1,1,215,0,0.650445," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a c^{4} + 160 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a c^{4} + 45 \, a c^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 120 \, a c^{4} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 240 \, a c^{4} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 720 \, a c^{4} \tan\left(f x + e\right)}{240 \, f}"," ",0,"1/240*(16*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a*c^4 + 160*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*c^4 + 45*a*c^4*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 120*a*c^4*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 240*a*c^4*log(sec(f*x + e) + tan(f*x + e)) - 720*a*c^4*tan(f*x + e))/f","B",0
2,1,133,0,0.418090," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a c^{3} + 3 \, a c^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 48 \, a c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 96 \, a c^{3} \tan\left(f x + e\right)}{48 \, f}"," ",0,"1/48*(32*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*c^3 + 3*a*c^3*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) + 48*a*c^3*log(sec(f*x + e) + tan(f*x + e)) - 96*a*c^3*tan(f*x + e))/f","A",0
3,1,108,0,0.588213," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a c^{2} + 3 \, a c^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 12 \, a c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 12 \, a c^{2} \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(4*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*c^2 + 3*a*c^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 12*a*c^2*log(sec(f*x + e) + tan(f*x + e)) - 12*a*c^2*tan(f*x + e))/f","A",0
4,1,68,0,0.460315," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","\frac{a c {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 4 \, a c \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{4 \, f}"," ",0,"1/4*(a*c*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 4*a*c*log(sec(f*x + e) + tan(f*x + e)))/f","A",0
5,1,101,0,1.172299," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{a {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c} - \frac{\cos\left(f x + e\right) + 1}{c \sin\left(f x + e\right)}\right)} - \frac{a {\left(\cos\left(f x + e\right) + 1\right)}}{c \sin\left(f x + e\right)}}{f}"," ",0,"-(a*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c - (cos(f*x + e) + 1)/(c*sin(f*x + e))) - a*(cos(f*x + e) + 1)/(c*sin(f*x + e)))/f","B",0
6,1,97,0,0.597691," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{\frac{a {\left(\frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{c^{2} \sin\left(f x + e\right)^{3}} - \frac{a {\left(\frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{c^{2} \sin\left(f x + e\right)^{3}}}{6 \, f}"," ",0,"-1/6*(a*(3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)*(cos(f*x + e) + 1)^3/(c^2*sin(f*x + e)^3) - a*(3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)*(cos(f*x + e) + 1)^3/(c^2*sin(f*x + e)^3))/f","B",0
7,1,117,0,0.338046," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{\frac{a {\left(\frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 3\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{c^{3} \sin\left(f x + e\right)^{5}} + \frac{3 \, a {\left(\frac{5 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{c^{3} \sin\left(f x + e\right)^{5}}}{60 \, f}"," ",0,"-1/60*(a*(10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3)*(cos(f*x + e) + 1)^5/(c^3*sin(f*x + e)^5) + 3*a*(5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1)*(cos(f*x + e) + 1)^5/(c^3*sin(f*x + e)^5))/f","A",0
8,1,177,0,0.458165," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{\frac{a {\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{105 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 15\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{c^{4} \sin\left(f x + e\right)^{7}} + \frac{3 \, a {\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 5\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{c^{4} \sin\left(f x + e\right)^{7}}}{840 \, f}"," ",0,"1/840*(a*(21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 105*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 15)*(cos(f*x + e) + 1)^7/(c^4*sin(f*x + e)^7) + 3*a*(21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 5)*(cos(f*x + e) + 1)^7/(c^4*sin(f*x + e)^7))/f","A",0
9,1,197,0,0.695612," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","-\frac{\frac{a {\left(\frac{180 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{378 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{420 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{315 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 35\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{c^{5} \sin\left(f x + e\right)^{9}} + \frac{5 \, a {\left(\frac{18 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{42 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 7\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{c^{5} \sin\left(f x + e\right)^{9}}}{5040 \, f}"," ",0,"-1/5040*(a*(180*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 378*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 420*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 315*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 35)*(cos(f*x + e) + 1)^9/(c^5*sin(f*x + e)^9) + 5*a*(18*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 42*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 7)*(cos(f*x + e) + 1)^9/(c^5*sin(f*x + e)^9))/f","A",0
10,1,368,0,0.337367," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","-\frac{96 \, {\left(5 \, \tan\left(f x + e\right)^{7} + 21 \, \tan\left(f x + e\right)^{5} + 35 \, \tan\left(f x + e\right)^{3} + 35 \, \tan\left(f x + e\right)\right)} a^{2} c^{5} + 224 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{2} c^{5} - 5600 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c^{5} + 105 \, a^{2} c^{5} {\left(\frac{2 \, {\left(15 \, \sin\left(f x + e\right)^{5} - 40 \, \sin\left(f x + e\right)^{3} + 33 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1} - 15 \, \log\left(\sin\left(f x + e\right) + 1\right) + 15 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 1050 \, a^{2} c^{5} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 840 \, a^{2} c^{5} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 3360 \, a^{2} c^{5} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 10080 \, a^{2} c^{5} \tan\left(f x + e\right)}{3360 \, f}"," ",0,"-1/3360*(96*(5*tan(f*x + e)^7 + 21*tan(f*x + e)^5 + 35*tan(f*x + e)^3 + 35*tan(f*x + e))*a^2*c^5 + 224*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^2*c^5 - 5600*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c^5 + 105*a^2*c^5*(2*(15*sin(f*x + e)^5 - 40*sin(f*x + e)^3 + 33*sin(f*x + e))/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1) - 15*log(sin(f*x + e) + 1) + 15*log(sin(f*x + e) - 1)) - 1050*a^2*c^5*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) + 840*a^2*c^5*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 3360*a^2*c^5*log(sec(f*x + e) + tan(f*x + e)) + 10080*a^2*c^5*tan(f*x + e))/f","B",0
11,1,321,0,0.563804," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","-\frac{64 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{2} c^{4} - 640 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c^{4} + 5 \, a^{2} c^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(f x + e\right)^{5} - 40 \, \sin\left(f x + e\right)^{3} + 33 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1} - 15 \, \log\left(\sin\left(f x + e\right) + 1\right) + 15 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 30 \, a^{2} c^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 120 \, a^{2} c^{4} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 480 \, a^{2} c^{4} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 960 \, a^{2} c^{4} \tan\left(f x + e\right)}{480 \, f}"," ",0,"-1/480*(64*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^2*c^4 - 640*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c^4 + 5*a^2*c^4*(2*(15*sin(f*x + e)^5 - 40*sin(f*x + e)^3 + 33*sin(f*x + e))/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1) - 15*log(sin(f*x + e) + 1) + 15*log(sin(f*x + e) - 1)) - 30*a^2*c^4*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 120*a^2*c^4*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 480*a^2*c^4*log(sec(f*x + e) + tan(f*x + e)) + 960*a^2*c^4*tan(f*x + e))/f","B",0
12,1,227,0,0.404940," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{16 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{2} c^{3} - 160 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c^{3} + 15 \, a^{2} c^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 120 \, a^{2} c^{3} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 240 \, a^{2} c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 240 \, a^{2} c^{3} \tan\left(f x + e\right)}{240 \, f}"," ",0,"-1/240*(16*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^2*c^3 - 160*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c^3 + 15*a^2*c^3*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 120*a^2*c^3*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 240*a^2*c^3*log(sec(f*x + e) + tan(f*x + e)) + 240*a^2*c^3*tan(f*x + e))/f","B",0
13,1,150,0,0.539903," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{a^{2} c^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 8 \, a^{2} c^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 16 \, a^{2} c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{16 \, f}"," ",0,"-1/16*(a^2*c^2*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 8*a^2*c^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 16*a^2*c^2*log(sec(f*x + e) + tan(f*x + e)))/f","B",0
14,1,108,0,0.378540," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{4 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c - 3 \, a^{2} c {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 12 \, a^{2} c \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 12 \, a^{2} c \tan\left(f x + e\right)}{12 \, f}"," ",0,"-1/12*(4*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c - 3*a^2*c*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 12*a^2*c*log(sec(f*x + e) + tan(f*x + e)) - 12*a^2*c*tan(f*x + e))/f","A",0
15,1,225,0,0.370694," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{\frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1}{\frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c}\right)} + 2 \, a^{2} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c} - \frac{\cos\left(f x + e\right) + 1}{c \sin\left(f x + e\right)}\right)} - \frac{a^{2} {\left(\cos\left(f x + e\right) + 1\right)}}{c \sin\left(f x + e\right)}}{f}"," ",0,"-(a^2*((3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)/(c*sin(f*x + e)/(cos(f*x + e) + 1) - c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c) + 2*a^2*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c - (cos(f*x + e) + 1)/(c*sin(f*x + e))) - a^2*(cos(f*x + e) + 1)/(c*sin(f*x + e)))/f","B",0
16,1,201,0,0.352196," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{2}} - \frac{{\left(\frac{9 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{c^{2} \sin\left(f x + e\right)^{3}}\right)} - \frac{2 \, a^{2} {\left(\frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{c^{2} \sin\left(f x + e\right)^{3}} + \frac{a^{2} {\left(\frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{c^{2} \sin\left(f x + e\right)^{3}}}{6 \, f}"," ",0,"1/6*(a^2*(6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^2 - (9*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)*(cos(f*x + e) + 1)^3/(c^2*sin(f*x + e)^3)) - 2*a^2*(3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)*(cos(f*x + e) + 1)^3/(c^2*sin(f*x + e)^3) + a^2*(3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)*(cos(f*x + e) + 1)^3/(c^2*sin(f*x + e)^3))/f","B",0
17,1,189,0,0.351079," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{a^{2} {\left(\frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 3\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{c^{3} \sin\left(f x + e\right)^{5}} - \frac{a^{2} {\left(\frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 3\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{c^{3} \sin\left(f x + e\right)^{5}} - \frac{6 \, a^{2} {\left(\frac{5 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{c^{3} \sin\left(f x + e\right)^{5}}}{60 \, f}"," ",0,"1/60*(a^2*(10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3)*(cos(f*x + e) + 1)^5/(c^3*sin(f*x + e)^5) - a^2*(10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3)*(cos(f*x + e) + 1)^5/(c^3*sin(f*x + e)^5) - 6*a^2*(5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1)*(cos(f*x + e) + 1)^5/(c^3*sin(f*x + e)^5))/f","B",0
18,1,270,0,0.351191," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{\frac{2 \, a^{2} {\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{105 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 15\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{c^{4} \sin\left(f x + e\right)^{7}} + \frac{3 \, a^{2} {\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 5\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{c^{4} \sin\left(f x + e\right)^{7}} - \frac{a^{2} {\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{105 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 15\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{c^{4} \sin\left(f x + e\right)^{7}}}{840 \, f}"," ",0,"1/840*(2*a^2*(21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 105*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 15)*(cos(f*x + e) + 1)^7/(c^4*sin(f*x + e)^7) + 3*a^2*(21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 5)*(cos(f*x + e) + 1)^7/(c^4*sin(f*x + e)^7) - a^2*(21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 105*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 15)*(cos(f*x + e) + 1)^7/(c^4*sin(f*x + e)^7))/f","B",0
19,1,269,0,0.360653," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","-\frac{\frac{a^{2} {\left(\frac{180 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{378 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{420 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{315 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 35\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{c^{5} \sin\left(f x + e\right)^{9}} + \frac{10 \, a^{2} {\left(\frac{18 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{42 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 7\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{c^{5} \sin\left(f x + e\right)^{9}} + \frac{7 \, a^{2} {\left(\frac{18 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{45 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 5\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{c^{5} \sin\left(f x + e\right)^{9}}}{5040 \, f}"," ",0,"-1/5040*(a^2*(180*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 378*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 420*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 315*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 35)*(cos(f*x + e) + 1)^9/(c^5*sin(f*x + e)^9) + 10*a^2*(18*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 42*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 7)*(cos(f*x + e) + 1)^9/(c^5*sin(f*x + e)^9) + 7*a^2*(18*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 45*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5)*(cos(f*x + e) + 1)^9/(c^5*sin(f*x + e)^9))/f","B",0
20,1,389,0,0.355045," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^6,x, algorithm=""maxima"")","\frac{\frac{a^{2} {\left(\frac{385 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{990 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1386 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{3465 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 315\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{11}}{c^{6} \sin\left(f x + e\right)^{11}} + \frac{6 \, a^{2} {\left(\frac{385 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{330 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{1155 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 105\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{11}}{c^{6} \sin\left(f x + e\right)^{11}} + \frac{5 \, a^{2} {\left(\frac{385 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{990 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1386 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{693 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 63\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{11}}{c^{6} \sin\left(f x + e\right)^{11}}}{110880 \, f}"," ",0,"1/110880*(a^2*(385*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 990*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1386*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 3465*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 315)*(cos(f*x + e) + 1)^11/(c^6*sin(f*x + e)^11) + 6*a^2*(385*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 330*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 1155*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 105)*(cos(f*x + e) + 1)^11/(c^6*sin(f*x + e)^11) + 5*a^2*(385*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 990*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1386*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 693*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 63)*(cos(f*x + e) + 1)^11/(c^6*sin(f*x + e)^11))/f","B",0
21,1,443,0,0.347887," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^6,x, algorithm=""maxima"")","\frac{256 \, {\left(35 \, \tan\left(f x + e\right)^{9} + 180 \, \tan\left(f x + e\right)^{7} + 378 \, \tan\left(f x + e\right)^{5} + 420 \, \tan\left(f x + e\right)^{3} + 315 \, \tan\left(f x + e\right)\right)} a^{3} c^{6} - 32256 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{3} c^{6} + 215040 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c^{6} + 315 \, a^{3} c^{6} {\left(\frac{2 \, {\left(105 \, \sin\left(f x + e\right)^{7} - 385 \, \sin\left(f x + e\right)^{5} + 511 \, \sin\left(f x + e\right)^{3} - 279 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{8} - 4 \, \sin\left(f x + e\right)^{6} + 6 \, \sin\left(f x + e\right)^{4} - 4 \, \sin\left(f x + e\right)^{2} + 1} - 105 \, \log\left(\sin\left(f x + e\right) + 1\right) + 105 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 6720 \, a^{3} c^{6} {\left(\frac{2 \, {\left(15 \, \sin\left(f x + e\right)^{5} - 40 \, \sin\left(f x + e\right)^{3} + 33 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1} - 15 \, \log\left(\sin\left(f x + e\right) + 1\right) + 15 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 30240 \, a^{3} c^{6} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 80640 \, a^{3} c^{6} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 241920 \, a^{3} c^{6} \tan\left(f x + e\right)}{80640 \, f}"," ",0,"1/80640*(256*(35*tan(f*x + e)^9 + 180*tan(f*x + e)^7 + 378*tan(f*x + e)^5 + 420*tan(f*x + e)^3 + 315*tan(f*x + e))*a^3*c^6 - 32256*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*c^6 + 215040*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c^6 + 315*a^3*c^6*(2*(105*sin(f*x + e)^7 - 385*sin(f*x + e)^5 + 511*sin(f*x + e)^3 - 279*sin(f*x + e))/(sin(f*x + e)^8 - 4*sin(f*x + e)^6 + 6*sin(f*x + e)^4 - 4*sin(f*x + e)^2 + 1) - 105*log(sin(f*x + e) + 1) + 105*log(sin(f*x + e) - 1)) - 6720*a^3*c^6*(2*(15*sin(f*x + e)^5 - 40*sin(f*x + e)^3 + 33*sin(f*x + e))/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1) - 15*log(sin(f*x + e) + 1) + 15*log(sin(f*x + e) - 1)) + 30240*a^3*c^6*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) + 80640*a^3*c^6*log(sec(f*x + e) + tan(f*x + e)) - 241920*a^3*c^6*tan(f*x + e))/f","B",0
22,1,408,0,0.348950," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","\frac{1536 \, {\left(5 \, \tan\left(f x + e\right)^{7} + 21 \, \tan\left(f x + e\right)^{5} + 35 \, \tan\left(f x + e\right)^{3} + 35 \, \tan\left(f x + e\right)\right)} a^{3} c^{5} - 10752 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{3} c^{5} + 53760 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c^{5} + 35 \, a^{3} c^{5} {\left(\frac{2 \, {\left(105 \, \sin\left(f x + e\right)^{7} - 385 \, \sin\left(f x + e\right)^{5} + 511 \, \sin\left(f x + e\right)^{3} - 279 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{8} - 4 \, \sin\left(f x + e\right)^{6} + 6 \, \sin\left(f x + e\right)^{4} - 4 \, \sin\left(f x + e\right)^{2} + 1} - 105 \, \log\left(\sin\left(f x + e\right) + 1\right) + 105 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 560 \, a^{3} c^{5} {\left(\frac{2 \, {\left(15 \, \sin\left(f x + e\right)^{5} - 40 \, \sin\left(f x + e\right)^{3} + 33 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1} - 15 \, \log\left(\sin\left(f x + e\right) + 1\right) + 15 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 13440 \, a^{3} c^{5} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 26880 \, a^{3} c^{5} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 53760 \, a^{3} c^{5} \tan\left(f x + e\right)}{26880 \, f}"," ",0,"1/26880*(1536*(5*tan(f*x + e)^7 + 21*tan(f*x + e)^5 + 35*tan(f*x + e)^3 + 35*tan(f*x + e))*a^3*c^5 - 10752*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*c^5 + 53760*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c^5 + 35*a^3*c^5*(2*(105*sin(f*x + e)^7 - 385*sin(f*x + e)^5 + 511*sin(f*x + e)^3 - 279*sin(f*x + e))/(sin(f*x + e)^8 - 4*sin(f*x + e)^6 + 6*sin(f*x + e)^4 - 4*sin(f*x + e)^2 + 1) - 105*log(sin(f*x + e) + 1) + 105*log(sin(f*x + e) - 1)) - 560*a^3*c^5*(2*(15*sin(f*x + e)^5 - 40*sin(f*x + e)^3 + 33*sin(f*x + e))/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1) - 15*log(sin(f*x + e) + 1) + 15*log(sin(f*x + e) - 1)) + 13440*a^3*c^5*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 26880*a^3*c^5*log(sec(f*x + e) + tan(f*x + e)) - 53760*a^3*c^5*tan(f*x + e))/f","B",0
23,1,368,0,0.356824," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{96 \, {\left(5 \, \tan\left(f x + e\right)^{7} + 21 \, \tan\left(f x + e\right)^{5} + 35 \, \tan\left(f x + e\right)^{3} + 35 \, \tan\left(f x + e\right)\right)} a^{3} c^{4} - 672 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{3} c^{4} + 3360 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c^{4} + 35 \, a^{3} c^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(f x + e\right)^{5} - 40 \, \sin\left(f x + e\right)^{3} + 33 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1} - 15 \, \log\left(\sin\left(f x + e\right) + 1\right) + 15 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 630 \, a^{3} c^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 2520 \, a^{3} c^{4} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 3360 \, a^{3} c^{4} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 3360 \, a^{3} c^{4} \tan\left(f x + e\right)}{3360 \, f}"," ",0,"1/3360*(96*(5*tan(f*x + e)^7 + 21*tan(f*x + e)^5 + 35*tan(f*x + e)^3 + 35*tan(f*x + e))*a^3*c^4 - 672*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*c^4 + 3360*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c^4 + 35*a^3*c^4*(2*(15*sin(f*x + e)^5 - 40*sin(f*x + e)^3 + 33*sin(f*x + e))/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1) - 15*log(sin(f*x + e) + 1) + 15*log(sin(f*x + e) - 1)) - 630*a^3*c^4*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) + 2520*a^3*c^4*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 3360*a^3*c^4*log(sec(f*x + e) + tan(f*x + e)) - 3360*a^3*c^4*tan(f*x + e))/f","B",0
24,1,244,0,0.346439," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{a^{3} c^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(f x + e\right)^{5} - 40 \, \sin\left(f x + e\right)^{3} + 33 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1} - 15 \, \log\left(\sin\left(f x + e\right) + 1\right) + 15 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 18 \, a^{3} c^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 72 \, a^{3} c^{3} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 96 \, a^{3} c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{96 \, f}"," ",0,"1/96*(a^3*c^3*(2*(15*sin(f*x + e)^5 - 40*sin(f*x + e)^3 + 33*sin(f*x + e))/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1) - 15*log(sin(f*x + e) + 1) + 15*log(sin(f*x + e) - 1)) - 18*a^3*c^3*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) + 72*a^3*c^3*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 96*a^3*c^3*log(sec(f*x + e) + tan(f*x + e)))/f","B",0
25,1,227,0,0.349303," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{3} c^{2} - 160 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c^{2} - 15 \, a^{3} c^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 120 \, a^{3} c^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 240 \, a^{3} c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 240 \, a^{3} c^{2} \tan\left(f x + e\right)}{240 \, f}"," ",0,"1/240*(16*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*c^2 - 160*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c^2 - 15*a^3*c^2*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) + 120*a^3*c^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 240*a^3*c^2*log(sec(f*x + e) + tan(f*x + e)) + 240*a^3*c^2*tan(f*x + e))/f","B",0
26,1,133,0,0.339238," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{32 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c - 3 \, a^{3} c {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 48 \, a^{3} c \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 96 \, a^{3} c \tan\left(f x + e\right)}{48 \, f}"," ",0,"-1/48*(32*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c - 3*a^3*c*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 48*a^3*c*log(sec(f*x + e) + tan(f*x + e)) - 96*a^3*c*tan(f*x + e))/f","A",0
27,1,387,0,0.344609," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{a^{3} {\left(\frac{2 \, {\left(\frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 1\right)}}{\frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{c \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c} - \frac{3 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c}\right)} + 6 \, a^{3} {\left(\frac{\frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1}{\frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c}\right)} + 6 \, a^{3} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c} - \frac{\cos\left(f x + e\right) + 1}{c \sin\left(f x + e\right)}\right)} - \frac{2 \, a^{3} {\left(\cos\left(f x + e\right) + 1\right)}}{c \sin\left(f x + e\right)}}{2 \, f}"," ",0,"-1/2*(a^3*(2*(5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1)/(c*sin(f*x + e)/(cos(f*x + e) + 1) - 2*c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + c*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c - 3*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c) + 6*a^3*((3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)/(c*sin(f*x + e)/(cos(f*x + e) + 1) - c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c) + 6*a^3*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c - (cos(f*x + e) + 1)/(c*sin(f*x + e))) - 2*a^3*(cos(f*x + e) + 1)/(c*sin(f*x + e)))/f","B",0
