 - 15*a^2*cos(f*x + e)^4 + 20*a^2*cos(f*x + e)^3 - 10*a^2*cos(f*x + e)^2 + 2*a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((c^6*f*cos(f*x + e)^5 - 5*c^6*f*cos(f*x + e)^4 + 10*c^6*f*cos(f*x + e)^3 - 10*c^6*f*cos(f*x + e)^2 + 5*c^6*f*cos(f*x + e) - c^6*f)*sin(f*x + e))","A",0
133,0,0,0,0.690294," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} \sec\left(f x + e\right)^{3} - 2 \, c^{2} \sec\left(f x + e\right)^{2} + c^{2} \sec\left(f x + e\right)\right)} \sqrt{-c \sec\left(f x + e\right) + c}}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral((c^2*sec(f*x + e)^3 - 2*c^2*sec(f*x + e)^2 + c^2*sec(f*x + e))*sqrt(-c*sec(f*x + e) + c)/sqrt(a*sec(f*x + e) + a), x)","F",0
134,0,0,0,0.638860," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c \sec\left(f x + e\right)^{2} - c \sec\left(f x + e\right)\right)} \sqrt{-c \sec\left(f x + e\right) + c}}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral(-(c*sec(f*x + e)^2 - c*sec(f*x + e))*sqrt(-c*sec(f*x + e) + c)/sqrt(a*sec(f*x + e) + a), x)","F",0
135,0,0,0,0.608715," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c \sec\left(f x + e\right) + c} \sec\left(f x + e\right)}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral(sqrt(-c*sec(f*x + e) + c)*sec(f*x + e)/sqrt(a*sec(f*x + e) + a), x)","F",0
136,1,204,0,0.565314," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a c} \log\left(-\frac{4 \, {\left(2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + {\left(a c \cos\left(f x + e\right)^{2} + a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right)}{2 \, a c f}, \frac{\sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{a c \sin\left(f x + e\right)}\right)}{a c f}\right]"," ",0,"[-1/2*sqrt(-a*c)*log(-4*(2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2 + (a*c*cos(f*x + e)^2 + a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))/(a*c*f), sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*c*sin(f*x + e)))/(a*c*f)]","A",0
137,1,382,0,0.549476," ","integrate(sec(f*x+e)/(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a c} {\left(\cos\left(f x + e\right) - 1\right)} \log\left(-\frac{4 \, {\left(2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + {\left(a c \cos\left(f x + e\right)^{2} + a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{4 \, {\left(a c^{2} f \cos\left(f x + e\right) - a c^{2} f\right)} \sin\left(f x + e\right)}, \frac{\sqrt{a c} {\left(\cos\left(f x + e\right) - 1\right)} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{a c \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{2 \, {\left(a c^{2} f \cos\left(f x + e\right) - a c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/4*(sqrt(-a*c)*(cos(f*x + e) - 1)*log(-4*(2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2 + (a*c*cos(f*x + e)^2 + a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))*sin(f*x + e) - 2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e))/((a*c^2*f*cos(f*x + e) - a*c^2*f)*sin(f*x + e)), 1/2*(sqrt(a*c)*(cos(f*x + e) - 1)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*c*sin(f*x + e)))*sin(f*x + e) + sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e))/((a*c^2*f*cos(f*x + e) - a*c^2*f)*sin(f*x + e))]","B",0
138,1,456,0,0.550749," ","integrate(sec(f*x+e)/(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a c} {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(-\frac{4 \, {\left(2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + {\left(a c \cos\left(f x + e\right)^{2} + a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(3 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{8 \, {\left(a c^{3} f \cos\left(f x + e\right)^{2} - 2 \, a c^{3} f \cos\left(f x + e\right) + a c^{3} f\right)} \sin\left(f x + e\right)}, \frac{\sqrt{a c} {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{a c \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + {\left(3 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{4 \, {\left(a c^{3} f \cos\left(f x + e\right)^{2} - 2 \, a c^{3} f \cos\left(f x + e\right) + a c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/8*(sqrt(-a*c)*(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*log(-4*(2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2 + (a*c*cos(f*x + e)^2 + a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))*sin(f*x + e) - 2*(3*cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a*c^3*f*cos(f*x + e)^2 - 2*a*c^3*f*cos(f*x + e) + a*c^3*f)*sin(f*x + e)), 1/4*(sqrt(a*c)*(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*c*sin(f*x + e)))*sin(f*x + e) + (3*cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a*c^3*f*cos(f*x + e)^2 - 2*a*c^3*f*cos(f*x + e) + a*c^3*f)*sin(f*x + e))]","A",0
139,0,0,0,0.928130," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} \sec\left(f x + e\right)^{3} - 2 \, c^{2} \sec\left(f x + e\right)^{2} + c^{2} \sec\left(f x + e\right)\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((c^2*sec(f*x + e)^3 - 2*c^2*sec(f*x + e)^2 + c^2*sec(f*x + e))*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
140,0,0,0,0.781811," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c \sec\left(f x + e\right)^{2} - c \sec\left(f x + e\right)\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(-(c*sec(f*x + e)^2 - c*sec(f*x + e))*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
141,1,78,0,0.445395," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/((a^2*f*cos(f*x + e) + a^2*f)*sin(f*x + e))","B",0
142,1,380,0,0.554894," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a c} {\left(\cos\left(f x + e\right) + 1\right)} \log\left(-\frac{4 \, {\left(2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + {\left(a c \cos\left(f x + e\right)^{2} + a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{4 \, {\left(a^{2} c f \cos\left(f x + e\right) + a^{2} c f\right)} \sin\left(f x + e\right)}, \frac{\sqrt{a c} {\left(\cos\left(f x + e\right) + 1\right)} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{a c \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{2 \, {\left(a^{2} c f \cos\left(f x + e\right) + a^{2} c f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/4*(sqrt(-a*c)*(cos(f*x + e) + 1)*log(-4*(2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2 + (a*c*cos(f*x + e)^2 + a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))*sin(f*x + e) - 2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e))/((a^2*c*f*cos(f*x + e) + a^2*c*f)*sin(f*x + e)), 1/2*(sqrt(a*c)*(cos(f*x + e) + 1)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*c*sin(f*x + e)))*sin(f*x + e) + sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e))/((a^2*c*f*cos(f*x + e) + a^2*c*f)*sin(f*x + e))]","B",0
143,1,402,0,0.595454," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a c} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(-\frac{4 \, {\left(2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + {\left(a c \cos\left(f x + e\right)^{2} + a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2}}{4 \, {\left(a^{2} c^{2} f \cos\left(f x + e\right)^{2} - a^{2} c^{2} f\right)} \sin\left(f x + e\right)}, \frac{\sqrt{a c} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{a c \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2}}{2 \, {\left(a^{2} c^{2} f \cos\left(f x + e\right)^{2} - a^{2} c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/4*(sqrt(-a*c)*(cos(f*x + e)^2 - 1)*log(-4*(2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2 + (a*c*cos(f*x + e)^2 + a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))*sin(f*x + e) - 2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2)/((a^2*c^2*f*cos(f*x + e)^2 - a^2*c^2*f)*sin(f*x + e)), 1/2*(sqrt(a*c)*(cos(f*x + e)^2 - 1)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*c*sin(f*x + e)))*sin(f*x + e) + sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2)/((a^2*c^2*f*cos(f*x + e)^2 - a^2*c^2*f)*sin(f*x + e))]","A",0
144,1,544,0,0.594017," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) + 1\right)} \sqrt{-a c} \log\left(-\frac{4 \, {\left(2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + {\left(a c \cos\left(f x + e\right)^{2} + a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(5 \, \cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{16 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} - a^{2} c^{3} f \cos\left(f x + e\right)^{2} - a^{2} c^{3} f \cos\left(f x + e\right) + a^{2} c^{3} f\right)} \sin\left(f x + e\right)}, \frac{3 \, {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) + 1\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{a c \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + {\left(5 \, \cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{8 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} - a^{2} c^{3} f \cos\left(f x + e\right)^{2} - a^{2} c^{3} f \cos\left(f x + e\right) + a^{2} c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/16*(3*(cos(f*x + e)^3 - cos(f*x + e)^2 - cos(f*x + e) + 1)*sqrt(-a*c)*log(-4*(2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2 + (a*c*cos(f*x + e)^2 + a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))*sin(f*x + e) - 2*(5*cos(f*x + e)^3 - cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^2*c^3*f*cos(f*x + e)^3 - a^2*c^3*f*cos(f*x + e)^2 - a^2*c^3*f*cos(f*x + e) + a^2*c^3*f)*sin(f*x + e)), 1/8*(3*(cos(f*x + e)^3 - cos(f*x + e)^2 - cos(f*x + e) + 1)*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*c*sin(f*x + e)))*sin(f*x + e) + (5*cos(f*x + e)^3 - cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^2*c^3*f*cos(f*x + e)^3 - a^2*c^3*f*cos(f*x + e)^2 - a^2*c^3*f*cos(f*x + e) + a^2*c^3*f)*sin(f*x + e))]","A",0
145,0,0,0,1.096306," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} \sec\left(f x + e\right)^{3} - 2 \, c^{2} \sec\left(f x + e\right)^{2} + c^{2} \sec\left(f x + e\right)\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{3} \sec\left(f x + e\right)^{3} + 3 \, a^{3} \sec\left(f x + e\right)^{2} + 3 \, a^{3} \sec\left(f x + e\right) + a^{3}}, x\right)"," ",0,"integral((c^2*sec(f*x + e)^3 - 2*c^2*sec(f*x + e)^2 + c^2*sec(f*x + e))*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^3*sec(f*x + e)^3 + 3*a^3*sec(f*x + e)^2 + 3*a^3*sec(f*x + e) + a^3), x)","F",0
146,1,95,0,0.439327," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2}}{{\left(a^{3} f \cos\left(f x + e\right)^{2} + 2 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2/((a^3*f*cos(f*x + e)^2 + 2*a^3*f*cos(f*x + e) + a^3*f)*sin(f*x + e))","B",0
147,1,104,0,0.451646," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{2 \, {\left(a^{3} f \cos\left(f x + e\right)^{2} + 2 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/2*(2*cos(f*x + e)^2 + cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((a^3*f*cos(f*x + e)^2 + 2*a^3*f*cos(f*x + e) + a^3*f)*sin(f*x + e))","B",0
148,1,456,0,0.561316," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a c} {\left(\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(-\frac{4 \, {\left(2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + {\left(a c \cos\left(f x + e\right)^{2} + a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{8 \, {\left(a^{3} c f \cos\left(f x + e\right)^{2} + 2 \, a^{3} c f \cos\left(f x + e\right) + a^{3} c f\right)} \sin\left(f x + e\right)}, \frac{\sqrt{a c} {\left(\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{a c \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + {\left(3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{4 \, {\left(a^{3} c f \cos\left(f x + e\right)^{2} + 2 \, a^{3} c f \cos\left(f x + e\right) + a^{3} c f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/8*(sqrt(-a*c)*(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)*log(-4*(2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2 + (a*c*cos(f*x + e)^2 + a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))*sin(f*x + e) - 2*(3*cos(f*x + e)^2 + 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c*f*cos(f*x + e)^2 + 2*a^3*c*f*cos(f*x + e) + a^3*c*f)*sin(f*x + e)), 1/4*(sqrt(a*c)*(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*c*sin(f*x + e)))*sin(f*x + e) + (3*cos(f*x + e)^2 + 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c*f*cos(f*x + e)^2 + 2*a^3*c*f*cos(f*x + e) + a^3*c*f)*sin(f*x + e))]","A",0
149,1,536,0,0.582026," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) - 1\right)} \sqrt{-a c} \log\left(-\frac{4 \, {\left(2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + {\left(a c \cos\left(f x + e\right)^{2} + a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(5 \, \cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{16 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} + a^{3} c^{2} f \cos\left(f x + e\right)^{2} - a^{3} c^{2} f \cos\left(f x + e\right) - a^{3} c^{2} f\right)} \sin\left(f x + e\right)}, \frac{3 \, {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) - 1\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{a c \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + {\left(5 \, \cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{8 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} + a^{3} c^{2} f \cos\left(f x + e\right)^{2} - a^{3} c^{2} f \cos\left(f x + e\right) - a^{3} c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/16*(3*(cos(f*x + e)^3 + cos(f*x + e)^2 - cos(f*x + e) - 1)*sqrt(-a*c)*log(-4*(2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2 + (a*c*cos(f*x + e)^2 + a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))*sin(f*x + e) - 2*(5*cos(f*x + e)^3 + cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c^2*f*cos(f*x + e)^3 + a^3*c^2*f*cos(f*x + e)^2 - a^3*c^2*f*cos(f*x + e) - a^3*c^2*f)*sin(f*x + e)), 1/8*(3*(cos(f*x + e)^3 + cos(f*x + e)^2 - cos(f*x + e) - 1)*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*c*sin(f*x + e)))*sin(f*x + e) + (5*cos(f*x + e)^3 + cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c^2*f*cos(f*x + e)^3 + a^3*c^2*f*cos(f*x + e)^2 - a^3*c^2*f*cos(f*x + e) - a^3*c^2*f)*sin(f*x + e))]","A",0
150,1,482,0,0.574929," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-a c} \log\left(-\frac{4 \, {\left(2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + {\left(a c \cos\left(f x + e\right)^{2} + a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 2 \, {\left(5 \, \cos\left(f x + e\right)^{4} - 3 \, \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{16 \, {\left(a^{3} c^{3} f \cos\left(f x + e\right)^{4} - 2 \, a^{3} c^{3} f \cos\left(f x + e\right)^{2} + a^{3} c^{3} f\right)} \sin\left(f x + e\right)}, \frac{3 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{a c \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + {\left(5 \, \cos\left(f x + e\right)^{4} - 3 \, \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{8 \, {\left(a^{3} c^{3} f \cos\left(f x + e\right)^{4} - 2 \, a^{3} c^{3} f \cos\left(f x + e\right)^{2} + a^{3} c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/16*(3*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-a*c)*log(-4*(2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)^2 + (a*c*cos(f*x + e)^2 + a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))*sin(f*x + e) - 2*(5*cos(f*x + e)^4 - 3*cos(f*x + e)^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c^3*f*cos(f*x + e)^4 - 2*a^3*c^3*f*cos(f*x + e)^2 + a^3*c^3*f)*sin(f*x + e)), 1/8*(3*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/(a*c*sin(f*x + e)))*sin(f*x + e) + (5*cos(f*x + e)^4 - 3*cos(f*x + e)^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c^3*f*cos(f*x + e)^4 - 2*a^3*c^3*f*cos(f*x + e)^2 + a^3*c^3*f)*sin(f*x + e))]","A",0
151,0,0,0,0.452124," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} {\left(-c \sec\left(f x + e\right) + c\right)}^{n} \sec\left(f x + e\right), x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*(-c*sec(f*x + e) + c)^n*sec(f*x + e), x)","F",0
152,0,0,0,0.415234," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} \sec\left(f x + e\right)^{3} - 2 \, c^{2} \sec\left(f x + e\right)^{2} + c^{2} \sec\left(f x + e\right)\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((c^2*sec(f*x + e)^3 - 2*c^2*sec(f*x + e)^2 + c^2*sec(f*x + e))*(a*sec(f*x + e) + a)^m, x)","F",0
153,0,0,0,0.444515," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c \sec\left(f x + e\right)^{2} - c \sec\left(f x + e\right)\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(c*sec(f*x + e)^2 - c*sec(f*x + e))*(a*sec(f*x + e) + a)^m, x)","F",0
154,0,0,0,0.460161," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)}{c \sec\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(a*sec(f*x + e) + a)^m*sec(f*x + e)/(c*sec(f*x + e) - c), x)","F",0
155,0,0,0,0.452168," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)}{c^{2} \sec\left(f x + e\right)^{2} - 2 \, c^{2} \sec\left(f x + e\right) + c^{2}}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*sec(f*x + e)/(c^2*sec(f*x + e)^2 - 2*c^2*sec(f*x + e) + c^2), x)","F",0
156,1,191,0,0.447769," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, c^{2} m^{2} + {\left(4 \, c^{2} m^{2} + 24 \, c^{2} m + 43 \, c^{2}\right)} \cos\left(f x + e\right)^{3} + 8 \, c^{2} m - {\left(4 \, c^{2} m^{2} + 8 \, c^{2} m - 29 \, c^{2}\right)} \cos\left(f x + e\right)^{2} + 3 \, c^{2} - {\left(4 \, c^{2} m^{2} + 24 \, c^{2} m + 11 \, c^{2}\right)} \cos\left(f x + e\right)\right)} \left(\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}\right)^{m} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{{\left(8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + 15 \, f\right)} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}"," ",0,"2*(4*c^2*m^2 + (4*c^2*m^2 + 24*c^2*m + 43*c^2)*cos(f*x + e)^3 + 8*c^2*m - (4*c^2*m^2 + 8*c^2*m - 29*c^2)*cos(f*x + e)^2 + 3*c^2 - (4*c^2*m^2 + 24*c^2*m + 11*c^2)*cos(f*x + e))*((a*cos(f*x + e) + a)/cos(f*x + e))^m*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((8*f*m^3 + 36*f*m^2 + 46*f*m + 15*f)*cos(f*x + e)^2*sin(f*x + e))","A",0
157,1,112,0,0.436689," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(2 \, c m + 5 \, c\right)} \cos\left(f x + e\right)^{2} - 2 \, c m + 4 \, c \cos\left(f x + e\right) - c\right)} \left(\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}\right)^{m} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{{\left(4 \, f m^{2} + 8 \, f m + 3 \, f\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)}"," ",0,"2*((2*c*m + 5*c)*cos(f*x + e)^2 - 2*c*m + 4*c*cos(f*x + e) - c)*((a*cos(f*x + e) + a)/cos(f*x + e))^m*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((4*f*m^2 + 8*f*m + 3*f)*cos(f*x + e)*sin(f*x + e))","A",0
158,1,70,0,0.473241," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \left(\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}\right)^{m} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + 1\right)}}{{\left(2 \, f m + f\right)} \sin\left(f x + e\right)}"," ",0,"2*((a*cos(f*x + e) + a)/cos(f*x + e))^m*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*(cos(f*x + e) + 1)/((2*f*m + f)*sin(f*x + e))","A",0
159,0,0,0,0.476037," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c \sec\left(f x + e\right) + c} {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)}{c \sec\left(f x + e\right) - c}, x\right)"," ",0,"integral(-sqrt(-c*sec(f*x + e) + c)*(a*sec(f*x + e) + a)^m*sec(f*x + e)/(c*sec(f*x + e) - c), x)","F",0
160,0,0,0,0.454581," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c \sec\left(f x + e\right) + c} {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)}{c^{2} \sec\left(f x + e\right)^{2} - 2 \, c^{2} \sec\left(f x + e\right) + c^{2}}, x\right)"," ",0,"integral(sqrt(-c*sec(f*x + e) + c)*(a*sec(f*x + e) + a)^m*sec(f*x + e)/(c^2*sec(f*x + e)^2 - 2*c^2*sec(f*x + e) + c^2), x)","F",0
161,0,0,0,0.502922," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c \sec\left(f x + e\right) + c} {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)}{c^{3} \sec\left(f x + e\right)^{3} - 3 \, c^{3} \sec\left(f x + e\right)^{2} + 3 \, c^{3} \sec\left(f x + e\right) - c^{3}}, x\right)"," ",0,"integral(-sqrt(-c*sec(f*x + e) + c)*(a*sec(f*x + e) + a)^m*sec(f*x + e)/(c^3*sec(f*x + e)^3 - 3*c^3*sec(f*x + e)^2 + 3*c^3*sec(f*x + e) - c^3), x)","F",0
162,1,120,0,0.526061," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-3-m),x, algorithm=""fricas"")","-\frac{{\left({\left(4 \, m^{2} + 12 \, m + 7\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(2 \, m + 3\right)} \cos\left(f x + e\right) + 2\right)} \left(\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}\right)^{m} \left(\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}\right)^{-m - 3} \sin\left(f x + e\right)}{{\left(8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + 15 \, f\right)} \cos\left(f x + e\right)^{3}}"," ",0,"-((4*m^2 + 12*m + 7)*cos(f*x + e)^2 - 2*(2*m + 3)*cos(f*x + e) + 2)*((a*cos(f*x + e) + a)/cos(f*x + e))^m*((c*cos(f*x + e) - c)/cos(f*x + e))^(-m - 3)*sin(f*x + e)/((8*f*m^3 + 36*f*m^2 + 46*f*m + 15*f)*cos(f*x + e)^3)","A",0
163,1,93,0,0.457141," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-2-m),x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(m + 1\right)} \cos\left(f x + e\right) - 1\right)} \left(\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}\right)^{m} \left(\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}\right)^{-m - 2} \sin\left(f x + e\right)}{{\left(4 \, f m^{2} + 8 \, f m + 3 \, f\right)} \cos\left(f x + e\right)^{2}}"," ",0,"-(2*(m + 1)*cos(f*x + e) - 1)*((a*cos(f*x + e) + a)/cos(f*x + e))^m*((c*cos(f*x + e) - c)/cos(f*x + e))^(-m - 2)*sin(f*x + e)/((4*f*m^2 + 8*f*m + 3*f)*cos(f*x + e)^2)","A",0
164,1,72,0,0.486789," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-1-m),x, algorithm=""fricas"")","-\frac{\left(\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}\right)^{m} \left(\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}\right)^{-m - 1} \sin\left(f x + e\right)}{{\left(2 \, f m + f\right)} \cos\left(f x + e\right)}"," ",0,"-((a*cos(f*x + e) + a)/cos(f*x + e))^m*((c*cos(f*x + e) - c)/cos(f*x + e))^(-m - 1)*sin(f*x + e)/((2*f*m + f)*cos(f*x + e))","A",0
165,0,0,0,0.438604," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/((c-c*sec(f*x+e))^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)}{{\left(-c \sec\left(f x + e\right) + c\right)}^{m}}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*sec(f*x + e)/(-c*sec(f*x + e) + c)^m, x)","F",0
166,0,0,0,0.465503," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(1-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} {\left(-c \sec\left(f x + e\right) + c\right)}^{-m + 1} \sec\left(f x + e\right), x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*(-c*sec(f*x + e) + c)^(-m + 1)*sec(f*x + e), x)","F",0
167,0,0,0,0.448021," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(2-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} {\left(-c \sec\left(f x + e\right) + c\right)}^{-m + 2} \sec\left(f x + e\right), x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*(-c*sec(f*x + e) + c)^(-m + 2)*sec(f*x + e), x)","F",0
168,1,131,0,0.430508," ","integrate(sec(f*x+e)^2*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{15 \, a^{3} c \cos\left(f x + e\right)^{5} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, a^{3} c \cos\left(f x + e\right)^{5} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(28 \, a^{3} c \cos\left(f x + e\right)^{4} + 15 \, a^{3} c \cos\left(f x + e\right)^{3} - 16 \, a^{3} c \cos\left(f x + e\right)^{2} - 30 \, a^{3} c \cos\left(f x + e\right) - 12 \, a^{3} c\right)} \sin\left(f x + e\right)}{120 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/120*(15*a^3*c*cos(f*x + e)^5*log(sin(f*x + e) + 1) - 15*a^3*c*cos(f*x + e)^5*log(-sin(f*x + e) + 1) + 2*(28*a^3*c*cos(f*x + e)^4 + 15*a^3*c*cos(f*x + e)^3 - 16*a^3*c*cos(f*x + e)^2 - 30*a^3*c*cos(f*x + e) - 12*a^3*c)*sin(f*x + e))/(f*cos(f*x + e)^5)","A",0
169,1,117,0,0.463908," ","integrate(sec(f*x+e)^2*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, a^{2} c \cos\left(f x + e\right)^{4} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, a^{2} c \cos\left(f x + e\right)^{4} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(8 \, a^{2} c \cos\left(f x + e\right)^{3} + 3 \, a^{2} c \cos\left(f x + e\right)^{2} - 8 \, a^{2} c \cos\left(f x + e\right) - 6 \, a^{2} c\right)} \sin\left(f x + e\right)}{48 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/48*(3*a^2*c*cos(f*x + e)^4*log(sin(f*x + e) + 1) - 3*a^2*c*cos(f*x + e)^4*log(-sin(f*x + e) + 1) + 2*(8*a^2*c*cos(f*x + e)^3 + 3*a^2*c*cos(f*x + e)^2 - 8*a^2*c*cos(f*x + e) - 6*a^2*c)*sin(f*x + e))/(f*cos(f*x + e)^4)","A",0
170,1,35,0,0.425864," ","integrate(sec(f*x+e)^2*(a+a*sec(f*x+e))*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a c \cos\left(f x + e\right)^{2} - a c\right)} \sin\left(f x + e\right)}{3 \, f \cos\left(f x + e\right)^{3}}"," ",0,"1/3*(a*c*cos(f*x + e)^2 - a*c)*sin(f*x + e)/(f*cos(f*x + e)^3)","B",0
171,1,105,0,0.438252," ","integrate(sec(f*x+e)^2*(c-c*sec(f*x+e))/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(c \cos\left(f x + e\right)^{2} + c \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(c \cos\left(f x + e\right)^{2} + c \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - {\left(3 \, c \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}{a f \cos\left(f x + e\right)^{2} + a f \cos\left(f x + e\right)}"," ",0,"((c*cos(f*x + e)^2 + c*cos(f*x + e))*log(sin(f*x + e) + 1) - (c*cos(f*x + e)^2 + c*cos(f*x + e))*log(-sin(f*x + e) + 1) - (3*c*cos(f*x + e) + c)*sin(f*x + e))/(a*f*cos(f*x + e)^2 + a*f*cos(f*x + e))","A",0
172,1,123,0,0.466139," ","integrate(sec(f*x+e)^2*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(c \cos\left(f x + e\right)^{2} + 2 \, c \cos\left(f x + e\right) + c\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(c \cos\left(f x + e\right)^{2} + 2 \, c \cos\left(f x + e\right) + c\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(5 \, c \cos\left(f x + e\right) + 7 \, c\right)} \sin\left(f x + e\right)}{6 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}"," ",0,"-1/6*(3*(c*cos(f*x + e)^2 + 2*c*cos(f*x + e) + c)*log(sin(f*x + e) + 1) - 3*(c*cos(f*x + e)^2 + 2*c*cos(f*x + e) + c)*log(-sin(f*x + e) + 1) - 2*(5*c*cos(f*x + e) + 7*c)*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)","A",0
173,1,78,0,0.404080," ","integrate(sec(f*x+e)^2*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(c \cos\left(f x + e\right)^{2} + 3 \, c \cos\left(f x + e\right) - 4 \, c\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"1/15*(c*cos(f*x + e)^2 + 3*c*cos(f*x + e) - 4*c)*sin(f*x + e)/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","A",0
174,0,0,0,0.437827," ","integrate((g*sec(f*x+e))^p*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c \sec\left(f x + e\right)^{3} + a^{2} c \sec\left(f x + e\right)^{2} - a^{2} c \sec\left(f x + e\right) - a^{2} c\right)} \left(g \sec\left(f x + e\right)\right)^{p}, x\right)"," ",0,"integral(-(a^2*c*sec(f*x + e)^3 + a^2*c*sec(f*x + e)^2 - a^2*c*sec(f*x + e) - a^2*c)*(g*sec(f*x + e))^p, x)","F",0
175,0,0,0,0.444221," ","integrate((g*sec(f*x+e))^p*(a+a*sec(f*x+e))*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c \sec\left(f x + e\right)^{2} - a c\right)} \left(g \sec\left(f x + e\right)\right)^{p}, x\right)"," ",0,"integral(-(a*c*sec(f*x + e)^2 - a*c)*(g*sec(f*x + e))^p, x)","F",0
176,0,0,0,0.485677," ","integrate((g*sec(f*x+e))^p*(c-c*sec(f*x+e))/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c \sec\left(f x + e\right) - c\right)} \left(g \sec\left(f x + e\right)\right)^{p}}{a \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral(-(c*sec(f*x + e) - c)*(g*sec(f*x + e))^p/(a*sec(f*x + e) + a), x)","F",0
177,0,0,0,0.462231," ","integrate((g*sec(f*x+e))^p*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c \sec\left(f x + e\right) - c\right)} \left(g \sec\left(f x + e\right)\right)^{p}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(-(c*sec(f*x + e) - c)*(g*sec(f*x + e))^p/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
178,1,340,0,0.583091," ","integrate((g*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{a g} g \log\left(\frac{a g \cos\left(f x + e\right)^{3} - 7 \, a g \cos\left(f x + e\right)^{2} + 4 \, \sqrt{a g} {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 8 \, a g}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right) \sin\left(f x + e\right) + 4 \, g \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{2 \, c f \sin\left(f x + e\right)}, -\frac{\sqrt{-a g} g \arctan\left(\frac{2 \, \sqrt{-a g} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a g \cos\left(f x + e\right)^{2} - a g \cos\left(f x + e\right) - 2 \, a g}\right) \sin\left(f x + e\right) - 2 \, g \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{c f \sin\left(f x + e\right)}\right]"," ",0,"[1/2*(sqrt(a*g)*g*log((a*g*cos(f*x + e)^3 - 7*a*g*cos(f*x + e)^2 + 4*sqrt(a*g)*(cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) + 8*a*g)/(cos(f*x + e)^3 + cos(f*x + e)^2))*sin(f*x + e) + 4*g*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e))/(c*f*sin(f*x + e)), -(sqrt(-a*g)*g*arctan(2*sqrt(-a*g)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*g*cos(f*x + e)^2 - a*g*cos(f*x + e) - 2*a*g))*sin(f*x + e) - 2*g*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e))/(c*f*sin(f*x + e))]","A",0
179,1,260,0,0.518852," ","integrate(sec(f*x+e)^2/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{4 \, a c f \sin\left(f x + e\right)}, \frac{\sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 2 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{2 \, a c f \sin\left(f x + e\right)}\right]"," ",0,"[1/4*(sqrt(2)*a*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 4*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e))/(a*c*f*sin(f*x + e)), 1/2*(sqrt(2)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))*sin(f*x + e) + 2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e))/(a*c*f*sin(f*x + e))]","A",0
180,1,462,0,0.506607," ","integrate(sec(f*x+e)^(5/2)/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{\cos\left(f x + e\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\cos\left(f x + e\right)} \sin\left(f x + e\right)}{\sqrt{a}} - 2 \, \cos\left(f x + e\right) - 3}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 2 \, \sqrt{a} \log\left(\frac{a \cos\left(f x + e\right)^{3} - 7 \, a \cos\left(f x + e\right)^{2} + \frac{4 \, {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{\sqrt{\cos\left(f x + e\right)}} + 8 \, a}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right) \sin\left(f x + e\right) + 4 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\cos\left(f x + e\right)}}{4 \, a c f \sin\left(f x + e\right)}, -\frac{\sqrt{2} a \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(f x + e\right)}}{\sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 2 \, \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\cos\left(f x + e\right)} \sin\left(f x + e\right)}{a \cos\left(f x + e\right)^{2} - a \cos\left(f x + e\right) - 2 \, a}\right) \sin\left(f x + e\right) - 2 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\cos\left(f x + e\right)}}{2 \, a c f \sin\left(f x + e\right)}\right]"," ",0,"[1/4*(sqrt(2)*sqrt(a)*log(-(cos(f*x + e)^2 - 2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(cos(f*x + e))*sin(f*x + e)/sqrt(a) - 2*cos(f*x + e) - 3)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 2*sqrt(a)*log((a*cos(f*x + e)^3 - 7*a*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e)/sqrt(cos(f*x + e)) + 8*a)/(cos(f*x + e)^3 + cos(f*x + e)^2))*sin(f*x + e) + 4*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(cos(f*x + e)))/(a*c*f*sin(f*x + e)), -1/2*(sqrt(2)*a*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*sqrt(cos(f*x + e))/sin(f*x + e))*sin(f*x + e) + 2*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(cos(f*x + e))*sin(f*x + e)/(a*cos(f*x + e)^2 - a*cos(f*x + e) - 2*a))*sin(f*x + e) - 2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(cos(f*x + e)))/(a*c*f*sin(f*x + e))]","A",0
181,1,330,0,0.447211," ","integrate((g*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a g \sqrt{\frac{g}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + g \cos\left(f x + e\right)^{2} - 2 \, g \cos\left(f x + e\right) - 3 \, g}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, g \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{4 \, a c f \sin\left(f x + e\right)}, \frac{\sqrt{2} a g \sqrt{-\frac{g}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{g \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 2 \, g \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{2 \, a c f \sin\left(f x + e\right)}\right]"," ",0,"[1/4*(sqrt(2)*a*g*sqrt(g/a)*log(-(2*sqrt(2)*sqrt(g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + g*cos(f*x + e)^2 - 2*g*cos(f*x + e) - 3*g)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 4*g*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e))/(a*c*f*sin(f*x + e)), 1/2*(sqrt(2)*a*g*sqrt(-g/a)*arctan(sqrt(2)*sqrt(-g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)/(g*sin(f*x + e)))*sin(f*x + e) + 2*g*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e))/(a*c*f*sin(f*x + e))]","A",0
182,1,569,0,0.600795," ","integrate((g*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a g^{2} \sqrt{\frac{g}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - g \cos\left(f x + e\right)^{2} + 2 \, g \cos\left(f x + e\right) + 3 \, g}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 2 \, a g^{2} \sqrt{\frac{g}{a}} \log\left(\frac{g \cos\left(f x + e\right)^{3} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, g \cos\left(f x + e\right)^{2} + 8 \, g}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right) \sin\left(f x + e\right) + 4 \, g^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{4 \, a c f \sin\left(f x + e\right)}, -\frac{\sqrt{2} a g^{2} \sqrt{-\frac{g}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{g \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 2 \, a g^{2} \sqrt{-\frac{g}{a}} \arctan\left(\frac{2 \, \sqrt{-\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{g \cos\left(f x + e\right)^{2} - g \cos\left(f x + e\right) - 2 \, g}\right) \sin\left(f x + e\right) - 2 \, g^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{2 \, a c f \sin\left(f x + e\right)}\right]"," ",0,"[1/4*(sqrt(2)*a*g^2*sqrt(g/a)*log((2*sqrt(2)*sqrt(g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - g*cos(f*x + e)^2 + 2*g*cos(f*x + e) + 3*g)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 2*a*g^2*sqrt(g/a)*log((g*cos(f*x + e)^3 + 4*(cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt(g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) - 7*g*cos(f*x + e)^2 + 8*g)/(cos(f*x + e)^3 + cos(f*x + e)^2))*sin(f*x + e) + 4*g^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e))/(a*c*f*sin(f*x + e)), -1/2*(sqrt(2)*a*g^2*sqrt(-g/a)*arctan(sqrt(2)*sqrt(-g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)/(g*sin(f*x + e)))*sin(f*x + e) + 2*a*g^2*sqrt(-g/a)*arctan(2*sqrt(-g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(g*cos(f*x + e)^2 - g*cos(f*x + e) - 2*g))*sin(f*x + e) - 2*g^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e))/(a*c*f*sin(f*x + e))]","A",0
183,1,255,0,0.551130," ","integrate(sec(f*x+e)^2/(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a c} \log\left(-\frac{8 \, {\left({\left(2 \, \cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} + {\left(2 \, a c \cos\left(f x + e\right)^{4} - 2 \, a c \cos\left(f x + e\right)^{2} + a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{4} - \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)}\right)}{2 \, a c f}, \frac{\sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(2 \, a c \cos\left(f x + e\right)^{2} - a c\right)} \sin\left(f x + e\right)}\right)}{a c f}\right]"," ",0,"[-1/2*sqrt(-a*c)*log(-8*((2*cos(f*x + e)^3 - cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) + (2*a*c*cos(f*x + e)^4 - 2*a*c*cos(f*x + e)^2 + a*c)*sin(f*x + e))/((cos(f*x + e)^4 - cos(f*x + e)^2)*sin(f*x + e)))/(a*c*f), sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)/((2*a*c*cos(f*x + e)^2 - a*c)*sin(f*x + e)))/(a*c*f)]","B",0
184,1,357,0,0.693811," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c-d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{a}{c d - d^{2}}} \log\left(-\frac{{\left(a c^{2} - 8 \, a c d + 8 \, a d^{2}\right)} \cos\left(f x + e\right)^{3} + a d^{2} + {\left(a c^{2} - 2 \, a c d\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(c^{2} d - 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c d^{2} - d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d - d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + {\left(6 \, a c d - 7 \, a d^{2}\right)} \cos\left(f x + e\right)}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} - 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} - {\left(2 \, c d - d^{2}\right)} \cos\left(f x + e\right)}\right)}{2 \, f}, -\frac{\sqrt{-\frac{a}{c d - d^{2}}} \arctan\left(\frac{2 \, {\left(c d - d^{2}\right)} \sqrt{-\frac{a}{c d - d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(a c - 2 \, a d\right)} \cos\left(f x + e\right)^{2} + a d + {\left(a c - a d\right)} \cos\left(f x + e\right)}\right)}{f}\right]"," ",0,"[1/2*sqrt(a/(c*d - d^2))*log(-((a*c^2 - 8*a*c*d + 8*a*d^2)*cos(f*x + e)^3 + a*d^2 + (a*c^2 - 2*a*c*d)*cos(f*x + e)^2 + 4*((c^2*d - 3*c*d^2 + 2*d^3)*cos(f*x + e)^2 + (c*d^2 - d^3)*cos(f*x + e))*sqrt(a/(c*d - d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) + (6*a*c*d - 7*a*d^2)*cos(f*x + e))/(c^2*cos(f*x + e)^3 + (c^2 - 2*c*d)*cos(f*x + e)^2 + d^2 - (2*c*d - d^2)*cos(f*x + e)))/f, -sqrt(-a/(c*d - d^2))*arctan(2*(c*d - d^2)*sqrt(-a/(c*d - d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((a*c - 2*a*d)*cos(f*x + e)^2 + a*d + (a*c - a*d)*cos(f*x + e)))/f]","B",0
185,1,281,0,0.442122," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, a c^{4} + 16 \, a c^{3} d + 24 \, a c^{2} d^{2} + 12 \, a c d^{3} + 3 \, a d^{4}\right)} \cos\left(f x + e\right)^{5} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(8 \, a c^{4} + 16 \, a c^{3} d + 24 \, a c^{2} d^{2} + 12 \, a c d^{3} + 3 \, a d^{4}\right)} \cos\left(f x + e\right)^{5} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(24 \, a d^{4} + 8 \, {\left(15 \, a c^{4} + 60 \, a c^{3} d + 60 \, a c^{2} d^{2} + 40 \, a c d^{3} + 8 \, a d^{4}\right)} \cos\left(f x + e\right)^{4} + 15 \, {\left(16 \, a c^{3} d + 24 \, a c^{2} d^{2} + 12 \, a c d^{3} + 3 \, a d^{4}\right)} \cos\left(f x + e\right)^{3} + 16 \, {\left(15 \, a c^{2} d^{2} + 10 \, a c d^{3} + 2 \, a d^{4}\right)} \cos\left(f x + e\right)^{2} + 30 \, {\left(4 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{240 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/240*(15*(8*a*c^4 + 16*a*c^3*d + 24*a*c^2*d^2 + 12*a*c*d^3 + 3*a*d^4)*cos(f*x + e)^5*log(sin(f*x + e) + 1) - 15*(8*a*c^4 + 16*a*c^3*d + 24*a*c^2*d^2 + 12*a*c*d^3 + 3*a*d^4)*cos(f*x + e)^5*log(-sin(f*x + e) + 1) + 2*(24*a*d^4 + 8*(15*a*c^4 + 60*a*c^3*d + 60*a*c^2*d^2 + 40*a*c*d^3 + 8*a*d^4)*cos(f*x + e)^4 + 15*(16*a*c^3*d + 24*a*c^2*d^2 + 12*a*c*d^3 + 3*a*d^4)*cos(f*x + e)^3 + 16*(15*a*c^2*d^2 + 10*a*c*d^3 + 2*a*d^4)*cos(f*x + e)^2 + 30*(4*a*c*d^3 + a*d^4)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^5)","A",0
186,1,211,0,0.474693," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, a c^{3} + 12 \, a c^{2} d + 12 \, a c d^{2} + 3 \, a d^{3}\right)} \cos\left(f x + e\right)^{4} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(8 \, a c^{3} + 12 \, a c^{2} d + 12 \, a c d^{2} + 3 \, a d^{3}\right)} \cos\left(f x + e\right)^{4} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(6 \, a d^{3} + 8 \, {\left(3 \, a c^{3} + 9 \, a c^{2} d + 6 \, a c d^{2} + 2 \, a d^{3}\right)} \cos\left(f x + e\right)^{3} + 9 \, {\left(4 \, a c^{2} d + 4 \, a c d^{2} + a d^{3}\right)} \cos\left(f x + e\right)^{2} + 8 \, {\left(3 \, a c d^{2} + a d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{48 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/48*(3*(8*a*c^3 + 12*a*c^2*d + 12*a*c*d^2 + 3*a*d^3)*cos(f*x + e)^4*log(sin(f*x + e) + 1) - 3*(8*a*c^3 + 12*a*c^2*d + 12*a*c*d^2 + 3*a*d^3)*cos(f*x + e)^4*log(-sin(f*x + e) + 1) + 2*(6*a*d^3 + 8*(3*a*c^3 + 9*a*c^2*d + 6*a*c*d^2 + 2*a*d^3)*cos(f*x + e)^3 + 9*(4*a*c^2*d + 4*a*c*d^2 + a*d^3)*cos(f*x + e)^2 + 8*(3*a*c*d^2 + a*d^3)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4)","A",0
187,1,150,0,0.480488," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, a c^{2} + 2 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)^{3} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(2 \, a c^{2} + 2 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)^{3} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, a d^{2} + 2 \, {\left(3 \, a c^{2} + 6 \, a c d + 2 \, a d^{2}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, f \cos\left(f x + e\right)^{3}}"," ",0,"1/12*(3*(2*a*c^2 + 2*a*c*d + a*d^2)*cos(f*x + e)^3*log(sin(f*x + e) + 1) - 3*(2*a*c^2 + 2*a*c*d + a*d^2)*cos(f*x + e)^3*log(-sin(f*x + e) + 1) + 2*(2*a*d^2 + 2*(3*a*c^2 + 6*a*c*d + 2*a*d^2)*cos(f*x + e)^2 + 3*(2*a*c*d + a*d^2)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3)","A",0
188,1,96,0,0.459763," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 \, a c + a d\right)} \cos\left(f x + e\right)^{2} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(2 \, a c + a d\right)} \cos\left(f x + e\right)^{2} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(a d + 2 \, {\left(a c + a d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, f \cos\left(f x + e\right)^{2}}"," ",0,"1/4*((2*a*c + a*d)*cos(f*x + e)^2*log(sin(f*x + e) + 1) - (2*a*c + a*d)*cos(f*x + e)^2*log(-sin(f*x + e) + 1) + 2*(a*d + 2*(a*c + a*d)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^2)","A",0
189,1,255,0,0.534254," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{a \sqrt{\frac{c - d}{c + d}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{2} + c d + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + a \log\left(\sin\left(f x + e\right) + 1\right) - a \log\left(-\sin\left(f x + e\right) + 1\right)}{2 \, d f}, -\frac{2 \, a \sqrt{-\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(d \cos\left(f x + e\right) + c\right)} \sqrt{-\frac{c - d}{c + d}}}{{\left(c - d\right)} \sin\left(f x + e\right)}\right) - a \log\left(\sin\left(f x + e\right) + 1\right) + a \log\left(-\sin\left(f x + e\right) + 1\right)}{2 \, d f}\right]"," ",0,"[1/2*(a*sqrt((c - d)/(c + d))*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*(c^2 + c*d + (c*d + d^2)*cos(f*x + e))*sqrt((c - d)/(c + d))*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + a*log(sin(f*x + e) + 1) - a*log(-sin(f*x + e) + 1))/(d*f), -1/2*(2*a*sqrt(-(c - d)/(c + d))*arctan(-(d*cos(f*x + e) + c)*sqrt(-(c - d)/(c + d))/((c - d)*sin(f*x + e))) - a*log(sin(f*x + e) + 1) + a*log(-sin(f*x + e) + 1))/(d*f)]","A",0
190,1,357,0,0.468709," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a c \cos\left(f x + e\right) + a d\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(a c^{2} - a d^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{4} + c^{3} d - c^{2} d^{2} - c d^{3}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d + c^{2} d^{2} - c d^{3} - d^{4}\right)} f\right)}}, \frac{{\left(a c \cos\left(f x + e\right) + a d\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(a c^{2} - a d^{2}\right)} \sin\left(f x + e\right)}{{\left(c^{4} + c^{3} d - c^{2} d^{2} - c d^{3}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d + c^{2} d^{2} - c d^{3} - d^{4}\right)} f}\right]"," ",0,"[1/2*((a*c*cos(f*x + e) + a*d)*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(a*c^2 - a*d^2)*sin(f*x + e))/((c^4 + c^3*d - c^2*d^2 - c*d^3)*f*cos(f*x + e) + (c^3*d + c^2*d^2 - c*d^3 - d^4)*f), ((a*c*cos(f*x + e) + a*d)*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (a*c^2 - a*d^2)*sin(f*x + e))/((c^4 + c^3*d - c^2*d^2 - c*d^3)*f*cos(f*x + e) + (c^3*d + c^2*d^2 - c*d^3 - d^4)*f)]","B",0
191,1,736,0,0.516633," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a c d^{2} - a d^{3} + {\left(2 \, a c^{3} - a c^{2} d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, a c^{2} d - a c d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(a c^{3} d - 2 \, a c^{2} d^{2} - a c d^{3} + 2 \, a d^{4} + {\left(2 \, a c^{4} - 2 \, a c^{3} d - 3 \, a c^{2} d^{2} + 2 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{7} + c^{6} d - 2 \, c^{5} d^{2} - 2 \, c^{4} d^{3} + c^{3} d^{4} + c^{2} d^{5}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{6} d + c^{5} d^{2} - 2 \, c^{4} d^{3} - 2 \, c^{3} d^{4} + c^{2} d^{5} + c d^{6}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{2} + c^{4} d^{3} - 2 \, c^{3} d^{4} - 2 \, c^{2} d^{5} + c d^{6} + d^{7}\right)} f\right)}}, \frac{{\left(2 \, a c d^{2} - a d^{3} + {\left(2 \, a c^{3} - a c^{2} d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, a c^{2} d - a c d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(a c^{3} d - 2 \, a c^{2} d^{2} - a c d^{3} + 2 \, a d^{4} + {\left(2 \, a c^{4} - 2 \, a c^{3} d - 3 \, a c^{2} d^{2} + 2 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{7} + c^{6} d - 2 \, c^{5} d^{2} - 2 \, c^{4} d^{3} + c^{3} d^{4} + c^{2} d^{5}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{6} d + c^{5} d^{2} - 2 \, c^{4} d^{3} - 2 \, c^{3} d^{4} + c^{2} d^{5} + c d^{6}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{2} + c^{4} d^{3} - 2 \, c^{3} d^{4} - 2 \, c^{2} d^{5} + c d^{6} + d^{7}\right)} f\right)}}\right]"," ",0,"[1/4*((2*a*c*d^2 - a*d^3 + (2*a*c^3 - a*c^2*d)*cos(f*x + e)^2 + 2*(2*a*c^2*d - a*c*d^2)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(a*c^3*d - 2*a*c^2*d^2 - a*c*d^3 + 2*a*d^4 + (2*a*c^4 - 2*a*c^3*d - 3*a*c^2*d^2 + 2*a*c*d^3 + a*d^4)*cos(f*x + e))*sin(f*x + e))/((c^7 + c^6*d - 2*c^5*d^2 - 2*c^4*d^3 + c^3*d^4 + c^2*d^5)*f*cos(f*x + e)^2 + 2*(c^6*d + c^5*d^2 - 2*c^4*d^3 - 2*c^3*d^4 + c^2*d^5 + c*d^6)*f*cos(f*x + e) + (c^5*d^2 + c^4*d^3 - 2*c^3*d^4 - 2*c^2*d^5 + c*d^6 + d^7)*f), 1/2*((2*a*c*d^2 - a*d^3 + (2*a*c^3 - a*c^2*d)*cos(f*x + e)^2 + 2*(2*a*c^2*d - a*c*d^2)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (a*c^3*d - 2*a*c^2*d^2 - a*c*d^3 + 2*a*d^4 + (2*a*c^4 - 2*a*c^3*d - 3*a*c^2*d^2 + 2*a*c*d^3 + a*d^4)*cos(f*x + e))*sin(f*x + e))/((c^7 + c^6*d - 2*c^5*d^2 - 2*c^4*d^3 + c^3*d^4 + c^2*d^5)*f*cos(f*x + e)^2 + 2*(c^6*d + c^5*d^2 - 2*c^4*d^3 - 2*c^3*d^4 + c^2*d^5 + c*d^6)*f*cos(f*x + e) + (c^5*d^2 + c^4*d^3 - 2*c^3*d^4 - 2*c^2*d^5 + c*d^6 + d^7)*f)]","B",0
192,1,1278,0,0.537277," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, a c^{2} d^{3} - 2 \, a c d^{4} + a d^{5} + {\left(2 \, a c^{5} - 2 \, a c^{4} d + a c^{3} d^{2}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(2 \, a c^{4} d - 2 \, a c^{3} d^{2} + a c^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, a c^{3} d^{2} - 2 \, a c^{2} d^{3} + a c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(2 \, a c^{4} d^{2} - 9 \, a c^{3} d^{3} + 2 \, a c^{2} d^{4} + 9 \, a c d^{5} - 4 \, a d^{6} + {\left(6 \, a c^{6} - 12 \, a c^{5} d - 8 \, a c^{4} d^{2} + 15 \, a c^{3} d^{3} + 4 \, a c^{2} d^{4} - 3 \, a c d^{5} - 2 \, a d^{6}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, a c^{5} d - 7 \, a c^{4} d^{2} + 8 \, a c^{2} d^{4} - 2 \, a c d^{5} - a d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left({\left(c^{10} + c^{9} d - 3 \, c^{8} d^{2} - 3 \, c^{7} d^{3} + 3 \, c^{6} d^{4} + 3 \, c^{5} d^{5} - c^{4} d^{6} - c^{3} d^{7}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{9} d + c^{8} d^{2} - 3 \, c^{7} d^{3} - 3 \, c^{6} d^{4} + 3 \, c^{5} d^{5} + 3 \, c^{4} d^{6} - c^{3} d^{7} - c^{2} d^{8}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{8} d^{2} + c^{7} d^{3} - 3 \, c^{6} d^{4} - 3 \, c^{5} d^{5} + 3 \, c^{4} d^{6} + 3 \, c^{3} d^{7} - c^{2} d^{8} - c d^{9}\right)} f \cos\left(f x + e\right) + {\left(c^{7} d^{3} + c^{6} d^{4} - 3 \, c^{5} d^{5} - 3 \, c^{4} d^{6} + 3 \, c^{3} d^{7} + 3 \, c^{2} d^{8} - c d^{9} - d^{10}\right)} f\right)}}, \frac{3 \, {\left(2 \, a c^{2} d^{3} - 2 \, a c d^{4} + a d^{5} + {\left(2 \, a c^{5} - 2 \, a c^{4} d + a c^{3} d^{2}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(2 \, a c^{4} d - 2 \, a c^{3} d^{2} + a c^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, a c^{3} d^{2} - 2 \, a c^{2} d^{3} + a c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(2 \, a c^{4} d^{2} - 9 \, a c^{3} d^{3} + 2 \, a c^{2} d^{4} + 9 \, a c d^{5} - 4 \, a d^{6} + {\left(6 \, a c^{6} - 12 \, a c^{5} d - 8 \, a c^{4} d^{2} + 15 \, a c^{3} d^{3} + 4 \, a c^{2} d^{4} - 3 \, a c d^{5} - 2 \, a d^{6}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, a c^{5} d - 7 \, a c^{4} d^{2} + 8 \, a c^{2} d^{4} - 2 \, a c d^{5} - a d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(c^{10} + c^{9} d - 3 \, c^{8} d^{2} - 3 \, c^{7} d^{3} + 3 \, c^{6} d^{4} + 3 \, c^{5} d^{5} - c^{4} d^{6} - c^{3} d^{7}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{9} d + c^{8} d^{2} - 3 \, c^{7} d^{3} - 3 \, c^{6} d^{4} + 3 \, c^{5} d^{5} + 3 \, c^{4} d^{6} - c^{3} d^{7} - c^{2} d^{8}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{8} d^{2} + c^{7} d^{3} - 3 \, c^{6} d^{4} - 3 \, c^{5} d^{5} + 3 \, c^{4} d^{6} + 3 \, c^{3} d^{7} - c^{2} d^{8} - c d^{9}\right)} f \cos\left(f x + e\right) + {\left(c^{7} d^{3} + c^{6} d^{4} - 3 \, c^{5} d^{5} - 3 \, c^{4} d^{6} + 3 \, c^{3} d^{7} + 3 \, c^{2} d^{8} - c d^{9} - d^{10}\right)} f\right)}}\right]"," ",0,"[1/12*(3*(2*a*c^2*d^3 - 2*a*c*d^4 + a*d^5 + (2*a*c^5 - 2*a*c^4*d + a*c^3*d^2)*cos(f*x + e)^3 + 3*(2*a*c^4*d - 2*a*c^3*d^2 + a*c^2*d^3)*cos(f*x + e)^2 + 3*(2*a*c^3*d^2 - 2*a*c^2*d^3 + a*c*d^4)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(2*a*c^4*d^2 - 9*a*c^3*d^3 + 2*a*c^2*d^4 + 9*a*c*d^5 - 4*a*d^6 + (6*a*c^6 - 12*a*c^5*d - 8*a*c^4*d^2 + 15*a*c^3*d^3 + 4*a*c^2*d^4 - 3*a*c*d^5 - 2*a*d^6)*cos(f*x + e)^2 + 3*(2*a*c^5*d - 7*a*c^4*d^2 + 8*a*c^2*d^4 - 2*a*c*d^5 - a*d^6)*cos(f*x + e))*sin(f*x + e))/((c^10 + c^9*d - 3*c^8*d^2 - 3*c^7*d^3 + 3*c^6*d^4 + 3*c^5*d^5 - c^4*d^6 - c^3*d^7)*f*cos(f*x + e)^3 + 3*(c^9*d + c^8*d^2 - 3*c^7*d^3 - 3*c^6*d^4 + 3*c^5*d^5 + 3*c^4*d^6 - c^3*d^7 - c^2*d^8)*f*cos(f*x + e)^2 + 3*(c^8*d^2 + c^7*d^3 - 3*c^6*d^4 - 3*c^5*d^5 + 3*c^4*d^6 + 3*c^3*d^7 - c^2*d^8 - c*d^9)*f*cos(f*x + e) + (c^7*d^3 + c^6*d^4 - 3*c^5*d^5 - 3*c^4*d^6 + 3*c^3*d^7 + 3*c^2*d^8 - c*d^9 - d^10)*f), 1/6*(3*(2*a*c^2*d^3 - 2*a*c*d^4 + a*d^5 + (2*a*c^5 - 2*a*c^4*d + a*c^3*d^2)*cos(f*x + e)^3 + 3*(2*a*c^4*d - 2*a*c^3*d^2 + a*c^2*d^3)*cos(f*x + e)^2 + 3*(2*a*c^3*d^2 - 2*a*c^2*d^3 + a*c*d^4)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (2*a*c^4*d^2 - 9*a*c^3*d^3 + 2*a*c^2*d^4 + 9*a*c*d^5 - 4*a*d^6 + (6*a*c^6 - 12*a*c^5*d - 8*a*c^4*d^2 + 15*a*c^3*d^3 + 4*a*c^2*d^4 - 3*a*c*d^5 - 2*a*d^6)*cos(f*x + e)^2 + 3*(2*a*c^5*d - 7*a*c^4*d^2 + 8*a*c^2*d^4 - 2*a*c*d^5 - a*d^6)*cos(f*x + e))*sin(f*x + e))/((c^10 + c^9*d - 3*c^8*d^2 - 3*c^7*d^3 + 3*c^6*d^4 + 3*c^5*d^5 - c^4*d^6 - c^3*d^7)*f*cos(f*x + e)^3 + 3*(c^9*d + c^8*d^2 - 3*c^7*d^3 - 3*c^6*d^4 + 3*c^5*d^5 + 3*c^4*d^6 - c^3*d^7 - c^2*d^8)*f*cos(f*x + e)^2 + 3*(c^8*d^2 + c^7*d^3 - 3*c^6*d^4 - 3*c^5*d^5 + 3*c^4*d^6 + 3*c^3*d^7 - c^2*d^8 - c*d^9)*f*cos(f*x + e) + (c^7*d^3 + c^6*d^4 - 3*c^5*d^5 - 3*c^4*d^6 + 3*c^3*d^7 + 3*c^2*d^8 - c*d^9 - d^10)*f)]","B",0
193,1,387,0,0.465982," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{15 \, {\left(24 \, a^{2} c^{4} + 64 \, a^{2} c^{3} d + 84 \, a^{2} c^{2} d^{2} + 48 \, a^{2} c d^{3} + 11 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)^{6} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(24 \, a^{2} c^{4} + 64 \, a^{2} c^{3} d + 84 \, a^{2} c^{2} d^{2} + 48 \, a^{2} c d^{3} + 11 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)^{6} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(40 \, a^{2} d^{4} + 32 \, {\left(15 \, a^{2} c^{4} + 50 \, a^{2} c^{3} d + 60 \, a^{2} c^{2} d^{2} + 36 \, a^{2} c d^{3} + 8 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)^{5} + 15 \, {\left(8 \, a^{2} c^{4} + 64 \, a^{2} c^{3} d + 84 \, a^{2} c^{2} d^{2} + 48 \, a^{2} c d^{3} + 11 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)^{4} + 64 \, {\left(5 \, a^{2} c^{3} d + 15 \, a^{2} c^{2} d^{2} + 9 \, a^{2} c d^{3} + 2 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)^{3} + 10 \, {\left(36 \, a^{2} c^{2} d^{2} + 48 \, a^{2} c d^{3} + 11 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} + 96 \, {\left(2 \, a^{2} c d^{3} + a^{2} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{480 \, f \cos\left(f x + e\right)^{6}}"," ",0,"1/480*(15*(24*a^2*c^4 + 64*a^2*c^3*d + 84*a^2*c^2*d^2 + 48*a^2*c*d^3 + 11*a^2*d^4)*cos(f*x + e)^6*log(sin(f*x + e) + 1) - 15*(24*a^2*c^4 + 64*a^2*c^3*d + 84*a^2*c^2*d^2 + 48*a^2*c*d^3 + 11*a^2*d^4)*cos(f*x + e)^6*log(-sin(f*x + e) + 1) + 2*(40*a^2*d^4 + 32*(15*a^2*c^4 + 50*a^2*c^3*d + 60*a^2*c^2*d^2 + 36*a^2*c*d^3 + 8*a^2*d^4)*cos(f*x + e)^5 + 15*(8*a^2*c^4 + 64*a^2*c^3*d + 84*a^2*c^2*d^2 + 48*a^2*c*d^3 + 11*a^2*d^4)*cos(f*x + e)^4 + 64*(5*a^2*c^3*d + 15*a^2*c^2*d^2 + 9*a^2*c*d^3 + 2*a^2*d^4)*cos(f*x + e)^3 + 10*(36*a^2*c^2*d^2 + 48*a^2*c*d^3 + 11*a^2*d^4)*cos(f*x + e)^2 + 96*(2*a^2*c*d^3 + a^2*d^4)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^6)","A",0
194,1,294,0,0.453683," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, a^{2} c^{3} + 8 \, a^{2} c^{2} d + 7 \, a^{2} c d^{2} + 2 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{5} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(4 \, a^{2} c^{3} + 8 \, a^{2} c^{2} d + 7 \, a^{2} c d^{2} + 2 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{5} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(8 \, a^{2} d^{3} + 8 \, {\left(10 \, a^{2} c^{3} + 25 \, a^{2} c^{2} d + 20 \, a^{2} c d^{2} + 6 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{4} + 5 \, {\left(4 \, a^{2} c^{3} + 24 \, a^{2} c^{2} d + 21 \, a^{2} c d^{2} + 6 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + 8 \, {\left(5 \, a^{2} c^{2} d + 10 \, a^{2} c d^{2} + 3 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + 10 \, {\left(3 \, a^{2} c d^{2} + 2 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{80 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/80*(15*(4*a^2*c^3 + 8*a^2*c^2*d + 7*a^2*c*d^2 + 2*a^2*d^3)*cos(f*x + e)^5*log(sin(f*x + e) + 1) - 15*(4*a^2*c^3 + 8*a^2*c^2*d + 7*a^2*c*d^2 + 2*a^2*d^3)*cos(f*x + e)^5*log(-sin(f*x + e) + 1) + 2*(8*a^2*d^3 + 8*(10*a^2*c^3 + 25*a^2*c^2*d + 20*a^2*c*d^2 + 6*a^2*d^3)*cos(f*x + e)^4 + 5*(4*a^2*c^3 + 24*a^2*c^2*d + 21*a^2*c*d^2 + 6*a^2*d^3)*cos(f*x + e)^3 + 8*(5*a^2*c^2*d + 10*a^2*c*d^2 + 3*a^2*d^3)*cos(f*x + e)^2 + 10*(3*a^2*c*d^2 + 2*a^2*d^3)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^5)","A",0
195,1,209,0,0.450030," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(12 \, a^{2} c^{2} + 16 \, a^{2} c d + 7 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)^{4} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(12 \, a^{2} c^{2} + 16 \, a^{2} c d + 7 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)^{4} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(6 \, a^{2} d^{2} + 16 \, {\left(3 \, a^{2} c^{2} + 5 \, a^{2} c d + 2 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(4 \, a^{2} c^{2} + 16 \, a^{2} c d + 7 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 16 \, {\left(a^{2} c d + a^{2} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{48 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/48*(3*(12*a^2*c^2 + 16*a^2*c*d + 7*a^2*d^2)*cos(f*x + e)^4*log(sin(f*x + e) + 1) - 3*(12*a^2*c^2 + 16*a^2*c*d + 7*a^2*d^2)*cos(f*x + e)^4*log(-sin(f*x + e) + 1) + 2*(6*a^2*d^2 + 16*(3*a^2*c^2 + 5*a^2*c*d + 2*a^2*d^2)*cos(f*x + e)^3 + 3*(4*a^2*c^2 + 16*a^2*c*d + 7*a^2*d^2)*cos(f*x + e)^2 + 16*(a^2*c*d + a^2*d^2)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4)","A",0
196,1,138,0,0.422500," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, a^{2} c + 2 \, a^{2} d\right)} \cos\left(f x + e\right)^{3} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(3 \, a^{2} c + 2 \, a^{2} d\right)} \cos\left(f x + e\right)^{3} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, a^{2} d + 2 \, {\left(6 \, a^{2} c + 5 \, a^{2} d\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(a^{2} c + 2 \, a^{2} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, f \cos\left(f x + e\right)^{3}}"," ",0,"1/12*(3*(3*a^2*c + 2*a^2*d)*cos(f*x + e)^3*log(sin(f*x + e) + 1) - 3*(3*a^2*c + 2*a^2*d)*cos(f*x + e)^3*log(-sin(f*x + e) + 1) + 2*(2*a^2*d + 2*(6*a^2*c + 5*a^2*d)*cos(f*x + e)^2 + 3*(a^2*c + 2*a^2*d)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3)","A",0
197,1,398,0,0.633964," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} d \sin\left(f x + e\right) - {\left(a^{2} c - a^{2} d\right)} \sqrt{\frac{c - d}{c + d}} \cos\left(f x + e\right) \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{2} + c d + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - {\left(a^{2} c - 2 \, a^{2} d\right)} \cos\left(f x + e\right) \log\left(\sin\left(f x + e\right) + 1\right) + {\left(a^{2} c - 2 \, a^{2} d\right)} \cos\left(f x + e\right) \log\left(-\sin\left(f x + e\right) + 1\right)}{2 \, d^{2} f \cos\left(f x + e\right)}, \frac{2 \, a^{2} d \sin\left(f x + e\right) + 2 \, {\left(a^{2} c - a^{2} d\right)} \sqrt{-\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(d \cos\left(f x + e\right) + c\right)} \sqrt{-\frac{c - d}{c + d}}}{{\left(c - d\right)} \sin\left(f x + e\right)}\right) \cos\left(f x + e\right) - {\left(a^{2} c - 2 \, a^{2} d\right)} \cos\left(f x + e\right) \log\left(\sin\left(f x + e\right) + 1\right) + {\left(a^{2} c - 2 \, a^{2} d\right)} \cos\left(f x + e\right) \log\left(-\sin\left(f x + e\right) + 1\right)}{2 \, d^{2} f \cos\left(f x + e\right)}\right]"," ",0,"[1/2*(2*a^2*d*sin(f*x + e) - (a^2*c - a^2*d)*sqrt((c - d)/(c + d))*cos(f*x + e)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*(c^2 + c*d + (c*d + d^2)*cos(f*x + e))*sqrt((c - d)/(c + d))*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - (a^2*c - 2*a^2*d)*cos(f*x + e)*log(sin(f*x + e) + 1) + (a^2*c - 2*a^2*d)*cos(f*x + e)*log(-sin(f*x + e) + 1))/(d^2*f*cos(f*x + e)), 1/2*(2*a^2*d*sin(f*x + e) + 2*(a^2*c - a^2*d)*sqrt(-(c - d)/(c + d))*arctan(-(d*cos(f*x + e) + c)*sqrt(-(c - d)/(c + d))/((c - d)*sin(f*x + e)))*cos(f*x + e) - (a^2*c - 2*a^2*d)*cos(f*x + e)*log(sin(f*x + e) + 1) + (a^2*c - 2*a^2*d)*cos(f*x + e)*log(-sin(f*x + e) + 1))/(d^2*f*cos(f*x + e))]","A",0
198,1,567,0,0.672617," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} c d + 2 \, a^{2} d^{2} + {\left(a^{2} c^{2} + 2 \, a^{2} c d\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{2} + c d + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + {\left(a^{2} c d + a^{2} d^{2} + {\left(a^{2} c^{2} + a^{2} c d\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(a^{2} c d + a^{2} d^{2} + {\left(a^{2} c^{2} + a^{2} c d\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(a^{2} c d - a^{2} d^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{2} d^{2} + c d^{3}\right)} f \cos\left(f x + e\right) + {\left(c d^{3} + d^{4}\right)} f\right)}}, -\frac{2 \, {\left(a^{2} c d + 2 \, a^{2} d^{2} + {\left(a^{2} c^{2} + 2 \, a^{2} c d\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(d \cos\left(f x + e\right) + c\right)} \sqrt{-\frac{c - d}{c + d}}}{{\left(c - d\right)} \sin\left(f x + e\right)}\right) - {\left(a^{2} c d + a^{2} d^{2} + {\left(a^{2} c^{2} + a^{2} c d\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) + {\left(a^{2} c d + a^{2} d^{2} + {\left(a^{2} c^{2} + a^{2} c d\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(a^{2} c d - a^{2} d^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{2} d^{2} + c d^{3}\right)} f \cos\left(f x + e\right) + {\left(c d^{3} + d^{4}\right)} f\right)}}\right]"," ",0,"[1/2*((a^2*c*d + 2*a^2*d^2 + (a^2*c^2 + 2*a^2*c*d)*cos(f*x + e))*sqrt((c - d)/(c + d))*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*(c^2 + c*d + (c*d + d^2)*cos(f*x + e))*sqrt((c - d)/(c + d))*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + (a^2*c*d + a^2*d^2 + (a^2*c^2 + a^2*c*d)*cos(f*x + e))*log(sin(f*x + e) + 1) - (a^2*c*d + a^2*d^2 + (a^2*c^2 + a^2*c*d)*cos(f*x + e))*log(-sin(f*x + e) + 1) - 2*(a^2*c*d - a^2*d^2)*sin(f*x + e))/((c^2*d^2 + c*d^3)*f*cos(f*x + e) + (c*d^3 + d^4)*f), -1/2*(2*(a^2*c*d + 2*a^2*d^2 + (a^2*c^2 + 2*a^2*c*d)*cos(f*x + e))*sqrt(-(c - d)/(c + d))*arctan(-(d*cos(f*x + e) + c)*sqrt(-(c - d)/(c + d))/((c - d)*sin(f*x + e))) - (a^2*c*d + a^2*d^2 + (a^2*c^2 + a^2*c*d)*cos(f*x + e))*log(sin(f*x + e) + 1) + (a^2*c*d + a^2*d^2 + (a^2*c^2 + a^2*c*d)*cos(f*x + e))*log(-sin(f*x + e) + 1) + 2*(a^2*c*d - a^2*d^2)*sin(f*x + e))/((c^2*d^2 + c*d^3)*f*cos(f*x + e) + (c*d^3 + d^4)*f)]","B",0
199,1,622,0,0.504781," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} c^{2} \cos\left(f x + e\right)^{2} + 2 \, a^{2} c d \cos\left(f x + e\right) + a^{2} d^{2}\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(a^{2} c^{3} + 4 \, a^{2} c^{2} d - a^{2} c d^{2} - 4 \, a^{2} d^{3} + {\left(4 \, a^{2} c^{3} + a^{2} c^{2} d - 4 \, a^{2} c d^{2} - a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{6} + 2 \, c^{5} d - 2 \, c^{3} d^{3} - c^{2} d^{4}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d + 2 \, c^{4} d^{2} - 2 \, c^{2} d^{4} - c d^{5}\right)} f \cos\left(f x + e\right) + {\left(c^{4} d^{2} + 2 \, c^{3} d^{3} - 2 \, c d^{5} - d^{6}\right)} f\right)}}, \frac{3 \, {\left(a^{2} c^{2} \cos\left(f x + e\right)^{2} + 2 \, a^{2} c d \cos\left(f x + e\right) + a^{2} d^{2}\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(a^{2} c^{3} + 4 \, a^{2} c^{2} d - a^{2} c d^{2} - 4 \, a^{2} d^{3} + {\left(4 \, a^{2} c^{3} + a^{2} c^{2} d - 4 \, a^{2} c d^{2} - a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{6} + 2 \, c^{5} d - 2 \, c^{3} d^{3} - c^{2} d^{4}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d + 2 \, c^{4} d^{2} - 2 \, c^{2} d^{4} - c d^{5}\right)} f \cos\left(f x + e\right) + {\left(c^{4} d^{2} + 2 \, c^{3} d^{3} - 2 \, c d^{5} - d^{6}\right)} f\right)}}\right]"," ",0,"[1/4*(3*(a^2*c^2*cos(f*x + e)^2 + 2*a^2*c*d*cos(f*x + e) + a^2*d^2)*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(a^2*c^3 + 4*a^2*c^2*d - a^2*c*d^2 - 4*a^2*d^3 + (4*a^2*c^3 + a^2*c^2*d - 4*a^2*c*d^2 - a^2*d^3)*cos(f*x + e))*sin(f*x + e))/((c^6 + 2*c^5*d - 2*c^3*d^3 - c^2*d^4)*f*cos(f*x + e)^2 + 2*(c^5*d + 2*c^4*d^2 - 2*c^2*d^4 - c*d^5)*f*cos(f*x + e) + (c^4*d^2 + 2*c^3*d^3 - 2*c*d^5 - d^6)*f), 1/2*(3*(a^2*c^2*cos(f*x + e)^2 + 2*a^2*c*d*cos(f*x + e) + a^2*d^2)*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (a^2*c^3 + 4*a^2*c^2*d - a^2*c*d^2 - 4*a^2*d^3 + (4*a^2*c^3 + a^2*c^2*d - 4*a^2*c*d^2 - a^2*d^3)*cos(f*x + e))*sin(f*x + e))/((c^6 + 2*c^5*d - 2*c^3*d^3 - c^2*d^4)*f*cos(f*x + e)^2 + 2*(c^5*d + 2*c^4*d^2 - 2*c^2*d^4 - c*d^5)*f*cos(f*x + e) + (c^4*d^2 + 2*c^3*d^3 - 2*c*d^5 - d^6)*f)]","B",0