28,1,349,0,0.357298," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{a^{3} {\left(\frac{\frac{14 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{27 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 1}{\frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{c^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c^{2}} + \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{2}}\right)} - 3 \, a^{3} {\left(\frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{2}} - \frac{{\left(\frac{9 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{c^{2} \sin\left(f x + e\right)^{3}}\right)} + \frac{3 \, a^{3} {\left(\frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{c^{2} \sin\left(f x + e\right)^{3}} - \frac{a^{3} {\left(\frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{c^{2} \sin\left(f x + e\right)^{3}}}{6 \, f}"," ",0,"-1/6*(a^3*((14*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 27*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1)/(c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - c^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 12*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c^2 + 12*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^2) - 3*a^3*(6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^2 - (9*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)*(cos(f*x + e) + 1)^3/(c^2*sin(f*x + e)^3)) + 3*a^3*(3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)*(cos(f*x + e) + 1)^3/(c^2*sin(f*x + e)^3) - a^3*(3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)*(cos(f*x + e) + 1)^3/(c^2*sin(f*x + e)^3))/f","B",0
29,1,309,0,0.363373," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{a^{3} {\left(\frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{3}} - \frac{{\left(\frac{20 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{105 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 3\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{c^{3} \sin\left(f x + e\right)^{5}}\right)} - \frac{3 \, a^{3} {\left(\frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 3\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{c^{3} \sin\left(f x + e\right)^{5}} + \frac{a^{3} {\left(\frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 3\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{c^{3} \sin\left(f x + e\right)^{5}} + \frac{9 \, a^{3} {\left(\frac{5 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{c^{3} \sin\left(f x + e\right)^{5}}}{60 \, f}"," ",0,"-1/60*(a^3*(60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^3 - (20*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 105*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3)*(cos(f*x + e) + 1)^5/(c^3*sin(f*x + e)^5)) - 3*a^3*(10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3)*(cos(f*x + e) + 1)^5/(c^3*sin(f*x + e)^5) + a^3*(10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3)*(cos(f*x + e) + 1)^5/(c^3*sin(f*x + e)^5) + 9*a^3*(5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1)*(cos(f*x + e) + 1)^5/(c^3*sin(f*x + e)^5))/f","B",0
30,1,356,0,0.371391," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","-\frac{\frac{a^{3} {\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 5\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{c^{4} \sin\left(f x + e\right)^{7}} - \frac{a^{3} {\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{105 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 15\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{c^{4} \sin\left(f x + e\right)^{7}} - \frac{a^{3} {\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 5\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{c^{4} \sin\left(f x + e\right)^{7}} + \frac{a^{3} {\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{105 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 15\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{c^{4} \sin\left(f x + e\right)^{7}}}{280 \, f}"," ",0,"-1/280*(a^3*(21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 5)*(cos(f*x + e) + 1)^7/(c^4*sin(f*x + e)^7) - a^3*(21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 105*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 15)*(cos(f*x + e) + 1)^7/(c^4*sin(f*x + e)^7) - a^3*(21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 5)*(cos(f*x + e) + 1)^7/(c^4*sin(f*x + e)^7) + a^3*(21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 105*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 15)*(cos(f*x + e) + 1)^7/(c^4*sin(f*x + e)^7))/f","B",0
31,1,357,0,0.367954," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","-\frac{\frac{a^{3} {\left(\frac{180 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{378 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{420 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{315 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 35\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{c^{5} \sin\left(f x + e\right)^{9}} + \frac{15 \, a^{3} {\left(\frac{18 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{42 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 7\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{c^{5} \sin\left(f x + e\right)^{9}} - \frac{5 \, a^{3} {\left(\frac{18 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{42 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{63 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 7\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{c^{5} \sin\left(f x + e\right)^{9}} + \frac{21 \, a^{3} {\left(\frac{18 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{45 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 5\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{c^{5} \sin\left(f x + e\right)^{9}}}{5040 \, f}"," ",0,"-1/5040*(a^3*(180*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 378*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 420*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 315*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 35)*(cos(f*x + e) + 1)^9/(c^5*sin(f*x + e)^9) + 15*a^3*(18*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 42*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 7)*(cos(f*x + e) + 1)^9/(c^5*sin(f*x + e)^9) - 5*a^3*(18*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 42*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 63*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 7)*(cos(f*x + e) + 1)^9/(c^5*sin(f*x + e)^9) + 21*a^3*(18*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 45*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5)*(cos(f*x + e) + 1)^9/(c^5*sin(f*x + e)^9))/f","B",0
32,1,518,0,0.380005," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^6,x, algorithm=""maxima"")","\frac{\frac{3 \, a^{3} {\left(\frac{385 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{990 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1386 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{3465 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 315\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{11}}{c^{6} \sin\left(f x + e\right)^{11}} + \frac{9 \, a^{3} {\left(\frac{385 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{330 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{1155 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 105\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{11}}{c^{6} \sin\left(f x + e\right)^{11}} + \frac{5 \, a^{3} {\left(\frac{385 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{990 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1386 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{693 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 63\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{11}}{c^{6} \sin\left(f x + e\right)^{11}} - \frac{a^{3} {\left(\frac{385 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{990 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1386 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{3465 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + 315\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{11}}{c^{6} \sin\left(f x + e\right)^{11}}}{110880 \, f}"," ",0,"1/110880*(3*a^3*(385*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 990*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1386*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 3465*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 315)*(cos(f*x + e) + 1)^11/(c^6*sin(f*x + e)^11) + 9*a^3*(385*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 330*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 1155*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 105)*(cos(f*x + e) + 1)^11/(c^6*sin(f*x + e)^11) + 5*a^3*(385*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 990*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1386*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 693*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 63)*(cos(f*x + e) + 1)^11/(c^6*sin(f*x + e)^11) - a^3*(385*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 990*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1386*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 3465*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 315)*(cos(f*x + e) + 1)^11/(c^6*sin(f*x + e)^11))/f","B",0
33,1,517,0,0.388447," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^7,x, algorithm=""maxima"")","-\frac{\frac{a^{3} {\left(\frac{8190 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5005 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{25740 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{9009 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{30030 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{45045 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 3465\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{13}}{c^{7} \sin\left(f x + e\right)^{13}} + \frac{5 \, a^{3} {\left(\frac{1638 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{5005 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{8580 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{9009 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{6006 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{3003 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 231\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{13}}{c^{7} \sin\left(f x + e\right)^{13}} + \frac{35 \, a^{3} {\left(\frac{468 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{715 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1287 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{1716 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{1287 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 99\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{13}}{c^{7} \sin\left(f x + e\right)^{13}} + \frac{77 \, a^{3} {\left(\frac{65 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{117 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{195 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 15\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{13}}{c^{7} \sin\left(f x + e\right)^{13}}}{960960 \, f}"," ",0,"-1/960960*(a^3*(8190*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5005*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 25740*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 9009*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 30030*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 45045*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 3465)*(cos(f*x + e) + 1)^13/(c^7*sin(f*x + e)^13) + 5*a^3*(1638*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 5005*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 8580*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 9009*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 6006*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 3003*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 231)*(cos(f*x + e) + 1)^13/(c^7*sin(f*x + e)^13) + 35*a^3*(468*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 715*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1287*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 1716*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 1287*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 99)*(cos(f*x + e) + 1)^13/(c^7*sin(f*x + e)^13) + 77*a^3*(65*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 117*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 195*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 15)*(cos(f*x + e) + 1)^13/(c^7*sin(f*x + e)^13))/f","B",0
34,1,591,0,0.347184," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^4/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{c^{4} {\left(\frac{2 \, {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{16 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a - \frac{3 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{a \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} - \frac{9 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} + \frac{6 \, \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + 12 \, c^{4} {\left(\frac{2 \, {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 36 \, c^{4} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(f x + e\right)}{{\left(a - \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 24 \, c^{4} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + \frac{6 \, c^{4} \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}}{6 \, f}"," ",0,"1/6*(c^4*(2*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 16*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a - 3*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - a*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) - 9*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a + 9*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a + 6*sin(f*x + e)/(a*(cos(f*x + e) + 1))) + 12*c^4*(2*(sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a - 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) - 3*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a + 3*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a + 2*sin(f*x + e)/(a*(cos(f*x + e) + 1))) - 36*c^4*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - 2*sin(f*x + e)/((a - a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) - sin(f*x + e)/(a*(cos(f*x + e) + 1))) - 24*c^4*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))) + 6*c^4*sin(f*x + e)/(a*(cos(f*x + e) + 1)))/f","B",0
35,1,386,0,0.346435," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^3/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{c^{3} {\left(\frac{2 \, {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 6 \, c^{3} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(f x + e\right)}{{\left(a - \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 6 \, c^{3} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + \frac{2 \, c^{3} \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}}{2 \, f}"," ",0,"1/2*(c^3*(2*(sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a - 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) - 3*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a + 3*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a + 2*sin(f*x + e)/(a*(cos(f*x + e) + 1))) - 6*c^3*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - 2*sin(f*x + e)/((a - a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) - sin(f*x + e)/(a*(cos(f*x + e) + 1))) - 6*c^3*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))) + 2*c^3*sin(f*x + e)/(a*(cos(f*x + e) + 1)))/f","B",0
36,1,224,0,0.346689," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^2/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{c^{2} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(f x + e\right)}{{\left(a - \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + 2 \, c^{2} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - \frac{c^{2} \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}}{f}"," ",0,"-(c^2*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - 2*sin(f*x + e)/((a - a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) - sin(f*x + e)/(a*(cos(f*x + e) + 1))) + 2*c^2*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))) - c^2*sin(f*x + e)/(a*(cos(f*x + e) + 1)))/f","B",0
37,1,101,0,0.330881," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{c {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - \frac{c \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}}{f}"," ",0,"-(c*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))) - c*sin(f*x + e)/(a*(cos(f*x + e) + 1)))/f","B",0
38,1,18,0,0.323874," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","\frac{1}{a c f \sin\left(f x + e\right)}"," ",0,"1/(a*c*f*sin(f*x + e))","A",0
39,1,77,0,0.338837," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{{\left(\frac{6 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{a c^{2} \sin\left(f x + e\right)^{3}} + \frac{3 \, \sin\left(f x + e\right)}{a c^{2} {\left(\cos\left(f x + e\right) + 1\right)}}}{12 \, f}"," ",0,"1/12*((6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)*(cos(f*x + e) + 1)^3/(a*c^2*sin(f*x + e)^3) + 3*sin(f*x + e)/(a*c^2*(cos(f*x + e) + 1)))/f","A",0
40,1,97,0,0.339972," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(\frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{a c^{3} \sin\left(f x + e\right)^{5}} - \frac{5 \, \sin\left(f x + e\right)}{a c^{3} {\left(\cos\left(f x + e\right) + 1\right)}}}{40 \, f}"," ",0,"-1/40*((5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1)*(cos(f*x + e) + 1)^5/(a*c^3*sin(f*x + e)^5) - 5*sin(f*x + e)/(a*c^3*(cos(f*x + e) + 1)))/f","A",0
41,1,117,0,0.337795," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{\frac{{\left(\frac{28 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{70 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{140 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 5\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{a c^{4} \sin\left(f x + e\right)^{7}} + \frac{35 \, \sin\left(f x + e\right)}{a c^{4} {\left(\cos\left(f x + e\right) + 1\right)}}}{560 \, f}"," ",0,"1/560*((28*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 70*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 140*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 5)*(cos(f*x + e) + 1)^7/(a*c^4*sin(f*x + e)^7) + 35*sin(f*x + e)/(a*c^4*(cos(f*x + e) + 1)))/f","A",0
42,1,765,0,0.352889," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{c^{5} {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{2} - \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{30 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{30 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + 5 \, c^{5} {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + 10 \, c^{5} {\left(\frac{\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(f x + e\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + 10 \, c^{5} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + \frac{5 \, c^{5} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{c^{5} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"-1/6*(c^5*(4*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^2 - 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) + (27*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 30*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 30*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + 5*c^5*(6*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2 - 2*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + (21*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 21*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 21*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + 10*c^5*((15*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 12*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 12*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2 + 12*sin(f*x + e)/((a^2 - a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1))) + 10*c^5*((9*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + 5*c^5*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - c^5*(3*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","B",0
43,1,531,0,0.353726," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{c^{4} {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + 4 \, c^{4} {\left(\frac{\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(f x + e\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + 6 \, c^{4} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + \frac{4 \, c^{4} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{c^{4} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"-1/6*(c^4*(6*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2 - 2*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + (21*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 21*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 21*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + 4*c^4*((15*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 12*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 12*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2 + 12*sin(f*x + e)/((a^2 - a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1))) + 6*c^4*((9*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + 4*c^4*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - c^4*(3*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","B",0
44,1,341,0,0.341680," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(f x + e\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + 3 \, c^{3} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + \frac{3 \, c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"-1/6*(c^3*((15*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 12*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 12*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2 + 12*sin(f*x + e)/((a^2 - a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1))) + 3*c^3*((9*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + 3*c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","B",0
45,1,196,0,0.328819," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{c^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + \frac{2 \, c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"-1/6*(c^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + 2*c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","B",0
46,1,94,0,0.331603," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{\frac{c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"-1/6*(c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - c*(3*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","B",0
47,1,76,0,0.334357," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{\frac{6 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2} c} + \frac{3 \, {\left(\cos\left(f x + e\right) + 1\right)}}{a^{2} c \sin\left(f x + e\right)}}{12 \, f}"," ",0,"1/12*((6*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*c) + 3*(cos(f*x + e) + 1)/(a^2*c*sin(f*x + e)))/f","A",0
48,1,31,0,0.335271," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, \sin\left(f x + e\right)^{2} - 1}{3 \, a^{2} c^{2} f \sin\left(f x + e\right)^{3}}"," ",0,"1/3*(3*sin(f*x + e)^2 - 1)/(a^2*c^2*f*sin(f*x + e)^3)","A",0
49,1,121,0,0.338683," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{5 \, {\left(\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2} c^{3}} - \frac{{\left(\frac{20 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{90 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 3\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{a^{2} c^{3} \sin\left(f x + e\right)^{5}}}{240 \, f}"," ",0,"1/240*(5*(12*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*c^3) - (20*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 90*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3)*(cos(f*x + e) + 1)^5/(a^2*c^3*sin(f*x + e)^5))/f","A",0
50,1,140,0,0.340789," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{\frac{7 \, {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2} c^{4}} + \frac{{\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{70 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{210 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 3\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{a^{2} c^{4} \sin\left(f x + e\right)^{7}}}{672 \, f}"," ",0,"1/672*(7*(15*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*c^4) + (21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 70*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 210*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 3)*(cos(f*x + e) + 1)^7/(a^2*c^4*sin(f*x + e)^7))/f","A",0
51,1,161,0,0.341799," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","\frac{\frac{21 \, {\left(\frac{18 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2} c^{5}} - \frac{{\left(\frac{54 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{189 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{420 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{945 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 7\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{a^{2} c^{5} \sin\left(f x + e\right)^{9}}}{4032 \, f}"," ",0,"1/4032*(21*(18*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*c^5) - (54*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 189*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 420*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 945*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 7)*(cos(f*x + e) + 1)^9/(a^2*c^5*sin(f*x + e)^9))/f","A",0
52,1,935,0,0.382983," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^6/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{c^{6} {\left(\frac{20 \, {\left(\frac{33 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{76 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{51 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3} - \frac{3 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} + \frac{\frac{735 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{50 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{690 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{690 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + 6 \, c^{6} {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{7 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + 45 \, c^{6} {\left(\frac{40 \, \sin\left(f x + e\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + 20 \, c^{6} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{15 \, c^{6} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{c^{6} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{18 \, c^{6} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"1/60*(c^6*(20*(33*sin(f*x + e)/(cos(f*x + e) + 1) - 76*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 51*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^3 - 3*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) + (735*sin(f*x + e)/(cos(f*x + e) + 1) + 50*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 690*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 690*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 6*c^6*(60*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^3 - 2*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + (465*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 390*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 390*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 45*c^6*(40*sin(f*x + e)/((a^3 - a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) + (85*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 20*c^6*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 15*c^6*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + c^6*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 18*c^6*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","B",0