200,1,1234,0,0.548409," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, a^{2} c d^{3} - 2 \, a^{2} d^{4} + {\left(3 \, a^{2} c^{4} - 2 \, a^{2} c^{3} d\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(3 \, a^{2} c^{3} d - 2 \, a^{2} c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(3 \, a^{2} c^{2} d^{2} - 2 \, a^{2} c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(a^{2} c^{4} d + 6 \, a^{2} c^{3} d^{2} - 11 \, a^{2} c^{2} d^{3} - 6 \, a^{2} c d^{4} + 10 \, a^{2} d^{5} + {\left(12 \, a^{2} c^{5} - 7 \, a^{2} c^{4} d - 18 \, a^{2} c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3} + 6 \, a^{2} c d^{4} + 2 \, a^{2} d^{5}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(a^{2} c^{5} + 6 \, a^{2} c^{4} d - 8 \, a^{2} c^{3} d^{2} - 8 \, a^{2} c^{2} d^{3} + 7 \, a^{2} c d^{4} + 2 \, a^{2} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left({\left(c^{9} + 2 \, c^{8} d - c^{7} d^{2} - 4 \, c^{6} d^{3} - c^{5} d^{4} + 2 \, c^{4} d^{5} + c^{3} d^{6}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{8} d + 2 \, c^{7} d^{2} - c^{6} d^{3} - 4 \, c^{5} d^{4} - c^{4} d^{5} + 2 \, c^{3} d^{6} + c^{2} d^{7}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{7} d^{2} + 2 \, c^{6} d^{3} - c^{5} d^{4} - 4 \, c^{4} d^{5} - c^{3} d^{6} + 2 \, c^{2} d^{7} + c d^{8}\right)} f \cos\left(f x + e\right) + {\left(c^{6} d^{3} + 2 \, c^{5} d^{4} - c^{4} d^{5} - 4 \, c^{3} d^{6} - c^{2} d^{7} + 2 \, c d^{8} + d^{9}\right)} f\right)}}, \frac{3 \, {\left(3 \, a^{2} c d^{3} - 2 \, a^{2} d^{4} + {\left(3 \, a^{2} c^{4} - 2 \, a^{2} c^{3} d\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(3 \, a^{2} c^{3} d - 2 \, a^{2} c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(3 \, a^{2} c^{2} d^{2} - 2 \, a^{2} c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(a^{2} c^{4} d + 6 \, a^{2} c^{3} d^{2} - 11 \, a^{2} c^{2} d^{3} - 6 \, a^{2} c d^{4} + 10 \, a^{2} d^{5} + {\left(12 \, a^{2} c^{5} - 7 \, a^{2} c^{4} d - 18 \, a^{2} c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3} + 6 \, a^{2} c d^{4} + 2 \, a^{2} d^{5}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(a^{2} c^{5} + 6 \, a^{2} c^{4} d - 8 \, a^{2} c^{3} d^{2} - 8 \, a^{2} c^{2} d^{3} + 7 \, a^{2} c d^{4} + 2 \, a^{2} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(c^{9} + 2 \, c^{8} d - c^{7} d^{2} - 4 \, c^{6} d^{3} - c^{5} d^{4} + 2 \, c^{4} d^{5} + c^{3} d^{6}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{8} d + 2 \, c^{7} d^{2} - c^{6} d^{3} - 4 \, c^{5} d^{4} - c^{4} d^{5} + 2 \, c^{3} d^{6} + c^{2} d^{7}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{7} d^{2} + 2 \, c^{6} d^{3} - c^{5} d^{4} - 4 \, c^{4} d^{5} - c^{3} d^{6} + 2 \, c^{2} d^{7} + c d^{8}\right)} f \cos\left(f x + e\right) + {\left(c^{6} d^{3} + 2 \, c^{5} d^{4} - c^{4} d^{5} - 4 \, c^{3} d^{6} - c^{2} d^{7} + 2 \, c d^{8} + d^{9}\right)} f\right)}}\right]"," ",0,"[1/12*(3*(3*a^2*c*d^3 - 2*a^2*d^4 + (3*a^2*c^4 - 2*a^2*c^3*d)*cos(f*x + e)^3 + 3*(3*a^2*c^3*d - 2*a^2*c^2*d^2)*cos(f*x + e)^2 + 3*(3*a^2*c^2*d^2 - 2*a^2*c*d^3)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(a^2*c^4*d + 6*a^2*c^3*d^2 - 11*a^2*c^2*d^3 - 6*a^2*c*d^4 + 10*a^2*d^5 + (12*a^2*c^5 - 7*a^2*c^4*d - 18*a^2*c^3*d^2 + 5*a^2*c^2*d^3 + 6*a^2*c*d^4 + 2*a^2*d^5)*cos(f*x + e)^2 + 3*(a^2*c^5 + 6*a^2*c^4*d - 8*a^2*c^3*d^2 - 8*a^2*c^2*d^3 + 7*a^2*c*d^4 + 2*a^2*d^5)*cos(f*x + e))*sin(f*x + e))/((c^9 + 2*c^8*d - c^7*d^2 - 4*c^6*d^3 - c^5*d^4 + 2*c^4*d^5 + c^3*d^6)*f*cos(f*x + e)^3 + 3*(c^8*d + 2*c^7*d^2 - c^6*d^3 - 4*c^5*d^4 - c^4*d^5 + 2*c^3*d^6 + c^2*d^7)*f*cos(f*x + e)^2 + 3*(c^7*d^2 + 2*c^6*d^3 - c^5*d^4 - 4*c^4*d^5 - c^3*d^6 + 2*c^2*d^7 + c*d^8)*f*cos(f*x + e) + (c^6*d^3 + 2*c^5*d^4 - c^4*d^5 - 4*c^3*d^6 - c^2*d^7 + 2*c*d^8 + d^9)*f), 1/6*(3*(3*a^2*c*d^3 - 2*a^2*d^4 + (3*a^2*c^4 - 2*a^2*c^3*d)*cos(f*x + e)^3 + 3*(3*a^2*c^3*d - 2*a^2*c^2*d^2)*cos(f*x + e)^2 + 3*(3*a^2*c^2*d^2 - 2*a^2*c*d^3)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (a^2*c^4*d + 6*a^2*c^3*d^2 - 11*a^2*c^2*d^3 - 6*a^2*c*d^4 + 10*a^2*d^5 + (12*a^2*c^5 - 7*a^2*c^4*d - 18*a^2*c^3*d^2 + 5*a^2*c^2*d^3 + 6*a^2*c*d^4 + 2*a^2*d^5)*cos(f*x + e)^2 + 3*(a^2*c^5 + 6*a^2*c^4*d - 8*a^2*c^3*d^2 - 8*a^2*c^2*d^3 + 7*a^2*c*d^4 + 2*a^2*d^5)*cos(f*x + e))*sin(f*x + e))/((c^9 + 2*c^8*d - c^7*d^2 - 4*c^6*d^3 - c^5*d^4 + 2*c^4*d^5 + c^3*d^6)*f*cos(f*x + e)^3 + 3*(c^8*d + 2*c^7*d^2 - c^6*d^3 - 4*c^5*d^4 - c^4*d^5 + 2*c^3*d^6 + c^2*d^7)*f*cos(f*x + e)^2 + 3*(c^7*d^2 + 2*c^6*d^3 - c^5*d^4 - 4*c^4*d^5 - c^3*d^6 + 2*c^2*d^7 + c*d^8)*f*cos(f*x + e) + (c^6*d^3 + 2*c^5*d^4 - c^4*d^5 - 4*c^3*d^6 - c^2*d^7 + 2*c*d^8 + d^9)*f)]","B",0
201,1,1908,0,0.589047," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(12 \, a^{2} c^{2} d^{4} - 16 \, a^{2} c d^{5} + 7 \, a^{2} d^{6} + {\left(12 \, a^{2} c^{6} - 16 \, a^{2} c^{5} d + 7 \, a^{2} c^{4} d^{2}\right)} \cos\left(f x + e\right)^{4} + 4 \, {\left(12 \, a^{2} c^{5} d - 16 \, a^{2} c^{4} d^{2} + 7 \, a^{2} c^{3} d^{3}\right)} \cos\left(f x + e\right)^{3} + 6 \, {\left(12 \, a^{2} c^{4} d^{2} - 16 \, a^{2} c^{3} d^{3} + 7 \, a^{2} c^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(12 \, a^{2} c^{3} d^{3} - 16 \, a^{2} c^{2} d^{4} + 7 \, a^{2} c d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(2 \, a^{2} c^{5} d^{2} + 16 \, a^{2} c^{4} d^{3} - 61 \, a^{2} c^{3} d^{4} + 16 \, a^{2} c^{2} d^{5} + 59 \, a^{2} c d^{6} - 32 \, a^{2} d^{7} + {\left(48 \, a^{2} c^{7} - 68 \, a^{2} c^{6} d - 64 \, a^{2} c^{5} d^{2} + 73 \, a^{2} c^{4} d^{3} + 32 \, a^{2} c^{3} d^{4} + a^{2} c^{2} d^{5} - 16 \, a^{2} c d^{6} - 6 \, a^{2} d^{7}\right)} \cos\left(f x + e\right)^{3} + {\left(12 \, a^{2} c^{7} + 96 \, a^{2} c^{6} d - 239 \, a^{2} c^{5} d^{2} - 64 \, a^{2} c^{4} d^{3} + 271 \, a^{2} c^{3} d^{4} - 16 \, a^{2} c^{2} d^{5} - 44 \, a^{2} c d^{6} - 16 \, a^{2} d^{7}\right)} \cos\left(f x + e\right)^{2} + {\left(8 \, a^{2} c^{6} d + 64 \, a^{2} c^{5} d^{2} - 208 \, a^{2} c^{4} d^{3} + 16 \, a^{2} c^{3} d^{4} + 221 \, a^{2} c^{2} d^{5} - 80 \, a^{2} c d^{6} - 21 \, a^{2} d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{48 \, {\left({\left(c^{12} + 2 \, c^{11} d - 2 \, c^{10} d^{2} - 6 \, c^{9} d^{3} + 6 \, c^{7} d^{5} + 2 \, c^{6} d^{6} - 2 \, c^{5} d^{7} - c^{4} d^{8}\right)} f \cos\left(f x + e\right)^{4} + 4 \, {\left(c^{11} d + 2 \, c^{10} d^{2} - 2 \, c^{9} d^{3} - 6 \, c^{8} d^{4} + 6 \, c^{6} d^{6} + 2 \, c^{5} d^{7} - 2 \, c^{4} d^{8} - c^{3} d^{9}\right)} f \cos\left(f x + e\right)^{3} + 6 \, {\left(c^{10} d^{2} + 2 \, c^{9} d^{3} - 2 \, c^{8} d^{4} - 6 \, c^{7} d^{5} + 6 \, c^{5} d^{7} + 2 \, c^{4} d^{8} - 2 \, c^{3} d^{9} - c^{2} d^{10}\right)} f \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{9} d^{3} + 2 \, c^{8} d^{4} - 2 \, c^{7} d^{5} - 6 \, c^{6} d^{6} + 6 \, c^{4} d^{8} + 2 \, c^{3} d^{9} - 2 \, c^{2} d^{10} - c d^{11}\right)} f \cos\left(f x + e\right) + {\left(c^{8} d^{4} + 2 \, c^{7} d^{5} - 2 \, c^{6} d^{6} - 6 \, c^{5} d^{7} + 6 \, c^{3} d^{9} + 2 \, c^{2} d^{10} - 2 \, c d^{11} - d^{12}\right)} f\right)}}, \frac{3 \, {\left(12 \, a^{2} c^{2} d^{4} - 16 \, a^{2} c d^{5} + 7 \, a^{2} d^{6} + {\left(12 \, a^{2} c^{6} - 16 \, a^{2} c^{5} d + 7 \, a^{2} c^{4} d^{2}\right)} \cos\left(f x + e\right)^{4} + 4 \, {\left(12 \, a^{2} c^{5} d - 16 \, a^{2} c^{4} d^{2} + 7 \, a^{2} c^{3} d^{3}\right)} \cos\left(f x + e\right)^{3} + 6 \, {\left(12 \, a^{2} c^{4} d^{2} - 16 \, a^{2} c^{3} d^{3} + 7 \, a^{2} c^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(12 \, a^{2} c^{3} d^{3} - 16 \, a^{2} c^{2} d^{4} + 7 \, a^{2} c d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(2 \, a^{2} c^{5} d^{2} + 16 \, a^{2} c^{4} d^{3} - 61 \, a^{2} c^{3} d^{4} + 16 \, a^{2} c^{2} d^{5} + 59 \, a^{2} c d^{6} - 32 \, a^{2} d^{7} + {\left(48 \, a^{2} c^{7} - 68 \, a^{2} c^{6} d - 64 \, a^{2} c^{5} d^{2} + 73 \, a^{2} c^{4} d^{3} + 32 \, a^{2} c^{3} d^{4} + a^{2} c^{2} d^{5} - 16 \, a^{2} c d^{6} - 6 \, a^{2} d^{7}\right)} \cos\left(f x + e\right)^{3} + {\left(12 \, a^{2} c^{7} + 96 \, a^{2} c^{6} d - 239 \, a^{2} c^{5} d^{2} - 64 \, a^{2} c^{4} d^{3} + 271 \, a^{2} c^{3} d^{4} - 16 \, a^{2} c^{2} d^{5} - 44 \, a^{2} c d^{6} - 16 \, a^{2} d^{7}\right)} \cos\left(f x + e\right)^{2} + {\left(8 \, a^{2} c^{6} d + 64 \, a^{2} c^{5} d^{2} - 208 \, a^{2} c^{4} d^{3} + 16 \, a^{2} c^{3} d^{4} + 221 \, a^{2} c^{2} d^{5} - 80 \, a^{2} c d^{6} - 21 \, a^{2} d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, {\left({\left(c^{12} + 2 \, c^{11} d - 2 \, c^{10} d^{2} - 6 \, c^{9} d^{3} + 6 \, c^{7} d^{5} + 2 \, c^{6} d^{6} - 2 \, c^{5} d^{7} - c^{4} d^{8}\right)} f \cos\left(f x + e\right)^{4} + 4 \, {\left(c^{11} d + 2 \, c^{10} d^{2} - 2 \, c^{9} d^{3} - 6 \, c^{8} d^{4} + 6 \, c^{6} d^{6} + 2 \, c^{5} d^{7} - 2 \, c^{4} d^{8} - c^{3} d^{9}\right)} f \cos\left(f x + e\right)^{3} + 6 \, {\left(c^{10} d^{2} + 2 \, c^{9} d^{3} - 2 \, c^{8} d^{4} - 6 \, c^{7} d^{5} + 6 \, c^{5} d^{7} + 2 \, c^{4} d^{8} - 2 \, c^{3} d^{9} - c^{2} d^{10}\right)} f \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{9} d^{3} + 2 \, c^{8} d^{4} - 2 \, c^{7} d^{5} - 6 \, c^{6} d^{6} + 6 \, c^{4} d^{8} + 2 \, c^{3} d^{9} - 2 \, c^{2} d^{10} - c d^{11}\right)} f \cos\left(f x + e\right) + {\left(c^{8} d^{4} + 2 \, c^{7} d^{5} - 2 \, c^{6} d^{6} - 6 \, c^{5} d^{7} + 6 \, c^{3} d^{9} + 2 \, c^{2} d^{10} - 2 \, c d^{11} - d^{12}\right)} f\right)}}\right]"," ",0,"[1/48*(3*(12*a^2*c^2*d^4 - 16*a^2*c*d^5 + 7*a^2*d^6 + (12*a^2*c^6 - 16*a^2*c^5*d + 7*a^2*c^4*d^2)*cos(f*x + e)^4 + 4*(12*a^2*c^5*d - 16*a^2*c^4*d^2 + 7*a^2*c^3*d^3)*cos(f*x + e)^3 + 6*(12*a^2*c^4*d^2 - 16*a^2*c^3*d^3 + 7*a^2*c^2*d^4)*cos(f*x + e)^2 + 4*(12*a^2*c^3*d^3 - 16*a^2*c^2*d^4 + 7*a^2*c*d^5)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(2*a^2*c^5*d^2 + 16*a^2*c^4*d^3 - 61*a^2*c^3*d^4 + 16*a^2*c^2*d^5 + 59*a^2*c*d^6 - 32*a^2*d^7 + (48*a^2*c^7 - 68*a^2*c^6*d - 64*a^2*c^5*d^2 + 73*a^2*c^4*d^3 + 32*a^2*c^3*d^4 + a^2*c^2*d^5 - 16*a^2*c*d^6 - 6*a^2*d^7)*cos(f*x + e)^3 + (12*a^2*c^7 + 96*a^2*c^6*d - 239*a^2*c^5*d^2 - 64*a^2*c^4*d^3 + 271*a^2*c^3*d^4 - 16*a^2*c^2*d^5 - 44*a^2*c*d^6 - 16*a^2*d^7)*cos(f*x + e)^2 + (8*a^2*c^6*d + 64*a^2*c^5*d^2 - 208*a^2*c^4*d^3 + 16*a^2*c^3*d^4 + 221*a^2*c^2*d^5 - 80*a^2*c*d^6 - 21*a^2*d^7)*cos(f*x + e))*sin(f*x + e))/((c^12 + 2*c^11*d - 2*c^10*d^2 - 6*c^9*d^3 + 6*c^7*d^5 + 2*c^6*d^6 - 2*c^5*d^7 - c^4*d^8)*f*cos(f*x + e)^4 + 4*(c^11*d + 2*c^10*d^2 - 2*c^9*d^3 - 6*c^8*d^4 + 6*c^6*d^6 + 2*c^5*d^7 - 2*c^4*d^8 - c^3*d^9)*f*cos(f*x + e)^3 + 6*(c^10*d^2 + 2*c^9*d^3 - 2*c^8*d^4 - 6*c^7*d^5 + 6*c^5*d^7 + 2*c^4*d^8 - 2*c^3*d^9 - c^2*d^10)*f*cos(f*x + e)^2 + 4*(c^9*d^3 + 2*c^8*d^4 - 2*c^7*d^5 - 6*c^6*d^6 + 6*c^4*d^8 + 2*c^3*d^9 - 2*c^2*d^10 - c*d^11)*f*cos(f*x + e) + (c^8*d^4 + 2*c^7*d^5 - 2*c^6*d^6 - 6*c^5*d^7 + 6*c^3*d^9 + 2*c^2*d^10 - 2*c*d^11 - d^12)*f), 1/24*(3*(12*a^2*c^2*d^4 - 16*a^2*c*d^5 + 7*a^2*d^6 + (12*a^2*c^6 - 16*a^2*c^5*d + 7*a^2*c^4*d^2)*cos(f*x + e)^4 + 4*(12*a^2*c^5*d - 16*a^2*c^4*d^2 + 7*a^2*c^3*d^3)*cos(f*x + e)^3 + 6*(12*a^2*c^4*d^2 - 16*a^2*c^3*d^3 + 7*a^2*c^2*d^4)*cos(f*x + e)^2 + 4*(12*a^2*c^3*d^3 - 16*a^2*c^2*d^4 + 7*a^2*c*d^5)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (2*a^2*c^5*d^2 + 16*a^2*c^4*d^3 - 61*a^2*c^3*d^4 + 16*a^2*c^2*d^5 + 59*a^2*c*d^6 - 32*a^2*d^7 + (48*a^2*c^7 - 68*a^2*c^6*d - 64*a^2*c^5*d^2 + 73*a^2*c^4*d^3 + 32*a^2*c^3*d^4 + a^2*c^2*d^5 - 16*a^2*c*d^6 - 6*a^2*d^7)*cos(f*x + e)^3 + (12*a^2*c^7 + 96*a^2*c^6*d - 239*a^2*c^5*d^2 - 64*a^2*c^4*d^3 + 271*a^2*c^3*d^4 - 16*a^2*c^2*d^5 - 44*a^2*c*d^6 - 16*a^2*d^7)*cos(f*x + e)^2 + (8*a^2*c^6*d + 64*a^2*c^5*d^2 - 208*a^2*c^4*d^3 + 16*a^2*c^3*d^4 + 221*a^2*c^2*d^5 - 80*a^2*c*d^6 - 21*a^2*d^7)*cos(f*x + e))*sin(f*x + e))/((c^12 + 2*c^11*d - 2*c^10*d^2 - 6*c^9*d^3 + 6*c^7*d^5 + 2*c^6*d^6 - 2*c^5*d^7 - c^4*d^8)*f*cos(f*x + e)^4 + 4*(c^11*d + 2*c^10*d^2 - 2*c^9*d^3 - 6*c^8*d^4 + 6*c^6*d^6 + 2*c^5*d^7 - 2*c^4*d^8 - c^3*d^9)*f*cos(f*x + e)^3 + 6*(c^10*d^2 + 2*c^9*d^3 - 2*c^8*d^4 - 6*c^7*d^5 + 6*c^5*d^7 + 2*c^4*d^8 - 2*c^3*d^9 - c^2*d^10)*f*cos(f*x + e)^2 + 4*(c^9*d^3 + 2*c^8*d^4 - 2*c^7*d^5 - 6*c^6*d^6 + 6*c^4*d^8 + 2*c^3*d^9 - 2*c^2*d^10 - c*d^11)*f*cos(f*x + e) + (c^8*d^4 + 2*c^7*d^5 - 2*c^6*d^6 - 6*c^5*d^7 + 6*c^3*d^9 + 2*c^2*d^10 - 2*c*d^11 - d^12)*f)]","B",0
202,1,337,0,0.458665," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(40 \, a^{3} c^{3} + 90 \, a^{3} c^{2} d + 78 \, a^{3} c d^{2} + 23 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)^{6} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(40 \, a^{3} c^{3} + 90 \, a^{3} c^{2} d + 78 \, a^{3} c d^{2} + 23 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)^{6} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(40 \, a^{3} d^{3} + 16 \, {\left(55 \, a^{3} c^{3} + 135 \, a^{3} c^{2} d + 114 \, a^{3} c d^{2} + 34 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)^{5} + 15 \, {\left(24 \, a^{3} c^{3} + 90 \, a^{3} c^{2} d + 78 \, a^{3} c d^{2} + 23 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)^{4} + 16 \, {\left(5 \, a^{3} c^{3} + 45 \, a^{3} c^{2} d + 57 \, a^{3} c d^{2} + 17 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)^{3} + 10 \, {\left(18 \, a^{3} c^{2} d + 54 \, a^{3} c d^{2} + 23 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)^{2} + 144 \, {\left(a^{3} c d^{2} + a^{3} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{480 \, f \cos\left(f x + e\right)^{6}}"," ",0,"1/480*(15*(40*a^3*c^3 + 90*a^3*c^2*d + 78*a^3*c*d^2 + 23*a^3*d^3)*cos(f*x + e)^6*log(sin(f*x + e) + 1) - 15*(40*a^3*c^3 + 90*a^3*c^2*d + 78*a^3*c*d^2 + 23*a^3*d^3)*cos(f*x + e)^6*log(-sin(f*x + e) + 1) + 2*(40*a^3*d^3 + 16*(55*a^3*c^3 + 135*a^3*c^2*d + 114*a^3*c*d^2 + 34*a^3*d^3)*cos(f*x + e)^5 + 15*(24*a^3*c^3 + 90*a^3*c^2*d + 78*a^3*c*d^2 + 23*a^3*d^3)*cos(f*x + e)^4 + 16*(5*a^3*c^3 + 45*a^3*c^2*d + 57*a^3*c*d^2 + 17*a^3*d^3)*cos(f*x + e)^3 + 10*(18*a^3*c^2*d + 54*a^3*c*d^2 + 23*a^3*d^3)*cos(f*x + e)^2 + 144*(a^3*c*d^2 + a^3*d^3)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^6)","A",0
203,1,245,0,0.469832," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{15 \, {\left(20 \, a^{3} c^{2} + 30 \, a^{3} c d + 13 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)^{5} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(20 \, a^{3} c^{2} + 30 \, a^{3} c d + 13 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)^{5} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(24 \, a^{3} d^{2} + 8 \, {\left(55 \, a^{3} c^{2} + 90 \, a^{3} c d + 38 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)^{4} + 15 \, {\left(12 \, a^{3} c^{2} + 30 \, a^{3} c d + 13 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)^{3} + 8 \, {\left(5 \, a^{3} c^{2} + 30 \, a^{3} c d + 19 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)^{2} + 30 \, {\left(2 \, a^{3} c d + 3 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{240 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/240*(15*(20*a^3*c^2 + 30*a^3*c*d + 13*a^3*d^2)*cos(f*x + e)^5*log(sin(f*x + e) + 1) - 15*(20*a^3*c^2 + 30*a^3*c*d + 13*a^3*d^2)*cos(f*x + e)^5*log(-sin(f*x + e) + 1) + 2*(24*a^3*d^2 + 8*(55*a^3*c^2 + 90*a^3*c*d + 38*a^3*d^2)*cos(f*x + e)^4 + 15*(12*a^3*c^2 + 30*a^3*c*d + 13*a^3*d^2)*cos(f*x + e)^3 + 8*(5*a^3*c^2 + 30*a^3*c*d + 19*a^3*d^2)*cos(f*x + e)^2 + 30*(2*a^3*c*d + 3*a^3*d^2)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^5)","A",0
204,1,161,0,0.433698," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, a^{3} c + 3 \, a^{3} d\right)} \cos\left(f x + e\right)^{4} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(4 \, a^{3} c + 3 \, a^{3} d\right)} \cos\left(f x + e\right)^{4} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(6 \, a^{3} d + 8 \, {\left(11 \, a^{3} c + 9 \, a^{3} d\right)} \cos\left(f x + e\right)^{3} + 9 \, {\left(4 \, a^{3} c + 5 \, a^{3} d\right)} \cos\left(f x + e\right)^{2} + 8 \, {\left(a^{3} c + 3 \, a^{3} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{48 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/48*(15*(4*a^3*c + 3*a^3*d)*cos(f*x + e)^4*log(sin(f*x + e) + 1) - 15*(4*a^3*c + 3*a^3*d)*cos(f*x + e)^4*log(-sin(f*x + e) + 1) + 2*(6*a^3*d + 8*(11*a^3*c + 9*a^3*d)*cos(f*x + e)^3 + 9*(4*a^3*c + 5*a^3*d)*cos(f*x + e)^2 + 8*(a^3*c + 3*a^3*d)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4)","A",0
205,1,532,0,0.892520," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{3} c^{2} - 2 \, a^{3} c d + a^{3} d^{2}\right)} \sqrt{\frac{c - d}{c + d}} \cos\left(f x + e\right)^{2} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{2} + c d + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + {\left(2 \, a^{3} c^{2} - 6 \, a^{3} c d + 7 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)^{2} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(2 \, a^{3} c^{2} - 6 \, a^{3} c d + 7 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)^{2} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(a^{3} d^{2} - 2 \, {\left(a^{3} c d - 3 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, d^{3} f \cos\left(f x + e\right)^{2}}, -\frac{4 \, {\left(a^{3} c^{2} - 2 \, a^{3} c d + a^{3} d^{2}\right)} \sqrt{-\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(d \cos\left(f x + e\right) + c\right)} \sqrt{-\frac{c - d}{c + d}}}{{\left(c - d\right)} \sin\left(f x + e\right)}\right) \cos\left(f x + e\right)^{2} - {\left(2 \, a^{3} c^{2} - 6 \, a^{3} c d + 7 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)^{2} \log\left(\sin\left(f x + e\right) + 1\right) + {\left(2 \, a^{3} c^{2} - 6 \, a^{3} c d + 7 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)^{2} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(a^{3} d^{2} - 2 \, {\left(a^{3} c d - 3 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, d^{3} f \cos\left(f x + e\right)^{2}}\right]"," ",0,"[1/4*(2*(a^3*c^2 - 2*a^3*c*d + a^3*d^2)*sqrt((c - d)/(c + d))*cos(f*x + e)^2*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*(c^2 + c*d + (c*d + d^2)*cos(f*x + e))*sqrt((c - d)/(c + d))*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + (2*a^3*c^2 - 6*a^3*c*d + 7*a^3*d^2)*cos(f*x + e)^2*log(sin(f*x + e) + 1) - (2*a^3*c^2 - 6*a^3*c*d + 7*a^3*d^2)*cos(f*x + e)^2*log(-sin(f*x + e) + 1) + 2*(a^3*d^2 - 2*(a^3*c*d - 3*a^3*d^2)*cos(f*x + e))*sin(f*x + e))/(d^3*f*cos(f*x + e)^2), -1/4*(4*(a^3*c^2 - 2*a^3*c*d + a^3*d^2)*sqrt(-(c - d)/(c + d))*arctan(-(d*cos(f*x + e) + c)*sqrt(-(c - d)/(c + d))/((c - d)*sin(f*x + e)))*cos(f*x + e)^2 - (2*a^3*c^2 - 6*a^3*c*d + 7*a^3*d^2)*cos(f*x + e)^2*log(sin(f*x + e) + 1) + (2*a^3*c^2 - 6*a^3*c*d + 7*a^3*d^2)*cos(f*x + e)^2*log(-sin(f*x + e) + 1) - 2*(a^3*d^2 - 2*(a^3*c*d - 3*a^3*d^2)*cos(f*x + e))*sin(f*x + e))/(d^3*f*cos(f*x + e)^2)]","A",0
206,1,859,0,0.924218," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, a^{3} c^{3} + a^{3} c^{2} d - 3 \, a^{3} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{3} c^{2} d + a^{3} c d^{2} - 3 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{2} + c d + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + {\left({\left(2 \, a^{3} c^{3} - a^{3} c^{2} d - 3 \, a^{3} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{3} c^{2} d - a^{3} c d^{2} - 3 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left({\left(2 \, a^{3} c^{3} - a^{3} c^{2} d - 3 \, a^{3} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{3} c^{2} d - a^{3} c d^{2} - 3 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(a^{3} c d^{2} + a^{3} d^{3} + {\left(2 \, a^{3} c^{2} d - a^{3} c d^{2} + a^{3} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{2} d^{3} + c d^{4}\right)} f \cos\left(f x + e\right)^{2} + {\left(c d^{4} + d^{5}\right)} f \cos\left(f x + e\right)\right)}}, \frac{2 \, {\left({\left(2 \, a^{3} c^{3} + a^{3} c^{2} d - 3 \, a^{3} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{3} c^{2} d + a^{3} c d^{2} - 3 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(d \cos\left(f x + e\right) + c\right)} \sqrt{-\frac{c - d}{c + d}}}{{\left(c - d\right)} \sin\left(f x + e\right)}\right) - {\left({\left(2 \, a^{3} c^{3} - a^{3} c^{2} d - 3 \, a^{3} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{3} c^{2} d - a^{3} c d^{2} - 3 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) + {\left({\left(2 \, a^{3} c^{3} - a^{3} c^{2} d - 3 \, a^{3} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{3} c^{2} d - a^{3} c d^{2} - 3 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(a^{3} c d^{2} + a^{3} d^{3} + {\left(2 \, a^{3} c^{2} d - a^{3} c d^{2} + a^{3} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{2} d^{3} + c d^{4}\right)} f \cos\left(f x + e\right)^{2} + {\left(c d^{4} + d^{5}\right)} f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[-1/2*(((2*a^3*c^3 + a^3*c^2*d - 3*a^3*c*d^2)*cos(f*x + e)^2 + (2*a^3*c^2*d + a^3*c*d^2 - 3*a^3*d^3)*cos(f*x + e))*sqrt((c - d)/(c + d))*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*(c^2 + c*d + (c*d + d^2)*cos(f*x + e))*sqrt((c - d)/(c + d))*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + ((2*a^3*c^3 - a^3*c^2*d - 3*a^3*c*d^2)*cos(f*x + e)^2 + (2*a^3*c^2*d - a^3*c*d^2 - 3*a^3*d^3)*cos(f*x + e))*log(sin(f*x + e) + 1) - ((2*a^3*c^3 - a^3*c^2*d - 3*a^3*c*d^2)*cos(f*x + e)^2 + (2*a^3*c^2*d - a^3*c*d^2 - 3*a^3*d^3)*cos(f*x + e))*log(-sin(f*x + e) + 1) - 2*(a^3*c*d^2 + a^3*d^3 + (2*a^3*c^2*d - a^3*c*d^2 + a^3*d^3)*cos(f*x + e))*sin(f*x + e))/((c^2*d^3 + c*d^4)*f*cos(f*x + e)^2 + (c*d^4 + d^5)*f*cos(f*x + e)), 1/2*(2*((2*a^3*c^3 + a^3*c^2*d - 3*a^3*c*d^2)*cos(f*x + e)^2 + (2*a^3*c^2*d + a^3*c*d^2 - 3*a^3*d^3)*cos(f*x + e))*sqrt(-(c - d)/(c + d))*arctan(-(d*cos(f*x + e) + c)*sqrt(-(c - d)/(c + d))/((c - d)*sin(f*x + e))) - ((2*a^3*c^3 - a^3*c^2*d - 3*a^3*c*d^2)*cos(f*x + e)^2 + (2*a^3*c^2*d - a^3*c*d^2 - 3*a^3*d^3)*cos(f*x + e))*log(sin(f*x + e) + 1) + ((2*a^3*c^3 - a^3*c^2*d - 3*a^3*c*d^2)*cos(f*x + e)^2 + (2*a^3*c^2*d - a^3*c*d^2 - 3*a^3*d^3)*cos(f*x + e))*log(-sin(f*x + e) + 1) + 2*(a^3*c*d^2 + a^3*d^3 + (2*a^3*c^2*d - a^3*c*d^2 + a^3*d^3)*cos(f*x + e))*sin(f*x + e))/((c^2*d^3 + c*d^4)*f*cos(f*x + e)^2 + (c*d^4 + d^5)*f*cos(f*x + e))]","B",0
207,1,1176,0,0.950077," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a^{3} c^{2} d^{2} + 6 \, a^{3} c d^{3} + 7 \, a^{3} d^{4} + {\left(2 \, a^{3} c^{4} + 6 \, a^{3} c^{3} d + 7 \, a^{3} c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, a^{3} c^{3} d + 6 \, a^{3} c^{2} d^{2} + 7 \, a^{3} c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{2} + c d + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(a^{3} c^{2} d^{2} + 2 \, a^{3} c d^{3} + a^{3} d^{4} + {\left(a^{3} c^{4} + 2 \, a^{3} c^{3} d + a^{3} c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{3} d + 2 \, a^{3} c^{2} d^{2} + a^{3} c d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 2 \, {\left(a^{3} c^{2} d^{2} + 2 \, a^{3} c d^{3} + a^{3} d^{4} + {\left(a^{3} c^{4} + 2 \, a^{3} c^{3} d + a^{3} c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{3} d + 2 \, a^{3} c^{2} d^{2} + a^{3} c d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(3 \, a^{3} c^{2} d^{2} + 3 \, a^{3} c d^{3} - 6 \, a^{3} d^{4} + {\left(2 \, a^{3} c^{3} d + 4 \, a^{3} c^{2} d^{2} - 5 \, a^{3} c d^{3} - a^{3} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{4} d^{3} + 2 \, c^{3} d^{4} + c^{2} d^{5}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{3} d^{4} + 2 \, c^{2} d^{5} + c d^{6}\right)} f \cos\left(f x + e\right) + {\left(c^{2} d^{5} + 2 \, c d^{6} + d^{7}\right)} f\right)}}, -\frac{{\left(2 \, a^{3} c^{2} d^{2} + 6 \, a^{3} c d^{3} + 7 \, a^{3} d^{4} + {\left(2 \, a^{3} c^{4} + 6 \, a^{3} c^{3} d + 7 \, a^{3} c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, a^{3} c^{3} d + 6 \, a^{3} c^{2} d^{2} + 7 \, a^{3} c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(d \cos\left(f x + e\right) + c\right)} \sqrt{-\frac{c - d}{c + d}}}{{\left(c - d\right)} \sin\left(f x + e\right)}\right) - {\left(a^{3} c^{2} d^{2} + 2 \, a^{3} c d^{3} + a^{3} d^{4} + {\left(a^{3} c^{4} + 2 \, a^{3} c^{3} d + a^{3} c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{3} d + 2 \, a^{3} c^{2} d^{2} + a^{3} c d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) + {\left(a^{3} c^{2} d^{2} + 2 \, a^{3} c d^{3} + a^{3} d^{4} + {\left(a^{3} c^{4} + 2 \, a^{3} c^{3} d + a^{3} c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{3} d + 2 \, a^{3} c^{2} d^{2} + a^{3} c d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + {\left(3 \, a^{3} c^{2} d^{2} + 3 \, a^{3} c d^{3} - 6 \, a^{3} d^{4} + {\left(2 \, a^{3} c^{3} d + 4 \, a^{3} c^{2} d^{2} - 5 \, a^{3} c d^{3} - a^{3} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{4} d^{3} + 2 \, c^{3} d^{4} + c^{2} d^{5}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{3} d^{4} + 2 \, c^{2} d^{5} + c d^{6}\right)} f \cos\left(f x + e\right) + {\left(c^{2} d^{5} + 2 \, c d^{6} + d^{7}\right)} f\right)}}\right]"," ",0,"[1/4*((2*a^3*c^2*d^2 + 6*a^3*c*d^3 + 7*a^3*d^4 + (2*a^3*c^4 + 6*a^3*c^3*d + 7*a^3*c^2*d^2)*cos(f*x + e)^2 + 2*(2*a^3*c^3*d + 6*a^3*c^2*d^2 + 7*a^3*c*d^3)*cos(f*x + e))*sqrt((c - d)/(c + d))*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*(c^2 + c*d + (c*d + d^2)*cos(f*x + e))*sqrt((c - d)/(c + d))*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(a^3*c^2*d^2 + 2*a^3*c*d^3 + a^3*d^4 + (a^3*c^4 + 2*a^3*c^3*d + a^3*c^2*d^2)*cos(f*x + e)^2 + 2*(a^3*c^3*d + 2*a^3*c^2*d^2 + a^3*c*d^3)*cos(f*x + e))*log(sin(f*x + e) + 1) - 2*(a^3*c^2*d^2 + 2*a^3*c*d^3 + a^3*d^4 + (a^3*c^4 + 2*a^3*c^3*d + a^3*c^2*d^2)*cos(f*x + e)^2 + 2*(a^3*c^3*d + 2*a^3*c^2*d^2 + a^3*c*d^3)*cos(f*x + e))*log(-sin(f*x + e) + 1) - 2*(3*a^3*c^2*d^2 + 3*a^3*c*d^3 - 6*a^3*d^4 + (2*a^3*c^3*d + 4*a^3*c^2*d^2 - 5*a^3*c*d^3 - a^3*d^4)*cos(f*x + e))*sin(f*x + e))/((c^4*d^3 + 2*c^3*d^4 + c^2*d^5)*f*cos(f*x + e)^2 + 2*(c^3*d^4 + 2*c^2*d^5 + c*d^6)*f*cos(f*x + e) + (c^2*d^5 + 2*c*d^6 + d^7)*f), -1/2*((2*a^3*c^2*d^2 + 6*a^3*c*d^3 + 7*a^3*d^4 + (2*a^3*c^4 + 6*a^3*c^3*d + 7*a^3*c^2*d^2)*cos(f*x + e)^2 + 2*(2*a^3*c^3*d + 6*a^3*c^2*d^2 + 7*a^3*c*d^3)*cos(f*x + e))*sqrt(-(c - d)/(c + d))*arctan(-(d*cos(f*x + e) + c)*sqrt(-(c - d)/(c + d))/((c - d)*sin(f*x + e))) - (a^3*c^2*d^2 + 2*a^3*c*d^3 + a^3*d^4 + (a^3*c^4 + 2*a^3*c^3*d + a^3*c^2*d^2)*cos(f*x + e)^2 + 2*(a^3*c^3*d + 2*a^3*c^2*d^2 + a^3*c*d^3)*cos(f*x + e))*log(sin(f*x + e) + 1) + (a^3*c^2*d^2 + 2*a^3*c*d^3 + a^3*d^4 + (a^3*c^4 + 2*a^3*c^3*d + a^3*c^2*d^2)*cos(f*x + e)^2 + 2*(a^3*c^3*d + 2*a^3*c^2*d^2 + a^3*c*d^3)*cos(f*x + e))*log(-sin(f*x + e) + 1) + (3*a^3*c^2*d^2 + 3*a^3*c*d^3 - 6*a^3*d^4 + (2*a^3*c^3*d + 4*a^3*c^2*d^2 - 5*a^3*c*d^3 - a^3*d^4)*cos(f*x + e))*sin(f*x + e))/((c^4*d^3 + 2*c^3*d^4 + c^2*d^5)*f*cos(f*x + e)^2 + 2*(c^3*d^4 + 2*c^2*d^5 + c*d^6)*f*cos(f*x + e) + (c^2*d^5 + 2*c*d^6 + d^7)*f)]","B",0
208,1,1012,0,0.558110," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^4,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{3} c^{3} \cos\left(f x + e\right)^{3} + 3 \, a^{3} c^{2} d \cos\left(f x + e\right)^{2} + 3 \, a^{3} c d^{2} \cos\left(f x + e\right) + a^{3} d^{3}\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(2 \, a^{3} c^{4} + 9 \, a^{3} c^{3} d + 20 \, a^{3} c^{2} d^{2} - 9 \, a^{3} c d^{3} - 22 \, a^{3} d^{4} + {\left(22 \, a^{3} c^{4} + 9 \, a^{3} c^{3} d - 20 \, a^{3} c^{2} d^{2} - 9 \, a^{3} c d^{3} - 2 \, a^{3} d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(3 \, a^{3} c^{4} + 16 \, a^{3} c^{3} d - 16 \, a^{3} c d^{3} - 3 \, a^{3} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left({\left(c^{8} + 3 \, c^{7} d + 2 \, c^{6} d^{2} - 2 \, c^{5} d^{3} - 3 \, c^{4} d^{4} - c^{3} d^{5}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{7} d + 3 \, c^{6} d^{2} + 2 \, c^{5} d^{3} - 2 \, c^{4} d^{4} - 3 \, c^{3} d^{5} - c^{2} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{6} d^{2} + 3 \, c^{5} d^{3} + 2 \, c^{4} d^{4} - 2 \, c^{3} d^{5} - 3 \, c^{2} d^{6} - c d^{7}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{3} + 3 \, c^{4} d^{4} + 2 \, c^{3} d^{5} - 2 \, c^{2} d^{6} - 3 \, c d^{7} - d^{8}\right)} f\right)}}, \frac{15 \, {\left(a^{3} c^{3} \cos\left(f x + e\right)^{3} + 3 \, a^{3} c^{2} d \cos\left(f x + e\right)^{2} + 3 \, a^{3} c d^{2} \cos\left(f x + e\right) + a^{3} d^{3}\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(2 \, a^{3} c^{4} + 9 \, a^{3} c^{3} d + 20 \, a^{3} c^{2} d^{2} - 9 \, a^{3} c d^{3} - 22 \, a^{3} d^{4} + {\left(22 \, a^{3} c^{4} + 9 \, a^{3} c^{3} d - 20 \, a^{3} c^{2} d^{2} - 9 \, a^{3} c d^{3} - 2 \, a^{3} d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(3 \, a^{3} c^{4} + 16 \, a^{3} c^{3} d - 16 \, a^{3} c d^{3} - 3 \, a^{3} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(c^{8} + 3 \, c^{7} d + 2 \, c^{6} d^{2} - 2 \, c^{5} d^{3} - 3 \, c^{4} d^{4} - c^{3} d^{5}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{7} d + 3 \, c^{6} d^{2} + 2 \, c^{5} d^{3} - 2 \, c^{4} d^{4} - 3 \, c^{3} d^{5} - c^{2} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{6} d^{2} + 3 \, c^{5} d^{3} + 2 \, c^{4} d^{4} - 2 \, c^{3} d^{5} - 3 \, c^{2} d^{6} - c d^{7}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{3} + 3 \, c^{4} d^{4} + 2 \, c^{3} d^{5} - 2 \, c^{2} d^{6} - 3 \, c d^{7} - d^{8}\right)} f\right)}}\right]"," ",0,"[1/12*(15*(a^3*c^3*cos(f*x + e)^3 + 3*a^3*c^2*d*cos(f*x + e)^2 + 3*a^3*c*d^2*cos(f*x + e) + a^3*d^3)*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(2*a^3*c^4 + 9*a^3*c^3*d + 20*a^3*c^2*d^2 - 9*a^3*c*d^3 - 22*a^3*d^4 + (22*a^3*c^4 + 9*a^3*c^3*d - 20*a^3*c^2*d^2 - 9*a^3*c*d^3 - 2*a^3*d^4)*cos(f*x + e)^2 + 3*(3*a^3*c^4 + 16*a^3*c^3*d - 16*a^3*c*d^3 - 3*a^3*d^4)*cos(f*x + e))*sin(f*x + e))/((c^8 + 3*c^7*d + 2*c^6*d^2 - 2*c^5*d^3 - 3*c^4*d^4 - c^3*d^5)*f*cos(f*x + e)^3 + 3*(c^7*d + 3*c^6*d^2 + 2*c^5*d^3 - 2*c^4*d^4 - 3*c^3*d^5 - c^2*d^6)*f*cos(f*x + e)^2 + 3*(c^6*d^2 + 3*c^5*d^3 + 2*c^4*d^4 - 2*c^3*d^5 - 3*c^2*d^6 - c*d^7)*f*cos(f*x + e) + (c^5*d^3 + 3*c^4*d^4 + 2*c^3*d^5 - 2*c^2*d^6 - 3*c*d^7 - d^8)*f), 1/6*(15*(a^3*c^3*cos(f*x + e)^3 + 3*a^3*c^2*d*cos(f*x + e)^2 + 3*a^3*c*d^2*cos(f*x + e) + a^3*d^3)*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (2*a^3*c^4 + 9*a^3*c^3*d + 20*a^3*c^2*d^2 - 9*a^3*c*d^3 - 22*a^3*d^4 + (22*a^3*c^4 + 9*a^3*c^3*d - 20*a^3*c^2*d^2 - 9*a^3*c*d^3 - 2*a^3*d^4)*cos(f*x + e)^2 + 3*(3*a^3*c^4 + 16*a^3*c^3*d - 16*a^3*c*d^3 - 3*a^3*d^4)*cos(f*x + e))*sin(f*x + e))/((c^8 + 3*c^7*d + 2*c^6*d^2 - 2*c^5*d^3 - 3*c^4*d^4 - c^3*d^5)*f*cos(f*x + e)^3 + 3*(c^7*d + 3*c^6*d^2 + 2*c^5*d^3 - 2*c^4*d^4 - 3*c^3*d^5 - c^2*d^6)*f*cos(f*x + e)^2 + 3*(c^6*d^2 + 3*c^5*d^3 + 2*c^4*d^4 - 2*c^3*d^5 - 3*c^2*d^6 - c*d^7)*f*cos(f*x + e) + (c^5*d^3 + 3*c^4*d^4 + 2*c^3*d^5 - 2*c^2*d^6 - 3*c*d^7 - d^8)*f)]","B",0
209,1,1714,0,0.581632," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(4 \, a^{3} c d^{4} - 3 \, a^{3} d^{5} + {\left(4 \, a^{3} c^{5} - 3 \, a^{3} c^{4} d\right)} \cos\left(f x + e\right)^{4} + 4 \, {\left(4 \, a^{3} c^{4} d - 3 \, a^{3} c^{3} d^{2}\right)} \cos\left(f x + e\right)^{3} + 6 \, {\left(4 \, a^{3} c^{3} d^{2} - 3 \, a^{3} c^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(4 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(2 \, a^{3} c^{5} d + 12 \, a^{3} c^{4} d^{2} + 41 \, a^{3} c^{3} d^{3} - 84 \, a^{3} c^{2} d^{4} - 43 \, a^{3} c d^{5} + 72 \, a^{3} d^{6} + {\left(88 \, a^{3} c^{6} - 36 \, a^{3} c^{5} d - 125 \, a^{3} c^{4} d^{2} + 12 \, a^{3} c^{3} d^{3} + 31 \, a^{3} c^{2} d^{4} + 24 \, a^{3} c d^{5} + 6 \, a^{3} d^{6}\right)} \cos\left(f x + e\right)^{3} + {\left(36 \, a^{3} c^{6} + 235 \, a^{3} c^{5} d - 228 \, a^{3} c^{4} d^{2} - 335 \, a^{3} c^{3} d^{3} + 168 \, a^{3} c^{2} d^{4} + 100 \, a^{3} c d^{5} + 24 \, a^{3} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(8 \, a^{3} c^{6} + 48 \, a^{3} c^{5} d + 164 \, a^{3} c^{4} d^{2} - 276 \, a^{3} c^{3} d^{3} - 217 \, a^{3} c^{2} d^{4} + 228 \, a^{3} c d^{5} + 45 \, a^{3} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{48 \, {\left({\left(c^{11} + 3 \, c^{10} d + c^{9} d^{2} - 5 \, c^{8} d^{3} - 5 \, c^{7} d^{4} + c^{6} d^{5} + 3 \, c^{5} d^{6} + c^{4} d^{7}\right)} f \cos\left(f x + e\right)^{4} + 4 \, {\left(c^{10} d + 3 \, c^{9} d^{2} + c^{8} d^{3} - 5 \, c^{7} d^{4} - 5 \, c^{6} d^{5} + c^{5} d^{6} + 3 \, c^{4} d^{7} + c^{3} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 6 \, {\left(c^{9} d^{2} + 3 \, c^{8} d^{3} + c^{7} d^{4} - 5 \, c^{6} d^{5} - 5 \, c^{5} d^{6} + c^{4} d^{7} + 3 \, c^{3} d^{8} + c^{2} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{8} d^{3} + 3 \, c^{7} d^{4} + c^{6} d^{5} - 5 \, c^{5} d^{6} - 5 \, c^{4} d^{7} + c^{3} d^{8} + 3 \, c^{2} d^{9} + c d^{10}\right)} f \cos\left(f x + e\right) + {\left(c^{7} d^{4} + 3 \, c^{6} d^{5} + c^{5} d^{6} - 5 \, c^{4} d^{7} - 5 \, c^{3} d^{8} + c^{2} d^{9} + 3 \, c d^{10} + d^{11}\right)} f\right)}}, \frac{15 \, {\left(4 \, a^{3} c d^{4} - 3 \, a^{3} d^{5} + {\left(4 \, a^{3} c^{5} - 3 \, a^{3} c^{4} d\right)} \cos\left(f x + e\right)^{4} + 4 \, {\left(4 \, a^{3} c^{4} d - 3 \, a^{3} c^{3} d^{2}\right)} \cos\left(f x + e\right)^{3} + 6 \, {\left(4 \, a^{3} c^{3} d^{2} - 3 \, a^{3} c^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(4 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(2 \, a^{3} c^{5} d + 12 \, a^{3} c^{4} d^{2} + 41 \, a^{3} c^{3} d^{3} - 84 \, a^{3} c^{2} d^{4} - 43 \, a^{3} c d^{5} + 72 \, a^{3} d^{6} + {\left(88 \, a^{3} c^{6} - 36 \, a^{3} c^{5} d - 125 \, a^{3} c^{4} d^{2} + 12 \, a^{3} c^{3} d^{3} + 31 \, a^{3} c^{2} d^{4} + 24 \, a^{3} c d^{5} + 6 \, a^{3} d^{6}\right)} \cos\left(f x + e\right)^{3} + {\left(36 \, a^{3} c^{6} + 235 \, a^{3} c^{5} d - 228 \, a^{3} c^{4} d^{2} - 335 \, a^{3} c^{3} d^{3} + 168 \, a^{3} c^{2} d^{4} + 100 \, a^{3} c d^{5} + 24 \, a^{3} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(8 \, a^{3} c^{6} + 48 \, a^{3} c^{5} d + 164 \, a^{3} c^{4} d^{2} - 276 \, a^{3} c^{3} d^{3} - 217 \, a^{3} c^{2} d^{4} + 228 \, a^{3} c d^{5} + 45 \, a^{3} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, {\left({\left(c^{11} + 3 \, c^{10} d + c^{9} d^{2} - 5 \, c^{8} d^{3} - 5 \, c^{7} d^{4} + c^{6} d^{5} + 3 \, c^{5} d^{6} + c^{4} d^{7}\right)} f \cos\left(f x + e\right)^{4} + 4 \, {\left(c^{10} d + 3 \, c^{9} d^{2} + c^{8} d^{3} - 5 \, c^{7} d^{4} - 5 \, c^{6} d^{5} + c^{5} d^{6} + 3 \, c^{4} d^{7} + c^{3} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 6 \, {\left(c^{9} d^{2} + 3 \, c^{8} d^{3} + c^{7} d^{4} - 5 \, c^{6} d^{5} - 5 \, c^{5} d^{6} + c^{4} d^{7} + 3 \, c^{3} d^{8} + c^{2} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{8} d^{3} + 3 \, c^{7} d^{4} + c^{6} d^{5} - 5 \, c^{5} d^{6} - 5 \, c^{4} d^{7} + c^{3} d^{8} + 3 \, c^{2} d^{9} + c d^{10}\right)} f \cos\left(f x + e\right) + {\left(c^{7} d^{4} + 3 \, c^{6} d^{5} + c^{5} d^{6} - 5 \, c^{4} d^{7} - 5 \, c^{3} d^{8} + c^{2} d^{9} + 3 \, c d^{10} + d^{11}\right)} f\right)}}\right]"," ",0,"[1/48*(15*(4*a^3*c*d^4 - 3*a^3*d^5 + (4*a^3*c^5 - 3*a^3*c^4*d)*cos(f*x + e)^4 + 4*(4*a^3*c^4*d - 3*a^3*c^3*d^2)*cos(f*x + e)^3 + 6*(4*a^3*c^3*d^2 - 3*a^3*c^2*d^3)*cos(f*x + e)^2 + 4*(4*a^3*c^2*d^3 - 3*a^3*c*d^4)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(2*a^3*c^5*d + 12*a^3*c^4*d^2 + 41*a^3*c^3*d^3 - 84*a^3*c^2*d^4 - 43*a^3*c*d^5 + 72*a^3*d^6 + (88*a^3*c^6 - 36*a^3*c^5*d - 125*a^3*c^4*d^2 + 12*a^3*c^3*d^3 + 31*a^3*c^2*d^4 + 24*a^3*c*d^5 + 6*a^3*d^6)*cos(f*x + e)^3 + (36*a^3*c^6 + 235*a^3*c^5*d - 228*a^3*c^4*d^2 - 335*a^3*c^3*d^3 + 168*a^3*c^2*d^4 + 100*a^3*c*d^5 + 24*a^3*d^6)*cos(f*x + e)^2 + (8*a^3*c^6 + 48*a^3*c^5*d + 164*a^3*c^4*d^2 - 276*a^3*c^3*d^3 - 217*a^3*c^2*d^4 + 228*a^3*c*d^5 + 45*a^3*d^6)*cos(f*x + e))*sin(f*x + e))/((c^11 + 3*c^10*d + c^9*d^2 - 5*c^8*d^3 - 5*c^7*d^4 + c^6*d^5 + 3*c^5*d^6 + c^4*d^7)*f*cos(f*x + e)^4 + 4*(c^10*d + 3*c^9*d^2 + c^8*d^3 - 5*c^7*d^4 - 5*c^6*d^5 + c^5*d^6 + 3*c^4*d^7 + c^3*d^8)*f*cos(f*x + e)^3 + 6*(c^9*d^2 + 3*c^8*d^3 + c^7*d^4 - 5*c^6*d^5 - 5*c^5*d^6 + c^4*d^7 + 3*c^3*d^8 + c^2*d^9)*f*cos(f*x + e)^2 + 4*(c^8*d^3 + 3*c^7*d^4 + c^6*d^5 - 5*c^5*d^6 - 5*c^4*d^7 + c^3*d^8 + 3*c^2*d^9 + c*d^10)*f*cos(f*x + e) + (c^7*d^4 + 3*c^6*d^5 + c^5*d^6 - 5*c^4*d^7 - 5*c^3*d^8 + c^2*d^9 + 3*c*d^10 + d^11)*f), 1/24*(15*(4*a^3*c*d^4 - 3*a^3*d^5 + (4*a^3*c^5 - 3*a^3*c^4*d)*cos(f*x + e)^4 + 4*(4*a^3*c^4*d - 3*a^3*c^3*d^2)*cos(f*x + e)^3 + 6*(4*a^3*c^3*d^2 - 3*a^3*c^2*d^3)*cos(f*x + e)^2 + 4*(4*a^3*c^2*d^3 - 3*a^3*c*d^4)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (2*a^3*c^5*d + 12*a^3*c^4*d^2 + 41*a^3*c^3*d^3 - 84*a^3*c^2*d^4 - 43*a^3*c*d^5 + 72*a^3*d^6 + (88*a^3*c^6 - 36*a^3*c^5*d - 125*a^3*c^4*d^2 + 12*a^3*c^3*d^3 + 31*a^3*c^2*d^4 + 24*a^3*c*d^5 + 6*a^3*d^6)*cos(f*x + e)^3 + (36*a^3*c^6 + 235*a^3*c^5*d - 228*a^3*c^4*d^2 - 335*a^3*c^3*d^3 + 168*a^3*c^2*d^4 + 100*a^3*c*d^5 + 24*a^3*d^6)*cos(f*x + e)^2 + (8*a^3*c^6 + 48*a^3*c^5*d + 164*a^3*c^4*d^2 - 276*a^3*c^3*d^3 - 217*a^3*c^2*d^4 + 228*a^3*c*d^5 + 45*a^3*d^6)*cos(f*x + e))*sin(f*x + e))/((c^11 + 3*c^10*d + c^9*d^2 - 5*c^8*d^3 - 5*c^7*d^4 + c^6*d^5 + 3*c^5*d^6 + c^4*d^7)*f*cos(f*x + e)^4 + 4*(c^10*d + 3*c^9*d^2 + c^8*d^3 - 5*c^7*d^4 - 5*c^6*d^5 + c^5*d^6 + 3*c^4*d^7 + c^3*d^8)*f*cos(f*x + e)^3 + 6*(c^9*d^2 + 3*c^8*d^3 + c^7*d^4 - 5*c^6*d^5 - 5*c^5*d^6 + c^4*d^7 + 3*c^3*d^8 + c^2*d^9)*f*cos(f*x + e)^2 + 4*(c^8*d^3 + 3*c^7*d^4 + c^6*d^5 - 5*c^5*d^6 - 5*c^4*d^7 + c^3*d^8 + 3*c^2*d^9 + c*d^10)*f*cos(f*x + e) + (c^7*d^4 + 3*c^6*d^5 + c^5*d^6 - 5*c^4*d^7 - 5*c^3*d^8 + c^2*d^9 + 3*c*d^10 + d^11)*f)]","B",0
210,1,297,0,0.477472," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(8 \, c^{3} d - 12 \, c^{2} d^{2} + 12 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)^{4} + {\left(8 \, c^{3} d - 12 \, c^{2} d^{2} + 12 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left({\left(8 \, c^{3} d - 12 \, c^{2} d^{2} + 12 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)^{4} + {\left(8 \, c^{3} d - 12 \, c^{2} d^{2} + 12 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, d^{4} + 2 \, {\left(3 \, c^{4} - 12 \, c^{3} d + 36 \, c^{2} d^{2} - 24 \, c d^{3} + 8 \, d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(36 \, c^{2} d^{2} - 12 \, c d^{3} + 7 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(12 \, c d^{3} - d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left(a f \cos\left(f x + e\right)^{4} + a f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"1/12*(3*((8*c^3*d - 12*c^2*d^2 + 12*c*d^3 - 3*d^4)*cos(f*x + e)^4 + (8*c^3*d - 12*c^2*d^2 + 12*c*d^3 - 3*d^4)*cos(f*x + e)^3)*log(sin(f*x + e) + 1) - 3*((8*c^3*d - 12*c^2*d^2 + 12*c*d^3 - 3*d^4)*cos(f*x + e)^4 + (8*c^3*d - 12*c^2*d^2 + 12*c*d^3 - 3*d^4)*cos(f*x + e)^3)*log(-sin(f*x + e) + 1) + 2*(2*d^4 + 2*(3*c^4 - 12*c^3*d + 36*c^2*d^2 - 24*c*d^3 + 8*d^4)*cos(f*x + e)^3 + (36*c^2*d^2 - 12*c*d^3 + 7*d^4)*cos(f*x + e)^2 + (12*c*d^3 - d^4)*cos(f*x + e))*sin(f*x + e))/(a*f*cos(f*x + e)^4 + a*f*cos(f*x + e)^3)","A",0
211,1,216,0,0.449397," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(2 \, c^{2} d - 2 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, c^{2} d - 2 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left({\left(2 \, c^{2} d - 2 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, c^{2} d - 2 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(d^{3} + 2 \, {\left(c^{3} - 3 \, c^{2} d + 6 \, c d^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left(a f \cos\left(f x + e\right)^{3} + a f \cos\left(f x + e\right)^{2}\right)}}"," ",0,"1/4*(3*((2*c^2*d - 2*c*d^2 + d^3)*cos(f*x + e)^3 + (2*c^2*d - 2*c*d^2 + d^3)*cos(f*x + e)^2)*log(sin(f*x + e) + 1) - 3*((2*c^2*d - 2*c*d^2 + d^3)*cos(f*x + e)^3 + (2*c^2*d - 2*c*d^2 + d^3)*cos(f*x + e)^2)*log(-sin(f*x + e) + 1) + 2*(d^3 + 2*(c^3 - 3*c^2*d + 6*c*d^2 - 2*d^3)*cos(f*x + e)^2 + (6*c*d^2 - d^3)*cos(f*x + e))*sin(f*x + e))/(a*f*cos(f*x + e)^3 + a*f*cos(f*x + e)^2)","A",0
212,1,155,0,0.444021," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{{\left({\left(2 \, c d - d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c d - d^{2}\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left({\left(2 \, c d - d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c d - d^{2}\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(d^{2} + {\left(c^{2} - 2 \, c d + 2 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left(a f \cos\left(f x + e\right)^{2} + a f \cos\left(f x + e\right)\right)}}"," ",0,"1/2*(((2*c*d - d^2)*cos(f*x + e)^2 + (2*c*d - d^2)*cos(f*x + e))*log(sin(f*x + e) + 1) - ((2*c*d - d^2)*cos(f*x + e)^2 + (2*c*d - d^2)*cos(f*x + e))*log(-sin(f*x + e) + 1) + 2*(d^2 + (c^2 - 2*c*d + 2*d^2)*cos(f*x + e))*sin(f*x + e))/(a*f*cos(f*x + e)^2 + a*f*cos(f*x + e))","B",0
213,1,74,0,0.476670," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(d \cos\left(f x + e\right) + d\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(d \cos\left(f x + e\right) + d\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(c - d\right)} \sin\left(f x + e\right)}{2 \, {\left(a f \cos\left(f x + e\right) + a f\right)}}"," ",0,"1/2*((d*cos(f*x + e) + d)*log(sin(f*x + e) + 1) - (d*cos(f*x + e) + d)*log(-sin(f*x + e) + 1) + 2*(c - d)*sin(f*x + e))/(a*f*cos(f*x + e) + a*f)","A",0
214,1,353,0,0.483575," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + d\right)} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - 2 \, {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} f \cos\left(f x + e\right) + {\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} f\right)}}, -\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + d\right)} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}{{\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} f \cos\left(f x + e\right) + {\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} f}\right]"," ",0,"[-1/2*(sqrt(c^2 - d^2)*(d*cos(f*x + e) + d)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - 2*(c^2 - d^2)*sin(f*x + e))/((a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*f*cos(f*x + e) + (a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*f), -(sqrt(-c^2 + d^2)*(d*cos(f*x + e) + d)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (c^2 - d^2)*sin(f*x + e))/((a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*f*cos(f*x + e) + (a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*f)]","A",0
215,1,691,0,0.484791," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, c d^{2} + d^{3} + {\left(2 \, c^{2} d + c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(c^{3} d + 2 \, c^{2} d^{2} - c d^{3} - 2 \, d^{4} + {\left(c^{4} + c^{3} d - c d^{3} - d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a c^{6} - a c^{5} d - 2 \, a c^{4} d^{2} + 2 \, a c^{3} d^{3} + a c^{2} d^{4} - a c d^{5}\right)} f \cos\left(f x + e\right)^{2} + {\left(a c^{6} - 3 \, a c^{4} d^{2} + 3 \, a c^{2} d^{4} - a d^{6}\right)} f \cos\left(f x + e\right) + {\left(a c^{5} d - a c^{4} d^{2} - 2 \, a c^{3} d^{3} + 2 \, a c^{2} d^{4} + a c d^{5} - a d^{6}\right)} f\right)}}, -\frac{{\left(2 \, c d^{2} + d^{3} + {\left(2 \, c^{2} d + c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(c^{3} d + 2 \, c^{2} d^{2} - c d^{3} - 2 \, d^{4} + {\left(c^{4} + c^{3} d - c d^{3} - d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{{\left(a c^{6} - a c^{5} d - 2 \, a c^{4} d^{2} + 2 \, a c^{3} d^{3} + a c^{2} d^{4} - a c d^{5}\right)} f \cos\left(f x + e\right)^{2} + {\left(a c^{6} - 3 \, a c^{4} d^{2} + 3 \, a c^{2} d^{4} - a d^{6}\right)} f \cos\left(f x + e\right) + {\left(a c^{5} d - a c^{4} d^{2} - 2 \, a c^{3} d^{3} + 2 \, a c^{2} d^{4} + a c d^{5} - a d^{6}\right)} f}\right]"," ",0,"[1/2*((2*c*d^2 + d^3 + (2*c^2*d + c*d^2)*cos(f*x + e)^2 + (2*c^2*d + 3*c*d^2 + d^3)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(c^3*d + 2*c^2*d^2 - c*d^3 - 2*d^4 + (c^4 + c^3*d - c*d^3 - d^4)*cos(f*x + e))*sin(f*x + e))/((a*c^6 - a*c^5*d - 2*a*c^4*d^2 + 2*a*c^3*d^3 + a*c^2*d^4 - a*c*d^5)*f*cos(f*x + e)^2 + (a*c^6 - 3*a*c^4*d^2 + 3*a*c^2*d^4 - a*d^6)*f*cos(f*x + e) + (a*c^5*d - a*c^4*d^2 - 2*a*c^3*d^3 + 2*a*c^2*d^4 + a*c*d^5 - a*d^6)*f), -((2*c*d^2 + d^3 + (2*c^2*d + c*d^2)*cos(f*x + e)^2 + (2*c^2*d + 3*c*d^2 + d^3)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (c^3*d + 2*c^2*d^2 - c*d^3 - 2*d^4 + (c^4 + c^3*d - c*d^3 - d^4)*cos(f*x + e))*sin(f*x + e))/((a*c^6 - a*c^5*d - 2*a*c^4*d^2 + 2*a*c^3*d^3 + a*c^2*d^4 - a*c*d^5)*f*cos(f*x + e)^2 + (a*c^6 - 3*a*c^4*d^2 + 3*a*c^2*d^4 - a*d^6)*f*cos(f*x + e) + (a*c^5*d - a*c^4*d^2 - 2*a*c^3*d^3 + 2*a*c^2*d^4 + a*c*d^5 - a*d^6)*f)]","B",0
216,1,1331,0,0.774394," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, c^{2} d^{3} + 2 \, c d^{4} + d^{5} + {\left(2 \, c^{4} d + 2 \, c^{3} d^{2} + c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, c^{4} d + 6 \, c^{3} d^{2} + 5 \, c^{2} d^{3} + 2 \, c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(4 \, c^{3} d^{2} + 6 \, c^{2} d^{3} + 4 \, c d^{4} + d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - 2 \, {\left(2 \, c^{4} d^{2} + 9 \, c^{3} d^{3} + 2 \, c^{2} d^{4} - 9 \, c d^{5} - 4 \, d^{6} + {\left(2 \, c^{6} + 4 \, c^{5} d + 6 \, c^{4} d^{2} - 2 \, c^{3} d^{3} - 9 \, c^{2} d^{4} - 2 \, c d^{5} + d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(4 \, c^{5} d + 14 \, c^{4} d^{2} + 7 \, c^{3} d^{3} - 13 \, c^{2} d^{4} - 11 \, c d^{5} - d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(a c^{9} - a c^{8} d - 3 \, a c^{7} d^{2} + 3 \, a c^{6} d^{3} + 3 \, a c^{5} d^{4} - 3 \, a c^{4} d^{5} - a c^{3} d^{6} + a c^{2} d^{7}\right)} f \cos\left(f x + e\right)^{3} + {\left(a c^{9} + a c^{8} d - 5 \, a c^{7} d^{2} - 3 \, a c^{6} d^{3} + 9 \, a c^{5} d^{4} + 3 \, a c^{4} d^{5} - 7 \, a c^{3} d^{6} - a c^{2} d^{7} + 2 \, a c d^{8}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, a c^{8} d - a c^{7} d^{2} - 7 \, a c^{6} d^{3} + 3 \, a c^{5} d^{4} + 9 \, a c^{4} d^{5} - 3 \, a c^{3} d^{6} - 5 \, a c^{2} d^{7} + a c d^{8} + a d^{9}\right)} f \cos\left(f x + e\right) + {\left(a c^{7} d^{2} - a c^{6} d^{3} - 3 \, a c^{5} d^{4} + 3 \, a c^{4} d^{5} + 3 \, a c^{3} d^{6} - 3 \, a c^{2} d^{7} - a c d^{8} + a d^{9}\right)} f\right)}}, -\frac{3 \, {\left(2 \, c^{2} d^{3} + 2 \, c d^{4} + d^{5} + {\left(2 \, c^{4} d + 2 \, c^{3} d^{2} + c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, c^{4} d + 6 \, c^{3} d^{2} + 5 \, c^{2} d^{3} + 2 \, c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(4 \, c^{3} d^{2} + 6 \, c^{2} d^{3} + 4 \, c d^{4} + d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(2 \, c^{4} d^{2} + 9 \, c^{3} d^{3} + 2 \, c^{2} d^{4} - 9 \, c d^{5} - 4 \, d^{6} + {\left(2 \, c^{6} + 4 \, c^{5} d + 6 \, c^{4} d^{2} - 2 \, c^{3} d^{3} - 9 \, c^{2} d^{4} - 2 \, c d^{5} + d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(4 \, c^{5} d + 14 \, c^{4} d^{2} + 7 \, c^{3} d^{3} - 13 \, c^{2} d^{4} - 11 \, c d^{5} - d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a c^{9} - a c^{8} d - 3 \, a c^{7} d^{2} + 3 \, a c^{6} d^{3} + 3 \, a c^{5} d^{4} - 3 \, a c^{4} d^{5} - a c^{3} d^{6} + a c^{2} d^{7}\right)} f \cos\left(f x + e\right)^{3} + {\left(a c^{9} + a c^{8} d - 5 \, a c^{7} d^{2} - 3 \, a c^{6} d^{3} + 9 \, a c^{5} d^{4} + 3 \, a c^{4} d^{5} - 7 \, a c^{3} d^{6} - a c^{2} d^{7} + 2 \, a c d^{8}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, a c^{8} d - a c^{7} d^{2} - 7 \, a c^{6} d^{3} + 3 \, a c^{5} d^{4} + 9 \, a c^{4} d^{5} - 3 \, a c^{3} d^{6} - 5 \, a c^{2} d^{7} + a c d^{8} + a d^{9}\right)} f \cos\left(f x + e\right) + {\left(a c^{7} d^{2} - a c^{6} d^{3} - 3 \, a c^{5} d^{4} + 3 \, a c^{4} d^{5} + 3 \, a c^{3} d^{6} - 3 \, a c^{2} d^{7} - a c d^{8} + a d^{9}\right)} f\right)}}\right]"," ",0,"[-1/4*(3*(2*c^2*d^3 + 2*c*d^4 + d^5 + (2*c^4*d + 2*c^3*d^2 + c^2*d^3)*cos(f*x + e)^3 + (2*c^4*d + 6*c^3*d^2 + 5*c^2*d^3 + 2*c*d^4)*cos(f*x + e)^2 + (4*c^3*d^2 + 6*c^2*d^3 + 4*c*d^4 + d^5)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - 2*(2*c^4*d^2 + 9*c^3*d^3 + 2*c^2*d^4 - 9*c*d^5 - 4*d^6 + (2*c^6 + 4*c^5*d + 6*c^4*d^2 - 2*c^3*d^3 - 9*c^2*d^4 - 2*c*d^5 + d^6)*cos(f*x + e)^2 + (4*c^5*d + 14*c^4*d^2 + 7*c^3*d^3 - 13*c^2*d^4 - 11*c*d^5 - d^6)*cos(f*x + e))*sin(f*x + e))/((a*c^9 - a*c^8*d - 3*a*c^7*d^2 + 3*a*c^6*d^3 + 3*a*c^5*d^4 - 3*a*c^4*d^5 - a*c^3*d^6 + a*c^2*d^7)*f*cos(f*x + e)^3 + (a*c^9 + a*c^8*d - 5*a*c^7*d^2 - 3*a*c^6*d^3 + 9*a*c^5*d^4 + 3*a*c^4*d^5 - 7*a*c^3*d^6 - a*c^2*d^7 + 2*a*c*d^8)*f*cos(f*x + e)^2 + (2*a*c^8*d - a*c^7*d^2 - 7*a*c^6*d^3 + 3*a*c^5*d^4 + 9*a*c^4*d^5 - 3*a*c^3*d^6 - 5*a*c^2*d^7 + a*c*d^8 + a*d^9)*f*cos(f*x + e) + (a*c^7*d^2 - a*c^6*d^3 - 3*a*c^5*d^4 + 3*a*c^4*d^5 + 3*a*c^3*d^6 - 3*a*c^2*d^7 - a*c*d^8 + a*d^9)*f), -1/2*(3*(2*c^2*d^3 + 2*c*d^4 + d^5 + (2*c^4*d + 2*c^3*d^2 + c^2*d^3)*cos(f*x + e)^3 + (2*c^4*d + 6*c^3*d^2 + 5*c^2*d^3 + 2*c*d^4)*cos(f*x + e)^2 + (4*c^3*d^2 + 6*c^2*d^3 + 4*c*d^4 + d^5)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (2*c^4*d^2 + 9*c^3*d^3 + 2*c^2*d^4 - 9*c*d^5 - 4*d^6 + (2*c^6 + 4*c^5*d + 6*c^4*d^2 - 2*c^3*d^3 - 9*c^2*d^4 - 2*c*d^5 + d^6)*cos(f*x + e)^2 + (4*c^5*d + 14*c^4*d^2 + 7*c^3*d^3 - 13*c^2*d^4 - 11*c*d^5 - d^6)*cos(f*x + e))*sin(f*x + e))/((a*c^9 - a*c^8*d - 3*a*c^7*d^2 + 3*a*c^6*d^3 + 3*a*c^5*d^4 - 3*a*c^4*d^5 - a*c^3*d^6 + a*c^2*d^7)*f*cos(f*x + e)^3 + (a*c^9 + a*c^8*d - 5*a*c^7*d^2 - 3*a*c^6*d^3 + 9*a*c^5*d^4 + 3*a*c^4*d^5 - 7*a*c^3*d^6 - a*c^2*d^7 + 2*a*c*d^8)*f*cos(f*x + e)^2 + (2*a*c^8*d - a*c^7*d^2 - 7*a*c^6*d^3 + 3*a*c^5*d^4 + 9*a*c^4*d^5 - 3*a*c^3*d^6 - 5*a*c^2*d^7 + a*c*d^8 + a*d^9)*f*cos(f*x + e) + (a*c^7*d^2 - a*c^6*d^3 - 3*a*c^5*d^4 + 3*a*c^4*d^5 + 3*a*c^3*d^6 - 3*a*c^2*d^7 - a*c*d^8 + a*d^9)*f)]","B",0
217,1,456,0,0.502274," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^5/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(4 \, c^{3} d^{2} - 8 \, c^{2} d^{3} + 7 \, c d^{4} - 2 \, d^{5}\right)} \cos\left(f x + e\right)^{5} + 2 \, {\left(4 \, c^{3} d^{2} - 8 \, c^{2} d^{3} + 7 \, c d^{4} - 2 \, d^{5}\right)} \cos\left(f x + e\right)^{4} + {\left(4 \, c^{3} d^{2} - 8 \, c^{2} d^{3} + 7 \, c d^{4} - 2 \, d^{5}\right)} \cos\left(f x + e\right)^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left({\left(4 \, c^{3} d^{2} - 8 \, c^{2} d^{3} + 7 \, c d^{4} - 2 \, d^{5}\right)} \cos\left(f x + e\right)^{5} + 2 \, {\left(4 \, c^{3} d^{2} - 8 \, c^{2} d^{3} + 7 \, c d^{4} - 2 \, d^{5}\right)} \cos\left(f x + e\right)^{4} + {\left(4 \, c^{3} d^{2} - 8 \, c^{2} d^{3} + 7 \, c d^{4} - 2 \, d^{5}\right)} \cos\left(f x + e\right)^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, d^{5} + 2 \, {\left(2 \, c^{5} + 5 \, c^{4} d - 40 \, c^{3} d^{2} + 100 \, c^{2} d^{3} - 80 \, c d^{4} + 24 \, d^{5}\right)} \cos\left(f x + e\right)^{4} + {\left(2 \, c^{5} + 20 \, c^{4} d - 100 \, c^{3} d^{2} + 280 \, c^{2} d^{3} - 215 \, c d^{4} + 66 \, d^{5}\right)} \cos\left(f x + e\right)^{3} + 6 \, {\left(10 \, c^{2} d^{3} - 5 \, c d^{4} + 2 \, d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, c d^{4} - 2 \, d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left(a^{2} f \cos\left(f x + e\right)^{5} + 2 \, a^{2} f \cos\left(f x + e\right)^{4} + a^{2} f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"1/12*(15*((4*c^3*d^2 - 8*c^2*d^3 + 7*c*d^4 - 2*d^5)*cos(f*x + e)^5 + 2*(4*c^3*d^2 - 8*c^2*d^3 + 7*c*d^4 - 2*d^5)*cos(f*x + e)^4 + (4*c^3*d^2 - 8*c^2*d^3 + 7*c*d^4 - 2*d^5)*cos(f*x + e)^3)*log(sin(f*x + e) + 1) - 15*((4*c^3*d^2 - 8*c^2*d^3 + 7*c*d^4 - 2*d^5)*cos(f*x + e)^5 + 2*(4*c^3*d^2 - 8*c^2*d^3 + 7*c*d^4 - 2*d^5)*cos(f*x + e)^4 + (4*c^3*d^2 - 8*c^2*d^3 + 7*c*d^4 - 2*d^5)*cos(f*x + e)^3)*log(-sin(f*x + e) + 1) + 2*(2*d^5 + 2*(2*c^5 + 5*c^4*d - 40*c^3*d^2 + 100*c^2*d^3 - 80*c*d^4 + 24*d^5)*cos(f*x + e)^4 + (2*c^5 + 20*c^4*d - 100*c^3*d^2 + 280*c^2*d^3 - 215*c*d^4 + 66*d^5)*cos(f*x + e)^3 + 6*(10*c^2*d^3 - 5*c*d^4 + 2*d^5)*cos(f*x + e)^2 + (15*c*d^4 - 2*d^5)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^5 + 2*a^2*f*cos(f*x + e)^4 + a^2*f*cos(f*x + e)^3)","A",0
218,1,361,0,0.460611," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(12 \, c^{2} d^{2} - 16 \, c d^{3} + 7 \, d^{4}\right)} \cos\left(f x + e\right)^{4} + 2 \, {\left(12 \, c^{2} d^{2} - 16 \, c d^{3} + 7 \, d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(12 \, c^{2} d^{2} - 16 \, c d^{3} + 7 \, d^{4}\right)} \cos\left(f x + e\right)^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left({\left(12 \, c^{2} d^{2} - 16 \, c d^{3} + 7 \, d^{4}\right)} \cos\left(f x + e\right)^{4} + 2 \, {\left(12 \, c^{2} d^{2} - 16 \, c d^{3} + 7 \, d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(12 \, c^{2} d^{2} - 16 \, c d^{3} + 7 \, d^{4}\right)} \cos\left(f x + e\right)^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(3 \, d^{4} + 4 \, {\left(c^{4} + 2 \, c^{3} d - 12 \, c^{2} d^{2} + 20 \, c d^{3} - 8 \, d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, c^{4} + 16 \, c^{3} d - 60 \, c^{2} d^{2} + 112 \, c d^{3} - 43 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(4 \, c d^{3} - d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left(a^{2} f \cos\left(f x + e\right)^{4} + 2 \, a^{2} f \cos\left(f x + e\right)^{3} + a^{2} f \cos\left(f x + e\right)^{2}\right)}}"," ",0,"1/12*(3*((12*c^2*d^2 - 16*c*d^3 + 7*d^4)*cos(f*x + e)^4 + 2*(12*c^2*d^2 - 16*c*d^3 + 7*d^4)*cos(f*x + e)^3 + (12*c^2*d^2 - 16*c*d^3 + 7*d^4)*cos(f*x + e)^2)*log(sin(f*x + e) + 1) - 3*((12*c^2*d^2 - 16*c*d^3 + 7*d^4)*cos(f*x + e)^4 + 2*(12*c^2*d^2 - 16*c*d^3 + 7*d^4)*cos(f*x + e)^3 + (12*c^2*d^2 - 16*c*d^3 + 7*d^4)*cos(f*x + e)^2)*log(-sin(f*x + e) + 1) + 2*(3*d^4 + 4*(c^4 + 2*c^3*d - 12*c^2*d^2 + 20*c*d^3 - 8*d^4)*cos(f*x + e)^3 + (2*c^4 + 16*c^3*d - 60*c^2*d^2 + 112*c*d^3 - 43*d^4)*cos(f*x + e)^2 + 6*(4*c*d^3 - d^4)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^4 + 2*a^2*f*cos(f*x + e)^3 + a^2*f*cos(f*x + e)^2)","A",0
219,1,268,0,0.471341," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(3 \, c d^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(3 \, c d^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, c d^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left({\left(3 \, c d^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(3 \, c d^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, c d^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(3 \, d^{3} + {\left(2 \, c^{3} + 3 \, c^{2} d - 12 \, c d^{2} + 10 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{3} + 6 \, c^{2} d - 15 \, c d^{2} + 14 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left(a^{2} f \cos\left(f x + e\right)^{3} + 2 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \cos\left(f x + e\right)\right)}}"," ",0,"1/6*(3*((3*c*d^2 - 2*d^3)*cos(f*x + e)^3 + 2*(3*c*d^2 - 2*d^3)*cos(f*x + e)^2 + (3*c*d^2 - 2*d^3)*cos(f*x + e))*log(sin(f*x + e) + 1) - 3*((3*c*d^2 - 2*d^3)*cos(f*x + e)^3 + 2*(3*c*d^2 - 2*d^3)*cos(f*x + e)^2 + (3*c*d^2 - 2*d^3)*cos(f*x + e))*log(-sin(f*x + e) + 1) + 2*(3*d^3 + (2*c^3 + 3*c^2*d - 12*c*d^2 + 10*d^3)*cos(f*x + e)^2 + (c^3 + 6*c^2*d - 15*c*d^2 + 14*d^3)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^3 + 2*a^2*f*cos(f*x + e)^2 + a^2*f*cos(f*x + e))","B",0
220,1,155,0,0.457434," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(d^{2} \cos\left(f x + e\right)^{2} + 2 \, d^{2} \cos\left(f x + e\right) + d^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(d^{2} \cos\left(f x + e\right)^{2} + 2 \, d^{2} \cos\left(f x + e\right) + d^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(c^{2} + 4 \, c d - 5 \, d^{2} + 2 \, {\left(c^{2} + c d - 2 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}"," ",0,"1/6*(3*(d^2*cos(f*x + e)^2 + 2*d^2*cos(f*x + e) + d^2)*log(sin(f*x + e) + 1) - 3*(d^2*cos(f*x + e)^2 + 2*d^2*cos(f*x + e) + d^2)*log(-sin(f*x + e) + 1) + 2*(c^2 + 4*c*d - 5*d^2 + 2*(c^2 + c*d - 2*d^2)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)","A",0
221,1,58,0,0.450294," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, c + d\right)} \cos\left(f x + e\right) + c + 2 \, d\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}"," ",0,"1/3*((2*c + d)*cos(f*x + e) + c + 2*d)*sin(f*x + e)/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)","A",0
222,1,598,0,0.481127," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(d^{2} \cos\left(f x + e\right)^{2} + 2 \, d^{2} \cos\left(f x + e\right) + d^{2}\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(c^{3} - 4 \, c^{2} d - c d^{2} + 4 \, d^{3} + {\left(2 \, c^{3} - 5 \, c^{2} d - 2 \, c d^{2} + 5 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f \cos\left(f x + e\right) + {\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f\right)}}, \frac{3 \, {\left(d^{2} \cos\left(f x + e\right)^{2} + 2 \, d^{2} \cos\left(f x + e\right) + d^{2}\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(c^{3} - 4 \, c^{2} d - c d^{2} + 4 \, d^{3} + {\left(2 \, c^{3} - 5 \, c^{2} d - 2 \, c d^{2} + 5 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left({\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f \cos\left(f x + e\right) + {\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f\right)}}\right]"," ",0,"[1/6*(3*(d^2*cos(f*x + e)^2 + 2*d^2*cos(f*x + e) + d^2)*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(c^3 - 4*c^2*d - c*d^2 + 4*d^3 + (2*c^3 - 5*c^2*d - 2*c*d^2 + 5*d^3)*cos(f*x + e))*sin(f*x + e))/((a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f*cos(f*x + e)^2 + 2*(a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f*cos(f*x + e) + (a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f), 1/3*(3*(d^2*cos(f*x + e)^2 + 2*d^2*cos(f*x + e) + d^2)*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (c^3 - 4*c^2*d - c*d^2 + 4*d^3 + (2*c^3 - 5*c^2*d - 2*c*d^2 + 5*d^3)*cos(f*x + e))*sin(f*x + e))/((a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f*cos(f*x + e)^2 + 2*(a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f*cos(f*x + e) + (a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f)]","B",0
223,1,1242,0,0.530065," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, c d^{3} + 2 \, d^{4} + {\left(3 \, c^{2} d^{2} + 2 \, c d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(6 \, c^{2} d^{2} + 7 \, c d^{3} + 2 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, c^{2} d^{2} + 8 \, c d^{3} + 4 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - 2 \, {\left(c^{4} d - 6 \, c^{3} d^{2} - 11 \, c^{2} d^{3} + 6 \, c d^{4} + 10 \, d^{5} + {\left(2 \, c^{5} - 6 \, c^{4} d - 10 \, c^{3} d^{2} + 3 \, c^{2} d^{3} + 8 \, c d^{4} + 3 \, d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{5} - 4 \, c^{4} d - 14 \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 13 \, c d^{4} + 14 \, d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(a^{2} c^{7} - 2 \, a^{2} c^{6} d - a^{2} c^{5} d^{2} + 4 \, a^{2} c^{4} d^{3} - a^{2} c^{3} d^{4} - 2 \, a^{2} c^{2} d^{5} + a^{2} c d^{6}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, a^{2} c^{7} - 3 \, a^{2} c^{6} d - 4 \, a^{2} c^{5} d^{2} + 7 \, a^{2} c^{4} d^{3} + 2 \, a^{2} c^{3} d^{4} - 5 \, a^{2} c^{2} d^{5} + a^{2} d^{7}\right)} f \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{7} - 5 \, a^{2} c^{5} d^{2} + 2 \, a^{2} c^{4} d^{3} + 7 \, a^{2} c^{3} d^{4} - 4 \, a^{2} c^{2} d^{5} - 3 \, a^{2} c d^{6} + 2 \, a^{2} d^{7}\right)} f \cos\left(f x + e\right) + {\left(a^{2} c^{6} d - 2 \, a^{2} c^{5} d^{2} - a^{2} c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4} - a^{2} c^{2} d^{5} - 2 \, a^{2} c d^{6} + a^{2} d^{7}\right)} f\right)}}, \frac{3 \, {\left(3 \, c d^{3} + 2 \, d^{4} + {\left(3 \, c^{2} d^{2} + 2 \, c d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(6 \, c^{2} d^{2} + 7 \, c d^{3} + 2 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, c^{2} d^{2} + 8 \, c d^{3} + 4 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(c^{4} d - 6 \, c^{3} d^{2} - 11 \, c^{2} d^{3} + 6 \, c d^{4} + 10 \, d^{5} + {\left(2 \, c^{5} - 6 \, c^{4} d - 10 \, c^{3} d^{2} + 3 \, c^{2} d^{3} + 8 \, c d^{4} + 3 \, d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{5} - 4 \, c^{4} d - 14 \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 13 \, c d^{4} + 14 \, d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left({\left(a^{2} c^{7} - 2 \, a^{2} c^{6} d - a^{2} c^{5} d^{2} + 4 \, a^{2} c^{4} d^{3} - a^{2} c^{3} d^{4} - 2 \, a^{2} c^{2} d^{5} + a^{2} c d^{6}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, a^{2} c^{7} - 3 \, a^{2} c^{6} d - 4 \, a^{2} c^{5} d^{2} + 7 \, a^{2} c^{4} d^{3} + 2 \, a^{2} c^{3} d^{4} - 5 \, a^{2} c^{2} d^{5} + a^{2} d^{7}\right)} f \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{7} - 5 \, a^{2} c^{5} d^{2} + 2 \, a^{2} c^{4} d^{3} + 7 \, a^{2} c^{3} d^{4} - 4 \, a^{2} c^{2} d^{5} - 3 \, a^{2} c d^{6} + 2 \, a^{2} d^{7}\right)} f \cos\left(f x + e\right) + {\left(a^{2} c^{6} d - 2 \, a^{2} c^{5} d^{2} - a^{2} c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4} - a^{2} c^{2} d^{5} - 2 \, a^{2} c d^{6} + a^{2} d^{7}\right)} f\right)}}\right]"," ",0,"[-1/6*(3*(3*c*d^3 + 2*d^4 + (3*c^2*d^2 + 2*c*d^3)*cos(f*x + e)^3 + (6*c^2*d^2 + 7*c*d^3 + 2*d^4)*cos(f*x + e)^2 + (3*c^2*d^2 + 8*c*d^3 + 4*d^4)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - 2*(c^4*d - 6*c^3*d^2 - 11*c^2*d^3 + 6*c*d^4 + 10*d^5 + (2*c^5 - 6*c^4*d - 10*c^3*d^2 + 3*c^2*d^3 + 8*c*d^4 + 3*d^5)*cos(f*x + e)^2 + (c^5 - 4*c^4*d - 14*c^3*d^2 - 10*c^2*d^3 + 13*c*d^4 + 14*d^5)*cos(f*x + e))*sin(f*x + e))/((a^2*c^7 - 2*a^2*c^6*d - a^2*c^5*d^2 + 4*a^2*c^4*d^3 - a^2*c^3*d^4 - 2*a^2*c^2*d^5 + a^2*c*d^6)*f*cos(f*x + e)^3 + (2*a^2*c^7 - 3*a^2*c^6*d - 4*a^2*c^5*d^2 + 7*a^2*c^4*d^3 + 2*a^2*c^3*d^4 - 5*a^2*c^2*d^5 + a^2*d^7)*f*cos(f*x + e)^2 + (a^2*c^7 - 5*a^2*c^5*d^2 + 2*a^2*c^4*d^3 + 7*a^2*c^3*d^4 - 4*a^2*c^2*d^5 - 3*a^2*c*d^6 + 2*a^2*d^7)*f*cos(f*x + e) + (a^2*c^6*d - 2*a^2*c^5*d^2 - a^2*c^4*d^3 + 4*a^2*c^3*d^4 - a^2*c^2*d^5 - 2*a^2*c*d^6 + a^2*d^7)*f), 1/3*(3*(3*c*d^3 + 2*d^4 + (3*c^2*d^2 + 2*c*d^3)*cos(f*x + e)^3 + (6*c^2*d^2 + 7*c*d^3 + 2*d^4)*cos(f*x + e)^2 + (3*c^2*d^2 + 8*c*d^3 + 4*d^4)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (c^4*d - 6*c^3*d^2 - 11*c^2*d^3 + 6*c*d^4 + 10*d^5 + (2*c^5 - 6*c^4*d - 10*c^3*d^2 + 3*c^2*d^3 + 8*c*d^4 + 3*d^5)*cos(f*x + e)^2 + (c^5 - 4*c^4*d - 14*c^3*d^2 - 10*c^2*d^3 + 13*c*d^4 + 14*d^5)*cos(f*x + e))*sin(f*x + e))/((a^2*c^7 - 2*a^2*c^6*d - a^2*c^5*d^2 + 4*a^2*c^4*d^3 - a^2*c^3*d^4 - 2*a^2*c^2*d^5 + a^2*c*d^6)*f*cos(f*x + e)^3 + (2*a^2*c^7 - 3*a^2*c^6*d - 4*a^2*c^5*d^2 + 7*a^2*c^4*d^3 + 2*a^2*c^3*d^4 - 5*a^2*c^2*d^5 + a^2*d^7)*f*cos(f*x + e)^2 + (a^2*c^7 - 5*a^2*c^5*d^2 + 2*a^2*c^4*d^3 + 7*a^2*c^3*d^4 - 4*a^2*c^2*d^5 - 3*a^2*c*d^6 + 2*a^2*d^7)*f*cos(f*x + e) + (a^2*c^6*d - 2*a^2*c^5*d^2 - a^2*c^4*d^3 + 4*a^2*c^3*d^4 - a^2*c^2*d^5 - 2*a^2*c*d^6 + a^2*d^7)*f)]","B",0