53,1,680,0,0.368747," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{c^{5} {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{7 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + 15 \, c^{5} {\left(\frac{40 \, \sin\left(f x + e\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + 10 \, c^{5} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{10 \, c^{5} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{c^{5} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{15 \, c^{5} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"1/60*(c^5*(60*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^3 - 2*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + (465*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 390*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 390*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 15*c^5*(40*sin(f*x + e)/((a^3 - a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) + (85*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 10*c^5*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 10*c^5*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + c^5*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 15*c^5*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","B",0
54,1,470,0,0.357728," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{3 \, c^{4} {\left(\frac{40 \, \sin\left(f x + e\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + 4 \, c^{4} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{6 \, c^{4} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{c^{4} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{12 \, c^{4} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"1/60*(3*c^4*(40*sin(f*x + e)/((a^3 - a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) + (85*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 4*c^4*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 6*c^4*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + c^4*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 12*c^4*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","B",0
55,1,304,0,0.349520," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{c^{3} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{3 \, c^{3} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{c^{3} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{9 \, c^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"1/60*(c^3*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 3*c^3*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + c^3*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 9*c^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","B",0
56,1,185,0,0.337370," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{c^{2} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{c^{2} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{6 \, c^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"1/60*(c^2*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + c^2*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 6*c^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","B",0
57,1,115,0,0.339487," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{c {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{3 \, c {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"1/60*(c*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 3*c*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","A",0
58,1,95,0,0.330996," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3} c} + \frac{5 \, {\left(\cos\left(f x + e\right) + 1\right)}}{a^{3} c \sin\left(f x + e\right)}}{40 \, f}"," ",0,"1/40*((15*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^3*c) + 5*(cos(f*x + e) + 1)/(a^3*c*sin(f*x + e)))/f","A",0
59,1,120,0,0.340150," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{90 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3} c^{2}} + \frac{5 \, {\left(\frac{12 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{a^{3} c^{2} \sin\left(f x + e\right)^{3}}}{240 \, f}"," ",0,"1/240*((90*sin(f*x + e)/(cos(f*x + e) + 1) - 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^3*c^2) + 5*(12*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)*(cos(f*x + e) + 1)^3/(a^3*c^2*sin(f*x + e)^3))/f","A",0
60,1,41,0,0.376783," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{15 \, \sin\left(f x + e\right)^{4} - 10 \, \sin\left(f x + e\right)^{2} + 3}{15 \, a^{3} c^{3} f \sin\left(f x + e\right)^{5}}"," ",0,"1/15*(15*sin(f*x + e)^4 - 10*sin(f*x + e)^2 + 3)/(a^3*c^3*f*sin(f*x + e)^5)","A",0
61,1,159,0,0.349587," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{\frac{7 \, {\left(\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3} c^{4}} + \frac{{\left(\frac{42 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{175 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{700 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 5\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{7}}{a^{3} c^{4} \sin\left(f x + e\right)^{7}}}{2240 \, f}"," ",0,"1/2240*(7*(75*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^3*c^4) + (42*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 175*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 700*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 5)*(cos(f*x + e) + 1)^7/(a^3*c^4*sin(f*x + e)^7))/f","A",0
62,1,181,0,0.338321," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(\frac{315 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3} c^{5}} - \frac{{\left(\frac{45 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{189 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{525 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1575 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 5\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{a^{3} c^{5} \sin\left(f x + e\right)^{9}}}{5760 \, f}"," ",0,"1/5760*(3*(315*sin(f*x + e)/(cos(f*x + e) + 1) - 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^3*c^5) - (45*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 189*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 525*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1575*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5)*(cos(f*x + e) + 1)^9/(a^3*c^5*sin(f*x + e)^9))/f","A",0
63,1,200,0,0.338885," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^6,x, algorithm=""maxima"")","\frac{\frac{33 \, {\left(\frac{420 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{40 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3} c^{6}} + \frac{{\left(\frac{440 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{1980 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5544 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{11550 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{27720 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 45\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{11}}{a^{3} c^{6} \sin\left(f x + e\right)^{11}}}{126720 \, f}"," ",0,"1/126720*(33*(420*sin(f*x + e)/(cos(f*x + e) + 1) - 40*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^3*c^6) + (440*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1980*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5544*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 11550*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 27720*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 45)*(cos(f*x + e) + 1)^11/(a^3*c^6*sin(f*x + e)^11))/f","A",0
64,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
68,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)} \sec\left(f x + e\right)}{\sqrt{-c \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)*sec(f*x + e)/sqrt(-c*sec(f*x + e) + c), x)","F",0
69,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)} \sec\left(f x + e\right)}{{\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)*sec(f*x + e)/(-c*sec(f*x + e) + c)^(3/2), x)","F",0
70,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)} \sec\left(f x + e\right)}{{\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)*sec(f*x + e)/(-c*sec(f*x + e) + c)^(5/2), x)","F",0
71,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{2} \sec\left(f x + e\right)}{\sqrt{-c \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^2*sec(f*x + e)/sqrt(-c*sec(f*x + e) + c), x)","F",0
76,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{2} \sec\left(f x + e\right)}{{\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^2*sec(f*x + e)/(-c*sec(f*x + e) + c)^(3/2), x)","F",0
77,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{3} \sec\left(f x + e\right)}{\sqrt{-c \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^3*sec(f*x + e)/sqrt(-c*sec(f*x + e) + c), x)","F",0
84,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{3} \sec\left(f x + e\right)}{{\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^3*sec(f*x + e)/(-c*sec(f*x + e) + c)^(3/2), x)","F",0
85,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,1,163,0,0.691352," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{8 \, {\left(16 \, \sqrt{2} c^{\frac{7}{2}} - \frac{56 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{70 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{35 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{5 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)}}{5 \, a f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{7}{2}}}"," ",0,"8/5*(16*sqrt(2)*c^(7/2) - 56*sqrt(2)*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 70*sqrt(2)*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 35*sqrt(2)*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 5*sqrt(2)*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)/(a*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(7/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(7/2))","A",0
87,1,137,0,0.637761," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{4 \, {\left(8 \, \sqrt{2} c^{\frac{5}{2}} - \frac{20 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)}}{3 \, a f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{5}{2}}}"," ",0,"-4/3*(8*sqrt(2)*c^(5/2) - 20*sqrt(2)*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*sqrt(2)*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3*sqrt(2)*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)/(a*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(5/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(5/2))","A",0
88,1,110,0,0.858019," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, \sqrt{2} c^{\frac{3}{2}} - \frac{3 \, \sqrt{2} c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sqrt{2} c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)}}{a f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{3}{2}}}"," ",0,"2*(2*sqrt(2)*c^(3/2) - 3*sqrt(2)*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sqrt(2)*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)/(a*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(3/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(3/2))","A",0
89,1,84,0,0.747395," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{c} - \frac{\sqrt{2} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}}{a f \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1} \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1}}"," ",0,"-(sqrt(2)*sqrt(c) - sqrt(2)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)/(a*f*sqrt(sin(f*x + e)/(cos(f*x + e) + 1) + 1)*sqrt(sin(f*x + e)/(cos(f*x + e) + 1) - 1))","B",0
90,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{{\left(a \sec\left(f x + e\right) + a\right)} \sqrt{-c \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sec(f*x + e)/((a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)), x)","F",0
91,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{{\left(a \sec\left(f x + e\right) + a\right)} {\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)/((a*sec(f*x + e) + a)*(-c*sec(f*x + e) + c)^(3/2)), x)","F",0
92,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{{\left(a \sec\left(f x + e\right) + a\right)} {\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)/((a*sec(f*x + e) + a)*(-c*sec(f*x + e) + c)^(5/2)), x)","F",0
93,1,188,0,0.495097," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(16 \, \sqrt{2} c^{\frac{7}{2}} - \frac{56 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{70 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{35 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{4 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{\sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}\right)}}{3 \, a^{2} f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{7}{2}}}"," ",0,"-4/3*(16*sqrt(2)*c^(7/2) - 56*sqrt(2)*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 70*sqrt(2)*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 35*sqrt(2)*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 4*sqrt(2)*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + sqrt(2)*c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)/(a^2*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(7/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(7/2))","A",0
94,1,163,0,0.615298," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(8 \, \sqrt{2} c^{\frac{5}{2}} - \frac{20 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{2 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{\sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)}}{3 \, a^{2} f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{5}{2}}}"," ",0,"2/3*(8*sqrt(2)*c^(5/2) - 20*sqrt(2)*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*sqrt(2)*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2*sqrt(2)*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - sqrt(2)*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)/(a^2*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(5/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(5/2))","A",0
95,1,110,0,0.673975," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} c^{\frac{3}{2}} - \frac{3 \, \sqrt{2} c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sqrt{2} c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}}{3 \, a^{2} f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{3}{2}}}"," ",0,"-1/3*(2*sqrt(2)*c^(3/2) - 3*sqrt(2)*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sqrt(2)*c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)/(a^2*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(3/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(3/2))","A",0
96,1,109,0,0.717258," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{c} - \frac{2 \, \sqrt{2} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sqrt{2} \sqrt{c} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}}{6 \, a^{2} f \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1} \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1}}"," ",0,"-1/6*(sqrt(2)*sqrt(c) - 2*sqrt(2)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sqrt(2)*sqrt(c)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)/(a^2*f*sqrt(sin(f*x + e)/(cos(f*x + e) + 1) + 1)*sqrt(sin(f*x + e)/(cos(f*x + e) + 1) - 1))","B",0
97,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{{\left(a \sec\left(f x + e\right) + a\right)}^{2} \sqrt{-c \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sec(f*x + e)/((a*sec(f*x + e) + a)^2*sqrt(-c*sec(f*x + e) + c)), x)","F",0
98,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{{\left(a \sec\left(f x + e\right) + a\right)}^{2} {\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)/((a*sec(f*x + e) + a)^2*(-c*sec(f*x + e) + c)^(3/2)), x)","F",0
99,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{{\left(a \sec\left(f x + e\right) + a\right)}^{2} {\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)/((a*sec(f*x + e) + a)^2*(-c*sec(f*x + e) + c)^(5/2)), x)","F",0
100,1,214,0,0.438900," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(16 \, \sqrt{2} c^{\frac{7}{2}} - \frac{56 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{70 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{35 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{5 \, \sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{\sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{\sqrt{2} c^{\frac{7}{2}} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}\right)}}{5 \, a^{3} f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{7}{2}}}"," ",0,"2/5*(16*sqrt(2)*c^(7/2) - 56*sqrt(2)*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 70*sqrt(2)*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 35*sqrt(2)*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 5*sqrt(2)*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - sqrt(2)*c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + sqrt(2)*c^(7/2)*sin(f*x + e)^12/(cos(f*x + e) + 1)^12)/(a^3*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(7/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(7/2))","A",0
101,1,189,0,0.442080," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{8 \, \sqrt{2} c^{\frac{5}{2}} - \frac{20 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{5 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{5 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{3 \, \sqrt{2} c^{\frac{5}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}}{15 \, a^{3} f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{5}{2}}}"," ",0,"-1/15*(8*sqrt(2)*c^(5/2) - 20*sqrt(2)*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*sqrt(2)*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5*sqrt(2)*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 5*sqrt(2)*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 3*sqrt(2)*c^(5/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)/(a^3*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(5/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(5/2))","A",0
102,1,163,0,0.435907," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} c^{\frac{3}{2}} - \frac{3 \, \sqrt{2} c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{3 \, \sqrt{2} c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{7 \, \sqrt{2} c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{3 \, \sqrt{2} c^{\frac{3}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}}{30 \, a^{3} f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{3}{2}}}"," ",0,"-1/30*(2*sqrt(2)*c^(3/2) - 3*sqrt(2)*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 3*sqrt(2)*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7*sqrt(2)*c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 3*sqrt(2)*c^(3/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)/(a^3*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(3/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(3/2))","B",0
103,1,136,0,0.439769," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{c} - \frac{3 \, \sqrt{2} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sqrt{2} \sqrt{c} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{\sqrt{2} \sqrt{c} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}}{20 \, a^{3} f \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1} \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1}}"," ",0,"-1/20*(sqrt(2)*sqrt(c) - 3*sqrt(2)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sqrt(2)*sqrt(c)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - sqrt(2)*sqrt(c)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)/(a^3*f*sqrt(sin(f*x + e)/(cos(f*x + e) + 1) + 1)*sqrt(sin(f*x + e)/(cos(f*x + e) + 1) - 1))","B",0
104,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{{\left(a \sec\left(f x + e\right) + a\right)}^{3} \sqrt{-c \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sec(f*x + e)/((a*sec(f*x + e) + a)^3*sqrt(-c*sec(f*x + e) + c)), x)","F",0
105,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{{\left(a \sec\left(f x + e\right) + a\right)}^{3} {\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)/((a*sec(f*x + e) + a)^3*(-c*sec(f*x + e) + c)^(3/2)), x)","F",0
106,-1,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,1,638,0,0.831550," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(30 \, c^{2} \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 9 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 3 \, c^{2} \sin\left(f x + e\right) - {\left(3 \, c^{2} \sin\left(5 \, f x + 5 \, e\right) - 6 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) + 10 \, c^{2} \sin\left(3 \, f x + 3 \, e\right) - 6 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) + 3 \, c^{2} \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 9 \, {\left(c^{2} \sin\left(4 \, f x + 4 \, e\right) + c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - 3 \, {\left(10 \, c^{2} \sin\left(3 \, f x + 3 \, e\right) + 3 \, c^{2} \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(3 \, c^{2} \cos\left(5 \, f x + 5 \, e\right) - 6 \, c^{2} \cos\left(4 \, f x + 4 \, e\right) + 10 \, c^{2} \cos\left(3 \, f x + 3 \, e\right) - 6 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, c^{2} \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 3 \, {\left(3 \, c^{2} \cos\left(4 \, f x + 4 \, e\right) + 3 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \sin\left(5 \, f x + 5 \, e\right) + 3 \, {\left(10 \, c^{2} \cos\left(3 \, f x + 3 \, e\right) + 3 \, c^{2} \cos\left(f x + e\right) + 2 \, c^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) - 10 \, {\left(3 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \sin\left(3 \, f x + 3 \, e\right) + 3 \, {\left(3 \, c^{2} \cos\left(f x + e\right) + 2 \, c^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a} \sqrt{c}}{3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, f x + 4 \, e\right) + 3 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + \cos\left(6 \, f x + 6 \, e\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 9 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 6 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + \sin\left(6 \, f x + 6 \, e\right)^{2} + 9 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 18 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 6 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"2/3*(30*c^2*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 9*c^2*cos(2*f*x + 2*e)*sin(f*x + e) - 3*c^2*sin(f*x + e) - (3*c^2*sin(5*f*x + 5*e) - 6*c^2*sin(4*f*x + 4*e) + 10*c^2*sin(3*f*x + 3*e) - 6*c^2*sin(2*f*x + 2*e) + 3*c^2*sin(f*x + e))*cos(6*f*x + 6*e) + 9*(c^2*sin(4*f*x + 4*e) + c^2*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - 3*(10*c^2*sin(3*f*x + 3*e) + 3*c^2*sin(f*x + e))*cos(4*f*x + 4*e) + (3*c^2*cos(5*f*x + 5*e) - 6*c^2*cos(4*f*x + 4*e) + 10*c^2*cos(3*f*x + 3*e) - 6*c^2*cos(2*f*x + 2*e) + 3*c^2*cos(f*x + e))*sin(6*f*x + 6*e) - 3*(3*c^2*cos(4*f*x + 4*e) + 3*c^2*cos(2*f*x + 2*e) + c^2)*sin(5*f*x + 5*e) + 3*(10*c^2*cos(3*f*x + 3*e) + 3*c^2*cos(f*x + e) + 2*c^2)*sin(4*f*x + 4*e) - 10*(3*c^2*cos(2*f*x + 2*e) + c^2)*sin(3*f*x + 3*e) + 3*(3*c^2*cos(f*x + e) + 2*c^2)*sin(2*f*x + 2*e))*sqrt(a)*sqrt(c)/((2*(3*cos(4*f*x + 4*e) + 3*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + cos(6*f*x + 6*e)^2 + 6*(3*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 9*cos(4*f*x + 4*e)^2 + 9*cos(2*f*x + 2*e)^2 + 6*(sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + sin(6*f*x + 6*e)^2 + 9*sin(4*f*x + 4*e)^2 + 18*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 9*sin(2*f*x + 2*e)^2 + 6*cos(2*f*x + 2*e) + 1)*f)","B",0
108,1,298,0,0.778949," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, c \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 2 \, c \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - {\left(c \sin\left(3 \, f x + 3 \, e\right) - c \sin\left(2 \, f x + 2 \, e\right) + c \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(c \cos\left(3 \, f x + 3 \, e\right) - c \cos\left(2 \, f x + 2 \, e\right) + c \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(2 \, c \cos\left(2 \, f x + 2 \, e\right) + c\right)} \sin\left(3 \, f x + 3 \, e\right) + {\left(2 \, c \cos\left(f x + e\right) + c\right)} \sin\left(2 \, f x + 2 \, e\right) - c \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{{\left(2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"2*(2*c*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 2*c*cos(2*f*x + 2*e)*sin(f*x + e) - (c*sin(3*f*x + 3*e) - c*sin(2*f*x + 2*e) + c*sin(f*x + e))*cos(4*f*x + 4*e) + (c*cos(3*f*x + 3*e) - c*cos(2*f*x + 2*e) + c*cos(f*x + e))*sin(4*f*x + 4*e) - (2*c*cos(2*f*x + 2*e) + c)*sin(3*f*x + 3*e) + (2*c*cos(f*x + e) + c)*sin(2*f*x + 2*e) - c*sin(f*x + e))*sqrt(a)*sqrt(c)/((2*(2*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + cos(4*f*x + 4*e)^2 + 4*cos(2*f*x + 2*e)^2 + sin(4*f*x + 4*e)^2 + 4*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*sin(2*f*x + 2*e)^2 + 4*cos(2*f*x + 2*e) + 1)*f)","B",0
109,1,55,0,0.847502," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)*(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a} \sqrt{c}}{f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}"," ",0,"2*sqrt(-a)*sqrt(c)/(f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1))","A",0
110,1,92,0,0.899369," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\sqrt{-a} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{\sqrt{c}} + \frac{\sqrt{-a} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{\sqrt{c}} - \frac{2 \, \sqrt{-a} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{\sqrt{c}}}{f}"," ",0,"-(sqrt(-a)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/sqrt(c) + sqrt(-a)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/sqrt(c) - 2*sqrt(-a)*log(sin(f*x + e)/(cos(f*x + e) + 1))/sqrt(c))/f","A",0