224,1,2030,0,0.608824," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(12 \, c^{2} d^{4} + 16 \, c d^{5} + 7 \, d^{6} + {\left(12 \, c^{4} d^{2} + 16 \, c^{3} d^{3} + 7 \, c^{2} d^{4}\right)} \cos\left(f x + e\right)^{4} + 2 \, {\left(12 \, c^{4} d^{2} + 28 \, c^{3} d^{3} + 23 \, c^{2} d^{4} + 7 \, c d^{5}\right)} \cos\left(f x + e\right)^{3} + {\left(12 \, c^{4} d^{2} + 64 \, c^{3} d^{3} + 83 \, c^{2} d^{4} + 44 \, c d^{5} + 7 \, d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(12 \, c^{3} d^{3} + 28 \, c^{2} d^{4} + 23 \, c d^{5} + 7 \, d^{6}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(2 \, c^{5} d^{2} - 16 \, c^{4} d^{3} - 61 \, c^{3} d^{4} - 16 \, c^{2} d^{5} + 59 \, c d^{6} + 32 \, d^{7} + {\left(4 \, c^{7} - 14 \, c^{6} d - 44 \, c^{5} d^{2} - 32 \, c^{4} d^{3} + 28 \, c^{3} d^{4} + 49 \, c^{2} d^{5} + 12 \, c d^{6} - 3 \, d^{7}\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, c^{7} - 8 \, c^{6} d - 68 \, c^{5} d^{2} - 140 \, c^{4} d^{3} - 23 \, c^{3} d^{4} + 142 \, c^{2} d^{5} + 89 \, c d^{6} + 6 \, d^{7}\right)} \cos\left(f x + e\right)^{2} + {\left(4 \, c^{6} d - 28 \, c^{5} d^{2} - 118 \, c^{4} d^{3} - 106 \, c^{3} d^{4} + 71 \, c^{2} d^{5} + 134 \, c d^{6} + 43 \, d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left({\left(a^{2} c^{10} - 2 \, a^{2} c^{9} d - 2 \, a^{2} c^{8} d^{2} + 6 \, a^{2} c^{7} d^{3} - 6 \, a^{2} c^{5} d^{5} + 2 \, a^{2} c^{4} d^{6} + 2 \, a^{2} c^{3} d^{7} - a^{2} c^{2} d^{8}\right)} f \cos\left(f x + e\right)^{4} + 2 \, {\left(a^{2} c^{10} - a^{2} c^{9} d - 4 \, a^{2} c^{8} d^{2} + 4 \, a^{2} c^{7} d^{3} + 6 \, a^{2} c^{6} d^{4} - 6 \, a^{2} c^{5} d^{5} - 4 \, a^{2} c^{4} d^{6} + 4 \, a^{2} c^{3} d^{7} + a^{2} c^{2} d^{8} - a^{2} c d^{9}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{10} + 2 \, a^{2} c^{9} d - 9 \, a^{2} c^{8} d^{2} - 4 \, a^{2} c^{7} d^{3} + 22 \, a^{2} c^{6} d^{4} - 22 \, a^{2} c^{4} d^{6} + 4 \, a^{2} c^{3} d^{7} + 9 \, a^{2} c^{2} d^{8} - 2 \, a^{2} c d^{9} - a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{2} c^{9} d - a^{2} c^{8} d^{2} - 4 \, a^{2} c^{7} d^{3} + 4 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 6 \, a^{2} c^{4} d^{6} - 4 \, a^{2} c^{3} d^{7} + 4 \, a^{2} c^{2} d^{8} + a^{2} c d^{9} - a^{2} d^{10}\right)} f \cos\left(f x + e\right) + {\left(a^{2} c^{8} d^{2} - 2 \, a^{2} c^{7} d^{3} - 2 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 6 \, a^{2} c^{3} d^{7} + 2 \, a^{2} c^{2} d^{8} + 2 \, a^{2} c d^{9} - a^{2} d^{10}\right)} f\right)}}, \frac{3 \, {\left(12 \, c^{2} d^{4} + 16 \, c d^{5} + 7 \, d^{6} + {\left(12 \, c^{4} d^{2} + 16 \, c^{3} d^{3} + 7 \, c^{2} d^{4}\right)} \cos\left(f x + e\right)^{4} + 2 \, {\left(12 \, c^{4} d^{2} + 28 \, c^{3} d^{3} + 23 \, c^{2} d^{4} + 7 \, c d^{5}\right)} \cos\left(f x + e\right)^{3} + {\left(12 \, c^{4} d^{2} + 64 \, c^{3} d^{3} + 83 \, c^{2} d^{4} + 44 \, c d^{5} + 7 \, d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(12 \, c^{3} d^{3} + 28 \, c^{2} d^{4} + 23 \, c d^{5} + 7 \, d^{6}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(2 \, c^{5} d^{2} - 16 \, c^{4} d^{3} - 61 \, c^{3} d^{4} - 16 \, c^{2} d^{5} + 59 \, c d^{6} + 32 \, d^{7} + {\left(4 \, c^{7} - 14 \, c^{6} d - 44 \, c^{5} d^{2} - 32 \, c^{4} d^{3} + 28 \, c^{3} d^{4} + 49 \, c^{2} d^{5} + 12 \, c d^{6} - 3 \, d^{7}\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, c^{7} - 8 \, c^{6} d - 68 \, c^{5} d^{2} - 140 \, c^{4} d^{3} - 23 \, c^{3} d^{4} + 142 \, c^{2} d^{5} + 89 \, c d^{6} + 6 \, d^{7}\right)} \cos\left(f x + e\right)^{2} + {\left(4 \, c^{6} d - 28 \, c^{5} d^{2} - 118 \, c^{4} d^{3} - 106 \, c^{3} d^{4} + 71 \, c^{2} d^{5} + 134 \, c d^{6} + 43 \, d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(a^{2} c^{10} - 2 \, a^{2} c^{9} d - 2 \, a^{2} c^{8} d^{2} + 6 \, a^{2} c^{7} d^{3} - 6 \, a^{2} c^{5} d^{5} + 2 \, a^{2} c^{4} d^{6} + 2 \, a^{2} c^{3} d^{7} - a^{2} c^{2} d^{8}\right)} f \cos\left(f x + e\right)^{4} + 2 \, {\left(a^{2} c^{10} - a^{2} c^{9} d - 4 \, a^{2} c^{8} d^{2} + 4 \, a^{2} c^{7} d^{3} + 6 \, a^{2} c^{6} d^{4} - 6 \, a^{2} c^{5} d^{5} - 4 \, a^{2} c^{4} d^{6} + 4 \, a^{2} c^{3} d^{7} + a^{2} c^{2} d^{8} - a^{2} c d^{9}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{10} + 2 \, a^{2} c^{9} d - 9 \, a^{2} c^{8} d^{2} - 4 \, a^{2} c^{7} d^{3} + 22 \, a^{2} c^{6} d^{4} - 22 \, a^{2} c^{4} d^{6} + 4 \, a^{2} c^{3} d^{7} + 9 \, a^{2} c^{2} d^{8} - 2 \, a^{2} c d^{9} - a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{2} c^{9} d - a^{2} c^{8} d^{2} - 4 \, a^{2} c^{7} d^{3} + 4 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 6 \, a^{2} c^{4} d^{6} - 4 \, a^{2} c^{3} d^{7} + 4 \, a^{2} c^{2} d^{8} + a^{2} c d^{9} - a^{2} d^{10}\right)} f \cos\left(f x + e\right) + {\left(a^{2} c^{8} d^{2} - 2 \, a^{2} c^{7} d^{3} - 2 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 6 \, a^{2} c^{3} d^{7} + 2 \, a^{2} c^{2} d^{8} + 2 \, a^{2} c d^{9} - a^{2} d^{10}\right)} f\right)}}\right]"," ",0,"[1/12*(3*(12*c^2*d^4 + 16*c*d^5 + 7*d^6 + (12*c^4*d^2 + 16*c^3*d^3 + 7*c^2*d^4)*cos(f*x + e)^4 + 2*(12*c^4*d^2 + 28*c^3*d^3 + 23*c^2*d^4 + 7*c*d^5)*cos(f*x + e)^3 + (12*c^4*d^2 + 64*c^3*d^3 + 83*c^2*d^4 + 44*c*d^5 + 7*d^6)*cos(f*x + e)^2 + 2*(12*c^3*d^3 + 28*c^2*d^4 + 23*c*d^5 + 7*d^6)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(2*c^5*d^2 - 16*c^4*d^3 - 61*c^3*d^4 - 16*c^2*d^5 + 59*c*d^6 + 32*d^7 + (4*c^7 - 14*c^6*d - 44*c^5*d^2 - 32*c^4*d^3 + 28*c^3*d^4 + 49*c^2*d^5 + 12*c*d^6 - 3*d^7)*cos(f*x + e)^3 + (2*c^7 - 8*c^6*d - 68*c^5*d^2 - 140*c^4*d^3 - 23*c^3*d^4 + 142*c^2*d^5 + 89*c*d^6 + 6*d^7)*cos(f*x + e)^2 + (4*c^6*d - 28*c^5*d^2 - 118*c^4*d^3 - 106*c^3*d^4 + 71*c^2*d^5 + 134*c*d^6 + 43*d^7)*cos(f*x + e))*sin(f*x + e))/((a^2*c^10 - 2*a^2*c^9*d - 2*a^2*c^8*d^2 + 6*a^2*c^7*d^3 - 6*a^2*c^5*d^5 + 2*a^2*c^4*d^6 + 2*a^2*c^3*d^7 - a^2*c^2*d^8)*f*cos(f*x + e)^4 + 2*(a^2*c^10 - a^2*c^9*d - 4*a^2*c^8*d^2 + 4*a^2*c^7*d^3 + 6*a^2*c^6*d^4 - 6*a^2*c^5*d^5 - 4*a^2*c^4*d^6 + 4*a^2*c^3*d^7 + a^2*c^2*d^8 - a^2*c*d^9)*f*cos(f*x + e)^3 + (a^2*c^10 + 2*a^2*c^9*d - 9*a^2*c^8*d^2 - 4*a^2*c^7*d^3 + 22*a^2*c^6*d^4 - 22*a^2*c^4*d^6 + 4*a^2*c^3*d^7 + 9*a^2*c^2*d^8 - 2*a^2*c*d^9 - a^2*d^10)*f*cos(f*x + e)^2 + 2*(a^2*c^9*d - a^2*c^8*d^2 - 4*a^2*c^7*d^3 + 4*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 6*a^2*c^4*d^6 - 4*a^2*c^3*d^7 + 4*a^2*c^2*d^8 + a^2*c*d^9 - a^2*d^10)*f*cos(f*x + e) + (a^2*c^8*d^2 - 2*a^2*c^7*d^3 - 2*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 6*a^2*c^3*d^7 + 2*a^2*c^2*d^8 + 2*a^2*c*d^9 - a^2*d^10)*f), 1/6*(3*(12*c^2*d^4 + 16*c*d^5 + 7*d^6 + (12*c^4*d^2 + 16*c^3*d^3 + 7*c^2*d^4)*cos(f*x + e)^4 + 2*(12*c^4*d^2 + 28*c^3*d^3 + 23*c^2*d^4 + 7*c*d^5)*cos(f*x + e)^3 + (12*c^4*d^2 + 64*c^3*d^3 + 83*c^2*d^4 + 44*c*d^5 + 7*d^6)*cos(f*x + e)^2 + 2*(12*c^3*d^3 + 28*c^2*d^4 + 23*c*d^5 + 7*d^6)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (2*c^5*d^2 - 16*c^4*d^3 - 61*c^3*d^4 - 16*c^2*d^5 + 59*c*d^6 + 32*d^7 + (4*c^7 - 14*c^6*d - 44*c^5*d^2 - 32*c^4*d^3 + 28*c^3*d^4 + 49*c^2*d^5 + 12*c*d^6 - 3*d^7)*cos(f*x + e)^3 + (2*c^7 - 8*c^6*d - 68*c^5*d^2 - 140*c^4*d^3 - 23*c^3*d^4 + 142*c^2*d^5 + 89*c*d^6 + 6*d^7)*cos(f*x + e)^2 + (4*c^6*d - 28*c^5*d^2 - 118*c^4*d^3 - 106*c^3*d^4 + 71*c^2*d^5 + 134*c*d^6 + 43*d^7)*cos(f*x + e))*sin(f*x + e))/((a^2*c^10 - 2*a^2*c^9*d - 2*a^2*c^8*d^2 + 6*a^2*c^7*d^3 - 6*a^2*c^5*d^5 + 2*a^2*c^4*d^6 + 2*a^2*c^3*d^7 - a^2*c^2*d^8)*f*cos(f*x + e)^4 + 2*(a^2*c^10 - a^2*c^9*d - 4*a^2*c^8*d^2 + 4*a^2*c^7*d^3 + 6*a^2*c^6*d^4 - 6*a^2*c^5*d^5 - 4*a^2*c^4*d^6 + 4*a^2*c^3*d^7 + a^2*c^2*d^8 - a^2*c*d^9)*f*cos(f*x + e)^3 + (a^2*c^10 + 2*a^2*c^9*d - 9*a^2*c^8*d^2 - 4*a^2*c^7*d^3 + 22*a^2*c^6*d^4 - 22*a^2*c^4*d^6 + 4*a^2*c^3*d^7 + 9*a^2*c^2*d^8 - 2*a^2*c*d^9 - a^2*d^10)*f*cos(f*x + e)^2 + 2*(a^2*c^9*d - a^2*c^8*d^2 - 4*a^2*c^7*d^3 + 4*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 6*a^2*c^4*d^6 - 4*a^2*c^3*d^7 + 4*a^2*c^2*d^8 + a^2*c*d^9 - a^2*d^10)*f*cos(f*x + e) + (a^2*c^8*d^2 - 2*a^2*c^7*d^3 - 2*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 6*a^2*c^3*d^7 + 2*a^2*c^2*d^8 + 2*a^2*c*d^9 - a^2*d^10)*f)]","B",0
225,1,620,0,0.500871," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^6/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(40 \, c^{3} d^{3} - 90 \, c^{2} d^{4} + 78 \, c d^{5} - 23 \, d^{6}\right)} \cos\left(f x + e\right)^{6} + 3 \, {\left(40 \, c^{3} d^{3} - 90 \, c^{2} d^{4} + 78 \, c d^{5} - 23 \, d^{6}\right)} \cos\left(f x + e\right)^{5} + 3 \, {\left(40 \, c^{3} d^{3} - 90 \, c^{2} d^{4} + 78 \, c d^{5} - 23 \, d^{6}\right)} \cos\left(f x + e\right)^{4} + {\left(40 \, c^{3} d^{3} - 90 \, c^{2} d^{4} + 78 \, c d^{5} - 23 \, d^{6}\right)} \cos\left(f x + e\right)^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left({\left(40 \, c^{3} d^{3} - 90 \, c^{2} d^{4} + 78 \, c d^{5} - 23 \, d^{6}\right)} \cos\left(f x + e\right)^{6} + 3 \, {\left(40 \, c^{3} d^{3} - 90 \, c^{2} d^{4} + 78 \, c d^{5} - 23 \, d^{6}\right)} \cos\left(f x + e\right)^{5} + 3 \, {\left(40 \, c^{3} d^{3} - 90 \, c^{2} d^{4} + 78 \, c d^{5} - 23 \, d^{6}\right)} \cos\left(f x + e\right)^{4} + {\left(40 \, c^{3} d^{3} - 90 \, c^{2} d^{4} + 78 \, c d^{5} - 23 \, d^{6}\right)} \cos\left(f x + e\right)^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(10 \, d^{6} + 2 \, {\left(7 \, c^{6} + 18 \, c^{5} d + 30 \, c^{4} d^{2} - 440 \, c^{3} d^{3} + 1080 \, c^{2} d^{4} - 912 \, c d^{5} + 272 \, d^{6}\right)} \cos\left(f x + e\right)^{5} + 3 \, {\left(4 \, c^{6} + 36 \, c^{5} d + 60 \, c^{4} d^{2} - 680 \, c^{3} d^{3} + 1710 \, c^{2} d^{4} - 1434 \, c d^{5} + 429 \, d^{6}\right)} \cos\left(f x + e\right)^{4} + {\left(4 \, c^{6} + 36 \, c^{5} d + 210 \, c^{4} d^{2} - 1280 \, c^{3} d^{3} + 3510 \, c^{2} d^{4} - 2874 \, c d^{5} + 869 \, d^{6}\right)} \cos\left(f x + e\right)^{3} + 5 \, {\left(90 \, c^{2} d^{4} - 54 \, c d^{5} + 19 \, d^{6}\right)} \cos\left(f x + e\right)^{2} + 15 \, {\left(6 \, c d^{5} - d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{60 \, {\left(a^{3} f \cos\left(f x + e\right)^{6} + 3 \, a^{3} f \cos\left(f x + e\right)^{5} + 3 \, a^{3} f \cos\left(f x + e\right)^{4} + a^{3} f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"1/60*(15*((40*c^3*d^3 - 90*c^2*d^4 + 78*c*d^5 - 23*d^6)*cos(f*x + e)^6 + 3*(40*c^3*d^3 - 90*c^2*d^4 + 78*c*d^5 - 23*d^6)*cos(f*x + e)^5 + 3*(40*c^3*d^3 - 90*c^2*d^4 + 78*c*d^5 - 23*d^6)*cos(f*x + e)^4 + (40*c^3*d^3 - 90*c^2*d^4 + 78*c*d^5 - 23*d^6)*cos(f*x + e)^3)*log(sin(f*x + e) + 1) - 15*((40*c^3*d^3 - 90*c^2*d^4 + 78*c*d^5 - 23*d^6)*cos(f*x + e)^6 + 3*(40*c^3*d^3 - 90*c^2*d^4 + 78*c*d^5 - 23*d^6)*cos(f*x + e)^5 + 3*(40*c^3*d^3 - 90*c^2*d^4 + 78*c*d^5 - 23*d^6)*cos(f*x + e)^4 + (40*c^3*d^3 - 90*c^2*d^4 + 78*c*d^5 - 23*d^6)*cos(f*x + e)^3)*log(-sin(f*x + e) + 1) + 2*(10*d^6 + 2*(7*c^6 + 18*c^5*d + 30*c^4*d^2 - 440*c^3*d^3 + 1080*c^2*d^4 - 912*c*d^5 + 272*d^6)*cos(f*x + e)^5 + 3*(4*c^6 + 36*c^5*d + 60*c^4*d^2 - 680*c^3*d^3 + 1710*c^2*d^4 - 1434*c*d^5 + 429*d^6)*cos(f*x + e)^4 + (4*c^6 + 36*c^5*d + 210*c^4*d^2 - 1280*c^3*d^3 + 3510*c^2*d^4 - 2874*c*d^5 + 869*d^6)*cos(f*x + e)^3 + 5*(90*c^2*d^4 - 54*c*d^5 + 19*d^6)*cos(f*x + e)^2 + 15*(6*c*d^5 - d^6)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^6 + 3*a^3*f*cos(f*x + e)^5 + 3*a^3*f*cos(f*x + e)^4 + a^3*f*cos(f*x + e)^3)","A",0
226,1,502,0,0.481072," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^5/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(20 \, c^{2} d^{3} - 30 \, c d^{4} + 13 \, d^{5}\right)} \cos\left(f x + e\right)^{5} + 3 \, {\left(20 \, c^{2} d^{3} - 30 \, c d^{4} + 13 \, d^{5}\right)} \cos\left(f x + e\right)^{4} + 3 \, {\left(20 \, c^{2} d^{3} - 30 \, c d^{4} + 13 \, d^{5}\right)} \cos\left(f x + e\right)^{3} + {\left(20 \, c^{2} d^{3} - 30 \, c d^{4} + 13 \, d^{5}\right)} \cos\left(f x + e\right)^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left({\left(20 \, c^{2} d^{3} - 30 \, c d^{4} + 13 \, d^{5}\right)} \cos\left(f x + e\right)^{5} + 3 \, {\left(20 \, c^{2} d^{3} - 30 \, c d^{4} + 13 \, d^{5}\right)} \cos\left(f x + e\right)^{4} + 3 \, {\left(20 \, c^{2} d^{3} - 30 \, c d^{4} + 13 \, d^{5}\right)} \cos\left(f x + e\right)^{3} + {\left(20 \, c^{2} d^{3} - 30 \, c d^{4} + 13 \, d^{5}\right)} \cos\left(f x + e\right)^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(15 \, d^{5} + 2 \, {\left(7 \, c^{5} + 15 \, c^{4} d + 20 \, c^{3} d^{2} - 220 \, c^{2} d^{3} + 360 \, c d^{4} - 152 \, d^{5}\right)} \cos\left(f x + e\right)^{4} + 3 \, {\left(4 \, c^{5} + 30 \, c^{4} d + 40 \, c^{3} d^{2} - 340 \, c^{2} d^{3} + 570 \, c d^{4} - 239 \, d^{5}\right)} \cos\left(f x + e\right)^{3} + {\left(4 \, c^{5} + 30 \, c^{4} d + 140 \, c^{3} d^{2} - 640 \, c^{2} d^{3} + 1170 \, c d^{4} - 479 \, d^{5}\right)} \cos\left(f x + e\right)^{2} + 15 \, {\left(10 \, c d^{4} - 3 \, d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{60 \, {\left(a^{3} f \cos\left(f x + e\right)^{5} + 3 \, a^{3} f \cos\left(f x + e\right)^{4} + 3 \, a^{3} f \cos\left(f x + e\right)^{3} + a^{3} f \cos\left(f x + e\right)^{2}\right)}}"," ",0,"1/60*(15*((20*c^2*d^3 - 30*c*d^4 + 13*d^5)*cos(f*x + e)^5 + 3*(20*c^2*d^3 - 30*c*d^4 + 13*d^5)*cos(f*x + e)^4 + 3*(20*c^2*d^3 - 30*c*d^4 + 13*d^5)*cos(f*x + e)^3 + (20*c^2*d^3 - 30*c*d^4 + 13*d^5)*cos(f*x + e)^2)*log(sin(f*x + e) + 1) - 15*((20*c^2*d^3 - 30*c*d^4 + 13*d^5)*cos(f*x + e)^5 + 3*(20*c^2*d^3 - 30*c*d^4 + 13*d^5)*cos(f*x + e)^4 + 3*(20*c^2*d^3 - 30*c*d^4 + 13*d^5)*cos(f*x + e)^3 + (20*c^2*d^3 - 30*c*d^4 + 13*d^5)*cos(f*x + e)^2)*log(-sin(f*x + e) + 1) + 2*(15*d^5 + 2*(7*c^5 + 15*c^4*d + 20*c^3*d^2 - 220*c^2*d^3 + 360*c*d^4 - 152*d^5)*cos(f*x + e)^4 + 3*(4*c^5 + 30*c^4*d + 40*c^3*d^2 - 340*c^2*d^3 + 570*c*d^4 - 239*d^5)*cos(f*x + e)^3 + (4*c^5 + 30*c^4*d + 140*c^3*d^2 - 640*c^2*d^3 + 1170*c*d^4 - 479*d^5)*cos(f*x + e)^2 + 15*(10*c*d^4 - 3*d^5)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^5 + 3*a^3*f*cos(f*x + e)^4 + 3*a^3*f*cos(f*x + e)^3 + a^3*f*cos(f*x + e)^2)","A",0
227,1,385,0,0.458158," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, {\left({\left(4 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)^{4} + 3 \, {\left(4 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(4 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(4 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left({\left(4 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)^{4} + 3 \, {\left(4 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(4 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(4 \, c d^{3} - 3 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(15 \, d^{4} + {\left(7 \, c^{4} + 12 \, c^{3} d + 12 \, c^{2} d^{2} - 88 \, c d^{3} + 72 \, d^{4}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(2 \, c^{4} + 12 \, c^{3} d + 12 \, c^{2} d^{2} - 68 \, c d^{3} + 57 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c^{4} + 12 \, c^{3} d + 42 \, c^{2} d^{2} - 128 \, c d^{3} + 117 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{30 \, {\left(a^{3} f \cos\left(f x + e\right)^{4} + 3 \, a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + a^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"1/30*(15*((4*c*d^3 - 3*d^4)*cos(f*x + e)^4 + 3*(4*c*d^3 - 3*d^4)*cos(f*x + e)^3 + 3*(4*c*d^3 - 3*d^4)*cos(f*x + e)^2 + (4*c*d^3 - 3*d^4)*cos(f*x + e))*log(sin(f*x + e) + 1) - 15*((4*c*d^3 - 3*d^4)*cos(f*x + e)^4 + 3*(4*c*d^3 - 3*d^4)*cos(f*x + e)^3 + 3*(4*c*d^3 - 3*d^4)*cos(f*x + e)^2 + (4*c*d^3 - 3*d^4)*cos(f*x + e))*log(-sin(f*x + e) + 1) + 2*(15*d^4 + (7*c^4 + 12*c^3*d + 12*c^2*d^2 - 88*c*d^3 + 72*d^4)*cos(f*x + e)^3 + 3*(2*c^4 + 12*c^3*d + 12*c^2*d^2 - 68*c*d^3 + 57*d^4)*cos(f*x + e)^2 + (2*c^4 + 12*c^3*d + 42*c^2*d^2 - 128*c*d^3 + 117*d^4)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^4 + 3*a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + a^3*f*cos(f*x + e))","A",0
228,1,248,0,0.497737," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(d^{3} \cos\left(f x + e\right)^{3} + 3 \, d^{3} \cos\left(f x + e\right)^{2} + 3 \, d^{3} \cos\left(f x + e\right) + d^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(d^{3} \cos\left(f x + e\right)^{3} + 3 \, d^{3} \cos\left(f x + e\right)^{2} + 3 \, d^{3} \cos\left(f x + e\right) + d^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, c^{3} + 9 \, c^{2} d + 21 \, c d^{2} - 32 \, d^{3} + {\left(7 \, c^{3} + 9 \, c^{2} d + 6 \, c d^{2} - 22 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, c^{3} + 9 \, c^{2} d + 6 \, c d^{2} - 17 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{30 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"1/30*(15*(d^3*cos(f*x + e)^3 + 3*d^3*cos(f*x + e)^2 + 3*d^3*cos(f*x + e) + d^3)*log(sin(f*x + e) + 1) - 15*(d^3*cos(f*x + e)^3 + 3*d^3*cos(f*x + e)^2 + 3*d^3*cos(f*x + e) + d^3)*log(-sin(f*x + e) + 1) + 2*(2*c^3 + 9*c^2*d + 21*c*d^2 - 32*d^3 + (7*c^3 + 9*c^2*d + 6*c*d^2 - 22*d^3)*cos(f*x + e)^2 + 3*(2*c^3 + 9*c^2*d + 6*c*d^2 - 17*d^3)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","A",0
229,1,113,0,0.420609," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left({\left(7 \, c^{2} + 6 \, c d + 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, c^{2} + 6 \, c d + 7 \, d^{2} + 6 \, {\left(c^{2} + 3 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"1/15*((7*c^2 + 6*c*d + 2*d^2)*cos(f*x + e)^2 + 2*c^2 + 6*c*d + 7*d^2 + 6*(c^2 + 3*c*d + d^2)*cos(f*x + e))*sin(f*x + e)/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","A",0
230,1,93,0,0.445766," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left({\left(7 \, c + 3 \, d\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, c + 3 \, d\right)} \cos\left(f x + e\right) + 2 \, c + 3 \, d\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"1/15*((7*c + 3*d)*cos(f*x + e)^2 + 3*(2*c + 3*d)*cos(f*x + e) + 2*c + 3*d)*sin(f*x + e)/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","A",0
231,1,1001,0,0.512448," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(d^{3} \cos\left(f x + e\right)^{3} + 3 \, d^{3} \cos\left(f x + e\right)^{2} + 3 \, d^{3} \cos\left(f x + e\right) + d^{3}\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - 2 \, {\left(2 \, c^{4} - 9 \, c^{3} d + 20 \, c^{2} d^{2} + 9 \, c d^{3} - 22 \, d^{4} + {\left(7 \, c^{4} - 24 \, c^{3} d + 25 \, c^{2} d^{2} + 24 \, c d^{3} - 32 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, c^{4} - 9 \, c^{3} d + 15 \, c^{2} d^{2} + 9 \, c d^{3} - 17 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{30 \, {\left({\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right) + {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f\right)}}, -\frac{15 \, {\left(d^{3} \cos\left(f x + e\right)^{3} + 3 \, d^{3} \cos\left(f x + e\right)^{2} + 3 \, d^{3} \cos\left(f x + e\right) + d^{3}\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(2 \, c^{4} - 9 \, c^{3} d + 20 \, c^{2} d^{2} + 9 \, c d^{3} - 22 \, d^{4} + {\left(7 \, c^{4} - 24 \, c^{3} d + 25 \, c^{2} d^{2} + 24 \, c d^{3} - 32 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, c^{4} - 9 \, c^{3} d + 15 \, c^{2} d^{2} + 9 \, c d^{3} - 17 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left({\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right) + {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f\right)}}\right]"," ",0,"[-1/30*(15*(d^3*cos(f*x + e)^3 + 3*d^3*cos(f*x + e)^2 + 3*d^3*cos(f*x + e) + d^3)*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - 2*(2*c^4 - 9*c^3*d + 20*c^2*d^2 + 9*c*d^3 - 22*d^4 + (7*c^4 - 24*c^3*d + 25*c^2*d^2 + 24*c*d^3 - 32*d^4)*cos(f*x + e)^2 + 3*(2*c^4 - 9*c^3*d + 15*c^2*d^2 + 9*c*d^3 - 17*d^4)*cos(f*x + e))*sin(f*x + e))/((a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e)^3 + 3*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e)^2 + 3*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e) + (a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f), -1/15*(15*(d^3*cos(f*x + e)^3 + 3*d^3*cos(f*x + e)^2 + 3*d^3*cos(f*x + e) + d^3)*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (2*c^4 - 9*c^3*d + 20*c^2*d^2 + 9*c*d^3 - 22*d^4 + (7*c^4 - 24*c^3*d + 25*c^2*d^2 + 24*c*d^3 - 32*d^4)*cos(f*x + e)^2 + 3*(2*c^4 - 9*c^3*d + 15*c^2*d^2 + 9*c*d^3 - 17*d^4)*cos(f*x + e))*sin(f*x + e))/((a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e)^3 + 3*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e)^2 + 3*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e) + (a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f)]","B",0
232,1,1693,0,0.538936," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(4 \, c d^{4} + 3 \, d^{5} + {\left(4 \, c^{2} d^{3} + 3 \, c d^{4}\right)} \cos\left(f x + e\right)^{4} + {\left(12 \, c^{2} d^{3} + 13 \, c d^{4} + 3 \, d^{5}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(4 \, c^{2} d^{3} + 7 \, c d^{4} + 3 \, d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(4 \, c^{2} d^{3} + 15 \, c d^{4} + 9 \, d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(2 \, c^{5} d - 12 \, c^{4} d^{2} + 41 \, c^{3} d^{3} + 84 \, c^{2} d^{4} - 43 \, c d^{5} - 72 \, d^{6} + {\left(7 \, c^{6} - 27 \, c^{5} d + 31 \, c^{4} d^{2} + 99 \, c^{3} d^{3} - 23 \, c^{2} d^{4} - 72 \, c d^{5} - 15 \, d^{6}\right)} \cos\left(f x + e\right)^{3} + {\left(6 \, c^{6} - 29 \, c^{5} d + 51 \, c^{4} d^{2} + 193 \, c^{3} d^{3} + 60 \, c^{2} d^{4} - 164 \, c d^{5} - 117 \, d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} - 6 \, c^{5} d + 5 \, c^{4} d^{2} + 147 \, c^{3} d^{3} + 164 \, c^{2} d^{4} - 141 \, c d^{5} - 171 \, d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{30 \, {\left({\left(a^{3} c^{8} - 3 \, a^{3} c^{7} d + a^{3} c^{6} d^{2} + 5 \, a^{3} c^{5} d^{3} - 5 \, a^{3} c^{4} d^{4} - a^{3} c^{3} d^{5} + 3 \, a^{3} c^{2} d^{6} - a^{3} c d^{7}\right)} f \cos\left(f x + e\right)^{4} + {\left(3 \, a^{3} c^{8} - 8 \, a^{3} c^{7} d + 16 \, a^{3} c^{5} d^{3} - 10 \, a^{3} c^{4} d^{4} - 8 \, a^{3} c^{3} d^{5} + 8 \, a^{3} c^{2} d^{6} - a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(a^{3} c^{8} - 2 \, a^{3} c^{7} d - 2 \, a^{3} c^{6} d^{2} + 6 \, a^{3} c^{5} d^{3} - 6 \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 2 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{2} + {\left(a^{3} c^{8} - 8 \, a^{3} c^{6} d^{2} + 8 \, a^{3} c^{5} d^{3} + 10 \, a^{3} c^{4} d^{4} - 16 \, a^{3} c^{3} d^{5} + 8 \, a^{3} c d^{7} - 3 \, a^{3} d^{8}\right)} f \cos\left(f x + e\right) + {\left(a^{3} c^{7} d - 3 \, a^{3} c^{6} d^{2} + a^{3} c^{5} d^{3} + 5 \, a^{3} c^{4} d^{4} - 5 \, a^{3} c^{3} d^{5} - a^{3} c^{2} d^{6} + 3 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f\right)}}, -\frac{15 \, {\left(4 \, c d^{4} + 3 \, d^{5} + {\left(4 \, c^{2} d^{3} + 3 \, c d^{4}\right)} \cos\left(f x + e\right)^{4} + {\left(12 \, c^{2} d^{3} + 13 \, c d^{4} + 3 \, d^{5}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(4 \, c^{2} d^{3} + 7 \, c d^{4} + 3 \, d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(4 \, c^{2} d^{3} + 15 \, c d^{4} + 9 \, d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(2 \, c^{5} d - 12 \, c^{4} d^{2} + 41 \, c^{3} d^{3} + 84 \, c^{2} d^{4} - 43 \, c d^{5} - 72 \, d^{6} + {\left(7 \, c^{6} - 27 \, c^{5} d + 31 \, c^{4} d^{2} + 99 \, c^{3} d^{3} - 23 \, c^{2} d^{4} - 72 \, c d^{5} - 15 \, d^{6}\right)} \cos\left(f x + e\right)^{3} + {\left(6 \, c^{6} - 29 \, c^{5} d + 51 \, c^{4} d^{2} + 193 \, c^{3} d^{3} + 60 \, c^{2} d^{4} - 164 \, c d^{5} - 117 \, d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} - 6 \, c^{5} d + 5 \, c^{4} d^{2} + 147 \, c^{3} d^{3} + 164 \, c^{2} d^{4} - 141 \, c d^{5} - 171 \, d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left({\left(a^{3} c^{8} - 3 \, a^{3} c^{7} d + a^{3} c^{6} d^{2} + 5 \, a^{3} c^{5} d^{3} - 5 \, a^{3} c^{4} d^{4} - a^{3} c^{3} d^{5} + 3 \, a^{3} c^{2} d^{6} - a^{3} c d^{7}\right)} f \cos\left(f x + e\right)^{4} + {\left(3 \, a^{3} c^{8} - 8 \, a^{3} c^{7} d + 16 \, a^{3} c^{5} d^{3} - 10 \, a^{3} c^{4} d^{4} - 8 \, a^{3} c^{3} d^{5} + 8 \, a^{3} c^{2} d^{6} - a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(a^{3} c^{8} - 2 \, a^{3} c^{7} d - 2 \, a^{3} c^{6} d^{2} + 6 \, a^{3} c^{5} d^{3} - 6 \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 2 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{2} + {\left(a^{3} c^{8} - 8 \, a^{3} c^{6} d^{2} + 8 \, a^{3} c^{5} d^{3} + 10 \, a^{3} c^{4} d^{4} - 16 \, a^{3} c^{3} d^{5} + 8 \, a^{3} c d^{7} - 3 \, a^{3} d^{8}\right)} f \cos\left(f x + e\right) + {\left(a^{3} c^{7} d - 3 \, a^{3} c^{6} d^{2} + a^{3} c^{5} d^{3} + 5 \, a^{3} c^{4} d^{4} - 5 \, a^{3} c^{3} d^{5} - a^{3} c^{2} d^{6} + 3 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f\right)}}\right]"," ",0,"[1/30*(15*(4*c*d^4 + 3*d^5 + (4*c^2*d^3 + 3*c*d^4)*cos(f*x + e)^4 + (12*c^2*d^3 + 13*c*d^4 + 3*d^5)*cos(f*x + e)^3 + 3*(4*c^2*d^3 + 7*c*d^4 + 3*d^5)*cos(f*x + e)^2 + (4*c^2*d^3 + 15*c*d^4 + 9*d^5)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(2*c^5*d - 12*c^4*d^2 + 41*c^3*d^3 + 84*c^2*d^4 - 43*c*d^5 - 72*d^6 + (7*c^6 - 27*c^5*d + 31*c^4*d^2 + 99*c^3*d^3 - 23*c^2*d^4 - 72*c*d^5 - 15*d^6)*cos(f*x + e)^3 + (6*c^6 - 29*c^5*d + 51*c^4*d^2 + 193*c^3*d^3 + 60*c^2*d^4 - 164*c*d^5 - 117*d^6)*cos(f*x + e)^2 + (2*c^6 - 6*c^5*d + 5*c^4*d^2 + 147*c^3*d^3 + 164*c^2*d^4 - 141*c*d^5 - 171*d^6)*cos(f*x + e))*sin(f*x + e))/((a^3*c^8 - 3*a^3*c^7*d + a^3*c^6*d^2 + 5*a^3*c^5*d^3 - 5*a^3*c^4*d^4 - a^3*c^3*d^5 + 3*a^3*c^2*d^6 - a^3*c*d^7)*f*cos(f*x + e)^4 + (3*a^3*c^8 - 8*a^3*c^7*d + 16*a^3*c^5*d^3 - 10*a^3*c^4*d^4 - 8*a^3*c^3*d^5 + 8*a^3*c^2*d^6 - a^3*d^8)*f*cos(f*x + e)^3 + 3*(a^3*c^8 - 2*a^3*c^7*d - 2*a^3*c^6*d^2 + 6*a^3*c^5*d^3 - 6*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 2*a^3*c*d^7 - a^3*d^8)*f*cos(f*x + e)^2 + (a^3*c^8 - 8*a^3*c^6*d^2 + 8*a^3*c^5*d^3 + 10*a^3*c^4*d^4 - 16*a^3*c^3*d^5 + 8*a^3*c*d^7 - 3*a^3*d^8)*f*cos(f*x + e) + (a^3*c^7*d - 3*a^3*c^6*d^2 + a^3*c^5*d^3 + 5*a^3*c^4*d^4 - 5*a^3*c^3*d^5 - a^3*c^2*d^6 + 3*a^3*c*d^7 - a^3*d^8)*f), -1/15*(15*(4*c*d^4 + 3*d^5 + (4*c^2*d^3 + 3*c*d^4)*cos(f*x + e)^4 + (12*c^2*d^3 + 13*c*d^4 + 3*d^5)*cos(f*x + e)^3 + 3*(4*c^2*d^3 + 7*c*d^4 + 3*d^5)*cos(f*x + e)^2 + (4*c^2*d^3 + 15*c*d^4 + 9*d^5)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (2*c^5*d - 12*c^4*d^2 + 41*c^3*d^3 + 84*c^2*d^4 - 43*c*d^5 - 72*d^6 + (7*c^6 - 27*c^5*d + 31*c^4*d^2 + 99*c^3*d^3 - 23*c^2*d^4 - 72*c*d^5 - 15*d^6)*cos(f*x + e)^3 + (6*c^6 - 29*c^5*d + 51*c^4*d^2 + 193*c^3*d^3 + 60*c^2*d^4 - 164*c*d^5 - 117*d^6)*cos(f*x + e)^2 + (2*c^6 - 6*c^5*d + 5*c^4*d^2 + 147*c^3*d^3 + 164*c^2*d^4 - 141*c*d^5 - 171*d^6)*cos(f*x + e))*sin(f*x + e))/((a^3*c^8 - 3*a^3*c^7*d + a^3*c^6*d^2 + 5*a^3*c^5*d^3 - 5*a^3*c^4*d^4 - a^3*c^3*d^5 + 3*a^3*c^2*d^6 - a^3*c*d^7)*f*cos(f*x + e)^4 + (3*a^3*c^8 - 8*a^3*c^7*d + 16*a^3*c^5*d^3 - 10*a^3*c^4*d^4 - 8*a^3*c^3*d^5 + 8*a^3*c^2*d^6 - a^3*d^8)*f*cos(f*x + e)^3 + 3*(a^3*c^8 - 2*a^3*c^7*d - 2*a^3*c^6*d^2 + 6*a^3*c^5*d^3 - 6*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 2*a^3*c*d^7 - a^3*d^8)*f*cos(f*x + e)^2 + (a^3*c^8 - 8*a^3*c^6*d^2 + 8*a^3*c^5*d^3 + 10*a^3*c^4*d^4 - 16*a^3*c^3*d^5 + 8*a^3*c*d^7 - 3*a^3*d^8)*f*cos(f*x + e) + (a^3*c^7*d - 3*a^3*c^6*d^2 + a^3*c^5*d^3 + 5*a^3*c^4*d^4 - 5*a^3*c^3*d^5 - a^3*c^2*d^6 + 3*a^3*c*d^7 - a^3*d^8)*f)]","B",0
233,1,2677,0,0.616279," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(20 \, c^{2} d^{5} + 30 \, c d^{6} + 13 \, d^{7} + {\left(20 \, c^{4} d^{3} + 30 \, c^{3} d^{4} + 13 \, c^{2} d^{5}\right)} \cos\left(f x + e\right)^{5} + {\left(60 \, c^{4} d^{3} + 130 \, c^{3} d^{4} + 99 \, c^{2} d^{5} + 26 \, c d^{6}\right)} \cos\left(f x + e\right)^{4} + {\left(60 \, c^{4} d^{3} + 210 \, c^{3} d^{4} + 239 \, c^{2} d^{5} + 108 \, c d^{6} + 13 \, d^{7}\right)} \cos\left(f x + e\right)^{3} + {\left(20 \, c^{4} d^{3} + 150 \, c^{3} d^{4} + 253 \, c^{2} d^{5} + 168 \, c d^{6} + 39 \, d^{7}\right)} \cos\left(f x + e\right)^{2} + {\left(40 \, c^{3} d^{4} + 120 \, c^{2} d^{5} + 116 \, c d^{6} + 39 \, d^{7}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - 2 \, {\left(4 \, c^{6} d^{2} - 30 \, c^{5} d^{3} + 138 \, c^{4} d^{4} + 555 \, c^{3} d^{5} + 162 \, c^{2} d^{6} - 525 \, c d^{7} - 304 \, d^{8} + {\left(14 \, c^{8} - 60 \, c^{7} d + 78 \, c^{6} d^{2} + 480 \, c^{5} d^{3} + 312 \, c^{4} d^{4} - 330 \, c^{3} d^{5} - 419 \, c^{2} d^{6} - 90 \, c d^{7} + 15 \, d^{8}\right)} \cos\left(f x + e\right)^{4} + {\left(12 \, c^{8} - 62 \, c^{7} d + 114 \, c^{6} d^{2} + 1056 \, c^{5} d^{3} + 1626 \, c^{4} d^{4} - 81 \, c^{3} d^{5} - 1707 \, c^{2} d^{6} - 913 \, c d^{7} - 45 \, d^{8}\right)} \cos\left(f x + e\right)^{3} + {\left(4 \, c^{8} - 6 \, c^{7} d - 28 \, c^{6} d^{2} + 828 \, c^{5} d^{3} + 2400 \, c^{4} d^{4} + 1197 \, c^{3} d^{5} - 1897 \, c^{2} d^{6} - 2019 \, c d^{7} - 479 \, d^{8}\right)} \cos\left(f x + e\right)^{2} + {\left(8 \, c^{7} d - 48 \, c^{6} d^{2} + 186 \, c^{5} d^{3} + 1224 \, c^{4} d^{4} + 1539 \, c^{3} d^{5} - 459 \, c^{2} d^{6} - 1733 \, c d^{7} - 717 \, d^{8}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{60 \, {\left({\left(a^{3} c^{11} - 3 \, a^{3} c^{10} d + 8 \, a^{3} c^{8} d^{3} - 6 \, a^{3} c^{7} d^{4} - 6 \, a^{3} c^{6} d^{5} + 8 \, a^{3} c^{5} d^{6} - 3 \, a^{3} c^{3} d^{8} + a^{3} c^{2} d^{9}\right)} f \cos\left(f x + e\right)^{5} + {\left(3 \, a^{3} c^{11} - 7 \, a^{3} c^{10} d - 6 \, a^{3} c^{9} d^{2} + 24 \, a^{3} c^{8} d^{3} - 2 \, a^{3} c^{7} d^{4} - 30 \, a^{3} c^{6} d^{5} + 12 \, a^{3} c^{5} d^{6} + 16 \, a^{3} c^{4} d^{7} - 9 \, a^{3} c^{3} d^{8} - 3 \, a^{3} c^{2} d^{9} + 2 \, a^{3} c d^{10}\right)} f \cos\left(f x + e\right)^{4} + {\left(3 \, a^{3} c^{11} - 3 \, a^{3} c^{10} d - 17 \, a^{3} c^{9} d^{2} + 21 \, a^{3} c^{8} d^{3} + 30 \, a^{3} c^{7} d^{4} - 46 \, a^{3} c^{6} d^{5} - 18 \, a^{3} c^{5} d^{6} + 42 \, a^{3} c^{4} d^{7} - a^{3} c^{3} d^{8} - 15 \, a^{3} c^{2} d^{9} + 3 \, a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{3} c^{11} + 3 \, a^{3} c^{10} d - 15 \, a^{3} c^{9} d^{2} - a^{3} c^{8} d^{3} + 42 \, a^{3} c^{7} d^{4} - 18 \, a^{3} c^{6} d^{5} - 46 \, a^{3} c^{5} d^{6} + 30 \, a^{3} c^{4} d^{7} + 21 \, a^{3} c^{3} d^{8} - 17 \, a^{3} c^{2} d^{9} - 3 \, a^{3} c d^{10} + 3 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, a^{3} c^{10} d - 3 \, a^{3} c^{9} d^{2} - 9 \, a^{3} c^{8} d^{3} + 16 \, a^{3} c^{7} d^{4} + 12 \, a^{3} c^{6} d^{5} - 30 \, a^{3} c^{5} d^{6} - 2 \, a^{3} c^{4} d^{7} + 24 \, a^{3} c^{3} d^{8} - 6 \, a^{3} c^{2} d^{9} - 7 \, a^{3} c d^{10} + 3 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right) + {\left(a^{3} c^{9} d^{2} - 3 \, a^{3} c^{8} d^{3} + 8 \, a^{3} c^{6} d^{5} - 6 \, a^{3} c^{5} d^{6} - 6 \, a^{3} c^{4} d^{7} + 8 \, a^{3} c^{3} d^{8} - 3 \, a^{3} c d^{10} + a^{3} d^{11}\right)} f\right)}}, -\frac{15 \, {\left(20 \, c^{2} d^{5} + 30 \, c d^{6} + 13 \, d^{7} + {\left(20 \, c^{4} d^{3} + 30 \, c^{3} d^{4} + 13 \, c^{2} d^{5}\right)} \cos\left(f x + e\right)^{5} + {\left(60 \, c^{4} d^{3} + 130 \, c^{3} d^{4} + 99 \, c^{2} d^{5} + 26 \, c d^{6}\right)} \cos\left(f x + e\right)^{4} + {\left(60 \, c^{4} d^{3} + 210 \, c^{3} d^{4} + 239 \, c^{2} d^{5} + 108 \, c d^{6} + 13 \, d^{7}\right)} \cos\left(f x + e\right)^{3} + {\left(20 \, c^{4} d^{3} + 150 \, c^{3} d^{4} + 253 \, c^{2} d^{5} + 168 \, c d^{6} + 39 \, d^{7}\right)} \cos\left(f x + e\right)^{2} + {\left(40 \, c^{3} d^{4} + 120 \, c^{2} d^{5} + 116 \, c d^{6} + 39 \, d^{7}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(4 \, c^{6} d^{2} - 30 \, c^{5} d^{3} + 138 \, c^{4} d^{4} + 555 \, c^{3} d^{5} + 162 \, c^{2} d^{6} - 525 \, c d^{7} - 304 \, d^{8} + {\left(14 \, c^{8} - 60 \, c^{7} d + 78 \, c^{6} d^{2} + 480 \, c^{5} d^{3} + 312 \, c^{4} d^{4} - 330 \, c^{3} d^{5} - 419 \, c^{2} d^{6} - 90 \, c d^{7} + 15 \, d^{8}\right)} \cos\left(f x + e\right)^{4} + {\left(12 \, c^{8} - 62 \, c^{7} d + 114 \, c^{6} d^{2} + 1056 \, c^{5} d^{3} + 1626 \, c^{4} d^{4} - 81 \, c^{3} d^{5} - 1707 \, c^{2} d^{6} - 913 \, c d^{7} - 45 \, d^{8}\right)} \cos\left(f x + e\right)^{3} + {\left(4 \, c^{8} - 6 \, c^{7} d - 28 \, c^{6} d^{2} + 828 \, c^{5} d^{3} + 2400 \, c^{4} d^{4} + 1197 \, c^{3} d^{5} - 1897 \, c^{2} d^{6} - 2019 \, c d^{7} - 479 \, d^{8}\right)} \cos\left(f x + e\right)^{2} + {\left(8 \, c^{7} d - 48 \, c^{6} d^{2} + 186 \, c^{5} d^{3} + 1224 \, c^{4} d^{4} + 1539 \, c^{3} d^{5} - 459 \, c^{2} d^{6} - 1733 \, c d^{7} - 717 \, d^{8}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{30 \, {\left({\left(a^{3} c^{11} - 3 \, a^{3} c^{10} d + 8 \, a^{3} c^{8} d^{3} - 6 \, a^{3} c^{7} d^{4} - 6 \, a^{3} c^{6} d^{5} + 8 \, a^{3} c^{5} d^{6} - 3 \, a^{3} c^{3} d^{8} + a^{3} c^{2} d^{9}\right)} f \cos\left(f x + e\right)^{5} + {\left(3 \, a^{3} c^{11} - 7 \, a^{3} c^{10} d - 6 \, a^{3} c^{9} d^{2} + 24 \, a^{3} c^{8} d^{3} - 2 \, a^{3} c^{7} d^{4} - 30 \, a^{3} c^{6} d^{5} + 12 \, a^{3} c^{5} d^{6} + 16 \, a^{3} c^{4} d^{7} - 9 \, a^{3} c^{3} d^{8} - 3 \, a^{3} c^{2} d^{9} + 2 \, a^{3} c d^{10}\right)} f \cos\left(f x + e\right)^{4} + {\left(3 \, a^{3} c^{11} - 3 \, a^{3} c^{10} d - 17 \, a^{3} c^{9} d^{2} + 21 \, a^{3} c^{8} d^{3} + 30 \, a^{3} c^{7} d^{4} - 46 \, a^{3} c^{6} d^{5} - 18 \, a^{3} c^{5} d^{6} + 42 \, a^{3} c^{4} d^{7} - a^{3} c^{3} d^{8} - 15 \, a^{3} c^{2} d^{9} + 3 \, a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{3} c^{11} + 3 \, a^{3} c^{10} d - 15 \, a^{3} c^{9} d^{2} - a^{3} c^{8} d^{3} + 42 \, a^{3} c^{7} d^{4} - 18 \, a^{3} c^{6} d^{5} - 46 \, a^{3} c^{5} d^{6} + 30 \, a^{3} c^{4} d^{7} + 21 \, a^{3} c^{3} d^{8} - 17 \, a^{3} c^{2} d^{9} - 3 \, a^{3} c d^{10} + 3 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, a^{3} c^{10} d - 3 \, a^{3} c^{9} d^{2} - 9 \, a^{3} c^{8} d^{3} + 16 \, a^{3} c^{7} d^{4} + 12 \, a^{3} c^{6} d^{5} - 30 \, a^{3} c^{5} d^{6} - 2 \, a^{3} c^{4} d^{7} + 24 \, a^{3} c^{3} d^{8} - 6 \, a^{3} c^{2} d^{9} - 7 \, a^{3} c d^{10} + 3 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right) + {\left(a^{3} c^{9} d^{2} - 3 \, a^{3} c^{8} d^{3} + 8 \, a^{3} c^{6} d^{5} - 6 \, a^{3} c^{5} d^{6} - 6 \, a^{3} c^{4} d^{7} + 8 \, a^{3} c^{3} d^{8} - 3 \, a^{3} c d^{10} + a^{3} d^{11}\right)} f\right)}}\right]"," ",0,"[-1/60*(15*(20*c^2*d^5 + 30*c*d^6 + 13*d^7 + (20*c^4*d^3 + 30*c^3*d^4 + 13*c^2*d^5)*cos(f*x + e)^5 + (60*c^4*d^3 + 130*c^3*d^4 + 99*c^2*d^5 + 26*c*d^6)*cos(f*x + e)^4 + (60*c^4*d^3 + 210*c^3*d^4 + 239*c^2*d^5 + 108*c*d^6 + 13*d^7)*cos(f*x + e)^3 + (20*c^4*d^3 + 150*c^3*d^4 + 253*c^2*d^5 + 168*c*d^6 + 39*d^7)*cos(f*x + e)^2 + (40*c^3*d^4 + 120*c^2*d^5 + 116*c*d^6 + 39*d^7)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - 2*(4*c^6*d^2 - 30*c^5*d^3 + 138*c^4*d^4 + 555*c^3*d^5 + 162*c^2*d^6 - 525*c*d^7 - 304*d^8 + (14*c^8 - 60*c^7*d + 78*c^6*d^2 + 480*c^5*d^3 + 312*c^4*d^4 - 330*c^3*d^5 - 419*c^2*d^6 - 90*c*d^7 + 15*d^8)*cos(f*x + e)^4 + (12*c^8 - 62*c^7*d + 114*c^6*d^2 + 1056*c^5*d^3 + 1626*c^4*d^4 - 81*c^3*d^5 - 1707*c^2*d^6 - 913*c*d^7 - 45*d^8)*cos(f*x + e)^3 + (4*c^8 - 6*c^7*d - 28*c^6*d^2 + 828*c^5*d^3 + 2400*c^4*d^4 + 1197*c^3*d^5 - 1897*c^2*d^6 - 2019*c*d^7 - 479*d^8)*cos(f*x + e)^2 + (8*c^7*d - 48*c^6*d^2 + 186*c^5*d^3 + 1224*c^4*d^4 + 1539*c^3*d^5 - 459*c^2*d^6 - 1733*c*d^7 - 717*d^8)*cos(f*x + e))*sin(f*x + e))/((a^3*c^11 - 3*a^3*c^10*d + 8*a^3*c^8*d^3 - 6*a^3*c^7*d^4 - 6*a^3*c^6*d^5 + 8*a^3*c^5*d^6 - 3*a^3*c^3*d^8 + a^3*c^2*d^9)*f*cos(f*x + e)^5 + (3*a^3*c^11 - 7*a^3*c^10*d - 6*a^3*c^9*d^2 + 24*a^3*c^8*d^3 - 2*a^3*c^7*d^4 - 30*a^3*c^6*d^5 + 12*a^3*c^5*d^6 + 16*a^3*c^4*d^7 - 9*a^3*c^3*d^8 - 3*a^3*c^2*d^9 + 2*a^3*c*d^10)*f*cos(f*x + e)^4 + (3*a^3*c^11 - 3*a^3*c^10*d - 17*a^3*c^9*d^2 + 21*a^3*c^8*d^3 + 30*a^3*c^7*d^4 - 46*a^3*c^6*d^5 - 18*a^3*c^5*d^6 + 42*a^3*c^4*d^7 - a^3*c^3*d^8 - 15*a^3*c^2*d^9 + 3*a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e)^3 + (a^3*c^11 + 3*a^3*c^10*d - 15*a^3*c^9*d^2 - a^3*c^8*d^3 + 42*a^3*c^7*d^4 - 18*a^3*c^6*d^5 - 46*a^3*c^5*d^6 + 30*a^3*c^4*d^7 + 21*a^3*c^3*d^8 - 17*a^3*c^2*d^9 - 3*a^3*c*d^10 + 3*a^3*d^11)*f*cos(f*x + e)^2 + (2*a^3*c^10*d - 3*a^3*c^9*d^2 - 9*a^3*c^8*d^3 + 16*a^3*c^7*d^4 + 12*a^3*c^6*d^5 - 30*a^3*c^5*d^6 - 2*a^3*c^4*d^7 + 24*a^3*c^3*d^8 - 6*a^3*c^2*d^9 - 7*a^3*c*d^10 + 3*a^3*d^11)*f*cos(f*x + e) + (a^3*c^9*d^2 - 3*a^3*c^8*d^3 + 8*a^3*c^6*d^5 - 6*a^3*c^5*d^6 - 6*a^3*c^4*d^7 + 8*a^3*c^3*d^8 - 3*a^3*c*d^10 + a^3*d^11)*f), -1/30*(15*(20*c^2*d^5 + 30*c*d^6 + 13*d^7 + (20*c^4*d^3 + 30*c^3*d^4 + 13*c^2*d^5)*cos(f*x + e)^5 + (60*c^4*d^3 + 130*c^3*d^4 + 99*c^2*d^5 + 26*c*d^6)*cos(f*x + e)^4 + (60*c^4*d^3 + 210*c^3*d^4 + 239*c^2*d^5 + 108*c*d^6 + 13*d^7)*cos(f*x + e)^3 + (20*c^4*d^3 + 150*c^3*d^4 + 253*c^2*d^5 + 168*c*d^6 + 39*d^7)*cos(f*x + e)^2 + (40*c^3*d^4 + 120*c^2*d^5 + 116*c*d^6 + 39*d^7)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (4*c^6*d^2 - 30*c^5*d^3 + 138*c^4*d^4 + 555*c^3*d^5 + 162*c^2*d^6 - 525*c*d^7 - 304*d^8 + (14*c^8 - 60*c^7*d + 78*c^6*d^2 + 480*c^5*d^3 + 312*c^4*d^4 - 330*c^3*d^5 - 419*c^2*d^6 - 90*c*d^7 + 15*d^8)*cos(f*x + e)^4 + (12*c^8 - 62*c^7*d + 114*c^6*d^2 + 1056*c^5*d^3 + 1626*c^4*d^4 - 81*c^3*d^5 - 1707*c^2*d^6 - 913*c*d^7 - 45*d^8)*cos(f*x + e)^3 + (4*c^8 - 6*c^7*d - 28*c^6*d^2 + 828*c^5*d^3 + 2400*c^4*d^4 + 1197*c^3*d^5 - 1897*c^2*d^6 - 2019*c*d^7 - 479*d^8)*cos(f*x + e)^2 + (8*c^7*d - 48*c^6*d^2 + 186*c^5*d^3 + 1224*c^4*d^4 + 1539*c^3*d^5 - 459*c^2*d^6 - 1733*c*d^7 - 717*d^8)*cos(f*x + e))*sin(f*x + e))/((a^3*c^11 - 3*a^3*c^10*d + 8*a^3*c^8*d^3 - 6*a^3*c^7*d^4 - 6*a^3*c^6*d^5 + 8*a^3*c^5*d^6 - 3*a^3*c^3*d^8 + a^3*c^2*d^9)*f*cos(f*x + e)^5 + (3*a^3*c^11 - 7*a^3*c^10*d - 6*a^3*c^9*d^2 + 24*a^3*c^8*d^3 - 2*a^3*c^7*d^4 - 30*a^3*c^6*d^5 + 12*a^3*c^5*d^6 + 16*a^3*c^4*d^7 - 9*a^3*c^3*d^8 - 3*a^3*c^2*d^9 + 2*a^3*c*d^10)*f*cos(f*x + e)^4 + (3*a^3*c^11 - 3*a^3*c^10*d - 17*a^3*c^9*d^2 + 21*a^3*c^8*d^3 + 30*a^3*c^7*d^4 - 46*a^3*c^6*d^5 - 18*a^3*c^5*d^6 + 42*a^3*c^4*d^7 - a^3*c^3*d^8 - 15*a^3*c^2*d^9 + 3*a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e)^3 + (a^3*c^11 + 3*a^3*c^10*d - 15*a^3*c^9*d^2 - a^3*c^8*d^3 + 42*a^3*c^7*d^4 - 18*a^3*c^6*d^5 - 46*a^3*c^5*d^6 + 30*a^3*c^4*d^7 + 21*a^3*c^3*d^8 - 17*a^3*c^2*d^9 - 3*a^3*c*d^10 + 3*a^3*d^11)*f*cos(f*x + e)^2 + (2*a^3*c^10*d - 3*a^3*c^9*d^2 - 9*a^3*c^8*d^3 + 16*a^3*c^7*d^4 + 12*a^3*c^6*d^5 - 30*a^3*c^5*d^6 - 2*a^3*c^4*d^7 + 24*a^3*c^3*d^8 - 6*a^3*c^2*d^9 - 7*a^3*c*d^10 + 3*a^3*d^11)*f*cos(f*x + e) + (a^3*c^9*d^2 - 3*a^3*c^8*d^3 + 8*a^3*c^6*d^5 - 6*a^3*c^5*d^6 - 6*a^3*c^4*d^7 + 8*a^3*c^3*d^8 - 3*a^3*c*d^10 + a^3*d^11)*f)]","B",0
234,1,307,0,0.673762," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{a}{d}} \log\left(-\frac{8 \, a c d \cos\left(f x + e\right) + {\left(a c^{2} - 6 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)^{3} + 4 \, {\left(2 \, d^{2} \cos\left(f x + e\right) + {\left(c d - d^{2}\right)} \cos\left(f x + e\right)^{2}\right)} \sqrt{\frac{a}{d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 8 \, a d^{2} + {\left(a c^{2} + 2 \, a c d - 7 \, a d^{2}\right)} \cos\left(f x + e\right)^{2}}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right)}{2 \, f}, \frac{\sqrt{-\frac{a}{d}} \arctan\left(-\frac{2 \, d \sqrt{-\frac{a}{d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(a c - a d\right)} \cos\left(f x + e\right)^{2} + 2 \, a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}\right)}{f}\right]"," ",0,"[1/2*sqrt(a/d)*log(-(8*a*c*d*cos(f*x + e) + (a*c^2 - 6*a*c*d + a*d^2)*cos(f*x + e)^3 + 4*(2*d^2*cos(f*x + e) + (c*d - d^2)*cos(f*x + e)^2)*sqrt(a/d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*sin(f*x + e) + 8*a*d^2 + (a*c^2 + 2*a*c*d - 7*a*d^2)*cos(f*x + e)^2)/(cos(f*x + e)^3 + cos(f*x + e)^2))/f, sqrt(-a/d)*arctan(-2*d*sqrt(-a/d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((a*c - a*d)*cos(f*x + e)^2 + 2*a*d + (a*c + a*d)*cos(f*x + e)))/f]","B",0
235,1,1048,0,0.774892," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-\frac{c - d}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-\frac{c - d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(3 \, c - d\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(c + d\right)} \cos\left(f x + e\right) + c - 3 \, d}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + \sqrt{\frac{d}{a}} \log\left(-\frac{{\left(c^{2} - 6 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{3} + 4 \, {\left({\left(c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, d \cos\left(f x + e\right)\right)} \sqrt{\frac{d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 8 \, c d \cos\left(f x + e\right) + {\left(c^{2} + 2 \, c d - 7 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 8 \, d^{2}}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right)}{2 \, f}, \frac{2 \, \sqrt{2} \sqrt{\frac{c - d}{a}} \arctan\left(-\frac{\sqrt{2} \sqrt{\frac{c - d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(c - d\right)} \sin\left(f x + e\right)}\right) + \sqrt{\frac{d}{a}} \log\left(-\frac{{\left(c^{2} - 6 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{3} + 4 \, {\left({\left(c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, d \cos\left(f x + e\right)\right)} \sqrt{\frac{d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 8 \, c d \cos\left(f x + e\right) + {\left(c^{2} + 2 \, c d - 7 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 8 \, d^{2}}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right)}{2 \, f}, \frac{\sqrt{2} \sqrt{-\frac{c - d}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-\frac{c - d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(3 \, c - d\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(c + d\right)} \cos\left(f x + e\right) + c - 3 \, d}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 2 \, \sqrt{-\frac{d}{a}} \arctan\left(-\frac{2 \, \sqrt{-\frac{d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(c - d\right)} \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + 2 \, d}\right)}{2 \, f}, \frac{\sqrt{2} \sqrt{\frac{c - d}{a}} \arctan\left(-\frac{\sqrt{2} \sqrt{\frac{c - d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(c - d\right)} \sin\left(f x + e\right)}\right) + \sqrt{-\frac{d}{a}} \arctan\left(-\frac{2 \, \sqrt{-\frac{d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(c - d\right)} \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + 2 \, d}\right)}{f}\right]"," ",0,"[1/2*(sqrt(2)*sqrt(-(c - d)/a)*log(-(2*sqrt(2)*sqrt(-(c - d)/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - (3*c - d)*cos(f*x + e)^2 - 2*(c + d)*cos(f*x + e) + c - 3*d)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + sqrt(d/a)*log(-((c^2 - 6*c*d + d^2)*cos(f*x + e)^3 + 4*((c - d)*cos(f*x + e)^2 + 2*d*cos(f*x + e))*sqrt(d/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*sin(f*x + e) + 8*c*d*cos(f*x + e) + (c^2 + 2*c*d - 7*d^2)*cos(f*x + e)^2 + 8*d^2)/(cos(f*x + e)^3 + cos(f*x + e)^2)))/f, 1/2*(2*sqrt(2)*sqrt((c - d)/a)*arctan(-sqrt(2)*sqrt((c - d)/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/((c - d)*sin(f*x + e))) + sqrt(d/a)*log(-((c^2 - 6*c*d + d^2)*cos(f*x + e)^3 + 4*((c - d)*cos(f*x + e)^2 + 2*d*cos(f*x + e))*sqrt(d/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*sin(f*x + e) + 8*c*d*cos(f*x + e) + (c^2 + 2*c*d - 7*d^2)*cos(f*x + e)^2 + 8*d^2)/(cos(f*x + e)^3 + cos(f*x + e)^2)))/f, 1/2*(sqrt(2)*sqrt(-(c - d)/a)*log(-(2*sqrt(2)*sqrt(-(c - d)/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - (3*c - d)*cos(f*x + e)^2 - 2*(c + d)*cos(f*x + e) + c - 3*d)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 2*sqrt(-d/a)*arctan(-2*sqrt(-d/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((c - d)*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + 2*d)))/f, (sqrt(2)*sqrt((c - d)/a)*arctan(-sqrt(2)*sqrt((c - d)/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/((c - d)*sin(f*x + e))) + sqrt(-d/a)*arctan(-2*sqrt(-d/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((c - d)*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + 2*d)))/f]","A",0
236,1,246,0,0.541005," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-\frac{1}{a c - a d}} \log\left(-\frac{2 \, \sqrt{2} {\left(c - d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a c - a d}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(3 \, c - d\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(c + d\right)} \cos\left(f x + e\right) + c - 3 \, d}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right)}{2 \, f}, -\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a c - a d} \sin\left(f x + e\right)}\right)}{\sqrt{a c - a d} f}\right]"," ",0,"[1/2*sqrt(2)*sqrt(-1/(a*c - a*d))*log(-(2*sqrt(2)*(c - d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*sqrt(-1/(a*c - a*d))*cos(f*x + e)*sin(f*x + e) - (3*c - d)*cos(f*x + e)^2 - 2*(c + d)*cos(f*x + e) + c - 3*d)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))/f, -sqrt(2)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(sqrt(a*c - a*d)*sin(f*x + e)))/(sqrt(a*c - a*d)*f)]","A",0
237,1,1100,0,0.812236," ","integrate(sec(f*x+e)^2/(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a d \sqrt{-\frac{1}{a c - a d}} \log\left(\frac{2 \, \sqrt{2} {\left(c - d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a c - a d}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(3 \, c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(c + d\right)} \cos\left(f x + e\right) - c + 3 \, d}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + \sqrt{a d} \log\left(-\frac{8 \, a c d \cos\left(f x + e\right) + {\left(a c^{2} - 6 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)^{3} + 4 \, {\left({\left(c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, d \cos\left(f x + e\right)\right)} \sqrt{a d} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 8 \, a d^{2} + {\left(a c^{2} + 2 \, a c d - 7 \, a d^{2}\right)} \cos\left(f x + e\right)^{2}}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right)}{2 \, a d f}, \frac{\frac{2 \, \sqrt{2} a d \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a c - a d} \sin\left(f x + e\right)}\right)}{\sqrt{a c - a d}} + \sqrt{a d} \log\left(-\frac{8 \, a c d \cos\left(f x + e\right) + {\left(a c^{2} - 6 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)^{3} + 4 \, {\left({\left(c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, d \cos\left(f x + e\right)\right)} \sqrt{a d} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 8 \, a d^{2} + {\left(a c^{2} + 2 \, a c d - 7 \, a d^{2}\right)} \cos\left(f x + e\right)^{2}}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right)}{2 \, a d f}, \frac{\sqrt{2} a d \sqrt{-\frac{1}{a c - a d}} \log\left(\frac{2 \, \sqrt{2} {\left(c - d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a c - a d}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(3 \, c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(c + d\right)} \cos\left(f x + e\right) - c + 3 \, d}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 2 \, \sqrt{-a d} \arctan\left(-\frac{2 \, \sqrt{-a d} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(a c - a d\right)} \cos\left(f x + e\right)^{2} + 2 \, a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}\right)}{2 \, a d f}, \frac{\frac{\sqrt{2} a d \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a c - a d} \sin\left(f x + e\right)}\right)}{\sqrt{a c - a d}} + \sqrt{-a d} \arctan\left(-\frac{2 \, \sqrt{-a d} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(a c - a d\right)} \cos\left(f x + e\right)^{2} + 2 \, a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}\right)}{a d f}\right]"," ",0,"[1/2*(sqrt(2)*a*d*sqrt(-1/(a*c - a*d))*log((2*sqrt(2)*(c - d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*sqrt(-1/(a*c - a*d))*cos(f*x + e)*sin(f*x + e) + (3*c - d)*cos(f*x + e)^2 + 2*(c + d)*cos(f*x + e) - c + 3*d)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + sqrt(a*d)*log(-(8*a*c*d*cos(f*x + e) + (a*c^2 - 6*a*c*d + a*d^2)*cos(f*x + e)^3 + 4*((c - d)*cos(f*x + e)^2 + 2*d*cos(f*x + e))*sqrt(a*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*sin(f*x + e) + 8*a*d^2 + (a*c^2 + 2*a*c*d - 7*a*d^2)*cos(f*x + e)^2)/(cos(f*x + e)^3 + cos(f*x + e)^2)))/(a*d*f), 1/2*(2*sqrt(2)*a*d*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(sqrt(a*c - a*d)*sin(f*x + e)))/sqrt(a*c - a*d) + sqrt(a*d)*log(-(8*a*c*d*cos(f*x + e) + (a*c^2 - 6*a*c*d + a*d^2)*cos(f*x + e)^3 + 4*((c - d)*cos(f*x + e)^2 + 2*d*cos(f*x + e))*sqrt(a*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*sin(f*x + e) + 8*a*d^2 + (a*c^2 + 2*a*c*d - 7*a*d^2)*cos(f*x + e)^2)/(cos(f*x + e)^3 + cos(f*x + e)^2)))/(a*d*f), 1/2*(sqrt(2)*a*d*sqrt(-1/(a*c - a*d))*log((2*sqrt(2)*(c - d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*sqrt(-1/(a*c - a*d))*cos(f*x + e)*sin(f*x + e) + (3*c - d)*cos(f*x + e)^2 + 2*(c + d)*cos(f*x + e) - c + 3*d)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 2*sqrt(-a*d)*arctan(-2*sqrt(-a*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((a*c - a*d)*cos(f*x + e)^2 + 2*a*d + (a*c + a*d)*cos(f*x + e))))/(a*d*f), (sqrt(2)*a*d*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(sqrt(a*c - a*d)*sin(f*x + e)))/sqrt(a*c - a*d) + sqrt(-a*d)*arctan(-2*sqrt(-a*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((a*c - a*d)*cos(f*x + e)^2 + 2*a*d + (a*c + a*d)*cos(f*x + e))))/(a*d*f)]","A",0
238,1,343,0,0.674851," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a}{c d + d^{2}}} \log\left(-\frac{{\left(a c^{2} + 8 \, a c d + 8 \, a d^{2}\right)} \cos\left(f x + e\right)^{3} + a d^{2} + {\left(a c^{2} + 2 \, a c d\right)} \cos\left(f x + e\right)^{2} - 4 \, {\left({\left(c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(c d^{2} + d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - {\left(6 \, a c d + 7 \, a d^{2}\right)} \cos\left(f x + e\right)}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right)}{2 \, f}, \frac{\sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}\right)}{f}\right]"," ",0,"[1/2*sqrt(-a/(c*d + d^2))*log(-((a*c^2 + 8*a*c*d + 8*a*d^2)*cos(f*x + e)^3 + a*d^2 + (a*c^2 + 2*a*c*d)*cos(f*x + e)^2 - 4*((c^2*d + 3*c*d^2 + 2*d^3)*cos(f*x + e)^2 - (c*d^2 + d^3)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - (6*a*c*d + 7*a*d^2)*cos(f*x + e))/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e)))/f, sqrt(a/(c*d + d^2))*arctan(2*(c*d + d^2)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e)))/f]","B",0
239,1,1126,0,7.933529," ","integrate((g*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{a c g}{c + d}} g \log\left(\frac{a c^{2} g \cos\left(f x + e\right)^{3} - {\left(7 \, a c^{2} + 6 \, a c d\right)} g \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, c^{2} + 3 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a c g}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + {\left(2 \, a c d + a d^{2}\right)} g \cos\left(f x + e\right) + {\left(8 \, a c^{2} + 8 \, a c d + a d^{2}\right)} g}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right) + \sqrt{a g} g \log\left(\frac{a g \cos\left(f x + e\right)^{3} - 7 \, a g \cos\left(f x + e\right)^{2} - 4 \, \sqrt{a g} {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 8 \, a g}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right)}{2 \, d f}, -\frac{2 \, \sqrt{-\frac{a c g}{c + d}} g \arctan\left(\frac{{\left(c \cos\left(f x + e\right)^{2} - {\left(2 \, c + d\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a c g}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}}}{2 \, a c g \sin\left(f x + e\right)}\right) - \sqrt{a g} g \log\left(\frac{a g \cos\left(f x + e\right)^{3} - 7 \, a g \cos\left(f x + e\right)^{2} - 4 \, \sqrt{a g} {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 8 \, a g}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right)}{2 \, d f}, \frac{2 \, \sqrt{-a g} g \arctan\left(\frac{2 \, \sqrt{-a g} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a g \cos\left(f x + e\right)^{2} - a g \cos\left(f x + e\right) - 2 \, a g}\right) + \sqrt{\frac{a c g}{c + d}} g \log\left(\frac{a c^{2} g \cos\left(f x + e\right)^{3} - {\left(7 \, a c^{2} + 6 \, a c d\right)} g \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, c^{2} + 3 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a c g}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + {\left(2 \, a c d + a d^{2}\right)} g \cos\left(f x + e\right) + {\left(8 \, a c^{2} + 8 \, a c d + a d^{2}\right)} g}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right)}{2 \, d f}, \frac{\sqrt{-a g} g \arctan\left(\frac{2 \, \sqrt{-a g} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a g \cos\left(f x + e\right)^{2} - a g \cos\left(f x + e\right) - 2 \, a g}\right) - \sqrt{-\frac{a c g}{c + d}} g \arctan\left(\frac{{\left(c \cos\left(f x + e\right)^{2} - {\left(2 \, c + d\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a c g}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}}}{2 \, a c g \sin\left(f x + e\right)}\right)}{d f}\right]"," ",0,"[1/2*(sqrt(a*c*g/(c + d))*g*log((a*c^2*g*cos(f*x + e)^3 - (7*a*c^2 + 6*a*c*d)*g*cos(f*x + e)^2 + 4*((c^2 + c*d)*cos(f*x + e)^2 - (2*c^2 + 3*c*d + d^2)*cos(f*x + e))*sqrt(a*c*g/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) + (2*a*c*d + a*d^2)*g*cos(f*x + e) + (8*a*c^2 + 8*a*c*d + a*d^2)*g)/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e))) + sqrt(a*g)*g*log((a*g*cos(f*x + e)^3 - 7*a*g*cos(f*x + e)^2 - 4*sqrt(a*g)*(cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) + 8*a*g)/(cos(f*x + e)^3 + cos(f*x + e)^2)))/(d*f), -1/2*(2*sqrt(-a*c*g/(c + d))*g*arctan(1/2*(c*cos(f*x + e)^2 - (2*c + d)*cos(f*x + e))*sqrt(-a*c*g/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))/(a*c*g*sin(f*x + e))) - sqrt(a*g)*g*log((a*g*cos(f*x + e)^3 - 7*a*g*cos(f*x + e)^2 - 4*sqrt(a*g)*(cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) + 8*a*g)/(cos(f*x + e)^3 + cos(f*x + e)^2)))/(d*f), 1/2*(2*sqrt(-a*g)*g*arctan(2*sqrt(-a*g)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*g*cos(f*x + e)^2 - a*g*cos(f*x + e) - 2*a*g)) + sqrt(a*c*g/(c + d))*g*log((a*c^2*g*cos(f*x + e)^3 - (7*a*c^2 + 6*a*c*d)*g*cos(f*x + e)^2 + 4*((c^2 + c*d)*cos(f*x + e)^2 - (2*c^2 + 3*c*d + d^2)*cos(f*x + e))*sqrt(a*c*g/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) + (2*a*c*d + a*d^2)*g*cos(f*x + e) + (8*a*c^2 + 8*a*c*d + a*d^2)*g)/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e))))/(d*f), (sqrt(-a*g)*g*arctan(2*sqrt(-a*g)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*g*cos(f*x + e)^2 - a*g*cos(f*x + e) - 2*a*g)) - sqrt(-a*c*g/(c + d))*g*arctan(1/2*(c*cos(f*x + e)^2 - (2*c + d)*cos(f*x + e))*sqrt(-a*c*g/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))/(a*c*g*sin(f*x + e))))/(d*f)]","A",0
240,1,963,0,0.779961," ","integrate(sec(f*x+e)/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + \sqrt{-\frac{d}{a c + a d}} \log\left(-\frac{{\left(c^{2} + 8 \, c d + 8 \, d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} - 4 \, {\left({\left(c^{2} + 3 \, c d + 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{d}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + d^{2} - {\left(6 \, c d + 7 \, d^{2}\right)} \cos\left(f x + e\right)}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right)}{2 \, {\left(c - d\right)} f}, -\frac{\sqrt{2} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 2 \, \sqrt{\frac{d}{a c + a d}} \arctan\left(\frac{2 \, {\left(c + d\right)} \sqrt{\frac{d}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(c + 2 \, d\right)} \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) - d}\right)}{2 \, {\left(c - d\right)} f}, -\frac{\sqrt{-\frac{d}{a c + a d}} \log\left(-\frac{{\left(c^{2} + 8 \, c d + 8 \, d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} - 4 \, {\left({\left(c^{2} + 3 \, c d + 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{d}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + d^{2} - {\left(6 \, c d + 7 \, d^{2}\right)} \cos\left(f x + e\right)}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right) + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}}{2 \, {\left(c - d\right)} f}, -\frac{\sqrt{\frac{d}{a c + a d}} \arctan\left(\frac{2 \, {\left(c + d\right)} \sqrt{\frac{d}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(c + 2 \, d\right)} \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) - d}\right) + \frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}}{{\left(c - d\right)} f}\right]"," ",0,"[-1/2*(sqrt(2)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + sqrt(-d/(a*c + a*d))*log(-((c^2 + 8*c*d + 8*d^2)*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 - 4*((c^2 + 3*c*d + 2*d^2)*cos(f*x + e)^2 - (c*d + d^2)*cos(f*x + e))*sqrt(-d/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) + d^2 - (6*c*d + 7*d^2)*cos(f*x + e))/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e))))/((c - d)*f), -1/2*(sqrt(2)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 2*sqrt(d/(a*c + a*d))*arctan(2*(c + d)*sqrt(d/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((c + 2*d)*cos(f*x + e)^2 + (c + d)*cos(f*x + e) - d)))/((c - d)*f), -1/2*(sqrt(-d/(a*c + a*d))*log(-((c^2 + 8*c*d + 8*d^2)*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 - 4*((c^2 + 3*c*d + 2*d^2)*cos(f*x + e)^2 - (c*d + d^2)*cos(f*x + e))*sqrt(-d/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) + d^2 - (6*c*d + 7*d^2)*cos(f*x + e))/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e))) + 2*sqrt(2)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/((c - d)*f), -(sqrt(d/(a*c + a*d))*arctan(2*(c + d)*sqrt(d/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((c + 2*d)*cos(f*x + e)^2 + (c + d)*cos(f*x + e) - d)) + sqrt(2)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/((c - d)*f)]","A",0
241,1,1041,0,0.870381," ","integrate(sec(f*x+e)^2/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(a c d + a d^{2}\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - \sqrt{-a c d - a d^{2}} c \log\left(-\frac{{\left(a c^{2} + 8 \, a c d + 8 \, a d^{2}\right)} \cos\left(f x + e\right)^{3} + a d^{2} + {\left(a c^{2} + 2 \, a c d\right)} \cos\left(f x + e\right)^{2} - 4 \, \sqrt{-a c d - a d^{2}} {\left({\left(c + 2 \, d\right)} \cos\left(f x + e\right)^{2} - d \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - {\left(6 \, a c d + 7 \, a d^{2}\right)} \cos\left(f x + e\right)}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right)}{2 \, {\left(a c^{2} d - a d^{3}\right)} f}, -\frac{\sqrt{2} {\left(a c d + a d^{2}\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 2 \, \sqrt{a c d + a d^{2}} c \arctan\left(\frac{2 \, \sqrt{a c d + a d^{2}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}\right)}{2 \, {\left(a c^{2} d - a d^{3}\right)} f}, \frac{\sqrt{-a c d - a d^{2}} c \log\left(-\frac{{\left(a c^{2} + 8 \, a c d + 8 \, a d^{2}\right)} \cos\left(f x + e\right)^{3} + a d^{2} + {\left(a c^{2} + 2 \, a c d\right)} \cos\left(f x + e\right)^{2} - 4 \, \sqrt{-a c d - a d^{2}} {\left({\left(c + 2 \, d\right)} \cos\left(f x + e\right)^{2} - d \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - {\left(6 \, a c d + 7 \, a d^{2}\right)} \cos\left(f x + e\right)}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right) + \frac{2 \, \sqrt{2} {\left(a c d + a d^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}}{2 \, {\left(a c^{2} d - a d^{3}\right)} f}, \frac{\sqrt{a c d + a d^{2}} c \arctan\left(\frac{2 \, \sqrt{a c d + a d^{2}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{{\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}\right) + \frac{\sqrt{2} {\left(a c d + a d^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}}{{\left(a c^{2} d - a d^{3}\right)} f}\right]"," ",0,"[-1/2*(sqrt(2)*(a*c*d + a*d^2)*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) - 3*cos(f*x + e)^2 - 2*cos(f*x + e) + 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - sqrt(-a*c*d - a*d^2)*c*log(-((a*c^2 + 8*a*c*d + 8*a*d^2)*cos(f*x + e)^3 + a*d^2 + (a*c^2 + 2*a*c*d)*cos(f*x + e)^2 - 4*sqrt(-a*c*d - a*d^2)*((c + 2*d)*cos(f*x + e)^2 - d*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - (6*a*c*d + 7*a*d^2)*cos(f*x + e))/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e))))/((a*c^2*d - a*d^3)*f), -1/2*(sqrt(2)*(a*c*d + a*d^2)*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) - 3*cos(f*x + e)^2 - 2*cos(f*x + e) + 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 2*sqrt(a*c*d + a*d^2)*c*arctan(2*sqrt(a*c*d + a*d^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))))/((a*c^2*d - a*d^3)*f), 1/2*(sqrt(-a*c*d - a*d^2)*c*log(-((a*c^2 + 8*a*c*d + 8*a*d^2)*cos(f*x + e)^3 + a*d^2 + (a*c^2 + 2*a*c*d)*cos(f*x + e)^2 - 4*sqrt(-a*c*d - a*d^2)*((c + 2*d)*cos(f*x + e)^2 - d*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - (6*a*c*d + 7*a*d^2)*cos(f*x + e))/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e))) + 2*sqrt(2)*(a*c*d + a*d^2)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/((a*c^2*d - a*d^3)*f), (sqrt(a*c*d + a*d^2)*c*arctan(2*sqrt(a*c*d + a*d^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/((a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))) + sqrt(2)*(a*c*d + a*d^2)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/((a*c^2*d - a*d^3)*f)]","A",0
242,1,1103,0,1.261659," ","integrate((g*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} g \sqrt{\frac{g}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - g \cos\left(f x + e\right)^{2} + 2 \, g \cos\left(f x + e\right) + 3 \, g}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + \sqrt{\frac{c g}{a c + a d}} g \log\left(\frac{c^{2} g \cos\left(f x + e\right)^{3} - {\left(7 \, c^{2} + 6 \, c d\right)} g \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, c^{2} + 3 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c g}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + {\left(2 \, c d + d^{2}\right)} g \cos\left(f x + e\right) + {\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} g}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right)}{2 \, {\left(c - d\right)} f}, \frac{2 \, \sqrt{2} g \sqrt{-\frac{g}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{g \sin\left(f x + e\right)}\right) - \sqrt{\frac{c g}{a c + a d}} g \log\left(\frac{c^{2} g \cos\left(f x + e\right)^{3} - {\left(7 \, c^{2} + 6 \, c d\right)} g \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, c^{2} + 3 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c g}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + {\left(2 \, c d + d^{2}\right)} g \cos\left(f x + e\right) + {\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} g}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right)}{2 \, {\left(c - d\right)} f}, -\frac{\sqrt{2} g \sqrt{\frac{g}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - g \cos\left(f x + e\right)^{2} + 2 \, g \cos\left(f x + e\right) + 3 \, g}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 2 \, \sqrt{-\frac{c g}{a c + a d}} g \arctan\left(\frac{{\left(c \cos\left(f x + e\right)^{2} - {\left(2 \, c + d\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c g}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}}}{2 \, c g \sin\left(f x + e\right)}\right)}{2 \, {\left(c - d\right)} f}, \frac{\sqrt{2} g \sqrt{-\frac{g}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{g \sin\left(f x + e\right)}\right) + \sqrt{-\frac{c g}{a c + a d}} g \arctan\left(\frac{{\left(c \cos\left(f x + e\right)^{2} - {\left(2 \, c + d\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c g}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}}}{2 \, c g \sin\left(f x + e\right)}\right)}{{\left(c - d\right)} f}\right]"," ",0,"[-1/2*(sqrt(2)*g*sqrt(g/a)*log((2*sqrt(2)*sqrt(g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - g*cos(f*x + e)^2 + 2*g*cos(f*x + e) + 3*g)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + sqrt(c*g/(a*c + a*d))*g*log((c^2*g*cos(f*x + e)^3 - (7*c^2 + 6*c*d)*g*cos(f*x + e)^2 + 4*((c^2 + c*d)*cos(f*x + e)^2 - (2*c^2 + 3*c*d + d^2)*cos(f*x + e))*sqrt(c*g/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) + (2*c*d + d^2)*g*cos(f*x + e) + (8*c^2 + 8*c*d + d^2)*g)/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e))))/((c - d)*f), 1/2*(2*sqrt(2)*g*sqrt(-g/a)*arctan(sqrt(2)*sqrt(-g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)/(g*sin(f*x + e))) - sqrt(c*g/(a*c + a*d))*g*log((c^2*g*cos(f*x + e)^3 - (7*c^2 + 6*c*d)*g*cos(f*x + e)^2 + 4*((c^2 + c*d)*cos(f*x + e)^2 - (2*c^2 + 3*c*d + d^2)*cos(f*x + e))*sqrt(c*g/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) + (2*c*d + d^2)*g*cos(f*x + e) + (8*c^2 + 8*c*d + d^2)*g)/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e))))/((c - d)*f), -1/2*(sqrt(2)*g*sqrt(g/a)*log((2*sqrt(2)*sqrt(g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - g*cos(f*x + e)^2 + 2*g*cos(f*x + e) + 3*g)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 2*sqrt(-c*g/(a*c + a*d))*g*arctan(1/2*(c*cos(f*x + e)^2 - (2*c + d)*cos(f*x + e))*sqrt(-c*g/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))/(c*g*sin(f*x + e))))/((c - d)*f), (sqrt(2)*g*sqrt(-g/a)*arctan(sqrt(2)*sqrt(-g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)/(g*sin(f*x + e))) + sqrt(-c*g/(a*c + a*d))*g*arctan(1/2*(c*cos(f*x + e)^2 - (2*c + d)*cos(f*x + e))*sqrt(-c*g/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))/(c*g*sin(f*x + e))))/((c - d)*f)]","A",0