111,1,514,0,1.326908," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(\sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - {\left(\cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(3 \, f x + 3 \, e\right) - 2 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 2 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 2 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{{\left(c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(3 \, f x + 3 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \cos\left(f x + e\right)^{2} + c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \sin\left(3 \, f x + 3 \, e\right)^{2} + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} - 8 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, c^{2} \sin\left(f x + e\right)^{2} - 4 \, c^{2} \cos\left(f x + e\right) + c^{2} - 2 \, {\left(2 \, c^{2} \cos\left(3 \, f x + 3 \, e\right) - 2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 2 \, c^{2} \cos\left(f x + e\right) - c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \cos\left(3 \, f x + 3 \, e\right) - 4 \, {\left(2 \, c^{2} \cos\left(f x + e\right) - c^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(c^{2} \sin\left(3 \, f x + 3 \, e\right) - c^{2} \sin\left(2 \, f x + 2 \, e\right) + c^{2} \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 8 \, {\left(c^{2} \sin\left(2 \, f x + 2 \, e\right) - c^{2} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} f}"," ",0,"-2*((sin(3*f*x + 3*e) + sin(f*x + e))*cos(4*f*x + 4*e) - (cos(3*f*x + 3*e) + cos(f*x + e))*sin(4*f*x + 4*e) + (2*cos(2*f*x + 2*e) + 1)*sin(3*f*x + 3*e) - 2*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 2*cos(f*x + e)*sin(2*f*x + 2*e) + 2*cos(2*f*x + 2*e)*sin(f*x + e) + sin(f*x + e))*sqrt(a)*sqrt(c)/((c^2*cos(4*f*x + 4*e)^2 + 4*c^2*cos(3*f*x + 3*e)^2 + 4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*cos(f*x + e)^2 + c^2*sin(4*f*x + 4*e)^2 + 4*c^2*sin(3*f*x + 3*e)^2 + 4*c^2*sin(2*f*x + 2*e)^2 - 8*c^2*sin(2*f*x + 2*e)*sin(f*x + e) + 4*c^2*sin(f*x + e)^2 - 4*c^2*cos(f*x + e) + c^2 - 2*(2*c^2*cos(3*f*x + 3*e) - 2*c^2*cos(2*f*x + 2*e) + 2*c^2*cos(f*x + e) - c^2)*cos(4*f*x + 4*e) - 4*(2*c^2*cos(2*f*x + 2*e) - 2*c^2*cos(f*x + e) + c^2)*cos(3*f*x + 3*e) - 4*(2*c^2*cos(f*x + e) - c^2)*cos(2*f*x + 2*e) - 4*(c^2*sin(3*f*x + 3*e) - c^2*sin(2*f*x + 2*e) + c^2*sin(f*x + e))*sin(4*f*x + 4*e) - 8*(c^2*sin(2*f*x + 2*e) - c^2*sin(f*x + e))*sin(3*f*x + 3*e))*f)","B",0
112,1,758,0,1.223845," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left({\left(\sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(\sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - \cos\left(2 \, f x + 2 \, e\right) \sin\left(4 \, f x + 4 \, e\right) + \cos\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - {\left(\cos\left(4 \, f x + 4 \, e\right) + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(\cos\left(4 \, f x + 4 \, e\right) + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a} \sqrt{c}}{{\left(c^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 36 \, c^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, c^{3} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 16 \, c^{3} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + c^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} + 12 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 36 \, c^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 16 \, c^{3} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 16 \, c^{3} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 12 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3} + 2 \, {\left(6 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\right)} \cos\left(4 \, f x + 4 \, e\right) - 8 \, {\left(c^{3} \cos\left(4 \, f x + 4 \, e\right) + 6 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) - 4 \, c^{3} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{3}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, {\left(c^{3} \cos\left(4 \, f x + 4 \, e\right) + 6 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, {\left(c^{3} \sin\left(4 \, f x + 4 \, e\right) + 6 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) - 4 \, c^{3} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, {\left(c^{3} \sin\left(4 \, f x + 4 \, e\right) + 6 \, c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} f}"," ",0,"2*((sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - cos(2*f*x + 2*e)*sin(4*f*x + 4*e) + cos(4*f*x + 4*e)*sin(2*f*x + 2*e) - (cos(4*f*x + 4*e) + 2*cos(2*f*x + 2*e) + 1)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (cos(4*f*x + 4*e) + 2*cos(2*f*x + 2*e) + 1)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sin(2*f*x + 2*e))*sqrt(a)*sqrt(c)/((c^3*cos(4*f*x + 4*e)^2 + 36*c^3*cos(2*f*x + 2*e)^2 + 16*c^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*c^3*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c^3*sin(4*f*x + 4*e)^2 + 12*c^3*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*c^3*sin(2*f*x + 2*e)^2 + 16*c^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*c^3*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 12*c^3*cos(2*f*x + 2*e) + c^3 + 2*(6*c^3*cos(2*f*x + 2*e) + c^3)*cos(4*f*x + 4*e) - 8*(c^3*cos(4*f*x + 4*e) + 6*c^3*cos(2*f*x + 2*e) - 4*c^3*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^3)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*(c^3*cos(4*f*x + 4*e) + 6*c^3*cos(2*f*x + 2*e) + c^3)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*(c^3*sin(4*f*x + 4*e) + 6*c^3*sin(2*f*x + 2*e) - 4*c^3*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*(c^3*sin(4*f*x + 4*e) + 6*c^3*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
113,1,1680,0,0.906971," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(100 \, a c^{3} \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 25 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 5 \, a c^{3} \sin\left(f x + e\right) - {\left(5 \, a c^{3} \sin\left(9 \, f x + 9 \, e\right) - 10 \, a c^{3} \sin\left(8 \, f x + 8 \, e\right) + 20 \, a c^{3} \sin\left(7 \, f x + 7 \, e\right) - 10 \, a c^{3} \sin\left(6 \, f x + 6 \, e\right) + 14 \, a c^{3} \sin\left(5 \, f x + 5 \, e\right) - 10 \, a c^{3} \sin\left(4 \, f x + 4 \, e\right) + 20 \, a c^{3} \sin\left(3 \, f x + 3 \, e\right) - 10 \, a c^{3} \sin\left(2 \, f x + 2 \, e\right) + 5 \, a c^{3} \sin\left(f x + e\right)\right)} \cos\left(10 \, f x + 10 \, e\right) + 25 \, {\left(a c^{3} \sin\left(8 \, f x + 8 \, e\right) + 2 \, a c^{3} \sin\left(6 \, f x + 6 \, e\right) + 2 \, a c^{3} \sin\left(4 \, f x + 4 \, e\right) + a c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(9 \, f x + 9 \, e\right) - 5 \, {\left(20 \, a c^{3} \sin\left(7 \, f x + 7 \, e\right) + 10 \, a c^{3} \sin\left(6 \, f x + 6 \, e\right) + 14 \, a c^{3} \sin\left(5 \, f x + 5 \, e\right) + 10 \, a c^{3} \sin\left(4 \, f x + 4 \, e\right) + 20 \, a c^{3} \sin\left(3 \, f x + 3 \, e\right) + 5 \, a c^{3} \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + 100 \, {\left(2 \, a c^{3} \sin\left(6 \, f x + 6 \, e\right) + 2 \, a c^{3} \sin\left(4 \, f x + 4 \, e\right) + a c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) - 10 \, {\left(14 \, a c^{3} \sin\left(5 \, f x + 5 \, e\right) + 20 \, a c^{3} \sin\left(3 \, f x + 3 \, e\right) - 5 \, a c^{3} \sin\left(2 \, f x + 2 \, e\right) + 5 \, a c^{3} \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 70 \, {\left(2 \, a c^{3} \sin\left(4 \, f x + 4 \, e\right) + a c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - 50 \, {\left(4 \, a c^{3} \sin\left(3 \, f x + 3 \, e\right) - a c^{3} \sin\left(2 \, f x + 2 \, e\right) + a c^{3} \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(5 \, a c^{3} \cos\left(9 \, f x + 9 \, e\right) - 10 \, a c^{3} \cos\left(8 \, f x + 8 \, e\right) + 20 \, a c^{3} \cos\left(7 \, f x + 7 \, e\right) - 10 \, a c^{3} \cos\left(6 \, f x + 6 \, e\right) + 14 \, a c^{3} \cos\left(5 \, f x + 5 \, e\right) - 10 \, a c^{3} \cos\left(4 \, f x + 4 \, e\right) + 20 \, a c^{3} \cos\left(3 \, f x + 3 \, e\right) - 10 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right) + 5 \, a c^{3} \cos\left(f x + e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) - 5 \, {\left(5 \, a c^{3} \cos\left(8 \, f x + 8 \, e\right) + 10 \, a c^{3} \cos\left(6 \, f x + 6 \, e\right) + 10 \, a c^{3} \cos\left(4 \, f x + 4 \, e\right) + 5 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right) + a c^{3}\right)} \sin\left(9 \, f x + 9 \, e\right) + 5 \, {\left(20 \, a c^{3} \cos\left(7 \, f x + 7 \, e\right) + 10 \, a c^{3} \cos\left(6 \, f x + 6 \, e\right) + 14 \, a c^{3} \cos\left(5 \, f x + 5 \, e\right) + 10 \, a c^{3} \cos\left(4 \, f x + 4 \, e\right) + 20 \, a c^{3} \cos\left(3 \, f x + 3 \, e\right) + 5 \, a c^{3} \cos\left(f x + e\right) + 2 \, a c^{3}\right)} \sin\left(8 \, f x + 8 \, e\right) - 20 \, {\left(10 \, a c^{3} \cos\left(6 \, f x + 6 \, e\right) + 10 \, a c^{3} \cos\left(4 \, f x + 4 \, e\right) + 5 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right) + a c^{3}\right)} \sin\left(7 \, f x + 7 \, e\right) + 10 \, {\left(14 \, a c^{3} \cos\left(5 \, f x + 5 \, e\right) + 20 \, a c^{3} \cos\left(3 \, f x + 3 \, e\right) - 5 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right) + 5 \, a c^{3} \cos\left(f x + e\right) + a c^{3}\right)} \sin\left(6 \, f x + 6 \, e\right) - 14 \, {\left(10 \, a c^{3} \cos\left(4 \, f x + 4 \, e\right) + 5 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right) + a c^{3}\right)} \sin\left(5 \, f x + 5 \, e\right) + 10 \, {\left(20 \, a c^{3} \cos\left(3 \, f x + 3 \, e\right) - 5 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right) + 5 \, a c^{3} \cos\left(f x + e\right) + a c^{3}\right)} \sin\left(4 \, f x + 4 \, e\right) - 20 \, {\left(5 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right) + a c^{3}\right)} \sin\left(3 \, f x + 3 \, e\right) + 5 \, {\left(5 \, a c^{3} \cos\left(f x + e\right) + 2 \, a c^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a} \sqrt{c}}{5 \, {\left(2 \, {\left(5 \, \cos\left(8 \, f x + 8 \, e\right) + 10 \, \cos\left(6 \, f x + 6 \, e\right) + 10 \, \cos\left(4 \, f x + 4 \, e\right) + 5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(10 \, f x + 10 \, e\right) + \cos\left(10 \, f x + 10 \, e\right)^{2} + 10 \, {\left(10 \, \cos\left(6 \, f x + 6 \, e\right) + 10 \, \cos\left(4 \, f x + 4 \, e\right) + 5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(8 \, f x + 8 \, e\right) + 25 \, \cos\left(8 \, f x + 8 \, e\right)^{2} + 20 \, {\left(10 \, \cos\left(4 \, f x + 4 \, e\right) + 5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + 100 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 20 \, {\left(5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 100 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 25 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 10 \, {\left(\sin\left(8 \, f x + 8 \, e\right) + 2 \, \sin\left(6 \, f x + 6 \, e\right) + 2 \, \sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + \sin\left(10 \, f x + 10 \, e\right)^{2} + 50 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 2 \, \sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 25 \, \sin\left(8 \, f x + 8 \, e\right)^{2} + 100 \, {\left(2 \, \sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 100 \, \sin\left(6 \, f x + 6 \, e\right)^{2} + 100 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 100 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 25 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 10 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"2/5*(100*a*c^3*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 25*a*c^3*cos(2*f*x + 2*e)*sin(f*x + e) - 5*a*c^3*sin(f*x + e) - (5*a*c^3*sin(9*f*x + 9*e) - 10*a*c^3*sin(8*f*x + 8*e) + 20*a*c^3*sin(7*f*x + 7*e) - 10*a*c^3*sin(6*f*x + 6*e) + 14*a*c^3*sin(5*f*x + 5*e) - 10*a*c^3*sin(4*f*x + 4*e) + 20*a*c^3*sin(3*f*x + 3*e) - 10*a*c^3*sin(2*f*x + 2*e) + 5*a*c^3*sin(f*x + e))*cos(10*f*x + 10*e) + 25*(a*c^3*sin(8*f*x + 8*e) + 2*a*c^3*sin(6*f*x + 6*e) + 2*a*c^3*sin(4*f*x + 4*e) + a*c^3*sin(2*f*x + 2*e))*cos(9*f*x + 9*e) - 5*(20*a*c^3*sin(7*f*x + 7*e) + 10*a*c^3*sin(6*f*x + 6*e) + 14*a*c^3*sin(5*f*x + 5*e) + 10*a*c^3*sin(4*f*x + 4*e) + 20*a*c^3*sin(3*f*x + 3*e) + 5*a*c^3*sin(f*x + e))*cos(8*f*x + 8*e) + 100*(2*a*c^3*sin(6*f*x + 6*e) + 2*a*c^3*sin(4*f*x + 4*e) + a*c^3*sin(2*f*x + 2*e))*cos(7*f*x + 7*e) - 10*(14*a*c^3*sin(5*f*x + 5*e) + 20*a*c^3*sin(3*f*x + 3*e) - 5*a*c^3*sin(2*f*x + 2*e) + 5*a*c^3*sin(f*x + e))*cos(6*f*x + 6*e) + 70*(2*a*c^3*sin(4*f*x + 4*e) + a*c^3*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - 50*(4*a*c^3*sin(3*f*x + 3*e) - a*c^3*sin(2*f*x + 2*e) + a*c^3*sin(f*x + e))*cos(4*f*x + 4*e) + (5*a*c^3*cos(9*f*x + 9*e) - 10*a*c^3*cos(8*f*x + 8*e) + 20*a*c^3*cos(7*f*x + 7*e) - 10*a*c^3*cos(6*f*x + 6*e) + 14*a*c^3*cos(5*f*x + 5*e) - 10*a*c^3*cos(4*f*x + 4*e) + 20*a*c^3*cos(3*f*x + 3*e) - 10*a*c^3*cos(2*f*x + 2*e) + 5*a*c^3*cos(f*x + e))*sin(10*f*x + 10*e) - 5*(5*a*c^3*cos(8*f*x + 8*e) + 10*a*c^3*cos(6*f*x + 6*e) + 10*a*c^3*cos(4*f*x + 4*e) + 5*a*c^3*cos(2*f*x + 2*e) + a*c^3)*sin(9*f*x + 9*e) + 5*(20*a*c^3*cos(7*f*x + 7*e) + 10*a*c^3*cos(6*f*x + 6*e) + 14*a*c^3*cos(5*f*x + 5*e) + 10*a*c^3*cos(4*f*x + 4*e) + 20*a*c^3*cos(3*f*x + 3*e) + 5*a*c^3*cos(f*x + e) + 2*a*c^3)*sin(8*f*x + 8*e) - 20*(10*a*c^3*cos(6*f*x + 6*e) + 10*a*c^3*cos(4*f*x + 4*e) + 5*a*c^3*cos(2*f*x + 2*e) + a*c^3)*sin(7*f*x + 7*e) + 10*(14*a*c^3*cos(5*f*x + 5*e) + 20*a*c^3*cos(3*f*x + 3*e) - 5*a*c^3*cos(2*f*x + 2*e) + 5*a*c^3*cos(f*x + e) + a*c^3)*sin(6*f*x + 6*e) - 14*(10*a*c^3*cos(4*f*x + 4*e) + 5*a*c^3*cos(2*f*x + 2*e) + a*c^3)*sin(5*f*x + 5*e) + 10*(20*a*c^3*cos(3*f*x + 3*e) - 5*a*c^3*cos(2*f*x + 2*e) + 5*a*c^3*cos(f*x + e) + a*c^3)*sin(4*f*x + 4*e) - 20*(5*a*c^3*cos(2*f*x + 2*e) + a*c^3)*sin(3*f*x + 3*e) + 5*(5*a*c^3*cos(f*x + e) + 2*a*c^3)*sin(2*f*x + 2*e))*sqrt(a)*sqrt(c)/((2*(5*cos(8*f*x + 8*e) + 10*cos(6*f*x + 6*e) + 10*cos(4*f*x + 4*e) + 5*cos(2*f*x + 2*e) + 1)*cos(10*f*x + 10*e) + cos(10*f*x + 10*e)^2 + 10*(10*cos(6*f*x + 6*e) + 10*cos(4*f*x + 4*e) + 5*cos(2*f*x + 2*e) + 1)*cos(8*f*x + 8*e) + 25*cos(8*f*x + 8*e)^2 + 20*(10*cos(4*f*x + 4*e) + 5*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + 100*cos(6*f*x + 6*e)^2 + 20*(5*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 100*cos(4*f*x + 4*e)^2 + 25*cos(2*f*x + 2*e)^2 + 10*(sin(8*f*x + 8*e) + 2*sin(6*f*x + 6*e) + 2*sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*sin(10*f*x + 10*e) + sin(10*f*x + 10*e)^2 + 50*(2*sin(6*f*x + 6*e) + 2*sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 25*sin(8*f*x + 8*e)^2 + 100*(2*sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 100*sin(6*f*x + 6*e)^2 + 100*sin(4*f*x + 4*e)^2 + 100*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 25*sin(2*f*x + 2*e)^2 + 10*cos(2*f*x + 2*e) + 1)*f)","B",0
114,1,1105,0,0.855983," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(20 \, a c^{2} \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 12 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 3 \, a c^{2} \sin\left(f x + e\right) - {\left(3 \, a c^{2} \sin\left(7 \, f x + 7 \, e\right) - 3 \, a c^{2} \sin\left(6 \, f x + 6 \, e\right) + 5 \, a c^{2} \sin\left(5 \, f x + 5 \, e\right) + 5 \, a c^{2} \sin\left(3 \, f x + 3 \, e\right) - 3 \, a c^{2} \sin\left(2 \, f x + 2 \, e\right) + 3 \, a c^{2} \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + 6 \, {\left(2 \, a c^{2} \sin\left(6 \, f x + 6 \, e\right) + 3 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) - 2 \, {\left(10 \, a c^{2} \sin\left(5 \, f x + 5 \, e\right) + 9 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 10 \, a c^{2} \sin\left(3 \, f x + 3 \, e\right) + 6 \, a c^{2} \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 10 \, {\left(3 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - 6 \, {\left(5 \, a c^{2} \sin\left(3 \, f x + 3 \, e\right) - 3 \, a c^{2} \sin\left(2 \, f x + 2 \, e\right) + 3 \, a c^{2} \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(3 \, a c^{2} \cos\left(7 \, f x + 7 \, e\right) - 3 \, a c^{2} \cos\left(6 \, f x + 6 \, e\right) + 5 \, a c^{2} \cos\left(5 \, f x + 5 \, e\right) + 5 \, a c^{2} \cos\left(3 \, f x + 3 \, e\right) - 3 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a c^{2} \cos\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 3 \, {\left(4 \, a c^{2} \cos\left(6 \, f x + 6 \, e\right) + 6 \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 4 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a c^{2}\right)} \sin\left(7 \, f x + 7 \, e\right) + {\left(20 \, a c^{2} \cos\left(5 \, f x + 5 \, e\right) + 18 \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 20 \, a c^{2} \cos\left(3 \, f x + 3 \, e\right) + 12 \, a c^{2} \cos\left(f x + e\right) + 3 \, a c^{2}\right)} \sin\left(6 \, f x + 6 \, e\right) - 5 \, {\left(6 \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 4 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a c^{2}\right)} \sin\left(5 \, f x + 5 \, e\right) + 6 \, {\left(5 \, a c^{2} \cos\left(3 \, f x + 3 \, e\right) - 3 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a c^{2} \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 5 \, {\left(4 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a c^{2}\right)} \sin\left(3 \, f x + 3 \, e\right) + 3 \, {\left(4 \, a c^{2} \cos\left(f x + e\right) + a c^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a} \sqrt{c}}{3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) + 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(8 \, f x + 8 \, e\right) + \cos\left(8 \, f x + 8 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + 16 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 36 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 16 \, \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"2/3*(20*a*c^2*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 12*a*c^2*cos(2*f*x + 2*e)*sin(f*x + e) - 3*a*c^2*sin(f*x + e) - (3*a*c^2*sin(7*f*x + 7*e) - 3*a*c^2*sin(6*f*x + 6*e) + 5*a*c^2*sin(5*f*x + 5*e) + 5*a*c^2*sin(3*f*x + 3*e) - 3*a*c^2*sin(2*f*x + 2*e) + 3*a*c^2*sin(f*x + e))*cos(8*f*x + 8*e) + 6*(2*a*c^2*sin(6*f*x + 6*e) + 3*a*c^2*sin(4*f*x + 4*e) + 2*a*c^2*sin(2*f*x + 2*e))*cos(7*f*x + 7*e) - 2*(10*a*c^2*sin(5*f*x + 5*e) + 9*a*c^2*sin(4*f*x + 4*e) + 10*a*c^2*sin(3*f*x + 3*e) + 6*a*c^2*sin(f*x + e))*cos(6*f*x + 6*e) + 10*(3*a*c^2*sin(4*f*x + 4*e) + 2*a*c^2*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - 6*(5*a*c^2*sin(3*f*x + 3*e) - 3*a*c^2*sin(2*f*x + 2*e) + 3*a*c^2*sin(f*x + e))*cos(4*f*x + 4*e) + (3*a*c^2*cos(7*f*x + 7*e) - 3*a*c^2*cos(6*f*x + 6*e) + 5*a*c^2*cos(5*f*x + 5*e) + 5*a*c^2*cos(3*f*x + 3*e) - 3*a*c^2*cos(2*f*x + 2*e) + 3*a*c^2*cos(f*x + e))*sin(8*f*x + 8*e) - 3*(4*a*c^2*cos(6*f*x + 6*e) + 6*a*c^2*cos(4*f*x + 4*e) + 4*a*c^2*cos(2*f*x + 2*e) + a*c^2)*sin(7*f*x + 7*e) + (20*a*c^2*cos(5*f*x + 5*e) + 18*a*c^2*cos(4*f*x + 4*e) + 20*a*c^2*cos(3*f*x + 3*e) + 12*a*c^2*cos(f*x + e) + 3*a*c^2)*sin(6*f*x + 6*e) - 5*(6*a*c^2*cos(4*f*x + 4*e) + 4*a*c^2*cos(2*f*x + 2*e) + a*c^2)*sin(5*f*x + 5*e) + 6*(5*a*c^2*cos(3*f*x + 3*e) - 3*a*c^2*cos(2*f*x + 2*e) + 3*a*c^2*cos(f*x + e))*sin(4*f*x + 4*e) - 5*(4*a*c^2*cos(2*f*x + 2*e) + a*c^2)*sin(3*f*x + 3*e) + 3*(4*a*c^2*cos(f*x + e) + a*c^2)*sin(2*f*x + 2*e))*sqrt(a)*sqrt(c)/((2*(4*cos(6*f*x + 6*e) + 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(8*f*x + 8*e) + cos(8*f*x + 8*e)^2 + 8*(6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + 16*cos(6*f*x + 6*e)^2 + 12*(4*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 36*cos(4*f*x + 4*e)^2 + 16*cos(2*f*x + 2*e)^2 + 4*(2*sin(6*f*x + 6*e) + 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + sin(8*f*x + 8*e)^2 + 16*(3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 16*sin(6*f*x + 6*e)^2 + 36*sin(4*f*x + 4*e)^2 + 48*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 16*sin(2*f*x + 2*e)^2 + 8*cos(2*f*x + 2*e) + 1)*f)","B",0
115,1,550,0,0.993428," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(6 \, a c \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, a c \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 9 \, a c \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 3 \, a c \sin\left(f x + e\right) - {\left(3 \, a c \sin\left(5 \, f x + 5 \, e\right) + 2 \, a c \sin\left(3 \, f x + 3 \, e\right) + 3 \, a c \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 9 \, {\left(a c \sin\left(4 \, f x + 4 \, e\right) + a c \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - 3 \, {\left(2 \, a c \sin\left(3 \, f x + 3 \, e\right) + 3 \, a c \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(3 \, a c \cos\left(5 \, f x + 5 \, e\right) + 2 \, a c \cos\left(3 \, f x + 3 \, e\right) + 3 \, a c \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 3 \, {\left(3 \, a c \cos\left(4 \, f x + 4 \, e\right) + 3 \, a c \cos\left(2 \, f x + 2 \, e\right) + a c\right)} \sin\left(5 \, f x + 5 \, e\right) + 3 \, {\left(2 \, a c \cos\left(3 \, f x + 3 \, e\right) + 3 \, a c \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 2 \, {\left(3 \, a c \cos\left(2 \, f x + 2 \, e\right) + a c\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} \sqrt{a} \sqrt{c}}{3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, f x + 4 \, e\right) + 3 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + \cos\left(6 \, f x + 6 \, e\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 9 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 6 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + \sin\left(6 \, f x + 6 \, e\right)^{2} + 9 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 18 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 6 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"2/3*(6*a*c*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) + 9*a*c*cos(f*x + e)*sin(2*f*x + 2*e) - 9*a*c*cos(2*f*x + 2*e)*sin(f*x + e) - 3*a*c*sin(f*x + e) - (3*a*c*sin(5*f*x + 5*e) + 2*a*c*sin(3*f*x + 3*e) + 3*a*c*sin(f*x + e))*cos(6*f*x + 6*e) + 9*(a*c*sin(4*f*x + 4*e) + a*c*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - 3*(2*a*c*sin(3*f*x + 3*e) + 3*a*c*sin(f*x + e))*cos(4*f*x + 4*e) + (3*a*c*cos(5*f*x + 5*e) + 2*a*c*cos(3*f*x + 3*e) + 3*a*c*cos(f*x + e))*sin(6*f*x + 6*e) - 3*(3*a*c*cos(4*f*x + 4*e) + 3*a*c*cos(2*f*x + 2*e) + a*c)*sin(5*f*x + 5*e) + 3*(2*a*c*cos(3*f*x + 3*e) + 3*a*c*cos(f*x + e))*sin(4*f*x + 4*e) - 2*(3*a*c*cos(2*f*x + 2*e) + a*c)*sin(3*f*x + 3*e))*sqrt(a)*sqrt(c)/((2*(3*cos(4*f*x + 4*e) + 3*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + cos(6*f*x + 6*e)^2 + 6*(3*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 9*cos(4*f*x + 4*e)^2 + 9*cos(2*f*x + 2*e)^2 + 6*(sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + sin(6*f*x + 6*e)^2 + 9*sin(4*f*x + 4*e)^2 + 18*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 9*sin(2*f*x + 2*e)^2 + 6*cos(2*f*x + 2*e) + 1)*f)","B",0
116,1,56,0,0.773328," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a} a \sqrt{c}}{f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{2} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{2}}"," ",0,"-2*sqrt(-a)*a*sqrt(c)/(f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^2*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^2)","A",0
117,1,275,0,1.026213," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) \sin\left(2 \, f x + 2 \, e\right) + {\left(a \cos\left(2 \, f x + 2 \, e\right)^{2} + a \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, {\left(a \cos\left(2 \, f x + 2 \, e\right)^{2} + a \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 1\right) - {\left(a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(c \cos\left(2 \, f x + 2 \, e\right)^{2} + c \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + c\right)} f}"," ",0,"-2*(a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(2*f*x + 2*e) + (a*cos(2*f*x + 2*e)^2 + a*sin(2*f*x + 2*e)^2 + 2*a*cos(2*f*x + 2*e) + a)*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*(a*cos(2*f*x + 2*e)^2 + a*sin(2*f*x + 2*e)^2 + 2*a*cos(2*f*x + 2*e) + a)*arctan2(sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1) - (a*cos(2*f*x + 2*e) + a)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((c*cos(2*f*x + 2*e)^2 + c*sin(2*f*x + 2*e)^2 + 2*c*cos(2*f*x + 2*e) + c)*f)","B",0
118,1,122,0,0.742449," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{\frac{\sqrt{-a} a \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{-a} a \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{3}{2}}} - \frac{2 \, \sqrt{-a} a \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{-a} a {\left(\cos\left(f x + e\right) + 1\right)}^{2}}{c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}}{f}"," ",0,"(sqrt(-a)*a*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c^(3/2) + sqrt(-a)*a*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(3/2) - 2*sqrt(-a)*a*log(sin(f*x + e)/(cos(f*x + e) + 1))/c^(3/2) + sqrt(-a)*a*(cos(f*x + e) + 1)^2/(c^(3/2)*sin(f*x + e)^2))/f","A",0
119,1,533,0,0.975931," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(6 \, a \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 6 \, a \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 6 \, a \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - {\left(a \sin\left(3 \, f x + 3 \, e\right) + a \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(a \cos\left(3 \, f x + 3 \, e\right) + a \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(6 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \sin\left(3 \, f x + 3 \, e\right) - a \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{{\left(c^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, c^{3} \cos\left(3 \, f x + 3 \, e\right)^{2} + 36 \, c^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, c^{3} \cos\left(f x + e\right)^{2} + c^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, c^{3} \sin\left(3 \, f x + 3 \, e\right)^{2} + 36 \, c^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} - 48 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 16 \, c^{3} \sin\left(f x + e\right)^{2} - 8 \, c^{3} \cos\left(f x + e\right) + c^{3} - 2 \, {\left(4 \, c^{3} \cos\left(3 \, f x + 3 \, e\right) - 6 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + 4 \, c^{3} \cos\left(f x + e\right) - c^{3}\right)} \cos\left(4 \, f x + 4 \, e\right) - 8 \, {\left(6 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) - 4 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \cos\left(3 \, f x + 3 \, e\right) - 12 \, {\left(4 \, c^{3} \cos\left(f x + e\right) - c^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(2 \, c^{3} \sin\left(3 \, f x + 3 \, e\right) - 3 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) + 2 \, c^{3} \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 16 \, {\left(3 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) - 2 \, c^{3} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} f}"," ",0,"2*(6*a*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) + 6*a*cos(f*x + e)*sin(2*f*x + 2*e) - 6*a*cos(2*f*x + 2*e)*sin(f*x + e) - (a*sin(3*f*x + 3*e) + a*sin(f*x + e))*cos(4*f*x + 4*e) + (a*cos(3*f*x + 3*e) + a*cos(f*x + e))*sin(4*f*x + 4*e) - (6*a*cos(2*f*x + 2*e) + a)*sin(3*f*x + 3*e) - a*sin(f*x + e))*sqrt(a)*sqrt(c)/((c^3*cos(4*f*x + 4*e)^2 + 16*c^3*cos(3*f*x + 3*e)^2 + 36*c^3*cos(2*f*x + 2*e)^2 + 16*c^3*cos(f*x + e)^2 + c^3*sin(4*f*x + 4*e)^2 + 16*c^3*sin(3*f*x + 3*e)^2 + 36*c^3*sin(2*f*x + 2*e)^2 - 48*c^3*sin(2*f*x + 2*e)*sin(f*x + e) + 16*c^3*sin(f*x + e)^2 - 8*c^3*cos(f*x + e) + c^3 - 2*(4*c^3*cos(3*f*x + 3*e) - 6*c^3*cos(2*f*x + 2*e) + 4*c^3*cos(f*x + e) - c^3)*cos(4*f*x + 4*e) - 8*(6*c^3*cos(2*f*x + 2*e) - 4*c^3*cos(f*x + e) + c^3)*cos(3*f*x + 3*e) - 12*(4*c^3*cos(f*x + e) - c^3)*cos(2*f*x + 2*e) - 4*(2*c^3*sin(3*f*x + 3*e) - 3*c^3*sin(2*f*x + 2*e) + 2*c^3*sin(f*x + e))*sin(4*f*x + 4*e) - 16*(3*c^3*sin(2*f*x + 2*e) - 2*c^3*sin(f*x + e))*sin(3*f*x + 3*e))*f)","B",0