243,1,1597,0,89.925916," ","integrate((g*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} d g^{2} \sqrt{\frac{g}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + g \cos\left(f x + e\right)^{2} - 2 \, g \cos\left(f x + e\right) - 3 \, g}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + c \sqrt{\frac{c g}{a c + a d}} g^{2} \log\left(\frac{c^{2} g \cos\left(f x + e\right)^{3} - {\left(7 \, c^{2} + 6 \, c d\right)} g \cos\left(f x + e\right)^{2} - 4 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, c^{2} + 3 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c g}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + {\left(2 \, c d + d^{2}\right)} g \cos\left(f x + e\right) + {\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} g}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right) - {\left(c - d\right)} g^{2} \sqrt{\frac{g}{a}} \log\left(\frac{g \cos\left(f x + e\right)^{3} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, g \cos\left(f x + e\right)^{2} + 8 \, g}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right)}{2 \, {\left(c d - d^{2}\right)} f}, -\frac{\sqrt{2} d g^{2} \sqrt{\frac{g}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + g \cos\left(f x + e\right)^{2} - 2 \, g \cos\left(f x + e\right) - 3 \, g}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 2 \, c \sqrt{-\frac{c g}{a c + a d}} g^{2} \arctan\left(\frac{{\left(c \cos\left(f x + e\right)^{2} - {\left(2 \, c + d\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c g}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}}}{2 \, c g \sin\left(f x + e\right)}\right) - {\left(c - d\right)} g^{2} \sqrt{\frac{g}{a}} \log\left(\frac{g \cos\left(f x + e\right)^{3} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, g \cos\left(f x + e\right)^{2} + 8 \, g}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right)}{2 \, {\left(c d - d^{2}\right)} f}, -\frac{2 \, \sqrt{2} d g^{2} \sqrt{-\frac{g}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{g \sin\left(f x + e\right)}\right) - 2 \, {\left(c - d\right)} g^{2} \sqrt{-\frac{g}{a}} \arctan\left(\frac{2 \, \sqrt{-\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{g \cos\left(f x + e\right)^{2} - g \cos\left(f x + e\right) - 2 \, g}\right) + c \sqrt{\frac{c g}{a c + a d}} g^{2} \log\left(\frac{c^{2} g \cos\left(f x + e\right)^{3} - {\left(7 \, c^{2} + 6 \, c d\right)} g \cos\left(f x + e\right)^{2} - 4 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, c^{2} + 3 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{c g}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + {\left(2 \, c d + d^{2}\right)} g \cos\left(f x + e\right) + {\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} g}{c^{2} \cos\left(f x + e\right)^{3} + {\left(c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + d^{2} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)}\right)}{2 \, {\left(c d - d^{2}\right)} f}, -\frac{\sqrt{2} d g^{2} \sqrt{-\frac{g}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{-\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{g \sin\left(f x + e\right)}\right) - {\left(c - d\right)} g^{2} \sqrt{-\frac{g}{a}} \arctan\left(\frac{2 \, \sqrt{-\frac{g}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{g \cos\left(f x + e\right)^{2} - g \cos\left(f x + e\right) - 2 \, g}\right) + c \sqrt{-\frac{c g}{a c + a d}} g^{2} \arctan\left(\frac{{\left(c \cos\left(f x + e\right)^{2} - {\left(2 \, c + d\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c g}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{g}{\cos\left(f x + e\right)}}}{2 \, c g \sin\left(f x + e\right)}\right)}{{\left(c d - d^{2}\right)} f}\right]"," ",0,"[-1/2*(sqrt(2)*d*g^2*sqrt(g/a)*log(-(2*sqrt(2)*sqrt(g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + g*cos(f*x + e)^2 - 2*g*cos(f*x + e) - 3*g)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + c*sqrt(c*g/(a*c + a*d))*g^2*log((c^2*g*cos(f*x + e)^3 - (7*c^2 + 6*c*d)*g*cos(f*x + e)^2 - 4*((c^2 + c*d)*cos(f*x + e)^2 - (2*c^2 + 3*c*d + d^2)*cos(f*x + e))*sqrt(c*g/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) + (2*c*d + d^2)*g*cos(f*x + e) + (8*c^2 + 8*c*d + d^2)*g)/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e))) - (c - d)*g^2*sqrt(g/a)*log((g*cos(f*x + e)^3 - 4*(cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt(g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) - 7*g*cos(f*x + e)^2 + 8*g)/(cos(f*x + e)^3 + cos(f*x + e)^2)))/((c*d - d^2)*f), -1/2*(sqrt(2)*d*g^2*sqrt(g/a)*log(-(2*sqrt(2)*sqrt(g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + g*cos(f*x + e)^2 - 2*g*cos(f*x + e) - 3*g)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 2*c*sqrt(-c*g/(a*c + a*d))*g^2*arctan(1/2*(c*cos(f*x + e)^2 - (2*c + d)*cos(f*x + e))*sqrt(-c*g/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))/(c*g*sin(f*x + e))) - (c - d)*g^2*sqrt(g/a)*log((g*cos(f*x + e)^3 - 4*(cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt(g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) - 7*g*cos(f*x + e)^2 + 8*g)/(cos(f*x + e)^3 + cos(f*x + e)^2)))/((c*d - d^2)*f), -1/2*(2*sqrt(2)*d*g^2*sqrt(-g/a)*arctan(sqrt(2)*sqrt(-g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)/(g*sin(f*x + e))) - 2*(c - d)*g^2*sqrt(-g/a)*arctan(2*sqrt(-g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(g*cos(f*x + e)^2 - g*cos(f*x + e) - 2*g)) + c*sqrt(c*g/(a*c + a*d))*g^2*log((c^2*g*cos(f*x + e)^3 - (7*c^2 + 6*c*d)*g*cos(f*x + e)^2 - 4*((c^2 + c*d)*cos(f*x + e)^2 - (2*c^2 + 3*c*d + d^2)*cos(f*x + e))*sqrt(c*g/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*sin(f*x + e) + (2*c*d + d^2)*g*cos(f*x + e) + (8*c^2 + 8*c*d + d^2)*g)/(c^2*cos(f*x + e)^3 + (c^2 + 2*c*d)*cos(f*x + e)^2 + d^2 + (2*c*d + d^2)*cos(f*x + e))))/((c*d - d^2)*f), -(sqrt(2)*d*g^2*sqrt(-g/a)*arctan(sqrt(2)*sqrt(-g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)/(g*sin(f*x + e))) - (c - d)*g^2*sqrt(-g/a)*arctan(2*sqrt(-g/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(g*cos(f*x + e)^2 - g*cos(f*x + e) - 2*g)) + c*sqrt(-c*g/(a*c + a*d))*g^2*arctan(1/2*(c*cos(f*x + e)^2 - (2*c + d)*cos(f*x + e))*sqrt(-c*g/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(g/cos(f*x + e))/(c*g*sin(f*x + e))))/((c*d - d^2)*f)]","A",0
244,1,281,0,0.469071," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, a c^{4} + 16 \, b c^{3} d + 24 \, a c^{2} d^{2} + 12 \, b c d^{3} + 3 \, a d^{4}\right)} \cos\left(f x + e\right)^{5} \log\left(\sin\left(f x + e\right) + 1\right) - 15 \, {\left(8 \, a c^{4} + 16 \, b c^{3} d + 24 \, a c^{2} d^{2} + 12 \, b c d^{3} + 3 \, a d^{4}\right)} \cos\left(f x + e\right)^{5} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(24 \, b d^{4} + 8 \, {\left(15 \, b c^{4} + 60 \, a c^{3} d + 60 \, b c^{2} d^{2} + 40 \, a c d^{3} + 8 \, b d^{4}\right)} \cos\left(f x + e\right)^{4} + 15 \, {\left(16 \, b c^{3} d + 24 \, a c^{2} d^{2} + 12 \, b c d^{3} + 3 \, a d^{4}\right)} \cos\left(f x + e\right)^{3} + 16 \, {\left(15 \, b c^{2} d^{2} + 10 \, a c d^{3} + 2 \, b d^{4}\right)} \cos\left(f x + e\right)^{2} + 30 \, {\left(4 \, b c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{240 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/240*(15*(8*a*c^4 + 16*b*c^3*d + 24*a*c^2*d^2 + 12*b*c*d^3 + 3*a*d^4)*cos(f*x + e)^5*log(sin(f*x + e) + 1) - 15*(8*a*c^4 + 16*b*c^3*d + 24*a*c^2*d^2 + 12*b*c*d^3 + 3*a*d^4)*cos(f*x + e)^5*log(-sin(f*x + e) + 1) + 2*(24*b*d^4 + 8*(15*b*c^4 + 60*a*c^3*d + 60*b*c^2*d^2 + 40*a*c*d^3 + 8*b*d^4)*cos(f*x + e)^4 + 15*(16*b*c^3*d + 24*a*c^2*d^2 + 12*b*c*d^3 + 3*a*d^4)*cos(f*x + e)^3 + 16*(15*b*c^2*d^2 + 10*a*c*d^3 + 2*b*d^4)*cos(f*x + e)^2 + 30*(4*b*c*d^3 + a*d^4)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^5)","A",0
245,1,211,0,0.455010," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, a c^{3} + 12 \, b c^{2} d + 12 \, a c d^{2} + 3 \, b d^{3}\right)} \cos\left(f x + e\right)^{4} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(8 \, a c^{3} + 12 \, b c^{2} d + 12 \, a c d^{2} + 3 \, b d^{3}\right)} \cos\left(f x + e\right)^{4} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(6 \, b d^{3} + 8 \, {\left(3 \, b c^{3} + 9 \, a c^{2} d + 6 \, b c d^{2} + 2 \, a d^{3}\right)} \cos\left(f x + e\right)^{3} + 9 \, {\left(4 \, b c^{2} d + 4 \, a c d^{2} + b d^{3}\right)} \cos\left(f x + e\right)^{2} + 8 \, {\left(3 \, b c d^{2} + a d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{48 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/48*(3*(8*a*c^3 + 12*b*c^2*d + 12*a*c*d^2 + 3*b*d^3)*cos(f*x + e)^4*log(sin(f*x + e) + 1) - 3*(8*a*c^3 + 12*b*c^2*d + 12*a*c*d^2 + 3*b*d^3)*cos(f*x + e)^4*log(-sin(f*x + e) + 1) + 2*(6*b*d^3 + 8*(3*b*c^3 + 9*a*c^2*d + 6*b*c*d^2 + 2*a*d^3)*cos(f*x + e)^3 + 9*(4*b*c^2*d + 4*a*c*d^2 + b*d^3)*cos(f*x + e)^2 + 8*(3*b*c*d^2 + a*d^3)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4)","A",0
246,1,150,0,0.473720," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, a c^{2} + 2 \, b c d + a d^{2}\right)} \cos\left(f x + e\right)^{3} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(2 \, a c^{2} + 2 \, b c d + a d^{2}\right)} \cos\left(f x + e\right)^{3} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, b d^{2} + 2 \, {\left(3 \, b c^{2} + 6 \, a c d + 2 \, b d^{2}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, b c d + a d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, f \cos\left(f x + e\right)^{3}}"," ",0,"1/12*(3*(2*a*c^2 + 2*b*c*d + a*d^2)*cos(f*x + e)^3*log(sin(f*x + e) + 1) - 3*(2*a*c^2 + 2*b*c*d + a*d^2)*cos(f*x + e)^3*log(-sin(f*x + e) + 1) + 2*(2*b*d^2 + 2*(3*b*c^2 + 6*a*c*d + 2*b*d^2)*cos(f*x + e)^2 + 3*(2*b*c*d + a*d^2)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3)","A",0
247,1,96,0,0.464131," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 \, a c + b d\right)} \cos\left(f x + e\right)^{2} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(2 \, a c + b d\right)} \cos\left(f x + e\right)^{2} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(b d + 2 \, {\left(b c + a d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, f \cos\left(f x + e\right)^{2}}"," ",0,"1/4*((2*a*c + b*d)*cos(f*x + e)^2*log(sin(f*x + e) + 1) - (2*a*c + b*d)*cos(f*x + e)^2*log(-sin(f*x + e) + 1) + 2*(b*d + 2*(b*c + a*d)*cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^2)","A",0
248,1,316,0,1.080337," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{{\left(b c - a d\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - {\left(b c^{2} - b d^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) + {\left(b c^{2} - b d^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right)}{2 \, {\left(c^{2} d - d^{3}\right)} f}, -\frac{2 \, {\left(b c - a d\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(b c^{2} - b d^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) + {\left(b c^{2} - b d^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right)}{2 \, {\left(c^{2} d - d^{3}\right)} f}\right]"," ",0,"[-1/2*((b*c - a*d)*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - (b*c^2 - b*d^2)*log(sin(f*x + e) + 1) + (b*c^2 - b*d^2)*log(-sin(f*x + e) + 1))/((c^2*d - d^3)*f), -1/2*(2*(b*c - a*d)*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (b*c^2 - b*d^2)*log(sin(f*x + e) + 1) + (b*c^2 - b*d^2)*log(-sin(f*x + e) + 1))/((c^2*d - d^3)*f)]","A",0
249,1,389,0,0.492204," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a c d - b d^{2} + {\left(a c^{2} - b c d\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(b c^{3} - a c^{2} d - b c d^{2} + a d^{3}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{5} - 2 \, c^{3} d^{2} + c d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{4} d - 2 \, c^{2} d^{3} + d^{5}\right)} f\right)}}, \frac{{\left(a c d - b d^{2} + {\left(a c^{2} - b c d\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(b c^{3} - a c^{2} d - b c d^{2} + a d^{3}\right)} \sin\left(f x + e\right)}{{\left(c^{5} - 2 \, c^{3} d^{2} + c d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{4} d - 2 \, c^{2} d^{3} + d^{5}\right)} f}\right]"," ",0,"[1/2*((a*c*d - b*d^2 + (a*c^2 - b*c*d)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(b*c^3 - a*c^2*d - b*c*d^2 + a*d^3)*sin(f*x + e))/((c^5 - 2*c^3*d^2 + c*d^4)*f*cos(f*x + e) + (c^4*d - 2*c^2*d^3 + d^5)*f), ((a*c*d - b*d^2 + (a*c^2 - b*c*d)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (b*c^3 - a*c^2*d - b*c*d^2 + a*d^3)*sin(f*x + e))/((c^5 - 2*c^3*d^2 + c*d^4)*f*cos(f*x + e) + (c^4*d - 2*c^2*d^3 + d^5)*f)]","A",0
250,1,752,0,0.543981," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a c^{2} d^{2} - 3 \, b c d^{3} + a d^{4} + {\left(2 \, a c^{4} - 3 \, b c^{3} d + a c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, a c^{3} d - 3 \, b c^{2} d^{2} + a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(b c^{4} d - 3 \, a c^{3} d^{2} + b c^{2} d^{3} + 3 \, a c d^{4} - 2 \, b d^{5} + {\left(2 \, b c^{5} - 4 \, a c^{4} d - b c^{3} d^{2} + 5 \, a c^{2} d^{3} - b c d^{4} - a d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{8} - 3 \, c^{6} d^{2} + 3 \, c^{4} d^{4} - c^{2} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{7} d - 3 \, c^{5} d^{3} + 3 \, c^{3} d^{5} - c d^{7}\right)} f \cos\left(f x + e\right) + {\left(c^{6} d^{2} - 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} - d^{8}\right)} f\right)}}, \frac{{\left(2 \, a c^{2} d^{2} - 3 \, b c d^{3} + a d^{4} + {\left(2 \, a c^{4} - 3 \, b c^{3} d + a c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, a c^{3} d - 3 \, b c^{2} d^{2} + a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(b c^{4} d - 3 \, a c^{3} d^{2} + b c^{2} d^{3} + 3 \, a c d^{4} - 2 \, b d^{5} + {\left(2 \, b c^{5} - 4 \, a c^{4} d - b c^{3} d^{2} + 5 \, a c^{2} d^{3} - b c d^{4} - a d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{8} - 3 \, c^{6} d^{2} + 3 \, c^{4} d^{4} - c^{2} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{7} d - 3 \, c^{5} d^{3} + 3 \, c^{3} d^{5} - c d^{7}\right)} f \cos\left(f x + e\right) + {\left(c^{6} d^{2} - 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} - d^{8}\right)} f\right)}}\right]"," ",0,"[1/4*((2*a*c^2*d^2 - 3*b*c*d^3 + a*d^4 + (2*a*c^4 - 3*b*c^3*d + a*c^2*d^2)*cos(f*x + e)^2 + 2*(2*a*c^3*d - 3*b*c^2*d^2 + a*c*d^3)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(b*c^4*d - 3*a*c^3*d^2 + b*c^2*d^3 + 3*a*c*d^4 - 2*b*d^5 + (2*b*c^5 - 4*a*c^4*d - b*c^3*d^2 + 5*a*c^2*d^3 - b*c*d^4 - a*d^5)*cos(f*x + e))*sin(f*x + e))/((c^8 - 3*c^6*d^2 + 3*c^4*d^4 - c^2*d^6)*f*cos(f*x + e)^2 + 2*(c^7*d - 3*c^5*d^3 + 3*c^3*d^5 - c*d^7)*f*cos(f*x + e) + (c^6*d^2 - 3*c^4*d^4 + 3*c^2*d^6 - d^8)*f), 1/2*((2*a*c^2*d^2 - 3*b*c*d^3 + a*d^4 + (2*a*c^4 - 3*b*c^3*d + a*c^2*d^2)*cos(f*x + e)^2 + 2*(2*a*c^3*d - 3*b*c^2*d^2 + a*c*d^3)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (b*c^4*d - 3*a*c^3*d^2 + b*c^2*d^3 + 3*a*c*d^4 - 2*b*d^5 + (2*b*c^5 - 4*a*c^4*d - b*c^3*d^2 + 5*a*c^2*d^3 - b*c*d^4 - a*d^5)*cos(f*x + e))*sin(f*x + e))/((c^8 - 3*c^6*d^2 + 3*c^4*d^4 - c^2*d^6)*f*cos(f*x + e)^2 + 2*(c^7*d - 3*c^5*d^3 + 3*c^3*d^5 - c*d^7)*f*cos(f*x + e) + (c^6*d^2 - 3*c^4*d^4 + 3*c^2*d^6 - d^8)*f)]","B",0
251,1,1238,0,0.566114," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, a c^{3} d^{3} - 4 \, b c^{2} d^{4} + 3 \, a c d^{5} - b d^{6} + {\left(2 \, a c^{6} - 4 \, b c^{5} d + 3 \, a c^{4} d^{2} - b c^{3} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(2 \, a c^{5} d - 4 \, b c^{4} d^{2} + 3 \, a c^{3} d^{3} - b c^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, a c^{4} d^{2} - 4 \, b c^{3} d^{3} + 3 \, a c^{2} d^{4} - b c d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(2 \, b c^{5} d^{2} - 11 \, a c^{4} d^{3} + 11 \, b c^{3} d^{4} + 7 \, a c^{2} d^{5} - 13 \, b c d^{6} + 4 \, a d^{7} + {\left(6 \, b c^{7} - 18 \, a c^{6} d + 4 \, b c^{5} d^{2} + 23 \, a c^{4} d^{3} - 11 \, b c^{3} d^{4} - 7 \, a c^{2} d^{5} + b c d^{6} + 2 \, a d^{7}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, b c^{6} d - 9 \, a c^{5} d^{2} + 7 \, b c^{4} d^{3} + 8 \, a c^{3} d^{4} - 10 \, b c^{2} d^{5} + a c d^{6} + b d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left({\left(c^{11} - 4 \, c^{9} d^{2} + 6 \, c^{7} d^{4} - 4 \, c^{5} d^{6} + c^{3} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{10} d - 4 \, c^{8} d^{3} + 6 \, c^{6} d^{5} - 4 \, c^{4} d^{7} + c^{2} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{9} d^{2} - 4 \, c^{7} d^{4} + 6 \, c^{5} d^{6} - 4 \, c^{3} d^{8} + c d^{10}\right)} f \cos\left(f x + e\right) + {\left(c^{8} d^{3} - 4 \, c^{6} d^{5} + 6 \, c^{4} d^{7} - 4 \, c^{2} d^{9} + d^{11}\right)} f\right)}}, \frac{3 \, {\left(2 \, a c^{3} d^{3} - 4 \, b c^{2} d^{4} + 3 \, a c d^{5} - b d^{6} + {\left(2 \, a c^{6} - 4 \, b c^{5} d + 3 \, a c^{4} d^{2} - b c^{3} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(2 \, a c^{5} d - 4 \, b c^{4} d^{2} + 3 \, a c^{3} d^{3} - b c^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, a c^{4} d^{2} - 4 \, b c^{3} d^{3} + 3 \, a c^{2} d^{4} - b c d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(2 \, b c^{5} d^{2} - 11 \, a c^{4} d^{3} + 11 \, b c^{3} d^{4} + 7 \, a c^{2} d^{5} - 13 \, b c d^{6} + 4 \, a d^{7} + {\left(6 \, b c^{7} - 18 \, a c^{6} d + 4 \, b c^{5} d^{2} + 23 \, a c^{4} d^{3} - 11 \, b c^{3} d^{4} - 7 \, a c^{2} d^{5} + b c d^{6} + 2 \, a d^{7}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, b c^{6} d - 9 \, a c^{5} d^{2} + 7 \, b c^{4} d^{3} + 8 \, a c^{3} d^{4} - 10 \, b c^{2} d^{5} + a c d^{6} + b d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(c^{11} - 4 \, c^{9} d^{2} + 6 \, c^{7} d^{4} - 4 \, c^{5} d^{6} + c^{3} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{10} d - 4 \, c^{8} d^{3} + 6 \, c^{6} d^{5} - 4 \, c^{4} d^{7} + c^{2} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{9} d^{2} - 4 \, c^{7} d^{4} + 6 \, c^{5} d^{6} - 4 \, c^{3} d^{8} + c d^{10}\right)} f \cos\left(f x + e\right) + {\left(c^{8} d^{3} - 4 \, c^{6} d^{5} + 6 \, c^{4} d^{7} - 4 \, c^{2} d^{9} + d^{11}\right)} f\right)}}\right]"," ",0,"[1/12*(3*(2*a*c^3*d^3 - 4*b*c^2*d^4 + 3*a*c*d^5 - b*d^6 + (2*a*c^6 - 4*b*c^5*d + 3*a*c^4*d^2 - b*c^3*d^3)*cos(f*x + e)^3 + 3*(2*a*c^5*d - 4*b*c^4*d^2 + 3*a*c^3*d^3 - b*c^2*d^4)*cos(f*x + e)^2 + 3*(2*a*c^4*d^2 - 4*b*c^3*d^3 + 3*a*c^2*d^4 - b*c*d^5)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(2*b*c^5*d^2 - 11*a*c^4*d^3 + 11*b*c^3*d^4 + 7*a*c^2*d^5 - 13*b*c*d^6 + 4*a*d^7 + (6*b*c^7 - 18*a*c^6*d + 4*b*c^5*d^2 + 23*a*c^4*d^3 - 11*b*c^3*d^4 - 7*a*c^2*d^5 + b*c*d^6 + 2*a*d^7)*cos(f*x + e)^2 + 3*(2*b*c^6*d - 9*a*c^5*d^2 + 7*b*c^4*d^3 + 8*a*c^3*d^4 - 10*b*c^2*d^5 + a*c*d^6 + b*d^7)*cos(f*x + e))*sin(f*x + e))/((c^11 - 4*c^9*d^2 + 6*c^7*d^4 - 4*c^5*d^6 + c^3*d^8)*f*cos(f*x + e)^3 + 3*(c^10*d - 4*c^8*d^3 + 6*c^6*d^5 - 4*c^4*d^7 + c^2*d^9)*f*cos(f*x + e)^2 + 3*(c^9*d^2 - 4*c^7*d^4 + 6*c^5*d^6 - 4*c^3*d^8 + c*d^10)*f*cos(f*x + e) + (c^8*d^3 - 4*c^6*d^5 + 6*c^4*d^7 - 4*c^2*d^9 + d^11)*f), 1/6*(3*(2*a*c^3*d^3 - 4*b*c^2*d^4 + 3*a*c*d^5 - b*d^6 + (2*a*c^6 - 4*b*c^5*d + 3*a*c^4*d^2 - b*c^3*d^3)*cos(f*x + e)^3 + 3*(2*a*c^5*d - 4*b*c^4*d^2 + 3*a*c^3*d^3 - b*c^2*d^4)*cos(f*x + e)^2 + 3*(2*a*c^4*d^2 - 4*b*c^3*d^3 + 3*a*c^2*d^4 - b*c*d^5)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (2*b*c^5*d^2 - 11*a*c^4*d^3 + 11*b*c^3*d^4 + 7*a*c^2*d^5 - 13*b*c*d^6 + 4*a*d^7 + (6*b*c^7 - 18*a*c^6*d + 4*b*c^5*d^2 + 23*a*c^4*d^3 - 11*b*c^3*d^4 - 7*a*c^2*d^5 + b*c*d^6 + 2*a*d^7)*cos(f*x + e)^2 + 3*(2*b*c^6*d - 9*a*c^5*d^2 + 7*b*c^4*d^3 + 8*a*c^3*d^4 - 10*b*c^2*d^5 + a*c*d^6 + b*d^7)*cos(f*x + e))*sin(f*x + e))/((c^11 - 4*c^9*d^2 + 6*c^7*d^4 - 4*c^5*d^6 + c^3*d^8)*f*cos(f*x + e)^3 + 3*(c^10*d - 4*c^8*d^3 + 6*c^6*d^5 - 4*c^4*d^7 + c^2*d^9)*f*cos(f*x + e)^2 + 3*(c^9*d^2 - 4*c^7*d^4 + 6*c^5*d^6 - 4*c^3*d^8 + c*d^10)*f*cos(f*x + e) + (c^8*d^3 - 4*c^6*d^5 + 6*c^4*d^7 - 4*c^2*d^9 + d^11)*f)]","B",0
252,1,1093,0,172.775640," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{a^{2} - b^{2}} \cos\left(f x + e\right)^{3} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right) + 3 \, {\left(8 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{3} d - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d^{2} + 4 \, {\left(2 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} c d^{3} - {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(8 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{3} d - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d^{2} + 4 \, {\left(2 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} c d^{3} - {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{4} + 2 \, {\left(18 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{2} d^{2} - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{3} + {\left(3 \, a^{4} b - a^{2} b^{3} - 2 \, b^{5}\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(4 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{3} - {\left(a^{3} b^{2} - a b^{4}\right)} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left(a^{2} b^{4} - b^{6}\right)} f \cos\left(f x + e\right)^{3}}, \frac{12 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right) \cos\left(f x + e\right)^{3} + 3 \, {\left(8 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{3} d - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d^{2} + 4 \, {\left(2 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} c d^{3} - {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(8 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{3} d - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d^{2} + 4 \, {\left(2 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} c d^{3} - {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{4} + 2 \, {\left(18 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{2} d^{2} - 12 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{3} + {\left(3 \, a^{4} b - a^{2} b^{3} - 2 \, b^{5}\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(4 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{3} - {\left(a^{3} b^{2} - a b^{4}\right)} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left(a^{2} b^{4} - b^{6}\right)} f \cos\left(f x + e\right)^{3}}\right]"," ",0,"[1/12*(6*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(a^2 - b^2)*cos(f*x + e)^3*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 + 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)) + 3*(8*(a^2*b^3 - b^5)*c^3*d - 12*(a^3*b^2 - a*b^4)*c^2*d^2 + 4*(2*a^4*b - a^2*b^3 - b^5)*c*d^3 - (2*a^5 - a^3*b^2 - a*b^4)*d^4)*cos(f*x + e)^3*log(sin(f*x + e) + 1) - 3*(8*(a^2*b^3 - b^5)*c^3*d - 12*(a^3*b^2 - a*b^4)*c^2*d^2 + 4*(2*a^4*b - a^2*b^3 - b^5)*c*d^3 - (2*a^5 - a^3*b^2 - a*b^4)*d^4)*cos(f*x + e)^3*log(-sin(f*x + e) + 1) + 2*(2*(a^2*b^3 - b^5)*d^4 + 2*(18*(a^2*b^3 - b^5)*c^2*d^2 - 12*(a^3*b^2 - a*b^4)*c*d^3 + (3*a^4*b - a^2*b^3 - 2*b^5)*d^4)*cos(f*x + e)^2 + 3*(4*(a^2*b^3 - b^5)*c*d^3 - (a^3*b^2 - a*b^4)*d^4)*cos(f*x + e))*sin(f*x + e))/((a^2*b^4 - b^6)*f*cos(f*x + e)^3), 1/12*(12*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e)))*cos(f*x + e)^3 + 3*(8*(a^2*b^3 - b^5)*c^3*d - 12*(a^3*b^2 - a*b^4)*c^2*d^2 + 4*(2*a^4*b - a^2*b^3 - b^5)*c*d^3 - (2*a^5 - a^3*b^2 - a*b^4)*d^4)*cos(f*x + e)^3*log(sin(f*x + e) + 1) - 3*(8*(a^2*b^3 - b^5)*c^3*d - 12*(a^3*b^2 - a*b^4)*c^2*d^2 + 4*(2*a^4*b - a^2*b^3 - b^5)*c*d^3 - (2*a^5 - a^3*b^2 - a*b^4)*d^4)*cos(f*x + e)^3*log(-sin(f*x + e) + 1) + 2*(2*(a^2*b^3 - b^5)*d^4 + 2*(18*(a^2*b^3 - b^5)*c^2*d^2 - 12*(a^3*b^2 - a*b^4)*c*d^3 + (3*a^4*b - a^2*b^3 - 2*b^5)*d^4)*cos(f*x + e)^2 + 3*(4*(a^2*b^3 - b^5)*c*d^3 - (a^3*b^2 - a*b^4)*d^4)*cos(f*x + e))*sin(f*x + e))/((a^2*b^4 - b^6)*f*cos(f*x + e)^3)]","B",0
253,1,779,0,37.602021," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a^{2} - b^{2}} \cos\left(f x + e\right)^{2} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right) - {\left(6 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{2} d - 6 \, {\left(a^{3} b - a b^{3}\right)} c d^{2} + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} \log\left(\sin\left(f x + e\right) + 1\right) + {\left(6 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{2} d - 6 \, {\left(a^{3} b - a b^{3}\right)} c d^{2} + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{3} + 2 \, {\left(3 \, {\left(a^{2} b^{2} - b^{4}\right)} c d^{2} - {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left(a^{2} b^{3} - b^{5}\right)} f \cos\left(f x + e\right)^{2}}, \frac{4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right) \cos\left(f x + e\right)^{2} + {\left(6 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{2} d - 6 \, {\left(a^{3} b - a b^{3}\right)} c d^{2} + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(6 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{2} d - 6 \, {\left(a^{3} b - a b^{3}\right)} c d^{2} + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{3} + 2 \, {\left(3 \, {\left(a^{2} b^{2} - b^{4}\right)} c d^{2} - {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left(a^{2} b^{3} - b^{5}\right)} f \cos\left(f x + e\right)^{2}}\right]"," ",0,"[-1/4*(2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a^2 - b^2)*cos(f*x + e)^2*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 - 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)) - (6*(a^2*b^2 - b^4)*c^2*d - 6*(a^3*b - a*b^3)*c*d^2 + (2*a^4 - a^2*b^2 - b^4)*d^3)*cos(f*x + e)^2*log(sin(f*x + e) + 1) + (6*(a^2*b^2 - b^4)*c^2*d - 6*(a^3*b - a*b^3)*c*d^2 + (2*a^4 - a^2*b^2 - b^4)*d^3)*cos(f*x + e)^2*log(-sin(f*x + e) + 1) - 2*((a^2*b^2 - b^4)*d^3 + 2*(3*(a^2*b^2 - b^4)*c*d^2 - (a^3*b - a*b^3)*d^3)*cos(f*x + e))*sin(f*x + e))/((a^2*b^3 - b^5)*f*cos(f*x + e)^2), 1/4*(4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e)))*cos(f*x + e)^2 + (6*(a^2*b^2 - b^4)*c^2*d - 6*(a^3*b - a*b^3)*c*d^2 + (2*a^4 - a^2*b^2 - b^4)*d^3)*cos(f*x + e)^2*log(sin(f*x + e) + 1) - (6*(a^2*b^2 - b^4)*c^2*d - 6*(a^3*b - a*b^3)*c*d^2 + (2*a^4 - a^2*b^2 - b^4)*d^3)*cos(f*x + e)^2*log(-sin(f*x + e) + 1) + 2*((a^2*b^2 - b^4)*d^3 + 2*(3*(a^2*b^2 - b^4)*c*d^2 - (a^3*b - a*b^3)*d^3)*cos(f*x + e))*sin(f*x + e))/((a^2*b^3 - b^5)*f*cos(f*x + e)^2)]","B",0
254,1,518,0,5.650673," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} b - b^{3}\right)} d^{2} \sin\left(f x + e\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a^{2} - b^{2}} \cos\left(f x + e\right) \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right) + {\left(2 \, {\left(a^{2} b - b^{3}\right)} c d - {\left(a^{3} - a b^{2}\right)} d^{2}\right)} \cos\left(f x + e\right) \log\left(\sin\left(f x + e\right) + 1\right) - {\left(2 \, {\left(a^{2} b - b^{3}\right)} c d - {\left(a^{3} - a b^{2}\right)} d^{2}\right)} \cos\left(f x + e\right) \log\left(-\sin\left(f x + e\right) + 1\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} f \cos\left(f x + e\right)}, \frac{2 \, {\left(a^{2} b - b^{3}\right)} d^{2} \sin\left(f x + e\right) + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right) \cos\left(f x + e\right) + {\left(2 \, {\left(a^{2} b - b^{3}\right)} c d - {\left(a^{3} - a b^{2}\right)} d^{2}\right)} \cos\left(f x + e\right) \log\left(\sin\left(f x + e\right) + 1\right) - {\left(2 \, {\left(a^{2} b - b^{3}\right)} c d - {\left(a^{3} - a b^{2}\right)} d^{2}\right)} \cos\left(f x + e\right) \log\left(-\sin\left(f x + e\right) + 1\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} f \cos\left(f x + e\right)}\right]"," ",0,"[1/2*(2*(a^2*b - b^3)*d^2*sin(f*x + e) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a^2 - b^2)*cos(f*x + e)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 + 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)) + (2*(a^2*b - b^3)*c*d - (a^3 - a*b^2)*d^2)*cos(f*x + e)*log(sin(f*x + e) + 1) - (2*(a^2*b - b^3)*c*d - (a^3 - a*b^2)*d^2)*cos(f*x + e)*log(-sin(f*x + e) + 1))/((a^2*b^2 - b^4)*f*cos(f*x + e)), 1/2*(2*(a^2*b - b^3)*d^2*sin(f*x + e) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e)))*cos(f*x + e) + (2*(a^2*b - b^3)*c*d - (a^3 - a*b^2)*d^2)*cos(f*x + e)*log(sin(f*x + e) + 1) - (2*(a^2*b - b^3)*c*d - (a^3 - a*b^2)*d^2)*cos(f*x + e)*log(-sin(f*x + e) + 1))/((a^2*b^2 - b^4)*f*cos(f*x + e))]","B",0
255,1,309,0,0.967573," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} - b^{2}\right)} d \log\left(\sin\left(f x + e\right) + 1\right) - {\left(a^{2} - b^{2}\right)} d \log\left(-\sin\left(f x + e\right) + 1\right) - \sqrt{a^{2} - b^{2}} {\left(b c - a d\right)} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right)}{2 \, {\left(a^{2} b - b^{3}\right)} f}, \frac{{\left(a^{2} - b^{2}\right)} d \log\left(\sin\left(f x + e\right) + 1\right) - {\left(a^{2} - b^{2}\right)} d \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(b c - a d\right)} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right)}{2 \, {\left(a^{2} b - b^{3}\right)} f}\right]"," ",0,"[1/2*((a^2 - b^2)*d*log(sin(f*x + e) + 1) - (a^2 - b^2)*d*log(-sin(f*x + e) + 1) - sqrt(a^2 - b^2)*(b*c - a*d)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 - 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)))/((a^2*b - b^3)*f), 1/2*((a^2 - b^2)*d*log(sin(f*x + e) + 1) - (a^2 - b^2)*d*log(-sin(f*x + e) + 1) + 2*sqrt(-a^2 + b^2)*(b*c - a*d)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e))))/((a^2*b - b^3)*f)]","A",0
256,1,1040,0,2.953279," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e))/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{{\left(a^{2} - b^{2}\right)} \sqrt{c^{2} - d^{2}} d \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + {\left(b c^{2} - b d^{2}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right)}{2 \, {\left({\left(a^{2} b - b^{3}\right)} c^{3} - {\left(a^{3} - a b^{2}\right)} c^{2} d - {\left(a^{2} b - b^{3}\right)} c d^{2} + {\left(a^{3} - a b^{2}\right)} d^{3}\right)} f}, -\frac{{\left(a^{2} - b^{2}\right)} \sqrt{c^{2} - d^{2}} d \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - 2 \, {\left(b c^{2} - b d^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right)}{2 \, {\left({\left(a^{2} b - b^{3}\right)} c^{3} - {\left(a^{3} - a b^{2}\right)} c^{2} d - {\left(a^{2} b - b^{3}\right)} c d^{2} + {\left(a^{3} - a b^{2}\right)} d^{3}\right)} f}, -\frac{2 \, {\left(a^{2} - b^{2}\right)} \sqrt{-c^{2} + d^{2}} d \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(b c^{2} - b d^{2}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right)}{2 \, {\left({\left(a^{2} b - b^{3}\right)} c^{3} - {\left(a^{3} - a b^{2}\right)} c^{2} d - {\left(a^{2} b - b^{3}\right)} c d^{2} + {\left(a^{3} - a b^{2}\right)} d^{3}\right)} f}, -\frac{{\left(a^{2} - b^{2}\right)} \sqrt{-c^{2} + d^{2}} d \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(b c^{2} - b d^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right)}{{\left({\left(a^{2} b - b^{3}\right)} c^{3} - {\left(a^{3} - a b^{2}\right)} c^{2} d - {\left(a^{2} b - b^{3}\right)} c d^{2} + {\left(a^{3} - a b^{2}\right)} d^{3}\right)} f}\right]"," ",0,"[-1/2*((a^2 - b^2)*sqrt(c^2 - d^2)*d*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + (b*c^2 - b*d^2)*sqrt(a^2 - b^2)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 - 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)))/(((a^2*b - b^3)*c^3 - (a^3 - a*b^2)*c^2*d - (a^2*b - b^3)*c*d^2 + (a^3 - a*b^2)*d^3)*f), -1/2*((a^2 - b^2)*sqrt(c^2 - d^2)*d*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - 2*(b*c^2 - b*d^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e))))/(((a^2*b - b^3)*c^3 - (a^3 - a*b^2)*c^2*d - (a^2*b - b^3)*c*d^2 + (a^3 - a*b^2)*d^3)*f), -1/2*(2*(a^2 - b^2)*sqrt(-c^2 + d^2)*d*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (b*c^2 - b*d^2)*sqrt(a^2 - b^2)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 - 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)))/(((a^2*b - b^3)*c^3 - (a^3 - a*b^2)*c^2*d - (a^2*b - b^3)*c*d^2 + (a^3 - a*b^2)*d^3)*f), -((a^2 - b^2)*sqrt(-c^2 + d^2)*d*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (b*c^2 - b*d^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e))))/(((a^2*b - b^3)*c^3 - (a^3 - a*b^2)*c^2*d - (a^2*b - b^3)*c*d^2 + (a^3 - a*b^2)*d^3)*f)]","A",0
257,1,2863,0,167.792491," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{4} d - 2 \, b^{2} c^{2} d^{3} + b^{2} d^{5} + {\left(b^{2} c^{5} - 2 \, b^{2} c^{3} d^{2} + b^{2} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right) + {\left(2 \, {\left(a^{2} b - b^{3}\right)} c^{2} d^{2} - {\left(a^{3} - a b^{2}\right)} c d^{3} - {\left(a^{2} b - b^{3}\right)} d^{4} + {\left(2 \, {\left(a^{2} b - b^{3}\right)} c^{3} d - {\left(a^{3} - a b^{2}\right)} c^{2} d^{2} - {\left(a^{2} b - b^{3}\right)} c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} c^{3} d^{2} - {\left(a^{3} - a b^{2}\right)} c^{2} d^{3} - {\left(a^{2} b - b^{3}\right)} c d^{4} + {\left(a^{3} - a b^{2}\right)} d^{5}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} c^{7} - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{6} d + {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{5} d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{4} d^{3} - {\left(2 \, a^{4} - 3 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{4} - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d^{5} + {\left(a^{4} - a^{2} b^{2}\right)} c d^{6}\right)} f \cos\left(f x + e\right) + {\left({\left(a^{2} b^{2} - b^{4}\right)} c^{6} d - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{5} d^{2} + {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{4} d^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{3} d^{4} - {\left(2 \, a^{4} - 3 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{5} - 2 \, {\left(a^{3} b - a b^{3}\right)} c d^{6} + {\left(a^{4} - a^{2} b^{2}\right)} d^{7}\right)} f\right)}}, \frac{2 \, {\left(b^{2} c^{4} d - 2 \, b^{2} c^{2} d^{3} + b^{2} d^{5} + {\left(b^{2} c^{5} - 2 \, b^{2} c^{3} d^{2} + b^{2} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(2 \, {\left(a^{2} b - b^{3}\right)} c^{2} d^{2} - {\left(a^{3} - a b^{2}\right)} c d^{3} - {\left(a^{2} b - b^{3}\right)} d^{4} + {\left(2 \, {\left(a^{2} b - b^{3}\right)} c^{3} d - {\left(a^{3} - a b^{2}\right)} c^{2} d^{2} - {\left(a^{2} b - b^{3}\right)} c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} c^{3} d^{2} - {\left(a^{3} - a b^{2}\right)} c^{2} d^{3} - {\left(a^{2} b - b^{3}\right)} c d^{4} + {\left(a^{3} - a b^{2}\right)} d^{5}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} c^{7} - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{6} d + {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{5} d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{4} d^{3} - {\left(2 \, a^{4} - 3 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{4} - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d^{5} + {\left(a^{4} - a^{2} b^{2}\right)} c d^{6}\right)} f \cos\left(f x + e\right) + {\left({\left(a^{2} b^{2} - b^{4}\right)} c^{6} d - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{5} d^{2} + {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{4} d^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{3} d^{4} - {\left(2 \, a^{4} - 3 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{5} - 2 \, {\left(a^{3} b - a b^{3}\right)} c d^{6} + {\left(a^{4} - a^{2} b^{2}\right)} d^{7}\right)} f\right)}}, -\frac{2 \, {\left(2 \, {\left(a^{2} b - b^{3}\right)} c^{2} d^{2} - {\left(a^{3} - a b^{2}\right)} c d^{3} - {\left(a^{2} b - b^{3}\right)} d^{4} + {\left(2 \, {\left(a^{2} b - b^{3}\right)} c^{3} d - {\left(a^{3} - a b^{2}\right)} c^{2} d^{2} - {\left(a^{2} b - b^{3}\right)} c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(b^{2} c^{4} d - 2 \, b^{2} c^{2} d^{3} + b^{2} d^{5} + {\left(b^{2} c^{5} - 2 \, b^{2} c^{3} d^{2} + b^{2} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} c^{3} d^{2} - {\left(a^{3} - a b^{2}\right)} c^{2} d^{3} - {\left(a^{2} b - b^{3}\right)} c d^{4} + {\left(a^{3} - a b^{2}\right)} d^{5}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} c^{7} - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{6} d + {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{5} d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{4} d^{3} - {\left(2 \, a^{4} - 3 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{4} - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d^{5} + {\left(a^{4} - a^{2} b^{2}\right)} c d^{6}\right)} f \cos\left(f x + e\right) + {\left({\left(a^{2} b^{2} - b^{4}\right)} c^{6} d - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{5} d^{2} + {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{4} d^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{3} d^{4} - {\left(2 \, a^{4} - 3 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{5} - 2 \, {\left(a^{3} b - a b^{3}\right)} c d^{6} + {\left(a^{4} - a^{2} b^{2}\right)} d^{7}\right)} f\right)}}, \frac{{\left(b^{2} c^{4} d - 2 \, b^{2} c^{2} d^{3} + b^{2} d^{5} + {\left(b^{2} c^{5} - 2 \, b^{2} c^{3} d^{2} + b^{2} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(2 \, {\left(a^{2} b - b^{3}\right)} c^{2} d^{2} - {\left(a^{3} - a b^{2}\right)} c d^{3} - {\left(a^{2} b - b^{3}\right)} d^{4} + {\left(2 \, {\left(a^{2} b - b^{3}\right)} c^{3} d - {\left(a^{3} - a b^{2}\right)} c^{2} d^{2} - {\left(a^{2} b - b^{3}\right)} c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left({\left(a^{2} b - b^{3}\right)} c^{3} d^{2} - {\left(a^{3} - a b^{2}\right)} c^{2} d^{3} - {\left(a^{2} b - b^{3}\right)} c d^{4} + {\left(a^{3} - a b^{2}\right)} d^{5}\right)} \sin\left(f x + e\right)}{{\left({\left(a^{2} b^{2} - b^{4}\right)} c^{7} - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{6} d + {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{5} d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{4} d^{3} - {\left(2 \, a^{4} - 3 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{4} - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d^{5} + {\left(a^{4} - a^{2} b^{2}\right)} c d^{6}\right)} f \cos\left(f x + e\right) + {\left({\left(a^{2} b^{2} - b^{4}\right)} c^{6} d - 2 \, {\left(a^{3} b - a b^{3}\right)} c^{5} d^{2} + {\left(a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{4} d^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{3} d^{4} - {\left(2 \, a^{4} - 3 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{5} - 2 \, {\left(a^{3} b - a b^{3}\right)} c d^{6} + {\left(a^{4} - a^{2} b^{2}\right)} d^{7}\right)} f}\right]"," ",0,"[1/2*((b^2*c^4*d - 2*b^2*c^2*d^3 + b^2*d^5 + (b^2*c^5 - 2*b^2*c^3*d^2 + b^2*c*d^4)*cos(f*x + e))*sqrt(a^2 - b^2)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 + 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)) + (2*(a^2*b - b^3)*c^2*d^2 - (a^3 - a*b^2)*c*d^3 - (a^2*b - b^3)*d^4 + (2*(a^2*b - b^3)*c^3*d - (a^3 - a*b^2)*c^2*d^2 - (a^2*b - b^3)*c*d^3)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*((a^2*b - b^3)*c^3*d^2 - (a^3 - a*b^2)*c^2*d^3 - (a^2*b - b^3)*c*d^4 + (a^3 - a*b^2)*d^5)*sin(f*x + e))/(((a^2*b^2 - b^4)*c^7 - 2*(a^3*b - a*b^3)*c^6*d + (a^4 - 3*a^2*b^2 + 2*b^4)*c^5*d^2 + 4*(a^3*b - a*b^3)*c^4*d^3 - (2*a^4 - 3*a^2*b^2 + b^4)*c^3*d^4 - 2*(a^3*b - a*b^3)*c^2*d^5 + (a^4 - a^2*b^2)*c*d^6)*f*cos(f*x + e) + ((a^2*b^2 - b^4)*c^6*d - 2*(a^3*b - a*b^3)*c^5*d^2 + (a^4 - 3*a^2*b^2 + 2*b^4)*c^4*d^3 + 4*(a^3*b - a*b^3)*c^3*d^4 - (2*a^4 - 3*a^2*b^2 + b^4)*c^2*d^5 - 2*(a^3*b - a*b^3)*c*d^6 + (a^4 - a^2*b^2)*d^7)*f), 1/2*(2*(b^2*c^4*d - 2*b^2*c^2*d^3 + b^2*d^5 + (b^2*c^5 - 2*b^2*c^3*d^2 + b^2*c*d^4)*cos(f*x + e))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e))) + (2*(a^2*b - b^3)*c^2*d^2 - (a^3 - a*b^2)*c*d^3 - (a^2*b - b^3)*d^4 + (2*(a^2*b - b^3)*c^3*d - (a^3 - a*b^2)*c^2*d^2 - (a^2*b - b^3)*c*d^3)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*((a^2*b - b^3)*c^3*d^2 - (a^3 - a*b^2)*c^2*d^3 - (a^2*b - b^3)*c*d^4 + (a^3 - a*b^2)*d^5)*sin(f*x + e))/(((a^2*b^2 - b^4)*c^7 - 2*(a^3*b - a*b^3)*c^6*d + (a^4 - 3*a^2*b^2 + 2*b^4)*c^5*d^2 + 4*(a^3*b - a*b^3)*c^4*d^3 - (2*a^4 - 3*a^2*b^2 + b^4)*c^3*d^4 - 2*(a^3*b - a*b^3)*c^2*d^5 + (a^4 - a^2*b^2)*c*d^6)*f*cos(f*x + e) + ((a^2*b^2 - b^4)*c^6*d - 2*(a^3*b - a*b^3)*c^5*d^2 + (a^4 - 3*a^2*b^2 + 2*b^4)*c^4*d^3 + 4*(a^3*b - a*b^3)*c^3*d^4 - (2*a^4 - 3*a^2*b^2 + b^4)*c^2*d^5 - 2*(a^3*b - a*b^3)*c*d^6 + (a^4 - a^2*b^2)*d^7)*f), -1/2*(2*(2*(a^2*b - b^3)*c^2*d^2 - (a^3 - a*b^2)*c*d^3 - (a^2*b - b^3)*d^4 + (2*(a^2*b - b^3)*c^3*d - (a^3 - a*b^2)*c^2*d^2 - (a^2*b - b^3)*c*d^3)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (b^2*c^4*d - 2*b^2*c^2*d^3 + b^2*d^5 + (b^2*c^5 - 2*b^2*c^3*d^2 + b^2*c*d^4)*cos(f*x + e))*sqrt(a^2 - b^2)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 + 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)) - 2*((a^2*b - b^3)*c^3*d^2 - (a^3 - a*b^2)*c^2*d^3 - (a^2*b - b^3)*c*d^4 + (a^3 - a*b^2)*d^5)*sin(f*x + e))/(((a^2*b^2 - b^4)*c^7 - 2*(a^3*b - a*b^3)*c^6*d + (a^4 - 3*a^2*b^2 + 2*b^4)*c^5*d^2 + 4*(a^3*b - a*b^3)*c^4*d^3 - (2*a^4 - 3*a^2*b^2 + b^4)*c^3*d^4 - 2*(a^3*b - a*b^3)*c^2*d^5 + (a^4 - a^2*b^2)*c*d^6)*f*cos(f*x + e) + ((a^2*b^2 - b^4)*c^6*d - 2*(a^3*b - a*b^3)*c^5*d^2 + (a^4 - 3*a^2*b^2 + 2*b^4)*c^4*d^3 + 4*(a^3*b - a*b^3)*c^3*d^4 - (2*a^4 - 3*a^2*b^2 + b^4)*c^2*d^5 - 2*(a^3*b - a*b^3)*c*d^6 + (a^4 - a^2*b^2)*d^7)*f), ((b^2*c^4*d - 2*b^2*c^2*d^3 + b^2*d^5 + (b^2*c^5 - 2*b^2*c^3*d^2 + b^2*c*d^4)*cos(f*x + e))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e))) - (2*(a^2*b - b^3)*c^2*d^2 - (a^3 - a*b^2)*c*d^3 - (a^2*b - b^3)*d^4 + (2*(a^2*b - b^3)*c^3*d - (a^3 - a*b^2)*c^2*d^2 - (a^2*b - b^3)*c*d^3)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + ((a^2*b - b^3)*c^3*d^2 - (a^3 - a*b^2)*c^2*d^3 - (a^2*b - b^3)*c*d^4 + (a^3 - a*b^2)*d^5)*sin(f*x + e))/(((a^2*b^2 - b^4)*c^7 - 2*(a^3*b - a*b^3)*c^6*d + (a^4 - 3*a^2*b^2 + 2*b^4)*c^5*d^2 + 4*(a^3*b - a*b^3)*c^4*d^3 - (2*a^4 - 3*a^2*b^2 + b^4)*c^3*d^4 - 2*(a^3*b - a*b^3)*c^2*d^5 + (a^4 - a^2*b^2)*c*d^6)*f*cos(f*x + e) + ((a^2*b^2 - b^4)*c^6*d - 2*(a^3*b - a*b^3)*c^5*d^2 + (a^4 - 3*a^2*b^2 + 2*b^4)*c^4*d^3 + 4*(a^3*b - a*b^3)*c^3*d^4 - (2*a^4 - 3*a^2*b^2 + b^4)*c^2*d^5 - 2*(a^3*b - a*b^3)*c*d^6 + (a^4 - a^2*b^2)*d^7)*f)]","B",0
258,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^5/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,1,1326,0,96.703694," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{2} b^{3} c^{3} - 3 \, a b^{4} c^{2} d - 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} c d^{2} + {\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a b^{4} c^{3} - 3 \, b^{5} c^{2} d - 3 \, {\left(a^{3} b^{2} - 2 \, a b^{4}\right)} c d^{2} + {\left(2 \, a^{4} b - 3 \, a^{2} b^{3}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right) + {\left({\left(3 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} c d^{2} - 2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c d^{2} - 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left({\left(3 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} c d^{2} - 2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c d^{2} - 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d^{3} - {\left({\left(a^{2} b^{4} - b^{6}\right)} c^{3} - 3 \, {\left(a^{3} b^{3} - a b^{5}\right)} c^{2} d + 3 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d^{2} - {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} f \cos\left(f x + e\right)^{2} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} f \cos\left(f x + e\right)\right)}}, \frac{2 \, {\left({\left(a^{2} b^{3} c^{3} - 3 \, a b^{4} c^{2} d - 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} c d^{2} + {\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a b^{4} c^{3} - 3 \, b^{5} c^{2} d - 3 \, {\left(a^{3} b^{2} - 2 \, a b^{4}\right)} c d^{2} + {\left(2 \, a^{4} b - 3 \, a^{2} b^{3}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right) + {\left({\left(3 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} c d^{2} - 2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c d^{2} - 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left({\left(3 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} c d^{2} - 2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c d^{2} - 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d^{3} - {\left({\left(a^{2} b^{4} - b^{6}\right)} c^{3} - 3 \, {\left(a^{3} b^{3} - a b^{5}\right)} c^{2} d + 3 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d^{2} - {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} f \cos\left(f x + e\right)^{2} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/2*(((a^2*b^3*c^3 - 3*a*b^4*c^2*d - 3*(a^4*b - 2*a^2*b^3)*c*d^2 + (2*a^5 - 3*a^3*b^2)*d^3)*cos(f*x + e)^2 + (a*b^4*c^3 - 3*b^5*c^2*d - 3*(a^3*b^2 - 2*a*b^4)*c*d^2 + (2*a^4*b - 3*a^2*b^3)*d^3)*cos(f*x + e))*sqrt(a^2 - b^2)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 + 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)) + ((3*(a^5*b - 2*a^3*b^3 + a*b^5)*c*d^2 - 2*(a^6 - 2*a^4*b^2 + a^2*b^4)*d^3)*cos(f*x + e)^2 + (3*(a^4*b^2 - 2*a^2*b^4 + b^6)*c*d^2 - 2*(a^5*b - 2*a^3*b^3 + a*b^5)*d^3)*cos(f*x + e))*log(sin(f*x + e) + 1) - ((3*(a^5*b - 2*a^3*b^3 + a*b^5)*c*d^2 - 2*(a^6 - 2*a^4*b^2 + a^2*b^4)*d^3)*cos(f*x + e)^2 + (3*(a^4*b^2 - 2*a^2*b^4 + b^6)*c*d^2 - 2*(a^5*b - 2*a^3*b^3 + a*b^5)*d^3)*cos(f*x + e))*log(-sin(f*x + e) + 1) + 2*((a^4*b^2 - 2*a^2*b^4 + b^6)*d^3 - ((a^2*b^4 - b^6)*c^3 - 3*(a^3*b^3 - a*b^5)*c^2*d + 3*(a^4*b^2 - a^2*b^4)*c*d^2 - (2*a^5*b - 3*a^3*b^3 + a*b^5)*d^3)*cos(f*x + e))*sin(f*x + e))/((a^5*b^3 - 2*a^3*b^5 + a*b^7)*f*cos(f*x + e)^2 + (a^4*b^4 - 2*a^2*b^6 + b^8)*f*cos(f*x + e)), 1/2*(2*((a^2*b^3*c^3 - 3*a*b^4*c^2*d - 3*(a^4*b - 2*a^2*b^3)*c*d^2 + (2*a^5 - 3*a^3*b^2)*d^3)*cos(f*x + e)^2 + (a*b^4*c^3 - 3*b^5*c^2*d - 3*(a^3*b^2 - 2*a*b^4)*c*d^2 + (2*a^4*b - 3*a^2*b^3)*d^3)*cos(f*x + e))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e))) + ((3*(a^5*b - 2*a^3*b^3 + a*b^5)*c*d^2 - 2*(a^6 - 2*a^4*b^2 + a^2*b^4)*d^3)*cos(f*x + e)^2 + (3*(a^4*b^2 - 2*a^2*b^4 + b^6)*c*d^2 - 2*(a^5*b - 2*a^3*b^3 + a*b^5)*d^3)*cos(f*x + e))*log(sin(f*x + e) + 1) - ((3*(a^5*b - 2*a^3*b^3 + a*b^5)*c*d^2 - 2*(a^6 - 2*a^4*b^2 + a^2*b^4)*d^3)*cos(f*x + e)^2 + (3*(a^4*b^2 - 2*a^2*b^4 + b^6)*c*d^2 - 2*(a^5*b - 2*a^3*b^3 + a*b^5)*d^3)*cos(f*x + e))*log(-sin(f*x + e) + 1) + 2*((a^4*b^2 - 2*a^2*b^4 + b^6)*d^3 - ((a^2*b^4 - b^6)*c^3 - 3*(a^3*b^3 - a*b^5)*c^2*d + 3*(a^4*b^2 - a^2*b^4)*c*d^2 - (2*a^5*b - 3*a^3*b^3 + a*b^5)*d^3)*cos(f*x + e))*sin(f*x + e))/((a^5*b^3 - 2*a^3*b^5 + a*b^7)*f*cos(f*x + e)^2 + (a^4*b^4 - 2*a^2*b^6 + b^8)*f*cos(f*x + e))]","B",0
261,1,798,0,9.540689," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(a b^{3} c^{2} - 2 \, b^{4} c d - {\left(a^{3} b - 2 \, a b^{3}\right)} d^{2} + {\left(a^{2} b^{2} c^{2} - 2 \, a b^{3} c d - {\left(a^{4} - 2 \, a^{2} b^{2}\right)} d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right) - {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cos\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) + {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cos\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left({\left(a^{2} b^{3} - b^{5}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d + {\left(a^{4} b - a^{2} b^{3}\right)} d^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} f \cos\left(f x + e\right) + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} f\right)}}, \frac{2 \, {\left(a b^{3} c^{2} - 2 \, b^{4} c d - {\left(a^{3} b - 2 \, a b^{3}\right)} d^{2} + {\left(a^{2} b^{2} c^{2} - 2 \, a b^{3} c d - {\left(a^{4} - 2 \, a^{2} b^{2}\right)} d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right) + {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cos\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cos\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left({\left(a^{2} b^{3} - b^{5}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d + {\left(a^{4} b - a^{2} b^{3}\right)} d^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} f \cos\left(f x + e\right) + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} f\right)}}\right]"," ",0,"[-1/2*((a*b^3*c^2 - 2*b^4*c*d - (a^3*b - 2*a*b^3)*d^2 + (a^2*b^2*c^2 - 2*a*b^3*c*d - (a^4 - 2*a^2*b^2)*d^2)*cos(f*x + e))*sqrt(a^2 - b^2)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 - 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)) - ((a^5 - 2*a^3*b^2 + a*b^4)*d^2*cos(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*d^2)*log(sin(f*x + e) + 1) + ((a^5 - 2*a^3*b^2 + a*b^4)*d^2*cos(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*d^2)*log(-sin(f*x + e) + 1) + 2*((a^2*b^3 - b^5)*c^2 - 2*(a^3*b^2 - a*b^4)*c*d + (a^4*b - a^2*b^3)*d^2)*sin(f*x + e))/((a^5*b^2 - 2*a^3*b^4 + a*b^6)*f*cos(f*x + e) + (a^4*b^3 - 2*a^2*b^5 + b^7)*f), 1/2*(2*(a*b^3*c^2 - 2*b^4*c*d - (a^3*b - 2*a*b^3)*d^2 + (a^2*b^2*c^2 - 2*a*b^3*c*d - (a^4 - 2*a^2*b^2)*d^2)*cos(f*x + e))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e))) + ((a^5 - 2*a^3*b^2 + a*b^4)*d^2*cos(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*d^2)*log(sin(f*x + e) + 1) - ((a^5 - 2*a^3*b^2 + a*b^4)*d^2*cos(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*d^2)*log(-sin(f*x + e) + 1) - 2*((a^2*b^3 - b^5)*c^2 - 2*(a^3*b^2 - a*b^4)*c*d + (a^4*b - a^2*b^3)*d^2)*sin(f*x + e))/((a^5*b^2 - 2*a^3*b^4 + a*b^6)*f*cos(f*x + e) + (a^4*b^3 - 2*a^2*b^5 + b^7)*f)]","B",0
262,1,394,0,0.507220," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a b c - b^{2} d + {\left(a^{2} c - a b d\right)} \cos\left(f x + e\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} c - {\left(a^{3} - a b^{2}\right)} d\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f \cos\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f\right)}}, \frac{{\left(a b c - b^{2} d + {\left(a^{2} c - a b d\right)} \cos\left(f x + e\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right) - {\left({\left(a^{2} b - b^{3}\right)} c - {\left(a^{3} - a b^{2}\right)} d\right)} \sin\left(f x + e\right)}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f \cos\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f}\right]"," ",0,"[1/2*((a*b*c - b^2*d + (a^2*c - a*b*d)*cos(f*x + e))*sqrt(a^2 - b^2)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 + 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)) - 2*((a^2*b - b^3)*c - (a^3 - a*b^2)*d)*sin(f*x + e))/((a^5 - 2*a^3*b^2 + a*b^4)*f*cos(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*f), ((a*b*c - b^2*d + (a^2*c - a*b*d)*cos(f*x + e))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e))) - ((a^2*b - b^3)*c - (a^3 - a*b^2)*d)*sin(f*x + e))/((a^5 - 2*a^3*b^2 + a*b^4)*f*cos(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*f)]","A",0
263,1,2852,0,108.507970," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e))^2/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{{\left(a b^{3} c^{3} - a b^{3} c d^{2} - {\left(2 \, a^{2} b^{2} - b^{4}\right)} c^{2} d + {\left(2 \, a^{2} b^{2} - b^{4}\right)} d^{3} + {\left(a^{2} b^{2} c^{3} - a^{2} b^{2} c d^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} d + {\left(2 \, a^{3} b - a b^{3}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right) - {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cos\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2}\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left({\left(a^{2} b^{3} - b^{5}\right)} c^{3} - {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d - {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} d^{3}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left({\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c^{4} - 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} d + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} c^{2} d^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c d^{3} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{4}\right)} f \cos\left(f x + e\right) + {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{4} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c^{3} d + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} c^{2} d^{2} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c d^{3} - {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{4}\right)} f\right)}}, \frac{2 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cos\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2}\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(a b^{3} c^{3} - a b^{3} c d^{2} - {\left(2 \, a^{2} b^{2} - b^{4}\right)} c^{2} d + {\left(2 \, a^{2} b^{2} - b^{4}\right)} d^{3} + {\left(a^{2} b^{2} c^{3} - a^{2} b^{2} c d^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} d + {\left(2 \, a^{3} b - a b^{3}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(f x + e\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(f x + e\right)^{2} + 2 \, a b \cos\left(f x + e\right) + b^{2}}\right) - 2 \, {\left({\left(a^{2} b^{3} - b^{5}\right)} c^{3} - {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d - {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} d^{3}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left({\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c^{4} - 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} d + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} c^{2} d^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c d^{3} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{4}\right)} f \cos\left(f x + e\right) + {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{4} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c^{3} d + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} c^{2} d^{2} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c d^{3} - {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{4}\right)} f\right)}}, \frac{2 \, {\left(a b^{3} c^{3} - a b^{3} c d^{2} - {\left(2 \, a^{2} b^{2} - b^{4}\right)} c^{2} d + {\left(2 \, a^{2} b^{2} - b^{4}\right)} d^{3} + {\left(a^{2} b^{2} c^{3} - a^{2} b^{2} c d^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} d + {\left(2 \, a^{3} b - a b^{3}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right) + {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cos\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2}\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - 2 \, {\left({\left(a^{2} b^{3} - b^{5}\right)} c^{3} - {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d - {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} d^{3}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left({\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c^{4} - 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} d + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} c^{2} d^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c d^{3} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{4}\right)} f \cos\left(f x + e\right) + {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{4} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c^{3} d + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} c^{2} d^{2} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c d^{3} - {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{4}\right)} f\right)}}, \frac{{\left(a b^{3} c^{3} - a b^{3} c d^{2} - {\left(2 \, a^{2} b^{2} - b^{4}\right)} c^{2} d + {\left(2 \, a^{2} b^{2} - b^{4}\right)} d^{3} + {\left(a^{2} b^{2} c^{3} - a^{2} b^{2} c d^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} d + {\left(2 \, a^{3} b - a b^{3}\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(f x + e\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)}\right) + {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cos\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2}\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left({\left(a^{2} b^{3} - b^{5}\right)} c^{3} - {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d - {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} d^{3}\right)} \sin\left(f x + e\right)}{{\left({\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c^{4} - 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} d + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} c^{2} d^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c d^{3} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{4}\right)} f \cos\left(f x + e\right) + {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{4} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c^{3} d + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} c^{2} d^{2} + 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} c d^{3} - {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{4}\right)} f}\right]"," ",0,"[-1/2*((a*b^3*c^3 - a*b^3*c*d^2 - (2*a^2*b^2 - b^4)*c^2*d + (2*a^2*b^2 - b^4)*d^3 + (a^2*b^2*c^3 - a^2*b^2*c*d^2 - (2*a^3*b - a*b^3)*c^2*d + (2*a^3*b - a*b^3)*d^3)*cos(f*x + e))*sqrt(a^2 - b^2)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 - 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)) - ((a^5 - 2*a^3*b^2 + a*b^4)*d^2*cos(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*d^2)*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*((a^2*b^3 - b^5)*c^3 - (a^3*b^2 - a*b^4)*c^2*d - (a^2*b^3 - b^5)*c*d^2 + (a^3*b^2 - a*b^4)*d^3)*sin(f*x + e))/(((a^5*b^2 - 2*a^3*b^4 + a*b^6)*c^4 - 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*c^3*d + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*c^2*d^2 + 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*c*d^3 - (a^7 - 2*a^5*b^2 + a^3*b^4)*d^4)*f*cos(f*x + e) + ((a^4*b^3 - 2*a^2*b^5 + b^7)*c^4 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*c^3*d + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*c^2*d^2 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*c*d^3 - (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^4)*f), 1/2*(2*((a^5 - 2*a^3*b^2 + a*b^4)*d^2*cos(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*d^2)*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (a*b^3*c^3 - a*b^3*c*d^2 - (2*a^2*b^2 - b^4)*c^2*d + (2*a^2*b^2 - b^4)*d^3 + (a^2*b^2*c^3 - a^2*b^2*c*d^2 - (2*a^3*b - a*b^3)*c^2*d + (2*a^3*b - a*b^3)*d^3)*cos(f*x + e))*sqrt(a^2 - b^2)*log((2*a*b*cos(f*x + e) - (a^2 - 2*b^2)*cos(f*x + e)^2 - 2*sqrt(a^2 - b^2)*(b*cos(f*x + e) + a)*sin(f*x + e) + 2*a^2 - b^2)/(a^2*cos(f*x + e)^2 + 2*a*b*cos(f*x + e) + b^2)) - 2*((a^2*b^3 - b^5)*c^3 - (a^3*b^2 - a*b^4)*c^2*d - (a^2*b^3 - b^5)*c*d^2 + (a^3*b^2 - a*b^4)*d^3)*sin(f*x + e))/(((a^5*b^2 - 2*a^3*b^4 + a*b^6)*c^4 - 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*c^3*d + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*c^2*d^2 + 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*c*d^3 - (a^7 - 2*a^5*b^2 + a^3*b^4)*d^4)*f*cos(f*x + e) + ((a^4*b^3 - 2*a^2*b^5 + b^7)*c^4 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*c^3*d + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*c^2*d^2 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*c*d^3 - (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^4)*f), 1/2*(2*(a*b^3*c^3 - a*b^3*c*d^2 - (2*a^2*b^2 - b^4)*c^2*d + (2*a^2*b^2 - b^4)*d^3 + (a^2*b^2*c^3 - a^2*b^2*c*d^2 - (2*a^3*b - a*b^3)*c^2*d + (2*a^3*b - a*b^3)*d^3)*cos(f*x + e))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e))) + ((a^5 - 2*a^3*b^2 + a*b^4)*d^2*cos(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*d^2)*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - 2*((a^2*b^3 - b^5)*c^3 - (a^3*b^2 - a*b^4)*c^2*d - (a^2*b^3 - b^5)*c*d^2 + (a^3*b^2 - a*b^4)*d^3)*sin(f*x + e))/(((a^5*b^2 - 2*a^3*b^4 + a*b^6)*c^4 - 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*c^3*d + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*c^2*d^2 + 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*c*d^3 - (a^7 - 2*a^5*b^2 + a^3*b^4)*d^4)*f*cos(f*x + e) + ((a^4*b^3 - 2*a^2*b^5 + b^7)*c^4 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*c^3*d + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*c^2*d^2 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*c*d^3 - (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^4)*f), ((a*b^3*c^3 - a*b^3*c*d^2 - (2*a^2*b^2 - b^4)*c^2*d + (2*a^2*b^2 - b^4)*d^3 + (a^2*b^2*c^3 - a^2*b^2*c*d^2 - (2*a^3*b - a*b^3)*c^2*d + (2*a^3*b - a*b^3)*d^3)*cos(f*x + e))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(f*x + e) + a)/((a^2 - b^2)*sin(f*x + e))) + ((a^5 - 2*a^3*b^2 + a*b^4)*d^2*cos(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*d^2)*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - ((a^2*b^3 - b^5)*c^3 - (a^3*b^2 - a*b^4)*c^2*d - (a^2*b^3 - b^5)*c*d^2 + (a^3*b^2 - a*b^4)*d^3)*sin(f*x + e))/(((a^5*b^2 - 2*a^3*b^4 + a*b^6)*c^4 - 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*c^3*d + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*c^2*d^2 + 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*c*d^3 - (a^7 - 2*a^5*b^2 + a^3*b^4)*d^4)*f*cos(f*x + e) + ((a^4*b^3 - 2*a^2*b^5 + b^7)*c^4 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*c^3*d + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*c^2*d^2 + 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*c*d^3 - (a^6*b - 2*a^4*b^3 + a^2*b^5)*d^4)*f)]","B",0
264,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,0,0,0,1.731079," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right) + a} \sqrt{d \sec\left(f x + e\right) + c} \sec\left(f x + e\right)}{b d \sec\left(f x + e\right)^{2} + a c + {\left(b c + a d\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)*sec(f*x + e)/(b*d*sec(f*x + e)^2 + a*c + (b*c + a*d)*sec(f*x + e)), x)","F",0
267,0,0,0,0.824061," ","integrate(sec(f*x+e)/(2+3*sec(f*x+e))^(1/2)/(-4+5*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, \sec\left(f x + e\right) - 4} \sqrt{3 \, \sec\left(f x + e\right) + 2} \sec\left(f x + e\right)}{15 \, \sec\left(f x + e\right)^{2} - 2 \, \sec\left(f x + e\right) - 8}, x\right)"," ",0,"integral(sqrt(5*sec(f*x + e) - 4)*sqrt(3*sec(f*x + e) + 2)*sec(f*x + e)/(15*sec(f*x + e)^2 - 2*sec(f*x + e) - 8), x)","F",0
268,0,0,0,0.921384," ","integrate(sec(f*x+e)/(4-5*sec(f*x+e))^(1/2)/(2+3*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, \sec\left(f x + e\right) + 2} \sqrt{-5 \, \sec\left(f x + e\right) + 4} \sec\left(f x + e\right)}{15 \, \sec\left(f x + e\right)^{2} - 2 \, \sec\left(f x + e\right) - 8}, x\right)"," ",0,"integral(-sqrt(3*sec(f*x + e) + 2)*sqrt(-5*sec(f*x + e) + 4)*sec(f*x + e)/(15*sec(f*x + e)^2 - 2*sec(f*x + e) - 8), x)","F",0
269,-1,0,0,0.000000," ","integrate(sec(f*x+e)^2/(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e))^(1/2)/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)/(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))^(1/2)*(c+d*sec(f*x+e))^(1/2)/(a+b*cos(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,0,0,0,0.945115," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^(1/2)/(c+c*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right) + a} \sec\left(f x + e\right)}{c \sec\left(f x + e\right) + c}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*sec(f*x + e)/(c*sec(f*x + e) + c), x)","F",0
274,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)*(a+b*sec(f*x+e))^(1/2)/(c+c*sec(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,0,0,0,0.692592," ","integrate(sec(f*x+e)/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right) + a} \sec\left(f x + e\right)}{b c \sec\left(f x + e\right)^{2} + {\left(a + b\right)} c \sec\left(f x + e\right) + a c}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*sec(f*x + e)/(b*c*sec(f*x + e)^2 + (a + b)*c*sec(f*x + e) + a*c), x)","F",0
276,0,0,0,0.878737," ","integrate(sec(f*x+e)^2/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right) + a} \sec\left(f x + e\right)^{2}}{b c \sec\left(f x + e\right)^{2} + {\left(a + b\right)} c \sec\left(f x + e\right) + a c}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*sec(f*x + e)^2/(b*c*sec(f*x + e)^2 + (a + b)*c*sec(f*x + e) + a*c), x)","F",0
277,0,0,0,0.688790," ","integrate((g*sec(f*x+e))^(3/2)/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right) + a} \sqrt{g \sec\left(f x + e\right)} g \sec\left(f x + e\right)}{b c \sec\left(f x + e\right)^{2} + {\left(a + b\right)} c \sec\left(f x + e\right) + a c}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*sqrt(g*sec(f*x + e))*g*sec(f*x + e)/(b*c*sec(f*x + e)^2 + (a + b)*c*sec(f*x + e) + a*c), x)","F",0
278,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))^(5/2)/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)*(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate(sec(f*x+e)/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate(sec(f*x+e)^2/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,1,121,0,1.183378," ","integrate(sec(f*x+e)*tan(f*x+e)^4/(c-c*sec(f*x+e))^7,x, algorithm=""fricas"")","\frac{47 \, \cos\left(f x + e\right)^{5} + 127 \, \cos\left(f x + e\right)^{4} + 101 \, \cos\left(f x + e\right)^{3} + 11 \, \cos\left(f x + e\right)^{2} - 8 \, \cos\left(f x + e\right) + 2}{315 \, {\left(c^{7} f \cos\left(f x + e\right)^{4} - 4 \, c^{7} f \cos\left(f x + e\right)^{3} + 6 \, c^{7} f \cos\left(f x + e\right)^{2} - 4 \, c^{7} f \cos\left(f x + e\right) + c^{7} f\right)} \sin\left(f x + e\right)}"," ",0,"1/315*(47*cos(f*x + e)^5 + 127*cos(f*x + e)^4 + 101*cos(f*x + e)^3 + 11*cos(f*x + e)^2 - 8*cos(f*x + e) + 2)/((c^7*f*cos(f*x + e)^4 - 4*c^7*f*cos(f*x + e)^3 + 6*c^7*f*cos(f*x + e)^2 - 4*c^7*f*cos(f*x + e) + c^7*f)*sin(f*x + e))","B",0
286,1,146,0,0.890777," ","integrate(sec(f*x+e)*tan(f*x+e)^4/(c-c*sec(f*x+e))^8,x, algorithm=""fricas"")","\frac{152 \, \cos\left(f x + e\right)^{6} + 395 \, \cos\left(f x + e\right)^{5} + 289 \, \cos\left(f x + e\right)^{4} + 15 \, \cos\left(f x + e\right)^{3} - 19 \, \cos\left(f x + e\right)^{2} + 10 \, \cos\left(f x + e\right) - 2}{1155 \, {\left(c^{8} f \cos\left(f x + e\right)^{5} - 5 \, c^{8} f \cos\left(f x + e\right)^{4} + 10 \, c^{8} f \cos\left(f x + e\right)^{3} - 10 \, c^{8} f \cos\left(f x + e\right)^{2} + 5 \, c^{8} f \cos\left(f x + e\right) - c^{8} f\right)} \sin\left(f x + e\right)}"," ",0,"1/1155*(152*cos(f*x + e)^6 + 395*cos(f*x + e)^5 + 289*cos(f*x + e)^4 + 15*cos(f*x + e)^3 - 19*cos(f*x + e)^2 + 10*cos(f*x + e) - 2)/((c^8*f*cos(f*x + e)^5 - 5*c^8*f*cos(f*x + e)^4 + 10*c^8*f*cos(f*x + e)^3 - 10*c^8*f*cos(f*x + e)^2 + 5*c^8*f*cos(f*x + e) - c^8*f)*sin(f*x + e))","A",0