120,1,1559,0,2.073688," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, {\left(a \sin\left(4 \, f x + 4 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 3 \, {\left(a \sin\left(6 \, f x + 6 \, e\right) + 9 \, a \sin\left(4 \, f x + 4 \, e\right) + 9 \, a \sin\left(2 \, f x + 2 \, e\right) - 4 \, a \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 \, {\left(2 \, a \sin\left(6 \, f x + 6 \, e\right) + 15 \, a \sin\left(4 \, f x + 4 \, e\right) + 15 \, a \sin\left(2 \, f x + 2 \, e\right) + 3 \, a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 3 \, {\left(a \sin\left(6 \, f x + 6 \, e\right) + 9 \, a \sin\left(4 \, f x + 4 \, e\right) + 9 \, a \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 3 \, {\left(a \cos\left(4 \, f x + 4 \, e\right) + a \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 3 \, a \sin\left(4 \, f x + 4 \, e\right) + 3 \, a \sin\left(2 \, f x + 2 \, e\right) - 3 \, {\left(a \cos\left(6 \, f x + 6 \, e\right) + 9 \, a \cos\left(4 \, f x + 4 \, e\right) + 9 \, a \cos\left(2 \, f x + 2 \, e\right) - 4 \, a \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + a\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, {\left(2 \, a \cos\left(6 \, f x + 6 \, e\right) + 15 \, a \cos\left(4 \, f x + 4 \, e\right) + 15 \, a \cos\left(2 \, f x + 2 \, e\right) + 3 \, a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2 \, a\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 3 \, {\left(a \cos\left(6 \, f x + 6 \, e\right) + 9 \, a \cos\left(4 \, f x + 4 \, e\right) + 9 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{3 \, {\left(c^{4} \cos\left(6 \, f x + 6 \, e\right)^{2} + 225 \, c^{4} \cos\left(4 \, f x + 4 \, e\right)^{2} + 225 \, c^{4} \cos\left(2 \, f x + 2 \, e\right)^{2} + 36 \, c^{4} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 400 \, c^{4} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 36 \, c^{4} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + c^{4} \sin\left(6 \, f x + 6 \, e\right)^{2} + 225 \, c^{4} \sin\left(4 \, f x + 4 \, e\right)^{2} + 450 \, c^{4} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 225 \, c^{4} \sin\left(2 \, f x + 2 \, e\right)^{2} + 36 \, c^{4} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 400 \, c^{4} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 36 \, c^{4} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 30 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) + c^{4} + 2 \, {\left(15 \, c^{4} \cos\left(4 \, f x + 4 \, e\right) + 15 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) + c^{4}\right)} \cos\left(6 \, f x + 6 \, e\right) + 30 \, {\left(15 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) + c^{4}\right)} \cos\left(4 \, f x + 4 \, e\right) - 12 \, {\left(c^{4} \cos\left(6 \, f x + 6 \, e\right) + 15 \, c^{4} \cos\left(4 \, f x + 4 \, e\right) + 15 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) - 20 \, c^{4} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 6 \, c^{4} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{4}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 40 \, {\left(c^{4} \cos\left(6 \, f x + 6 \, e\right) + 15 \, c^{4} \cos\left(4 \, f x + 4 \, e\right) + 15 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) - 6 \, c^{4} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{4}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12 \, {\left(c^{4} \cos\left(6 \, f x + 6 \, e\right) + 15 \, c^{4} \cos\left(4 \, f x + 4 \, e\right) + 15 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) + c^{4}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 30 \, {\left(c^{4} \sin\left(4 \, f x + 4 \, e\right) + c^{4} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 12 \, {\left(c^{4} \sin\left(6 \, f x + 6 \, e\right) + 15 \, c^{4} \sin\left(4 \, f x + 4 \, e\right) + 15 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) - 20 \, c^{4} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 6 \, c^{4} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 40 \, {\left(c^{4} \sin\left(6 \, f x + 6 \, e\right) + 15 \, c^{4} \sin\left(4 \, f x + 4 \, e\right) + 15 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) - 6 \, c^{4} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12 \, {\left(c^{4} \sin\left(6 \, f x + 6 \, e\right) + 15 \, c^{4} \sin\left(4 \, f x + 4 \, e\right) + 15 \, c^{4} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} f}"," ",0,"2/3*(3*(a*sin(4*f*x + 4*e) + a*sin(2*f*x + 2*e))*cos(6*f*x + 6*e) + 3*(a*sin(6*f*x + 6*e) + 9*a*sin(4*f*x + 4*e) + 9*a*sin(2*f*x + 2*e) - 4*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(2*a*sin(6*f*x + 6*e) + 15*a*sin(4*f*x + 4*e) + 15*a*sin(2*f*x + 2*e) + 3*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*(a*sin(6*f*x + 6*e) + 9*a*sin(4*f*x + 4*e) + 9*a*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3*(a*cos(4*f*x + 4*e) + a*cos(2*f*x + 2*e))*sin(6*f*x + 6*e) + 3*a*sin(4*f*x + 4*e) + 3*a*sin(2*f*x + 2*e) - 3*(a*cos(6*f*x + 6*e) + 9*a*cos(4*f*x + 4*e) + 9*a*cos(2*f*x + 2*e) - 4*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(2*a*cos(6*f*x + 6*e) + 15*a*cos(4*f*x + 4*e) + 15*a*cos(2*f*x + 2*e) + 3*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*a)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3*(a*cos(6*f*x + 6*e) + 9*a*cos(4*f*x + 4*e) + 9*a*cos(2*f*x + 2*e) + a)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((c^4*cos(6*f*x + 6*e)^2 + 225*c^4*cos(4*f*x + 4*e)^2 + 225*c^4*cos(2*f*x + 2*e)^2 + 36*c^4*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 400*c^4*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 36*c^4*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c^4*sin(6*f*x + 6*e)^2 + 225*c^4*sin(4*f*x + 4*e)^2 + 450*c^4*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 225*c^4*sin(2*f*x + 2*e)^2 + 36*c^4*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 400*c^4*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 36*c^4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 30*c^4*cos(2*f*x + 2*e) + c^4 + 2*(15*c^4*cos(4*f*x + 4*e) + 15*c^4*cos(2*f*x + 2*e) + c^4)*cos(6*f*x + 6*e) + 30*(15*c^4*cos(2*f*x + 2*e) + c^4)*cos(4*f*x + 4*e) - 12*(c^4*cos(6*f*x + 6*e) + 15*c^4*cos(4*f*x + 4*e) + 15*c^4*cos(2*f*x + 2*e) - 20*c^4*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*c^4*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^4)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 40*(c^4*cos(6*f*x + 6*e) + 15*c^4*cos(4*f*x + 4*e) + 15*c^4*cos(2*f*x + 2*e) - 6*c^4*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^4)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*(c^4*cos(6*f*x + 6*e) + 15*c^4*cos(4*f*x + 4*e) + 15*c^4*cos(2*f*x + 2*e) + c^4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 30*(c^4*sin(4*f*x + 4*e) + c^4*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 12*(c^4*sin(6*f*x + 6*e) + 15*c^4*sin(4*f*x + 4*e) + 15*c^4*sin(2*f*x + 2*e) - 20*c^4*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*c^4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 40*(c^4*sin(6*f*x + 6*e) + 15*c^4*sin(4*f*x + 4*e) + 15*c^4*sin(2*f*x + 2*e) - 6*c^4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*(c^4*sin(6*f*x + 6*e) + 15*c^4*sin(4*f*x + 4*e) + 15*c^4*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
121,1,2608,0,7.888633," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(9/2),x, algorithm=""maxima"")","\frac{2 \, {\left(28 \, a \cos\left(6 \, f x + 6 \, e\right) \sin\left(4 \, f x + 4 \, e\right) - 28 \, a \cos\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(3 \, a \sin\left(6 \, f x + 6 \, e\right) + 8 \, a \sin\left(4 \, f x + 4 \, e\right) + 3 \, a \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + {\left(3 \, a \sin\left(8 \, f x + 8 \, e\right) + 36 \, a \sin\left(6 \, f x + 6 \, e\right) + 82 \, a \sin\left(4 \, f x + 4 \, e\right) + 36 \, a \sin\left(2 \, f x + 2 \, e\right) - 32 \, a \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 32 \, a \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(17 \, a \sin\left(8 \, f x + 8 \, e\right) + 140 \, a \sin\left(6 \, f x + 6 \, e\right) + 294 \, a \sin\left(4 \, f x + 4 \, e\right) + 140 \, a \sin\left(2 \, f x + 2 \, e\right) + 32 \, a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(17 \, a \sin\left(8 \, f x + 8 \, e\right) + 140 \, a \sin\left(6 \, f x + 6 \, e\right) + 294 \, a \sin\left(4 \, f x + 4 \, e\right) + 140 \, a \sin\left(2 \, f x + 2 \, e\right) + 32 \, a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(3 \, a \sin\left(8 \, f x + 8 \, e\right) + 36 \, a \sin\left(6 \, f x + 6 \, e\right) + 82 \, a \sin\left(4 \, f x + 4 \, e\right) + 36 \, a \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 2 \, {\left(3 \, a \cos\left(6 \, f x + 6 \, e\right) + 8 \, a \cos\left(4 \, f x + 4 \, e\right) + 3 \, a \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 2 \, {\left(14 \, a \cos\left(4 \, f x + 4 \, e\right) - 3 \, a\right)} \sin\left(6 \, f x + 6 \, e\right) + 4 \, {\left(7 \, a \cos\left(2 \, f x + 2 \, e\right) + 4 \, a\right)} \sin\left(4 \, f x + 4 \, e\right) + 6 \, a \sin\left(2 \, f x + 2 \, e\right) - {\left(3 \, a \cos\left(8 \, f x + 8 \, e\right) + 36 \, a \cos\left(6 \, f x + 6 \, e\right) + 82 \, a \cos\left(4 \, f x + 4 \, e\right) + 36 \, a \cos\left(2 \, f x + 2 \, e\right) - 32 \, a \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 32 \, a \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 3 \, a\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(17 \, a \cos\left(8 \, f x + 8 \, e\right) + 140 \, a \cos\left(6 \, f x + 6 \, e\right) + 294 \, a \cos\left(4 \, f x + 4 \, e\right) + 140 \, a \cos\left(2 \, f x + 2 \, e\right) + 32 \, a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 17 \, a\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(17 \, a \cos\left(8 \, f x + 8 \, e\right) + 140 \, a \cos\left(6 \, f x + 6 \, e\right) + 294 \, a \cos\left(4 \, f x + 4 \, e\right) + 140 \, a \cos\left(2 \, f x + 2 \, e\right) + 32 \, a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 17 \, a\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(3 \, a \cos\left(8 \, f x + 8 \, e\right) + 36 \, a \cos\left(6 \, f x + 6 \, e\right) + 82 \, a \cos\left(4 \, f x + 4 \, e\right) + 36 \, a \cos\left(2 \, f x + 2 \, e\right) + 3 \, a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{3 \, {\left(c^{5} \cos\left(8 \, f x + 8 \, e\right)^{2} + 784 \, c^{5} \cos\left(6 \, f x + 6 \, e\right)^{2} + 4900 \, c^{5} \cos\left(4 \, f x + 4 \, e\right)^{2} + 784 \, c^{5} \cos\left(2 \, f x + 2 \, e\right)^{2} + 64 \, c^{5} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 3136 \, c^{5} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 3136 \, c^{5} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 64 \, c^{5} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + c^{5} \sin\left(8 \, f x + 8 \, e\right)^{2} + 784 \, c^{5} \sin\left(6 \, f x + 6 \, e\right)^{2} + 4900 \, c^{5} \sin\left(4 \, f x + 4 \, e\right)^{2} + 3920 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 784 \, c^{5} \sin\left(2 \, f x + 2 \, e\right)^{2} + 64 \, c^{5} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 3136 \, c^{5} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 3136 \, c^{5} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 64 \, c^{5} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 56 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + c^{5} + 2 \, {\left(28 \, c^{5} \cos\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + c^{5}\right)} \cos\left(8 \, f x + 8 \, e\right) + 56 \, {\left(70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + c^{5}\right)} \cos\left(6 \, f x + 6 \, e\right) + 140 \, {\left(28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + c^{5}\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(c^{5} \cos\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \cos\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) - 56 \, c^{5} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 56 \, c^{5} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, c^{5} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{5}\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(c^{5} \cos\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \cos\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) - 56 \, c^{5} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, c^{5} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{5}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(c^{5} \cos\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \cos\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) - 8 \, c^{5} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{5}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 16 \, {\left(c^{5} \cos\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \cos\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + c^{5}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 28 \, {\left(2 \, c^{5} \sin\left(6 \, f x + 6 \, e\right) + 5 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{5} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 784 \, {\left(5 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{5} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, {\left(c^{5} \sin\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \sin\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \sin\left(2 \, f x + 2 \, e\right) - 56 \, c^{5} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 56 \, c^{5} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, c^{5} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(c^{5} \sin\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \sin\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \sin\left(2 \, f x + 2 \, e\right) - 56 \, c^{5} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, c^{5} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(c^{5} \sin\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \sin\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \sin\left(2 \, f x + 2 \, e\right) - 8 \, c^{5} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 16 \, {\left(c^{5} \sin\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \sin\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} f}"," ",0,"2/3*(28*a*cos(6*f*x + 6*e)*sin(4*f*x + 4*e) - 28*a*cos(4*f*x + 4*e)*sin(2*f*x + 2*e) + 2*(3*a*sin(6*f*x + 6*e) + 8*a*sin(4*f*x + 4*e) + 3*a*sin(2*f*x + 2*e))*cos(8*f*x + 8*e) + (3*a*sin(8*f*x + 8*e) + 36*a*sin(6*f*x + 6*e) + 82*a*sin(4*f*x + 4*e) + 36*a*sin(2*f*x + 2*e) - 32*a*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (17*a*sin(8*f*x + 8*e) + 140*a*sin(6*f*x + 6*e) + 294*a*sin(4*f*x + 4*e) + 140*a*sin(2*f*x + 2*e) + 32*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (17*a*sin(8*f*x + 8*e) + 140*a*sin(6*f*x + 6*e) + 294*a*sin(4*f*x + 4*e) + 140*a*sin(2*f*x + 2*e) + 32*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (3*a*sin(8*f*x + 8*e) + 36*a*sin(6*f*x + 6*e) + 82*a*sin(4*f*x + 4*e) + 36*a*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*(3*a*cos(6*f*x + 6*e) + 8*a*cos(4*f*x + 4*e) + 3*a*cos(2*f*x + 2*e))*sin(8*f*x + 8*e) - 2*(14*a*cos(4*f*x + 4*e) - 3*a)*sin(6*f*x + 6*e) + 4*(7*a*cos(2*f*x + 2*e) + 4*a)*sin(4*f*x + 4*e) + 6*a*sin(2*f*x + 2*e) - (3*a*cos(8*f*x + 8*e) + 36*a*cos(6*f*x + 6*e) + 82*a*cos(4*f*x + 4*e) + 36*a*cos(2*f*x + 2*e) - 32*a*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*a)*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (17*a*cos(8*f*x + 8*e) + 140*a*cos(6*f*x + 6*e) + 294*a*cos(4*f*x + 4*e) + 140*a*cos(2*f*x + 2*e) + 32*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 17*a)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (17*a*cos(8*f*x + 8*e) + 140*a*cos(6*f*x + 6*e) + 294*a*cos(4*f*x + 4*e) + 140*a*cos(2*f*x + 2*e) + 32*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 17*a)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (3*a*cos(8*f*x + 8*e) + 36*a*cos(6*f*x + 6*e) + 82*a*cos(4*f*x + 4*e) + 36*a*cos(2*f*x + 2*e) + 3*a)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((c^5*cos(8*f*x + 8*e)^2 + 784*c^5*cos(6*f*x + 6*e)^2 + 4900*c^5*cos(4*f*x + 4*e)^2 + 784*c^5*cos(2*f*x + 2*e)^2 + 64*c^5*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*c^5*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*c^5*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*c^5*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c^5*sin(8*f*x + 8*e)^2 + 784*c^5*sin(6*f*x + 6*e)^2 + 4900*c^5*sin(4*f*x + 4*e)^2 + 3920*c^5*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 784*c^5*sin(2*f*x + 2*e)^2 + 64*c^5*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*c^5*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*c^5*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*c^5*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 56*c^5*cos(2*f*x + 2*e) + c^5 + 2*(28*c^5*cos(6*f*x + 6*e) + 70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) + c^5)*cos(8*f*x + 8*e) + 56*(70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) + c^5)*cos(6*f*x + 6*e) + 140*(28*c^5*cos(2*f*x + 2*e) + c^5)*cos(4*f*x + 4*e) - 16*(c^5*cos(8*f*x + 8*e) + 28*c^5*cos(6*f*x + 6*e) + 70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) - 56*c^5*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 56*c^5*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*c^5*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^5)*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 112*(c^5*cos(8*f*x + 8*e) + 28*c^5*cos(6*f*x + 6*e) + 70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) - 56*c^5*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*c^5*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^5)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 112*(c^5*cos(8*f*x + 8*e) + 28*c^5*cos(6*f*x + 6*e) + 70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) - 8*c^5*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^5)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 16*(c^5*cos(8*f*x + 8*e) + 28*c^5*cos(6*f*x + 6*e) + 70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) + c^5)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 28*(2*c^5*sin(6*f*x + 6*e) + 5*c^5*sin(4*f*x + 4*e) + 2*c^5*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 784*(5*c^5*sin(4*f*x + 4*e) + 2*c^5*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 16*(c^5*sin(8*f*x + 8*e) + 28*c^5*sin(6*f*x + 6*e) + 70*c^5*sin(4*f*x + 4*e) + 28*c^5*sin(2*f*x + 2*e) - 56*c^5*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 56*c^5*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*c^5*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 112*(c^5*sin(8*f*x + 8*e) + 28*c^5*sin(6*f*x + 6*e) + 70*c^5*sin(4*f*x + 4*e) + 28*c^5*sin(2*f*x + 2*e) - 56*c^5*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*c^5*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 112*(c^5*sin(8*f*x + 8*e) + 28*c^5*sin(6*f*x + 6*e) + 70*c^5*sin(4*f*x + 4*e) + 28*c^5*sin(2*f*x + 2*e) - 8*c^5*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 16*(c^5*sin(8*f*x + 8*e) + 28*c^5*sin(6*f*x + 6*e) + 70*c^5*sin(4*f*x + 4*e) + 28*c^5*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
122,1,3906,0,38.317138," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(11/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(225 \, a \cos\left(6 \, f x + 6 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 225 \, a \cos\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 15 \, {\left(a \sin\left(8 \, f x + 8 \, e\right) + 5 \, a \sin\left(6 \, f x + 6 \, e\right) + 5 \, a \sin\left(4 \, f x + 4 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(10 \, f x + 10 \, e\right) - 225 \, {\left(a \sin\left(6 \, f x + 6 \, e\right) + a \sin\left(4 \, f x + 4 \, e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) - 5 \, {\left(a \sin\left(10 \, f x + 10 \, e\right) + 15 \, a \sin\left(8 \, f x + 8 \, e\right) + 60 \, a \sin\left(6 \, f x + 6 \, e\right) + 60 \, a \sin\left(4 \, f x + 4 \, e\right) + 15 \, a \sin\left(2 \, f x + 2 \, e\right) - 20 \, a \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 48 \, a \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 20 \, a \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, {\left(5 \, a \sin\left(10 \, f x + 10 \, e\right) + 45 \, a \sin\left(8 \, f x + 8 \, e\right) + 150 \, a \sin\left(6 \, f x + 6 \, e\right) + 150 \, a \sin\left(4 \, f x + 4 \, e\right) + 45 \, a \sin\left(2 \, f x + 2 \, e\right) - 36 \, a \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 10 \, a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 6 \, {\left(17 \, a \sin\left(10 \, f x + 10 \, e\right) + 135 \, a \sin\left(8 \, f x + 8 \, e\right) + 420 \, a \sin\left(6 \, f x + 6 \, e\right) + 420 \, a \sin\left(4 \, f x + 4 \, e\right) + 135 \, a \sin\left(2 \, f x + 2 \, e\right) + 60 \, a \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 40 \, a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 50 \, {\left(a \sin\left(10 \, f x + 10 \, e\right) + 9 \, a \sin\left(8 \, f x + 8 \, e\right) + 30 \, a \sin\left(6 \, f x + 6 \, e\right) + 30 \, a \sin\left(4 \, f x + 4 \, e\right) + 9 \, a \sin\left(2 \, f x + 2 \, e\right) + 2 \, a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 5 \, {\left(a \sin\left(10 \, f x + 10 \, e\right) + 15 \, a \sin\left(8 \, f x + 8 \, e\right) + 60 \, a \sin\left(6 \, f x + 6 \, e\right) + 60 \, a \sin\left(4 \, f x + 4 \, e\right) + 15 \, a \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 15 \, {\left(a \cos\left(8 \, f x + 8 \, e\right) + 5 \, a \cos\left(6 \, f x + 6 \, e\right) + 5 \, a \cos\left(4 \, f x + 4 \, e\right) + a \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + 15 \, {\left(15 \, a \cos\left(6 \, f x + 6 \, e\right) + 15 \, a \cos\left(4 \, f x + 4 \, e\right) - a\right)} \sin\left(8 \, f x + 8 \, e\right) - 75 \, {\left(3 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \sin\left(6 \, f x + 6 \, e\right) - 75 \, {\left(3 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \sin\left(4 \, f x + 4 \, e\right) - 15 \, a \sin\left(2 \, f x + 2 \, e\right) + 5 \, {\left(a \cos\left(10 \, f x + 10 \, e\right) + 15 \, a \cos\left(8 \, f x + 8 \, e\right) + 60 \, a \cos\left(6 \, f x + 6 \, e\right) + 60 \, a \cos\left(4 \, f x + 4 \, e\right) + 15 \, a \cos\left(2 \, f x + 2 \, e\right) - 20 \, a \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 48 \, a \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 20 \, a \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + a\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 10 \, {\left(5 \, a \cos\left(10 \, f x + 10 \, e\right) + 45 \, a \cos\left(8 \, f x + 8 \, e\right) + 150 \, a \cos\left(6 \, f x + 6 \, e\right) + 150 \, a \cos\left(4 \, f x + 4 \, e\right) + 45 \, a \cos\left(2 \, f x + 2 \, e\right) - 36 \, a \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 10 \, a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 5 \, a\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 6 \, {\left(17 \, a \cos\left(10 \, f x + 10 \, e\right) + 135 \, a \cos\left(8 \, f x + 8 \, e\right) + 420 \, a \cos\left(6 \, f x + 6 \, e\right) + 420 \, a \cos\left(4 \, f x + 4 \, e\right) + 135 \, a \cos\left(2 \, f x + 2 \, e\right) + 60 \, a \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 40 \, a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 17 \, a\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 50 \, {\left(a \cos\left(10 \, f x + 10 \, e\right) + 9 \, a \cos\left(8 \, f x + 8 \, e\right) + 30 \, a \cos\left(6 \, f x + 6 \, e\right) + 30 \, a \cos\left(4 \, f x + 4 \, e\right) + 9 \, a \cos\left(2 \, f x + 2 \, e\right) + 2 \, a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + a\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 5 \, {\left(a \cos\left(10 \, f x + 10 \, e\right) + 15 \, a \cos\left(8 \, f x + 8 \, e\right) + 60 \, a \cos\left(6 \, f x + 6 \, e\right) + 60 \, a \cos\left(4 \, f x + 4 \, e\right) + 15 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{5 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right)^{2} + 2025 \, c^{6} \cos\left(8 \, f x + 8 \, e\right)^{2} + 44100 \, c^{6} \cos\left(6 \, f x + 6 \, e\right)^{2} + 44100 \, c^{6} \cos\left(4 \, f x + 4 \, e\right)^{2} + 2025 \, c^{6} \cos\left(2 \, f x + 2 \, e\right)^{2} + 100 \, c^{6} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 14400 \, c^{6} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 63504 \, c^{6} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 14400 \, c^{6} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 100 \, c^{6} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + c^{6} \sin\left(10 \, f x + 10 \, e\right)^{2} + 2025 \, c^{6} \sin\left(8 \, f x + 8 \, e\right)^{2} + 44100 \, c^{6} \sin\left(6 \, f x + 6 \, e\right)^{2} + 44100 \, c^{6} \sin\left(4 \, f x + 4 \, e\right)^{2} + 18900 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 2025 \, c^{6} \sin\left(2 \, f x + 2 \, e\right)^{2} + 100 \, c^{6} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 14400 \, c^{6} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 63504 \, c^{6} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 14400 \, c^{6} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 100 \, c^{6} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 90 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6} + 2 \, {\left(45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6}\right)} \cos\left(10 \, f x + 10 \, e\right) + 90 \, {\left(210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6}\right)} \cos\left(8 \, f x + 8 \, e\right) + 420 \, {\left(210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6}\right)} \cos\left(6 \, f x + 6 \, e\right) + 420 \, {\left(45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6}\right)} \cos\left(4 \, f x + 4 \, e\right) - 20 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) - 120 \, c^{6} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 252 \, c^{6} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 120 \, c^{6} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{6}\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) - 252 \, c^{6} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 120 \, c^{6} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{6}\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 504 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) - 120 \, c^{6} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{6}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) - 10 \, c^{6} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{6}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 20 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 30 \, {\left(3 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 14 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 14 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 3 \, c^{6} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + 1350 \, {\left(14 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 14 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 3 \, c^{6} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 6300 \, {\left(14 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 3 \, c^{6} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 20 \, {\left(c^{6} \sin\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \sin\left(2 \, f x + 2 \, e\right) - 120 \, c^{6} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 252 \, c^{6} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 120 \, c^{6} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(c^{6} \sin\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \sin\left(2 \, f x + 2 \, e\right) - 252 \, c^{6} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 120 \, c^{6} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 504 \, {\left(c^{6} \sin\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \sin\left(2 \, f x + 2 \, e\right) - 120 \, c^{6} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(c^{6} \sin\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \sin\left(2 \, f x + 2 \, e\right) - 10 \, c^{6} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 20 \, {\left(c^{6} \sin\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} f}"," ",0,"-2/5*(225*a*cos(6*f*x + 6*e)*sin(2*f*x + 2*e) + 225*a*cos(4*f*x + 4*e)*sin(2*f*x + 2*e) - 15*(a*sin(8*f*x + 8*e) + 5*a*sin(6*f*x + 6*e) + 5*a*sin(4*f*x + 4*e) + a*sin(2*f*x + 2*e))*cos(10*f*x + 10*e) - 225*(a*sin(6*f*x + 6*e) + a*sin(4*f*x + 4*e))*cos(8*f*x + 8*e) - 5*(a*sin(10*f*x + 10*e) + 15*a*sin(8*f*x + 8*e) + 60*a*sin(6*f*x + 6*e) + 60*a*sin(4*f*x + 4*e) + 15*a*sin(2*f*x + 2*e) - 20*a*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 48*a*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*(5*a*sin(10*f*x + 10*e) + 45*a*sin(8*f*x + 8*e) + 150*a*sin(6*f*x + 6*e) + 150*a*sin(4*f*x + 4*e) + 45*a*sin(2*f*x + 2*e) - 36*a*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 10*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*(17*a*sin(10*f*x + 10*e) + 135*a*sin(8*f*x + 8*e) + 420*a*sin(6*f*x + 6*e) + 420*a*sin(4*f*x + 4*e) + 135*a*sin(2*f*x + 2*e) + 60*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 40*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 50*(a*sin(10*f*x + 10*e) + 9*a*sin(8*f*x + 8*e) + 30*a*sin(6*f*x + 6*e) + 30*a*sin(4*f*x + 4*e) + 9*a*sin(2*f*x + 2*e) + 2*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*(a*sin(10*f*x + 10*e) + 15*a*sin(8*f*x + 8*e) + 60*a*sin(6*f*x + 6*e) + 60*a*sin(4*f*x + 4*e) + 15*a*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 15*(a*cos(8*f*x + 8*e) + 5*a*cos(6*f*x + 6*e) + 5*a*cos(4*f*x + 4*e) + a*cos(2*f*x + 2*e))*sin(10*f*x + 10*e) + 15*(15*a*cos(6*f*x + 6*e) + 15*a*cos(4*f*x + 4*e) - a)*sin(8*f*x + 8*e) - 75*(3*a*cos(2*f*x + 2*e) + a)*sin(6*f*x + 6*e) - 75*(3*a*cos(2*f*x + 2*e) + a)*sin(4*f*x + 4*e) - 15*a*sin(2*f*x + 2*e) + 5*(a*cos(10*f*x + 10*e) + 15*a*cos(8*f*x + 8*e) + 60*a*cos(6*f*x + 6*e) + 60*a*cos(4*f*x + 4*e) + 15*a*cos(2*f*x + 2*e) - 20*a*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 48*a*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a)*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 10*(5*a*cos(10*f*x + 10*e) + 45*a*cos(8*f*x + 8*e) + 150*a*cos(6*f*x + 6*e) + 150*a*cos(4*f*x + 4*e) + 45*a*cos(2*f*x + 2*e) - 36*a*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 10*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 5*a)*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 6*(17*a*cos(10*f*x + 10*e) + 135*a*cos(8*f*x + 8*e) + 420*a*cos(6*f*x + 6*e) + 420*a*cos(4*f*x + 4*e) + 135*a*cos(2*f*x + 2*e) + 60*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 40*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 17*a)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 50*(a*cos(10*f*x + 10*e) + 9*a*cos(8*f*x + 8*e) + 30*a*cos(6*f*x + 6*e) + 30*a*cos(4*f*x + 4*e) + 9*a*cos(2*f*x + 2*e) + 2*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 5*(a*cos(10*f*x + 10*e) + 15*a*cos(8*f*x + 8*e) + 60*a*cos(6*f*x + 6*e) + 60*a*cos(4*f*x + 4*e) + 15*a*cos(2*f*x + 2*e) + a)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((c^6*cos(10*f*x + 10*e)^2 + 2025*c^6*cos(8*f*x + 8*e)^2 + 44100*c^6*cos(6*f*x + 6*e)^2 + 44100*c^6*cos(4*f*x + 4*e)^2 + 2025*c^6*cos(2*f*x + 2*e)^2 + 100*c^6*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*c^6*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 63504*c^6*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*c^6*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 100*c^6*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c^6*sin(10*f*x + 10*e)^2 + 2025*c^6*sin(8*f*x + 8*e)^2 + 44100*c^6*sin(6*f*x + 6*e)^2 + 44100*c^6*sin(4*f*x + 4*e)^2 + 18900*c^6*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 2025*c^6*sin(2*f*x + 2*e)^2 + 100*c^6*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*c^6*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 63504*c^6*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*c^6*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 100*c^6*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 90*c^6*cos(2*f*x + 2*e) + c^6 + 2*(45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) + c^6)*cos(10*f*x + 10*e) + 90*(210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) + c^6)*cos(8*f*x + 8*e) + 420*(210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) + c^6)*cos(6*f*x + 6*e) + 420*(45*c^6*cos(2*f*x + 2*e) + c^6)*cos(4*f*x + 4*e) - 20*(c^6*cos(10*f*x + 10*e) + 45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) - 120*c^6*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 252*c^6*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*c^6*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^6)*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 240*(c^6*cos(10*f*x + 10*e) + 45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) - 252*c^6*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*c^6*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^6)*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 504*(c^6*cos(10*f*x + 10*e) + 45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) - 120*c^6*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^6)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 240*(c^6*cos(10*f*x + 10*e) + 45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) - 10*c^6*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^6)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*(c^6*cos(10*f*x + 10*e) + 45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) + c^6)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 30*(3*c^6*sin(8*f*x + 8*e) + 14*c^6*sin(6*f*x + 6*e) + 14*c^6*sin(4*f*x + 4*e) + 3*c^6*sin(2*f*x + 2*e))*sin(10*f*x + 10*e) + 1350*(14*c^6*sin(6*f*x + 6*e) + 14*c^6*sin(4*f*x + 4*e) + 3*c^6*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 6300*(14*c^6*sin(4*f*x + 4*e) + 3*c^6*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 20*(c^6*sin(10*f*x + 10*e) + 45*c^6*sin(8*f*x + 8*e) + 210*c^6*sin(6*f*x + 6*e) + 210*c^6*sin(4*f*x + 4*e) + 45*c^6*sin(2*f*x + 2*e) - 120*c^6*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 252*c^6*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*c^6*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 240*(c^6*sin(10*f*x + 10*e) + 45*c^6*sin(8*f*x + 8*e) + 210*c^6*sin(6*f*x + 6*e) + 210*c^6*sin(4*f*x + 4*e) + 45*c^6*sin(2*f*x + 2*e) - 252*c^6*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*c^6*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 504*(c^6*sin(10*f*x + 10*e) + 45*c^6*sin(8*f*x + 8*e) + 210*c^6*sin(6*f*x + 6*e) + 210*c^6*sin(4*f*x + 4*e) + 45*c^6*sin(2*f*x + 2*e) - 120*c^6*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 240*(c^6*sin(10*f*x + 10*e) + 45*c^6*sin(8*f*x + 8*e) + 210*c^6*sin(6*f*x + 6*e) + 210*c^6*sin(4*f*x + 4*e) + 45*c^6*sin(2*f*x + 2*e) - 10*c^6*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*(c^6*sin(10*f*x + 10*e) + 45*c^6*sin(8*f*x + 8*e) + 210*c^6*sin(6*f*x + 6*e) + 210*c^6*sin(4*f*x + 4*e) + 45*c^6*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
123,1,2454,0,0.606411," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(210 \, a^{2} c^{3} \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 90 \, a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 15 \, a^{2} c^{3} \sin\left(f x + e\right) - {\left(15 \, a^{2} c^{3} \sin\left(11 \, f x + 11 \, e\right) - 15 \, a^{2} c^{3} \sin\left(10 \, f x + 10 \, e\right) + 35 \, a^{2} c^{3} \sin\left(9 \, f x + 9 \, e\right) + 78 \, a^{2} c^{3} \sin\left(7 \, f x + 7 \, e\right) - 50 \, a^{2} c^{3} \sin\left(6 \, f x + 6 \, e\right) + 78 \, a^{2} c^{3} \sin\left(5 \, f x + 5 \, e\right) + 35 \, a^{2} c^{3} \sin\left(3 \, f x + 3 \, e\right) - 15 \, a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 15 \, a^{2} c^{3} \sin\left(f x + e\right)\right)} \cos\left(12 \, f x + 12 \, e\right) + 15 \, {\left(6 \, a^{2} c^{3} \sin\left(10 \, f x + 10 \, e\right) + 15 \, a^{2} c^{3} \sin\left(8 \, f x + 8 \, e\right) + 20 \, a^{2} c^{3} \sin\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(11 \, f x + 11 \, e\right) - 3 \, {\left(70 \, a^{2} c^{3} \sin\left(9 \, f x + 9 \, e\right) + 75 \, a^{2} c^{3} \sin\left(8 \, f x + 8 \, e\right) + 156 \, a^{2} c^{3} \sin\left(7 \, f x + 7 \, e\right) + 156 \, a^{2} c^{3} \sin\left(5 \, f x + 5 \, e\right) + 75 \, a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 70 \, a^{2} c^{3} \sin\left(3 \, f x + 3 \, e\right) + 30 \, a^{2} c^{3} \sin\left(f x + e\right)\right)} \cos\left(10 \, f x + 10 \, e\right) + 35 \, {\left(15 \, a^{2} c^{3} \sin\left(8 \, f x + 8 \, e\right) + 20 \, a^{2} c^{3} \sin\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(9 \, f x + 9 \, e\right) - 15 \, {\left(78 \, a^{2} c^{3} \sin\left(7 \, f x + 7 \, e\right) - 50 \, a^{2} c^{3} \sin\left(6 \, f x + 6 \, e\right) + 78 \, a^{2} c^{3} \sin\left(5 \, f x + 5 \, e\right) + 35 \, a^{2} c^{3} \sin\left(3 \, f x + 3 \, e\right) - 15 \, a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 15 \, a^{2} c^{3} \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + 78 \, {\left(20 \, a^{2} c^{3} \sin\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) - 10 \, {\left(156 \, a^{2} c^{3} \sin\left(5 \, f x + 5 \, e\right) + 75 \, a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 70 \, a^{2} c^{3} \sin\left(3 \, f x + 3 \, e\right) + 30 \, a^{2} c^{3} \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 234 \, {\left(5 \, a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - 75 \, {\left(7 \, a^{2} c^{3} \sin\left(3 \, f x + 3 \, e\right) - 3 \, a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} c^{3} \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(15 \, a^{2} c^{3} \cos\left(11 \, f x + 11 \, e\right) - 15 \, a^{2} c^{3} \cos\left(10 \, f x + 10 \, e\right) + 35 \, a^{2} c^{3} \cos\left(9 \, f x + 9 \, e\right) + 78 \, a^{2} c^{3} \cos\left(7 \, f x + 7 \, e\right) - 50 \, a^{2} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 78 \, a^{2} c^{3} \cos\left(5 \, f x + 5 \, e\right) + 35 \, a^{2} c^{3} \cos\left(3 \, f x + 3 \, e\right) - 15 \, a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 15 \, a^{2} c^{3} \cos\left(f x + e\right)\right)} \sin\left(12 \, f x + 12 \, e\right) - 15 \, {\left(6 \, a^{2} c^{3} \cos\left(10 \, f x + 10 \, e\right) + 15 \, a^{2} c^{3} \cos\left(8 \, f x + 8 \, e\right) + 20 \, a^{2} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{3}\right)} \sin\left(11 \, f x + 11 \, e\right) + 3 \, {\left(70 \, a^{2} c^{3} \cos\left(9 \, f x + 9 \, e\right) + 75 \, a^{2} c^{3} \cos\left(8 \, f x + 8 \, e\right) + 156 \, a^{2} c^{3} \cos\left(7 \, f x + 7 \, e\right) + 156 \, a^{2} c^{3} \cos\left(5 \, f x + 5 \, e\right) + 75 \, a^{2} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 70 \, a^{2} c^{3} \cos\left(3 \, f x + 3 \, e\right) + 30 \, a^{2} c^{3} \cos\left(f x + e\right) + 5 \, a^{2} c^{3}\right)} \sin\left(10 \, f x + 10 \, e\right) - 35 \, {\left(15 \, a^{2} c^{3} \cos\left(8 \, f x + 8 \, e\right) + 20 \, a^{2} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{3}\right)} \sin\left(9 \, f x + 9 \, e\right) + 15 \, {\left(78 \, a^{2} c^{3} \cos\left(7 \, f x + 7 \, e\right) - 50 \, a^{2} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 78 \, a^{2} c^{3} \cos\left(5 \, f x + 5 \, e\right) + 35 \, a^{2} c^{3} \cos\left(3 \, f x + 3 \, e\right) - 15 \, a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 15 \, a^{2} c^{3} \cos\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 78 \, {\left(20 \, a^{2} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{3}\right)} \sin\left(7 \, f x + 7 \, e\right) + 10 \, {\left(156 \, a^{2} c^{3} \cos\left(5 \, f x + 5 \, e\right) + 75 \, a^{2} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 70 \, a^{2} c^{3} \cos\left(3 \, f x + 3 \, e\right) + 30 \, a^{2} c^{3} \cos\left(f x + e\right) + 5 \, a^{2} c^{3}\right)} \sin\left(6 \, f x + 6 \, e\right) - 78 \, {\left(15 \, a^{2} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{3}\right)} \sin\left(5 \, f x + 5 \, e\right) + 75 \, {\left(7 \, a^{2} c^{3} \cos\left(3 \, f x + 3 \, e\right) - 3 \, a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} c^{3} \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 35 \, {\left(6 \, a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{3}\right)} \sin\left(3 \, f x + 3 \, e\right) + 15 \, {\left(6 \, a^{2} c^{3} \cos\left(f x + e\right) + a^{2} c^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a} \sqrt{c}}{15 \, {\left(2 \, {\left(6 \, \cos\left(10 \, f x + 10 \, e\right) + 15 \, \cos\left(8 \, f x + 8 \, e\right) + 20 \, \cos\left(6 \, f x + 6 \, e\right) + 15 \, \cos\left(4 \, f x + 4 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(12 \, f x + 12 \, e\right) + \cos\left(12 \, f x + 12 \, e\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, f x + 8 \, e\right) + 20 \, \cos\left(6 \, f x + 6 \, e\right) + 15 \, \cos\left(4 \, f x + 4 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(10 \, f x + 10 \, e\right) + 36 \, \cos\left(10 \, f x + 10 \, e\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, f x + 6 \, e\right) + 15 \, \cos\left(4 \, f x + 4 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(8 \, f x + 8 \, e\right) + 225 \, \cos\left(8 \, f x + 8 \, e\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, f x + 4 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + 400 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 225 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 36 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, f x + 10 \, e\right) + 15 \, \sin\left(8 \, f x + 8 \, e\right) + 20 \, \sin\left(6 \, f x + 6 \, e\right) + 15 \, \sin\left(4 \, f x + 4 \, e\right) + 6 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(12 \, f x + 12 \, e\right) + \sin\left(12 \, f x + 12 \, e\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, f x + 8 \, e\right) + 20 \, \sin\left(6 \, f x + 6 \, e\right) + 15 \, \sin\left(4 \, f x + 4 \, e\right) + 6 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + 36 \, \sin\left(10 \, f x + 10 \, e\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, f x + 6 \, e\right) + 15 \, \sin\left(4 \, f x + 4 \, e\right) + 6 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 225 \, \sin\left(8 \, f x + 8 \, e\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 400 \, \sin\left(6 \, f x + 6 \, e\right)^{2} + 225 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 180 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 36 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 12 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"2/15*(210*a^2*c^3*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 90*a^2*c^3*cos(2*f*x + 2*e)*sin(f*x + e) - 15*a^2*c^3*sin(f*x + e) - (15*a^2*c^3*sin(11*f*x + 11*e) - 15*a^2*c^3*sin(10*f*x + 10*e) + 35*a^2*c^3*sin(9*f*x + 9*e) + 78*a^2*c^3*sin(7*f*x + 7*e) - 50*a^2*c^3*sin(6*f*x + 6*e) + 78*a^2*c^3*sin(5*f*x + 5*e) + 35*a^2*c^3*sin(3*f*x + 3*e) - 15*a^2*c^3*sin(2*f*x + 2*e) + 15*a^2*c^3*sin(f*x + e))*cos(12*f*x + 12*e) + 15*(6*a^2*c^3*sin(10*f*x + 10*e) + 15*a^2*c^3*sin(8*f*x + 8*e) + 20*a^2*c^3*sin(6*f*x + 6*e) + 15*a^2*c^3*sin(4*f*x + 4*e) + 6*a^2*c^3*sin(2*f*x + 2*e))*cos(11*f*x + 11*e) - 3*(70*a^2*c^3*sin(9*f*x + 9*e) + 75*a^2*c^3*sin(8*f*x + 8*e) + 156*a^2*c^3*sin(7*f*x + 7*e) + 156*a^2*c^3*sin(5*f*x + 5*e) + 75*a^2*c^3*sin(4*f*x + 4*e) + 70*a^2*c^3*sin(3*f*x + 3*e) + 30*a^2*c^3*sin(f*x + e))*cos(10*f*x + 10*e) + 35*(15*a^2*c^3*sin(8*f*x + 8*e) + 20*a^2*c^3*sin(6*f*x + 6*e) + 15*a^2*c^3*sin(4*f*x + 4*e) + 6*a^2*c^3*sin(2*f*x + 2*e))*cos(9*f*x + 9*e) - 15*(78*a^2*c^3*sin(7*f*x + 7*e) - 50*a^2*c^3*sin(6*f*x + 6*e) + 78*a^2*c^3*sin(5*f*x + 5*e) + 35*a^2*c^3*sin(3*f*x + 3*e) - 15*a^2*c^3*sin(2*f*x + 2*e) + 15*a^2*c^3*sin(f*x + e))*cos(8*f*x + 8*e) + 78*(20*a^2*c^3*sin(6*f*x + 6*e) + 15*a^2*c^3*sin(4*f*x + 4*e) + 6*a^2*c^3*sin(2*f*x + 2*e))*cos(7*f*x + 7*e) - 10*(156*a^2*c^3*sin(5*f*x + 5*e) + 75*a^2*c^3*sin(4*f*x + 4*e) + 70*a^2*c^3*sin(3*f*x + 3*e) + 30*a^2*c^3*sin(f*x + e))*cos(6*f*x + 6*e) + 234*(5*a^2*c^3*sin(4*f*x + 4*e) + 2*a^2*c^3*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - 75*(7*a^2*c^3*sin(3*f*x + 3*e) - 3*a^2*c^3*sin(2*f*x + 2*e) + 3*a^2*c^3*sin(f*x + e))*cos(4*f*x + 4*e) + (15*a^2*c^3*cos(11*f*x + 11*e) - 15*a^2*c^3*cos(10*f*x + 10*e) + 35*a^2*c^3*cos(9*f*x + 9*e) + 78*a^2*c^3*cos(7*f*x + 7*e) - 50*a^2*c^3*cos(6*f*x + 6*e) + 78*a^2*c^3*cos(5*f*x + 5*e) + 35*a^2*c^3*cos(3*f*x + 3*e) - 15*a^2*c^3*cos(2*f*x + 2*e) + 15*a^2*c^3*cos(f*x + e))*sin(12*f*x + 12*e) - 15*(6*a^2*c^3*cos(10*f*x + 10*e) + 15*a^2*c^3*cos(8*f*x + 8*e) + 20*a^2*c^3*cos(6*f*x + 6*e) + 15*a^2*c^3*cos(4*f*x + 4*e) + 6*a^2*c^3*cos(2*f*x + 2*e) + a^2*c^3)*sin(11*f*x + 11*e) + 3*(70*a^2*c^3*cos(9*f*x + 9*e) + 75*a^2*c^3*cos(8*f*x + 8*e) + 156*a^2*c^3*cos(7*f*x + 7*e) + 156*a^2*c^3*cos(5*f*x + 5*e) + 75*a^2*c^3*cos(4*f*x + 4*e) + 70*a^2*c^3*cos(3*f*x + 3*e) + 30*a^2*c^3*cos(f*x + e) + 5*a^2*c^3)*sin(10*f*x + 10*e) - 35*(15*a^2*c^3*cos(8*f*x + 8*e) + 20*a^2*c^3*cos(6*f*x + 6*e) + 15*a^2*c^3*cos(4*f*x + 4*e) + 6*a^2*c^3*cos(2*f*x + 2*e) + a^2*c^3)*sin(9*f*x + 9*e) + 15*(78*a^2*c^3*cos(7*f*x + 7*e) - 50*a^2*c^3*cos(6*f*x + 6*e) + 78*a^2*c^3*cos(5*f*x + 5*e) + 35*a^2*c^3*cos(3*f*x + 3*e) - 15*a^2*c^3*cos(2*f*x + 2*e) + 15*a^2*c^3*cos(f*x + e))*sin(8*f*x + 8*e) - 78*(20*a^2*c^3*cos(6*f*x + 6*e) + 15*a^2*c^3*cos(4*f*x + 4*e) + 6*a^2*c^3*cos(2*f*x + 2*e) + a^2*c^3)*sin(7*f*x + 7*e) + 10*(156*a^2*c^3*cos(5*f*x + 5*e) + 75*a^2*c^3*cos(4*f*x + 4*e) + 70*a^2*c^3*cos(3*f*x + 3*e) + 30*a^2*c^3*cos(f*x + e) + 5*a^2*c^3)*sin(6*f*x + 6*e) - 78*(15*a^2*c^3*cos(4*f*x + 4*e) + 6*a^2*c^3*cos(2*f*x + 2*e) + a^2*c^3)*sin(5*f*x + 5*e) + 75*(7*a^2*c^3*cos(3*f*x + 3*e) - 3*a^2*c^3*cos(2*f*x + 2*e) + 3*a^2*c^3*cos(f*x + e))*sin(4*f*x + 4*e) - 35*(6*a^2*c^3*cos(2*f*x + 2*e) + a^2*c^3)*sin(3*f*x + 3*e) + 15*(6*a^2*c^3*cos(f*x + e) + a^2*c^3)*sin(2*f*x + 2*e))*sqrt(a)*sqrt(c)/((2*(6*cos(10*f*x + 10*e) + 15*cos(8*f*x + 8*e) + 20*cos(6*f*x + 6*e) + 15*cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) + 1)*cos(12*f*x + 12*e) + cos(12*f*x + 12*e)^2 + 12*(15*cos(8*f*x + 8*e) + 20*cos(6*f*x + 6*e) + 15*cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) + 1)*cos(10*f*x + 10*e) + 36*cos(10*f*x + 10*e)^2 + 30*(20*cos(6*f*x + 6*e) + 15*cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) + 1)*cos(8*f*x + 8*e) + 225*cos(8*f*x + 8*e)^2 + 40*(15*cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + 400*cos(6*f*x + 6*e)^2 + 30*(6*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 225*cos(4*f*x + 4*e)^2 + 36*cos(2*f*x + 2*e)^2 + 2*(6*sin(10*f*x + 10*e) + 15*sin(8*f*x + 8*e) + 20*sin(6*f*x + 6*e) + 15*sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e))*sin(12*f*x + 12*e) + sin(12*f*x + 12*e)^2 + 12*(15*sin(8*f*x + 8*e) + 20*sin(6*f*x + 6*e) + 15*sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e))*sin(10*f*x + 10*e) + 36*sin(10*f*x + 10*e)^2 + 30*(20*sin(6*f*x + 6*e) + 15*sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 225*sin(8*f*x + 8*e)^2 + 120*(5*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 400*sin(6*f*x + 6*e)^2 + 225*sin(4*f*x + 4*e)^2 + 180*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*sin(2*f*x + 2*e)^2 + 12*cos(2*f*x + 2*e) + 1)*f)","B",0
124,1,1526,0,0.585982," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(100 \, a^{2} c^{2} \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 75 \, a^{2} c^{2} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 75 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 15 \, a^{2} c^{2} \sin\left(f x + e\right) - {\left(15 \, a^{2} c^{2} \sin\left(9 \, f x + 9 \, e\right) + 20 \, a^{2} c^{2} \sin\left(7 \, f x + 7 \, e\right) + 58 \, a^{2} c^{2} \sin\left(5 \, f x + 5 \, e\right) + 20 \, a^{2} c^{2} \sin\left(3 \, f x + 3 \, e\right) + 15 \, a^{2} c^{2} \sin\left(f x + e\right)\right)} \cos\left(10 \, f x + 10 \, e\right) + 75 \, {\left(a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right) + 2 \, a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 2 \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(9 \, f x + 9 \, e\right) - 5 \, {\left(20 \, a^{2} c^{2} \sin\left(7 \, f x + 7 \, e\right) + 58 \, a^{2} c^{2} \sin\left(5 \, f x + 5 \, e\right) + 20 \, a^{2} c^{2} \sin\left(3 \, f x + 3 \, e\right) + 15 \, a^{2} c^{2} \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + 100 \, {\left(2 \, a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 2 \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) - 10 \, {\left(58 \, a^{2} c^{2} \sin\left(5 \, f x + 5 \, e\right) + 20 \, a^{2} c^{2} \sin\left(3 \, f x + 3 \, e\right) + 15 \, a^{2} c^{2} \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 290 \, {\left(2 \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - 50 \, {\left(4 \, a^{2} c^{2} \sin\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} c^{2} \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(15 \, a^{2} c^{2} \cos\left(9 \, f x + 9 \, e\right) + 20 \, a^{2} c^{2} \cos\left(7 \, f x + 7 \, e\right) + 58 \, a^{2} c^{2} \cos\left(5 \, f x + 5 \, e\right) + 20 \, a^{2} c^{2} \cos\left(3 \, f x + 3 \, e\right) + 15 \, a^{2} c^{2} \cos\left(f x + e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) - 15 \, {\left(5 \, a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right) + 10 \, a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 10 \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 5 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{2}\right)} \sin\left(9 \, f x + 9 \, e\right) + 5 \, {\left(20 \, a^{2} c^{2} \cos\left(7 \, f x + 7 \, e\right) + 58 \, a^{2} c^{2} \cos\left(5 \, f x + 5 \, e\right) + 20 \, a^{2} c^{2} \cos\left(3 \, f x + 3 \, e\right) + 15 \, a^{2} c^{2} \cos\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 20 \, {\left(10 \, a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 10 \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 5 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{2}\right)} \sin\left(7 \, f x + 7 \, e\right) + 10 \, {\left(58 \, a^{2} c^{2} \cos\left(5 \, f x + 5 \, e\right) + 20 \, a^{2} c^{2} \cos\left(3 \, f x + 3 \, e\right) + 15 \, a^{2} c^{2} \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 58 \, {\left(10 \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 5 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{2}\right)} \sin\left(5 \, f x + 5 \, e\right) + 50 \, {\left(4 \, a^{2} c^{2} \cos\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} c^{2} \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 20 \, {\left(5 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{2}\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} \sqrt{a} \sqrt{c}}{15 \, {\left(2 \, {\left(5 \, \cos\left(8 \, f x + 8 \, e\right) + 10 \, \cos\left(6 \, f x + 6 \, e\right) + 10 \, \cos\left(4 \, f x + 4 \, e\right) + 5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(10 \, f x + 10 \, e\right) + \cos\left(10 \, f x + 10 \, e\right)^{2} + 10 \, {\left(10 \, \cos\left(6 \, f x + 6 \, e\right) + 10 \, \cos\left(4 \, f x + 4 \, e\right) + 5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(8 \, f x + 8 \, e\right) + 25 \, \cos\left(8 \, f x + 8 \, e\right)^{2} + 20 \, {\left(10 \, \cos\left(4 \, f x + 4 \, e\right) + 5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + 100 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 20 \, {\left(5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 100 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 25 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 10 \, {\left(\sin\left(8 \, f x + 8 \, e\right) + 2 \, \sin\left(6 \, f x + 6 \, e\right) + 2 \, \sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + \sin\left(10 \, f x + 10 \, e\right)^{2} + 50 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 2 \, \sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 25 \, \sin\left(8 \, f x + 8 \, e\right)^{2} + 100 \, {\left(2 \, \sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 100 \, \sin\left(6 \, f x + 6 \, e\right)^{2} + 100 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 100 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 25 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 10 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"2/15*(100*a^2*c^2*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) + 75*a^2*c^2*cos(f*x + e)*sin(2*f*x + 2*e) - 75*a^2*c^2*cos(2*f*x + 2*e)*sin(f*x + e) - 15*a^2*c^2*sin(f*x + e) - (15*a^2*c^2*sin(9*f*x + 9*e) + 20*a^2*c^2*sin(7*f*x + 7*e) + 58*a^2*c^2*sin(5*f*x + 5*e) + 20*a^2*c^2*sin(3*f*x + 3*e) + 15*a^2*c^2*sin(f*x + e))*cos(10*f*x + 10*e) + 75*(a^2*c^2*sin(8*f*x + 8*e) + 2*a^2*c^2*sin(6*f*x + 6*e) + 2*a^2*c^2*sin(4*f*x + 4*e) + a^2*c^2*sin(2*f*x + 2*e))*cos(9*f*x + 9*e) - 5*(20*a^2*c^2*sin(7*f*x + 7*e) + 58*a^2*c^2*sin(5*f*x + 5*e) + 20*a^2*c^2*sin(3*f*x + 3*e) + 15*a^2*c^2*sin(f*x + e))*cos(8*f*x + 8*e) + 100*(2*a^2*c^2*sin(6*f*x + 6*e) + 2*a^2*c^2*sin(4*f*x + 4*e) + a^2*c^2*sin(2*f*x + 2*e))*cos(7*f*x + 7*e) - 10*(58*a^2*c^2*sin(5*f*x + 5*e) + 20*a^2*c^2*sin(3*f*x + 3*e) + 15*a^2*c^2*sin(f*x + e))*cos(6*f*x + 6*e) + 290*(2*a^2*c^2*sin(4*f*x + 4*e) + a^2*c^2*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - 50*(4*a^2*c^2*sin(3*f*x + 3*e) + 3*a^2*c^2*sin(f*x + e))*cos(4*f*x + 4*e) + (15*a^2*c^2*cos(9*f*x + 9*e) + 20*a^2*c^2*cos(7*f*x + 7*e) + 58*a^2*c^2*cos(5*f*x + 5*e) + 20*a^2*c^2*cos(3*f*x + 3*e) + 15*a^2*c^2*cos(f*x + e))*sin(10*f*x + 10*e) - 15*(5*a^2*c^2*cos(8*f*x + 8*e) + 10*a^2*c^2*cos(6*f*x + 6*e) + 10*a^2*c^2*cos(4*f*x + 4*e) + 5*a^2*c^2*cos(2*f*x + 2*e) + a^2*c^2)*sin(9*f*x + 9*e) + 5*(20*a^2*c^2*cos(7*f*x + 7*e) + 58*a^2*c^2*cos(5*f*x + 5*e) + 20*a^2*c^2*cos(3*f*x + 3*e) + 15*a^2*c^2*cos(f*x + e))*sin(8*f*x + 8*e) - 20*(10*a^2*c^2*cos(6*f*x + 6*e) + 10*a^2*c^2*cos(4*f*x + 4*e) + 5*a^2*c^2*cos(2*f*x + 2*e) + a^2*c^2)*sin(7*f*x + 7*e) + 10*(58*a^2*c^2*cos(5*f*x + 5*e) + 20*a^2*c^2*cos(3*f*x + 3*e) + 15*a^2*c^2*cos(f*x + e))*sin(6*f*x + 6*e) - 58*(10*a^2*c^2*cos(4*f*x + 4*e) + 5*a^2*c^2*cos(2*f*x + 2*e) + a^2*c^2)*sin(5*f*x + 5*e) + 50*(4*a^2*c^2*cos(3*f*x + 3*e) + 3*a^2*c^2*cos(f*x + e))*sin(4*f*x + 4*e) - 20*(5*a^2*c^2*cos(2*f*x + 2*e) + a^2*c^2)*sin(3*f*x + 3*e))*sqrt(a)*sqrt(c)/((2*(5*cos(8*f*x + 8*e) + 10*cos(6*f*x + 6*e) + 10*cos(4*f*x + 4*e) + 5*cos(2*f*x + 2*e) + 1)*cos(10*f*x + 10*e) + cos(10*f*x + 10*e)^2 + 10*(10*cos(6*f*x + 6*e) + 10*cos(4*f*x + 4*e) + 5*cos(2*f*x + 2*e) + 1)*cos(8*f*x + 8*e) + 25*cos(8*f*x + 8*e)^2 + 20*(10*cos(4*f*x + 4*e) + 5*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + 100*cos(6*f*x + 6*e)^2 + 20*(5*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 100*cos(4*f*x + 4*e)^2 + 25*cos(2*f*x + 2*e)^2 + 10*(sin(8*f*x + 8*e) + 2*sin(6*f*x + 6*e) + 2*sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*sin(10*f*x + 10*e) + sin(10*f*x + 10*e)^2 + 50*(2*sin(6*f*x + 6*e) + 2*sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 25*sin(8*f*x + 8*e)^2 + 100*(2*sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 100*sin(6*f*x + 6*e)^2 + 100*sin(4*f*x + 4*e)^2 + 100*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 25*sin(2*f*x + 2*e)^2 + 10*cos(2*f*x + 2*e) + 1)*f)","B",0
125,1,1106,0,0.559903," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(20 \, a^{2} c \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 12 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 3 \, a^{2} c \sin\left(f x + e\right) - {\left(3 \, a^{2} c \sin\left(7 \, f x + 7 \, e\right) + 3 \, a^{2} c \sin\left(6 \, f x + 6 \, e\right) + 5 \, a^{2} c \sin\left(5 \, f x + 5 \, e\right) + 5 \, a^{2} c \sin\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} c \sin\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} c \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + 6 \, {\left(2 \, a^{2} c \sin\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} c \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) - 2 \, {\left(10 \, a^{2} c \sin\left(5 \, f x + 5 \, e\right) - 9 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 10 \, a^{2} c \sin\left(3 \, f x + 3 \, e\right) + 6 \, a^{2} c \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 10 \, {\left(3 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} c \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - 6 \, {\left(5 \, a^{2} c \sin\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} c \sin\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} c \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(3 \, a^{2} c \cos\left(7 \, f x + 7 \, e\right) + 3 \, a^{2} c \cos\left(6 \, f x + 6 \, e\right) + 5 \, a^{2} c \cos\left(5 \, f x + 5 \, e\right) + 5 \, a^{2} c \cos\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} c \cos\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 3 \, {\left(4 \, a^{2} c \cos\left(6 \, f x + 6 \, e\right) + 6 \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 4 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} c\right)} \sin\left(7 \, f x + 7 \, e\right) + {\left(20 \, a^{2} c \cos\left(5 \, f x + 5 \, e\right) - 18 \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 20 \, a^{2} c \cos\left(3 \, f x + 3 \, e\right) + 12 \, a^{2} c \cos\left(f x + e\right) - 3 \, a^{2} c\right)} \sin\left(6 \, f x + 6 \, e\right) - 5 \, {\left(6 \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 4 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} c\right)} \sin\left(5 \, f x + 5 \, e\right) + 6 \, {\left(5 \, a^{2} c \cos\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} c \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 5 \, {\left(4 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} c\right)} \sin\left(3 \, f x + 3 \, e\right) + 3 \, {\left(4 \, a^{2} c \cos\left(f x + e\right) - a^{2} c\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a} \sqrt{c}}{3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) + 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(8 \, f x + 8 \, e\right) + \cos\left(8 \, f x + 8 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + 16 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 36 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 16 \, \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"2/3*(20*a^2*c*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 12*a^2*c*cos(2*f*x + 2*e)*sin(f*x + e) - 3*a^2*c*sin(f*x + e) - (3*a^2*c*sin(7*f*x + 7*e) + 3*a^2*c*sin(6*f*x + 6*e) + 5*a^2*c*sin(5*f*x + 5*e) + 5*a^2*c*sin(3*f*x + 3*e) + 3*a^2*c*sin(2*f*x + 2*e) + 3*a^2*c*sin(f*x + e))*cos(8*f*x + 8*e) + 6*(2*a^2*c*sin(6*f*x + 6*e) + 3*a^2*c*sin(4*f*x + 4*e) + 2*a^2*c*sin(2*f*x + 2*e))*cos(7*f*x + 7*e) - 2*(10*a^2*c*sin(5*f*x + 5*e) - 9*a^2*c*sin(4*f*x + 4*e) + 10*a^2*c*sin(3*f*x + 3*e) + 6*a^2*c*sin(f*x + e))*cos(6*f*x + 6*e) + 10*(3*a^2*c*sin(4*f*x + 4*e) + 2*a^2*c*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - 6*(5*a^2*c*sin(3*f*x + 3*e) + 3*a^2*c*sin(2*f*x + 2*e) + 3*a^2*c*sin(f*x + e))*cos(4*f*x + 4*e) + (3*a^2*c*cos(7*f*x + 7*e) + 3*a^2*c*cos(6*f*x + 6*e) + 5*a^2*c*cos(5*f*x + 5*e) + 5*a^2*c*cos(3*f*x + 3*e) + 3*a^2*c*cos(2*f*x + 2*e) + 3*a^2*c*cos(f*x + e))*sin(8*f*x + 8*e) - 3*(4*a^2*c*cos(6*f*x + 6*e) + 6*a^2*c*cos(4*f*x + 4*e) + 4*a^2*c*cos(2*f*x + 2*e) + a^2*c)*sin(7*f*x + 7*e) + (20*a^2*c*cos(5*f*x + 5*e) - 18*a^2*c*cos(4*f*x + 4*e) + 20*a^2*c*cos(3*f*x + 3*e) + 12*a^2*c*cos(f*x + e) - 3*a^2*c)*sin(6*f*x + 6*e) - 5*(6*a^2*c*cos(4*f*x + 4*e) + 4*a^2*c*cos(2*f*x + 2*e) + a^2*c)*sin(5*f*x + 5*e) + 6*(5*a^2*c*cos(3*f*x + 3*e) + 3*a^2*c*cos(2*f*x + 2*e) + 3*a^2*c*cos(f*x + e))*sin(4*f*x + 4*e) - 5*(4*a^2*c*cos(2*f*x + 2*e) + a^2*c)*sin(3*f*x + 3*e) + 3*(4*a^2*c*cos(f*x + e) - a^2*c)*sin(2*f*x + 2*e))*sqrt(a)*sqrt(c)/((2*(4*cos(6*f*x + 6*e) + 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(8*f*x + 8*e) + cos(8*f*x + 8*e)^2 + 8*(6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + 16*cos(6*f*x + 6*e)^2 + 12*(4*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 36*cos(4*f*x + 4*e)^2 + 16*cos(2*f*x + 2*e)^2 + 4*(2*sin(6*f*x + 6*e) + 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + sin(8*f*x + 8*e)^2 + 16*(3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 16*sin(6*f*x + 6*e)^2 + 36*sin(4*f*x + 4*e)^2 + 48*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 16*sin(2*f*x + 2*e)^2 + 8*cos(2*f*x + 2*e) + 1)*f)","B",0
126,1,58,0,0.457201," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{8 \, \sqrt{-a} a^{2} \sqrt{c}}{3 \, f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{3} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{3}}"," ",0,"8/3*sqrt(-a)*a^2*sqrt(c)/(f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^3*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^3)","A",0
127,1,737,0,0.592016," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{2} \cos\left(2 \, f x + 2 \, e\right) \sin\left(4 \, f x + 4 \, e\right) - a^{2} \cos\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - a^{2} \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} + 2 \, {\left(2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} + 2 \, {\left(2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)\right)} \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 1\right) + 3 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 3 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 3 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 3 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(c \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c \cos\left(2 \, f x + 2 \, e\right)^{2} + c \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, c \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(2 \, c \cos\left(2 \, f x + 2 \, e\right) + c\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, c \cos\left(2 \, f x + 2 \, e\right) + c\right)} f}"," ",0,"-2*(a^2*cos(2*f*x + 2*e)*sin(4*f*x + 4*e) - a^2*cos(4*f*x + 4*e)*sin(2*f*x + 2*e) - a^2*sin(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + 4*a^2*cos(2*f*x + 2*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*a^2*sin(2*f*x + 2*e)^2 + 4*a^2*cos(2*f*x + 2*e) + a^2 + 2*(2*a^2*cos(2*f*x + 2*e) + a^2)*cos(4*f*x + 4*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*(a^2*cos(4*f*x + 4*e)^2 + 4*a^2*cos(2*f*x + 2*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*a^2*sin(2*f*x + 2*e)^2 + 4*a^2*cos(2*f*x + 2*e) + a^2 + 2*(2*a^2*cos(2*f*x + 2*e) + a^2)*cos(4*f*x + 4*e))*arctan2(sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1) + 3*(a^2*sin(4*f*x + 4*e) + 2*a^2*sin(2*f*x + 2*e))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*(a^2*sin(4*f*x + 4*e) + 2*a^2*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3*(a^2*cos(4*f*x + 4*e) + 2*a^2*cos(2*f*x + 2*e) + a^2)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3*(a^2*cos(4*f*x + 4*e) + 2*a^2*cos(2*f*x + 2*e) + a^2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((c*cos(4*f*x + 4*e)^2 + 4*c*cos(2*f*x + 2*e)^2 + c*sin(4*f*x + 4*e)^2 + 4*c*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*c*sin(2*f*x + 2*e)^2 + 2*(2*c*cos(2*f*x + 2*e) + c)*cos(4*f*x + 4*e) + 4*c*cos(2*f*x + 2*e) + c)*f)","B",0
128,1,2035,0,0.737883," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(8 \, a^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 8 \, a^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 8 \, a^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 8 \, a^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} + 2 \, {\left(2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} + 2 \, {\left(2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 2 \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 1\right) + {\left(16 \, a^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 5 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 8 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(5 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 8 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(16 \, a^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 5 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 6 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 5 \, a^{2} - 8 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(5 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 5 \, a^{2} + 8 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, c^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, c^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, {\left(c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) - 2 \, c^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, {\left(c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} f}"," ",0,"2*(8*a^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*a^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*a^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*a^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*a^2*cos(2*f*x + 2*e)*sin(4*f*x + 4*e) + 2*a^2*cos(4*f*x + 4*e)*sin(2*f*x + 2*e) + 2*a^2*sin(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + 4*a^2*cos(2*f*x + 2*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*a^2*sin(2*f*x + 2*e)^2 + 4*a^2*cos(2*f*x + 2*e) + a^2 + 2*(2*a^2*cos(2*f*x + 2*e) + a^2)*cos(4*f*x + 4*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*(a^2*cos(4*f*x + 4*e)^2 + 4*a^2*cos(2*f*x + 2*e)^2 + 4*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a^2*sin(4*f*x + 4*e)^2 + 4*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*a^2*sin(2*f*x + 2*e)^2 + 4*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a^2*cos(2*f*x + 2*e) + a^2 + 2*(2*a^2*cos(2*f*x + 2*e) + a^2)*cos(4*f*x + 4*e) - 4*(a^2*cos(4*f*x + 4*e) + 2*a^2*cos(2*f*x + 2*e) - 2*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^2)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(a^2*cos(4*f*x + 4*e) + 2*a^2*cos(2*f*x + 2*e) + a^2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(a^2*sin(4*f*x + 4*e) + 2*a^2*sin(2*f*x + 2*e) - 2*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(a^2*sin(4*f*x + 4*e) + 2*a^2*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*arctan2(sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1) + (16*a^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 5*a^2*sin(4*f*x + 4*e) + 6*a^2*sin(2*f*x + 2*e) - 8*(a^2*cos(4*f*x + 4*e) + 2*a^2*cos(2*f*x + 2*e) + a^2)*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (5*a^2*sin(4*f*x + 4*e) + 6*a^2*sin(2*f*x + 2*e) - 8*(a^2*cos(4*f*x + 4*e) + 2*a^2*cos(2*f*x + 2*e) + a^2)*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (16*a^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*a^2*cos(4*f*x + 4*e) - 6*a^2*cos(2*f*x + 2*e) - 5*a^2 - 8*(a^2*sin(4*f*x + 4*e) + 2*a^2*sin(2*f*x + 2*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (5*a^2*cos(4*f*x + 4*e) + 6*a^2*cos(2*f*x + 2*e) + 5*a^2 + 8*(a^2*sin(4*f*x + 4*e) + 2*a^2*sin(2*f*x + 2*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((c^2*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c^2*sin(4*f*x + 4*e)^2 + 4*c^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*c^2*sin(2*f*x + 2*e)^2 + 4*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*c^2*cos(2*f*x + 2*e) + c^2 + 2*(2*c^2*cos(2*f*x + 2*e) + c^2)*cos(4*f*x + 4*e) - 4*(c^2*cos(4*f*x + 4*e) + 2*c^2*cos(2*f*x + 2*e) - 2*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^2)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(c^2*cos(4*f*x + 4*e) + 2*c^2*cos(2*f*x + 2*e) + c^2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(c^2*sin(4*f*x + 4*e) + 2*c^2*sin(2*f*x + 2*e) - 2*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(c^2*sin(4*f*x + 4*e) + 2*c^2*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
129,1,169,0,0.453031," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{-a} a^{2} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{c^{\frac{5}{2}}} + \frac{2 \, \sqrt{-a} a^{2} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{5}{2}}} - \frac{4 \, \sqrt{-a} a^{2} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{\frac{5}{2}}} + \frac{{\left(\sqrt{-a} a^{2} \sqrt{c} + \frac{2 \, \sqrt{-a} a^{2} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{4}}{c^{3} \sin\left(f x + e\right)^{4}}}{2 \, f}"," ",0,"-1/2*(2*sqrt(-a)*a^2*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/c^(5/2) + 2*sqrt(-a)*a^2*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(5/2) - 4*sqrt(-a)*a^2*log(sin(f*x + e)/(cos(f*x + e) + 1))/c^(5/2) + (sqrt(-a)*a^2*sqrt(c) + 2*sqrt(-a)*a^2*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)^4/(c^3*sin(f*x + e)^4))/f","A",0
130,1,1815,0,0.582602," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(208 \, a^{2} \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 48 \, a^{2} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 48 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 3 \, a^{2} \sin\left(f x + e\right) - {\left(3 \, a^{2} \sin\left(7 \, f x + 7 \, e\right) + 13 \, a^{2} \sin\left(5 \, f x + 5 \, e\right) + 13 \, a^{2} \sin\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + 6 \, {\left(8 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 8 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) - 16 \, {\left(13 \, a^{2} \sin\left(5 \, f x + 5 \, e\right) + 13 \, a^{2} \sin\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 26 \, {\left(15 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 8 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - 30 \, {\left(13 \, a^{2} \sin\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(3 \, a^{2} \cos\left(7 \, f x + 7 \, e\right) + 13 \, a^{2} \cos\left(5 \, f x + 5 \, e\right) + 13 \, a^{2} \cos\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} \cos\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 3 \, {\left(16 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 30 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 16 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \sin\left(7 \, f x + 7 \, e\right) + 16 \, {\left(13 \, a^{2} \cos\left(5 \, f x + 5 \, e\right) + 13 \, a^{2} \cos\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 13 \, {\left(30 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 16 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \sin\left(5 \, f x + 5 \, e\right) + 30 \, {\left(13 \, a^{2} \cos\left(3 \, f x + 3 \, e\right) + 3 \, a^{2} \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 13 \, {\left(16 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} \sqrt{a} \sqrt{c}}{3 \, {\left(c^{4} \cos\left(8 \, f x + 8 \, e\right)^{2} + 36 \, c^{4} \cos\left(7 \, f x + 7 \, e\right)^{2} + 256 \, c^{4} \cos\left(6 \, f x + 6 \, e\right)^{2} + 676 \, c^{4} \cos\left(5 \, f x + 5 \, e\right)^{2} + 900 \, c^{4} \cos\left(4 \, f x + 4 \, e\right)^{2} + 676 \, c^{4} \cos\left(3 \, f x + 3 \, e\right)^{2} + 256 \, c^{4} \cos\left(2 \, f x + 2 \, e\right)^{2} + 36 \, c^{4} \cos\left(f x + e\right)^{2} + c^{4} \sin\left(8 \, f x + 8 \, e\right)^{2} + 36 \, c^{4} \sin\left(7 \, f x + 7 \, e\right)^{2} + 256 \, c^{4} \sin\left(6 \, f x + 6 \, e\right)^{2} + 676 \, c^{4} \sin\left(5 \, f x + 5 \, e\right)^{2} + 900 \, c^{4} \sin\left(4 \, f x + 4 \, e\right)^{2} + 676 \, c^{4} \sin\left(3 \, f x + 3 \, e\right)^{2} + 256 \, c^{4} \sin\left(2 \, f x + 2 \, e\right)^{2} - 192 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 36 \, c^{4} \sin\left(f x + e\right)^{2} - 12 \, c^{4} \cos\left(f x + e\right) + c^{4} - 2 \, {\left(6 \, c^{4} \cos\left(7 \, f x + 7 \, e\right) - 16 \, c^{4} \cos\left(6 \, f x + 6 \, e\right) + 26 \, c^{4} \cos\left(5 \, f x + 5 \, e\right) - 30 \, c^{4} \cos\left(4 \, f x + 4 \, e\right) + 26 \, c^{4} \cos\left(3 \, f x + 3 \, e\right) - 16 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) + 6 \, c^{4} \cos\left(f x + e\right) - c^{4}\right)} \cos\left(8 \, f x + 8 \, e\right) - 12 \, {\left(16 \, c^{4} \cos\left(6 \, f x + 6 \, e\right) - 26 \, c^{4} \cos\left(5 \, f x + 5 \, e\right) + 30 \, c^{4} \cos\left(4 \, f x + 4 \, e\right) - 26 \, c^{4} \cos\left(3 \, f x + 3 \, e\right) + 16 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) - 6 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \cos\left(7 \, f x + 7 \, e\right) - 32 \, {\left(26 \, c^{4} \cos\left(5 \, f x + 5 \, e\right) - 30 \, c^{4} \cos\left(4 \, f x + 4 \, e\right) + 26 \, c^{4} \cos\left(3 \, f x + 3 \, e\right) - 16 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) + 6 \, c^{4} \cos\left(f x + e\right) - c^{4}\right)} \cos\left(6 \, f x + 6 \, e\right) - 52 \, {\left(30 \, c^{4} \cos\left(4 \, f x + 4 \, e\right) - 26 \, c^{4} \cos\left(3 \, f x + 3 \, e\right) + 16 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) - 6 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \cos\left(5 \, f x + 5 \, e\right) - 60 \, {\left(26 \, c^{4} \cos\left(3 \, f x + 3 \, e\right) - 16 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) + 6 \, c^{4} \cos\left(f x + e\right) - c^{4}\right)} \cos\left(4 \, f x + 4 \, e\right) - 52 \, {\left(16 \, c^{4} \cos\left(2 \, f x + 2 \, e\right) - 6 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \cos\left(3 \, f x + 3 \, e\right) - 32 \, {\left(6 \, c^{4} \cos\left(f x + e\right) - c^{4}\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(3 \, c^{4} \sin\left(7 \, f x + 7 \, e\right) - 8 \, c^{4} \sin\left(6 \, f x + 6 \, e\right) + 13 \, c^{4} \sin\left(5 \, f x + 5 \, e\right) - 15 \, c^{4} \sin\left(4 \, f x + 4 \, e\right) + 13 \, c^{4} \sin\left(3 \, f x + 3 \, e\right) - 8 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) + 3 \, c^{4} \sin\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 24 \, {\left(8 \, c^{4} \sin\left(6 \, f x + 6 \, e\right) - 13 \, c^{4} \sin\left(5 \, f x + 5 \, e\right) + 15 \, c^{4} \sin\left(4 \, f x + 4 \, e\right) - 13 \, c^{4} \sin\left(3 \, f x + 3 \, e\right) + 8 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) - 3 \, c^{4} \sin\left(f x + e\right)\right)} \sin\left(7 \, f x + 7 \, e\right) - 64 \, {\left(13 \, c^{4} \sin\left(5 \, f x + 5 \, e\right) - 15 \, c^{4} \sin\left(4 \, f x + 4 \, e\right) + 13 \, c^{4} \sin\left(3 \, f x + 3 \, e\right) - 8 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) + 3 \, c^{4} \sin\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 104 \, {\left(15 \, c^{4} \sin\left(4 \, f x + 4 \, e\right) - 13 \, c^{4} \sin\left(3 \, f x + 3 \, e\right) + 8 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) - 3 \, c^{4} \sin\left(f x + e\right)\right)} \sin\left(5 \, f x + 5 \, e\right) - 120 \, {\left(13 \, c^{4} \sin\left(3 \, f x + 3 \, e\right) - 8 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) + 3 \, c^{4} \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 104 \, {\left(8 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) - 3 \, c^{4} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} f}"," ",0,"2/3*(208*a^2*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) + 48*a^2*cos(f*x + e)*sin(2*f*x + 2*e) - 48*a^2*cos(2*f*x + 2*e)*sin(f*x + e) - 3*a^2*sin(f*x + e) - (3*a^2*sin(7*f*x + 7*e) + 13*a^2*sin(5*f*x + 5*e) + 13*a^2*sin(3*f*x + 3*e) + 3*a^2*sin(f*x + e))*cos(8*f*x + 8*e) + 6*(8*a^2*sin(6*f*x + 6*e) + 15*a^2*sin(4*f*x + 4*e) + 8*a^2*sin(2*f*x + 2*e))*cos(7*f*x + 7*e) - 16*(13*a^2*sin(5*f*x + 5*e) + 13*a^2*sin(3*f*x + 3*e) + 3*a^2*sin(f*x + e))*cos(6*f*x + 6*e) + 26*(15*a^2*sin(4*f*x + 4*e) + 8*a^2*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - 30*(13*a^2*sin(3*f*x + 3*e) + 3*a^2*sin(f*x + e))*cos(4*f*x + 4*e) + (3*a^2*cos(7*f*x + 7*e) + 13*a^2*cos(5*f*x + 5*e) + 13*a^2*cos(3*f*x + 3*e) + 3*a^2*cos(f*x + e))*sin(8*f*x + 8*e) - 3*(16*a^2*cos(6*f*x + 6*e) + 30*a^2*cos(4*f*x + 4*e) + 16*a^2*cos(2*f*x + 2*e) + a^2)*sin(7*f*x + 7*e) + 16*(13*a^2*cos(5*f*x + 5*e) + 13*a^2*cos(3*f*x + 3*e) + 3*a^2*cos(f*x + e))*sin(6*f*x + 6*e) - 13*(30*a^2*cos(4*f*x + 4*e) + 16*a^2*cos(2*f*x + 2*e) + a^2)*sin(5*f*x + 5*e) + 30*(13*a^2*cos(3*f*x + 3*e) + 3*a^2*cos(f*x + e))*sin(4*f*x + 4*e) - 13*(16*a^2*cos(2*f*x + 2*e) + a^2)*sin(3*f*x + 3*e))*sqrt(a)*sqrt(c)/((c^4*cos(8*f*x + 8*e)^2 + 36*c^4*cos(7*f*x + 7*e)^2 + 256*c^4*cos(6*f*x + 6*e)^2 + 676*c^4*cos(5*f*x + 5*e)^2 + 900*c^4*cos(4*f*x + 4*e)^2 + 676*c^4*cos(3*f*x + 3*e)^2 + 256*c^4*cos(2*f*x + 2*e)^2 + 36*c^4*cos(f*x + e)^2 + c^4*sin(8*f*x + 8*e)^2 + 36*c^4*sin(7*f*x + 7*e)^2 + 256*c^4*sin(6*f*x + 6*e)^2 + 676*c^4*sin(5*f*x + 5*e)^2 + 900*c^4*sin(4*f*x + 4*e)^2 + 676*c^4*sin(3*f*x + 3*e)^2 + 256*c^4*sin(2*f*x + 2*e)^2 - 192*c^4*sin(2*f*x + 2*e)*sin(f*x + e) + 36*c^4*sin(f*x + e)^2 - 12*c^4*cos(f*x + e) + c^4 - 2*(6*c^4*cos(7*f*x + 7*e) - 16*c^4*cos(6*f*x + 6*e) + 26*c^4*cos(5*f*x + 5*e) - 30*c^4*cos(4*f*x + 4*e) + 26*c^4*cos(3*f*x + 3*e) - 16*c^4*cos(2*f*x + 2*e) + 6*c^4*cos(f*x + e) - c^4)*cos(8*f*x + 8*e) - 12*(16*c^4*cos(6*f*x + 6*e) - 26*c^4*cos(5*f*x + 5*e) + 30*c^4*cos(4*f*x + 4*e) - 26*c^4*cos(3*f*x + 3*e) + 16*c^4*cos(2*f*x + 2*e) - 6*c^4*cos(f*x + e) + c^4)*cos(7*f*x + 7*e) - 32*(26*c^4*cos(5*f*x + 5*e) - 30*c^4*cos(4*f*x + 4*e) + 26*c^4*cos(3*f*x + 3*e) - 16*c^4*cos(2*f*x + 2*e) + 6*c^4*cos(f*x + e) - c^4)*cos(6*f*x + 6*e) - 52*(30*c^4*cos(4*f*x + 4*e) - 26*c^4*cos(3*f*x + 3*e) + 16*c^4*cos(2*f*x + 2*e) - 6*c^4*cos(f*x + e) + c^4)*cos(5*f*x + 5*e) - 60*(26*c^4*cos(3*f*x + 3*e) - 16*c^4*cos(2*f*x + 2*e) + 6*c^4*cos(f*x + e) - c^4)*cos(4*f*x + 4*e) - 52*(16*c^4*cos(2*f*x + 2*e) - 6*c^4*cos(f*x + e) + c^4)*cos(3*f*x + 3*e) - 32*(6*c^4*cos(f*x + e) - c^4)*cos(2*f*x + 2*e) - 4*(3*c^4*sin(7*f*x + 7*e) - 8*c^4*sin(6*f*x + 6*e) + 13*c^4*sin(5*f*x + 5*e) - 15*c^4*sin(4*f*x + 4*e) + 13*c^4*sin(3*f*x + 3*e) - 8*c^4*sin(2*f*x + 2*e) + 3*c^4*sin(f*x + e))*sin(8*f*x + 8*e) - 24*(8*c^4*sin(6*f*x + 6*e) - 13*c^4*sin(5*f*x + 5*e) + 15*c^4*sin(4*f*x + 4*e) - 13*c^4*sin(3*f*x + 3*e) + 8*c^4*sin(2*f*x + 2*e) - 3*c^4*sin(f*x + e))*sin(7*f*x + 7*e) - 64*(13*c^4*sin(5*f*x + 5*e) - 15*c^4*sin(4*f*x + 4*e) + 13*c^4*sin(3*f*x + 3*e) - 8*c^4*sin(2*f*x + 2*e) + 3*c^4*sin(f*x + e))*sin(6*f*x + 6*e) - 104*(15*c^4*sin(4*f*x + 4*e) - 13*c^4*sin(3*f*x + 3*e) + 8*c^4*sin(2*f*x + 2*e) - 3*c^4*sin(f*x + e))*sin(5*f*x + 5*e) - 120*(13*c^4*sin(3*f*x + 3*e) - 8*c^4*sin(2*f*x + 2*e) + 3*c^4*sin(f*x + e))*sin(4*f*x + 4*e) - 104*(8*c^4*sin(2*f*x + 2*e) - 3*c^4*sin(f*x + e))*sin(3*f*x + 3*e))*f)","B",0
131,1,2719,0,4.434151," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(9/2),x, algorithm=""maxima"")","\frac{2 \, {\left(70 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) \sin\left(4 \, f x + 4 \, e\right) - 70 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(3 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 10 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + {\left(3 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 60 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 130 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 60 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 32 \, a^{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 32 \, a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(17 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 308 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 630 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 308 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 32 \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(17 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 308 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 630 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 308 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 32 \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(3 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 60 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 130 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 60 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(3 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 10 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - {\left(70 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 3 \, a^{2}\right)} \sin\left(6 \, f x + 6 \, e\right) + 10 \, {\left(7 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(3 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 60 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 130 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 60 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 32 \, a^{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 32 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 3 \, a^{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(17 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 308 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 630 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 308 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 32 \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 17 \, a^{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(17 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 308 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 630 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 308 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 32 \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 17 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(3 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 60 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 130 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 60 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{3 \, {\left(c^{5} \cos\left(8 \, f x + 8 \, e\right)^{2} + 784 \, c^{5} \cos\left(6 \, f x + 6 \, e\right)^{2} + 4900 \, c^{5} \cos\left(4 \, f x + 4 \, e\right)^{2} + 784 \, c^{5} \cos\left(2 \, f x + 2 \, e\right)^{2} + 64 \, c^{5} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 3136 \, c^{5} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 3136 \, c^{5} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 64 \, c^{5} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + c^{5} \sin\left(8 \, f x + 8 \, e\right)^{2} + 784 \, c^{5} \sin\left(6 \, f x + 6 \, e\right)^{2} + 4900 \, c^{5} \sin\left(4 \, f x + 4 \, e\right)^{2} + 3920 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 784 \, c^{5} \sin\left(2 \, f x + 2 \, e\right)^{2} + 64 \, c^{5} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 3136 \, c^{5} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 3136 \, c^{5} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 64 \, c^{5} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 56 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + c^{5} + 2 \, {\left(28 \, c^{5} \cos\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + c^{5}\right)} \cos\left(8 \, f x + 8 \, e\right) + 56 \, {\left(70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + c^{5}\right)} \cos\left(6 \, f x + 6 \, e\right) + 140 \, {\left(28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + c^{5}\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(c^{5} \cos\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \cos\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) - 56 \, c^{5} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 56 \, c^{5} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, c^{5} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{5}\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(c^{5} \cos\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \cos\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) - 56 \, c^{5} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, c^{5} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{5}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(c^{5} \cos\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \cos\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) - 8 \, c^{5} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{5}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 16 \, {\left(c^{5} \cos\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \cos\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \cos\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + c^{5}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 28 \, {\left(2 \, c^{5} \sin\left(6 \, f x + 6 \, e\right) + 5 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{5} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 784 \, {\left(5 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{5} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, {\left(c^{5} \sin\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \sin\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \sin\left(2 \, f x + 2 \, e\right) - 56 \, c^{5} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 56 \, c^{5} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, c^{5} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(c^{5} \sin\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \sin\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \sin\left(2 \, f x + 2 \, e\right) - 56 \, c^{5} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 8 \, c^{5} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(c^{5} \sin\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \sin\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \sin\left(2 \, f x + 2 \, e\right) - 8 \, c^{5} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 16 \, {\left(c^{5} \sin\left(8 \, f x + 8 \, e\right) + 28 \, c^{5} \sin\left(6 \, f x + 6 \, e\right) + 70 \, c^{5} \sin\left(4 \, f x + 4 \, e\right) + 28 \, c^{5} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} f}"," ",0,"2/3*(70*a^2*cos(6*f*x + 6*e)*sin(4*f*x + 4*e) - 70*a^2*cos(4*f*x + 4*e)*sin(2*f*x + 2*e) + 3*a^2*sin(2*f*x + 2*e) + (3*a^2*sin(6*f*x + 6*e) + 10*a^2*sin(4*f*x + 4*e) + 3*a^2*sin(2*f*x + 2*e))*cos(8*f*x + 8*e) + (3*a^2*sin(8*f*x + 8*e) + 60*a^2*sin(6*f*x + 6*e) + 130*a^2*sin(4*f*x + 4*e) + 60*a^2*sin(2*f*x + 2*e) - 32*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (17*a^2*sin(8*f*x + 8*e) + 308*a^2*sin(6*f*x + 6*e) + 630*a^2*sin(4*f*x + 4*e) + 308*a^2*sin(2*f*x + 2*e) + 32*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (17*a^2*sin(8*f*x + 8*e) + 308*a^2*sin(6*f*x + 6*e) + 630*a^2*sin(4*f*x + 4*e) + 308*a^2*sin(2*f*x + 2*e) + 32*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (3*a^2*sin(8*f*x + 8*e) + 60*a^2*sin(6*f*x + 6*e) + 130*a^2*sin(4*f*x + 4*e) + 60*a^2*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (3*a^2*cos(6*f*x + 6*e) + 10*a^2*cos(4*f*x + 4*e) + 3*a^2*cos(2*f*x + 2*e))*sin(8*f*x + 8*e) - (70*a^2*cos(4*f*x + 4*e) - 3*a^2)*sin(6*f*x + 6*e) + 10*(7*a^2*cos(2*f*x + 2*e) + a^2)*sin(4*f*x + 4*e) - (3*a^2*cos(8*f*x + 8*e) + 60*a^2*cos(6*f*x + 6*e) + 130*a^2*cos(4*f*x + 4*e) + 60*a^2*cos(2*f*x + 2*e) - 32*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*a^2)*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (17*a^2*cos(8*f*x + 8*e) + 308*a^2*cos(6*f*x + 6*e) + 630*a^2*cos(4*f*x + 4*e) + 308*a^2*cos(2*f*x + 2*e) + 32*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 17*a^2)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (17*a^2*cos(8*f*x + 8*e) + 308*a^2*cos(6*f*x + 6*e) + 630*a^2*cos(4*f*x + 4*e) + 308*a^2*cos(2*f*x + 2*e) + 32*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 17*a^2)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (3*a^2*cos(8*f*x + 8*e) + 60*a^2*cos(6*f*x + 6*e) + 130*a^2*cos(4*f*x + 4*e) + 60*a^2*cos(2*f*x + 2*e) + 3*a^2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((c^5*cos(8*f*x + 8*e)^2 + 784*c^5*cos(6*f*x + 6*e)^2 + 4900*c^5*cos(4*f*x + 4*e)^2 + 784*c^5*cos(2*f*x + 2*e)^2 + 64*c^5*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*c^5*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*c^5*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*c^5*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c^5*sin(8*f*x + 8*e)^2 + 784*c^5*sin(6*f*x + 6*e)^2 + 4900*c^5*sin(4*f*x + 4*e)^2 + 3920*c^5*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 784*c^5*sin(2*f*x + 2*e)^2 + 64*c^5*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*c^5*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*c^5*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*c^5*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 56*c^5*cos(2*f*x + 2*e) + c^5 + 2*(28*c^5*cos(6*f*x + 6*e) + 70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) + c^5)*cos(8*f*x + 8*e) + 56*(70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) + c^5)*cos(6*f*x + 6*e) + 140*(28*c^5*cos(2*f*x + 2*e) + c^5)*cos(4*f*x + 4*e) - 16*(c^5*cos(8*f*x + 8*e) + 28*c^5*cos(6*f*x + 6*e) + 70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) - 56*c^5*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 56*c^5*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*c^5*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^5)*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 112*(c^5*cos(8*f*x + 8*e) + 28*c^5*cos(6*f*x + 6*e) + 70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) - 56*c^5*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*c^5*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^5)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 112*(c^5*cos(8*f*x + 8*e) + 28*c^5*cos(6*f*x + 6*e) + 70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) - 8*c^5*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^5)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 16*(c^5*cos(8*f*x + 8*e) + 28*c^5*cos(6*f*x + 6*e) + 70*c^5*cos(4*f*x + 4*e) + 28*c^5*cos(2*f*x + 2*e) + c^5)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 28*(2*c^5*sin(6*f*x + 6*e) + 5*c^5*sin(4*f*x + 4*e) + 2*c^5*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 784*(5*c^5*sin(4*f*x + 4*e) + 2*c^5*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 16*(c^5*sin(8*f*x + 8*e) + 28*c^5*sin(6*f*x + 6*e) + 70*c^5*sin(4*f*x + 4*e) + 28*c^5*sin(2*f*x + 2*e) - 56*c^5*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 56*c^5*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*c^5*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 112*(c^5*sin(8*f*x + 8*e) + 28*c^5*sin(6*f*x + 6*e) + 70*c^5*sin(4*f*x + 4*e) + 28*c^5*sin(2*f*x + 2*e) - 56*c^5*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*c^5*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 112*(c^5*sin(8*f*x + 8*e) + 28*c^5*sin(6*f*x + 6*e) + 70*c^5*sin(4*f*x + 4*e) + 28*c^5*sin(2*f*x + 2*e) - 8*c^5*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 16*(c^5*sin(8*f*x + 8*e) + 28*c^5*sin(6*f*x + 6*e) + 70*c^5*sin(4*f*x + 4*e) + 28*c^5*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
132,1,4108,0,23.290117," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(11/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(1350 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 1350 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 30 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 10 \, {\left(3 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 17 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 17 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(10 \, f x + 10 \, e\right) - 1350 \, {\left(a^{2} \sin\left(6 \, f x + 6 \, e\right) + a^{2} \sin\left(4 \, f x + 4 \, e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) - 5 \, {\left(3 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) + 75 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 290 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 290 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 75 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 80 \, a^{2} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 192 \, a^{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 80 \, a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 20 \, {\left(7 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) + 135 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 450 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 450 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 135 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 72 \, a^{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 20 \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 6 \, {\left(47 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) + 855 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 2730 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 2730 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 855 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 240 \, a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 160 \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 20 \, {\left(7 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) + 135 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 450 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 450 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 135 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 20 \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 5 \, {\left(3 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) + 75 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 290 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 290 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 75 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 10 \, {\left(3 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 17 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 17 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + 30 \, {\left(45 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 45 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - a^{2}\right)} \sin\left(8 \, f x + 8 \, e\right) - 10 \, {\left(135 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 17 \, a^{2}\right)} \sin\left(6 \, f x + 6 \, e\right) - 10 \, {\left(135 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 17 \, a^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) + 5 \, {\left(3 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) + 75 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 290 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 290 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 75 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 80 \, a^{2} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 192 \, a^{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 80 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 3 \, a^{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 20 \, {\left(7 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) + 135 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 450 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 450 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 135 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 72 \, a^{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 20 \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 7 \, a^{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 6 \, {\left(47 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) + 855 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 2730 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 2730 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 855 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 240 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 160 \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 47 \, a^{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 20 \, {\left(7 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) + 135 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 450 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 450 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 135 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 20 \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 7 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 5 \, {\left(3 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) + 75 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 290 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 290 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 75 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{15 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right)^{2} + 2025 \, c^{6} \cos\left(8 \, f x + 8 \, e\right)^{2} + 44100 \, c^{6} \cos\left(6 \, f x + 6 \, e\right)^{2} + 44100 \, c^{6} \cos\left(4 \, f x + 4 \, e\right)^{2} + 2025 \, c^{6} \cos\left(2 \, f x + 2 \, e\right)^{2} + 100 \, c^{6} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 14400 \, c^{6} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 63504 \, c^{6} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 14400 \, c^{6} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 100 \, c^{6} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + c^{6} \sin\left(10 \, f x + 10 \, e\right)^{2} + 2025 \, c^{6} \sin\left(8 \, f x + 8 \, e\right)^{2} + 44100 \, c^{6} \sin\left(6 \, f x + 6 \, e\right)^{2} + 44100 \, c^{6} \sin\left(4 \, f x + 4 \, e\right)^{2} + 18900 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 2025 \, c^{6} \sin\left(2 \, f x + 2 \, e\right)^{2} + 100 \, c^{6} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 14400 \, c^{6} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 63504 \, c^{6} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 14400 \, c^{6} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 100 \, c^{6} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 90 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6} + 2 \, {\left(45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6}\right)} \cos\left(10 \, f x + 10 \, e\right) + 90 \, {\left(210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6}\right)} \cos\left(8 \, f x + 8 \, e\right) + 420 \, {\left(210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6}\right)} \cos\left(6 \, f x + 6 \, e\right) + 420 \, {\left(45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6}\right)} \cos\left(4 \, f x + 4 \, e\right) - 20 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) - 120 \, c^{6} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 252 \, c^{6} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 120 \, c^{6} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{6}\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) - 252 \, c^{6} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 120 \, c^{6} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{6}\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 504 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) - 120 \, c^{6} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{6}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) - 10 \, c^{6} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{6}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 20 \, {\left(c^{6} \cos\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \cos\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \cos\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \cos\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \cos\left(2 \, f x + 2 \, e\right) + c^{6}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 30 \, {\left(3 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 14 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 14 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 3 \, c^{6} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + 1350 \, {\left(14 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 14 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 3 \, c^{6} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 6300 \, {\left(14 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 3 \, c^{6} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 20 \, {\left(c^{6} \sin\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \sin\left(2 \, f x + 2 \, e\right) - 120 \, c^{6} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 252 \, c^{6} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 120 \, c^{6} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(c^{6} \sin\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \sin\left(2 \, f x + 2 \, e\right) - 252 \, c^{6} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 120 \, c^{6} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 504 \, {\left(c^{6} \sin\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \sin\left(2 \, f x + 2 \, e\right) - 120 \, c^{6} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10 \, c^{6} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(c^{6} \sin\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \sin\left(2 \, f x + 2 \, e\right) - 10 \, c^{6} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 20 \, {\left(c^{6} \sin\left(10 \, f x + 10 \, e\right) + 45 \, c^{6} \sin\left(8 \, f x + 8 \, e\right) + 210 \, c^{6} \sin\left(6 \, f x + 6 \, e\right) + 210 \, c^{6} \sin\left(4 \, f x + 4 \, e\right) + 45 \, c^{6} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} f}"," ",0,"-2/15*(1350*a^2*cos(6*f*x + 6*e)*sin(2*f*x + 2*e) + 1350*a^2*cos(4*f*x + 4*e)*sin(2*f*x + 2*e) - 30*a^2*sin(2*f*x + 2*e) - 10*(3*a^2*sin(8*f*x + 8*e) + 17*a^2*sin(6*f*x + 6*e) + 17*a^2*sin(4*f*x + 4*e) + 3*a^2*sin(2*f*x + 2*e))*cos(10*f*x + 10*e) - 1350*(a^2*sin(6*f*x + 6*e) + a^2*sin(4*f*x + 4*e))*cos(8*f*x + 8*e) - 5*(3*a^2*sin(10*f*x + 10*e) + 75*a^2*sin(8*f*x + 8*e) + 290*a^2*sin(6*f*x + 6*e) + 290*a^2*sin(4*f*x + 4*e) + 75*a^2*sin(2*f*x + 2*e) - 80*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 192*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 80*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*(7*a^2*sin(10*f*x + 10*e) + 135*a^2*sin(8*f*x + 8*e) + 450*a^2*sin(6*f*x + 6*e) + 450*a^2*sin(4*f*x + 4*e) + 135*a^2*sin(2*f*x + 2*e) - 72*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 20*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*(47*a^2*sin(10*f*x + 10*e) + 855*a^2*sin(8*f*x + 8*e) + 2730*a^2*sin(6*f*x + 6*e) + 2730*a^2*sin(4*f*x + 4*e) + 855*a^2*sin(2*f*x + 2*e) + 240*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 160*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*(7*a^2*sin(10*f*x + 10*e) + 135*a^2*sin(8*f*x + 8*e) + 450*a^2*sin(6*f*x + 6*e) + 450*a^2*sin(4*f*x + 4*e) + 135*a^2*sin(2*f*x + 2*e) + 20*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*(3*a^2*sin(10*f*x + 10*e) + 75*a^2*sin(8*f*x + 8*e) + 290*a^2*sin(6*f*x + 6*e) + 290*a^2*sin(4*f*x + 4*e) + 75*a^2*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 10*(3*a^2*cos(8*f*x + 8*e) + 17*a^2*cos(6*f*x + 6*e) + 17*a^2*cos(4*f*x + 4*e) + 3*a^2*cos(2*f*x + 2*e))*sin(10*f*x + 10*e) + 30*(45*a^2*cos(6*f*x + 6*e) + 45*a^2*cos(4*f*x + 4*e) - a^2)*sin(8*f*x + 8*e) - 10*(135*a^2*cos(2*f*x + 2*e) + 17*a^2)*sin(6*f*x + 6*e) - 10*(135*a^2*cos(2*f*x + 2*e) + 17*a^2)*sin(4*f*x + 4*e) + 5*(3*a^2*cos(10*f*x + 10*e) + 75*a^2*cos(8*f*x + 8*e) + 290*a^2*cos(6*f*x + 6*e) + 290*a^2*cos(4*f*x + 4*e) + 75*a^2*cos(2*f*x + 2*e) - 80*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 192*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 80*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*a^2)*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 20*(7*a^2*cos(10*f*x + 10*e) + 135*a^2*cos(8*f*x + 8*e) + 450*a^2*cos(6*f*x + 6*e) + 450*a^2*cos(4*f*x + 4*e) + 135*a^2*cos(2*f*x + 2*e) - 72*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 20*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 7*a^2)*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 6*(47*a^2*cos(10*f*x + 10*e) + 855*a^2*cos(8*f*x + 8*e) + 2730*a^2*cos(6*f*x + 6*e) + 2730*a^2*cos(4*f*x + 4*e) + 855*a^2*cos(2*f*x + 2*e) + 240*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 160*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 47*a^2)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 20*(7*a^2*cos(10*f*x + 10*e) + 135*a^2*cos(8*f*x + 8*e) + 450*a^2*cos(6*f*x + 6*e) + 450*a^2*cos(4*f*x + 4*e) + 135*a^2*cos(2*f*x + 2*e) + 20*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 7*a^2)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 5*(3*a^2*cos(10*f*x + 10*e) + 75*a^2*cos(8*f*x + 8*e) + 290*a^2*cos(6*f*x + 6*e) + 290*a^2*cos(4*f*x + 4*e) + 75*a^2*cos(2*f*x + 2*e) + 3*a^2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((c^6*cos(10*f*x + 10*e)^2 + 2025*c^6*cos(8*f*x + 8*e)^2 + 44100*c^6*cos(6*f*x + 6*e)^2 + 44100*c^6*cos(4*f*x + 4*e)^2 + 2025*c^6*cos(2*f*x + 2*e)^2 + 100*c^6*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*c^6*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 63504*c^6*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*c^6*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 100*c^6*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c^6*sin(10*f*x + 10*e)^2 + 2025*c^6*sin(8*f*x + 8*e)^2 + 44100*c^6*sin(6*f*x + 6*e)^2 + 44100*c^6*sin(4*f*x + 4*e)^2 + 18900*c^6*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 2025*c^6*sin(2*f*x + 2*e)^2 + 100*c^6*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*c^6*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 63504*c^6*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*c^6*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 100*c^6*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 90*c^6*cos(2*f*x + 2*e) + c^6 + 2*(45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) + c^6)*cos(10*f*x + 10*e) + 90*(210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) + c^6)*cos(8*f*x + 8*e) + 420*(210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) + c^6)*cos(6*f*x + 6*e) + 420*(45*c^6*cos(2*f*x + 2*e) + c^6)*cos(4*f*x + 4*e) - 20*(c^6*cos(10*f*x + 10*e) + 45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) - 120*c^6*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 252*c^6*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*c^6*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^6)*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 240*(c^6*cos(10*f*x + 10*e) + 45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) - 252*c^6*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*c^6*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^6)*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 504*(c^6*cos(10*f*x + 10*e) + 45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) - 120*c^6*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^6)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 240*(c^6*cos(10*f*x + 10*e) + 45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) - 10*c^6*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^6)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*(c^6*cos(10*f*x + 10*e) + 45*c^6*cos(8*f*x + 8*e) + 210*c^6*cos(6*f*x + 6*e) + 210*c^6*cos(4*f*x + 4*e) + 45*c^6*cos(2*f*x + 2*e) + c^6)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 30*(3*c^6*sin(8*f*x + 8*e) + 14*c^6*sin(6*f*x + 6*e) + 14*c^6*sin(4*f*x + 4*e) + 3*c^6*sin(2*f*x + 2*e))*sin(10*f*x + 10*e) + 1350*(14*c^6*sin(6*f*x + 6*e) + 14*c^6*sin(4*f*x + 4*e) + 3*c^6*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 6300*(14*c^6*sin(4*f*x + 4*e) + 3*c^6*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 20*(c^6*sin(10*f*x + 10*e) + 45*c^6*sin(8*f*x + 8*e) + 210*c^6*sin(6*f*x + 6*e) + 210*c^6*sin(4*f*x + 4*e) + 45*c^6*sin(2*f*x + 2*e) - 120*c^6*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 252*c^6*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*c^6*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 240*(c^6*sin(10*f*x + 10*e) + 45*c^6*sin(8*f*x + 8*e) + 210*c^6*sin(6*f*x + 6*e) + 210*c^6*sin(4*f*x + 4*e) + 45*c^6*sin(2*f*x + 2*e) - 252*c^6*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*c^6*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 504*(c^6*sin(10*f*x + 10*e) + 45*c^6*sin(8*f*x + 8*e) + 210*c^6*sin(6*f*x + 6*e) + 210*c^6*sin(4*f*x + 4*e) + 45*c^6*sin(2*f*x + 2*e) - 120*c^6*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*c^6*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 240*(c^6*sin(10*f*x + 10*e) + 45*c^6*sin(8*f*x + 8*e) + 210*c^6*sin(6*f*x + 6*e) + 210*c^6*sin(4*f*x + 4*e) + 45*c^6*sin(2*f*x + 2*e) - 10*c^6*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*(c^6*sin(10*f*x + 10*e) + 45*c^6*sin(8*f*x + 8*e) + 210*c^6*sin(6*f*x + 6*e) + 210*c^6*sin(4*f*x + 4*e) + 45*c^6*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
133,1,737,0,0.603138," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(c^{2} \cos\left(2 \, f x + 2 \, e\right) \sin\left(4 \, f x + 4 \, e\right) - c^{2} \cos\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - c^{2} \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)\right)} \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 3 \, {\left(c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 3 \, {\left(c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 3 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 3 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(a \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a \cos\left(2 \, f x + 2 \, e\right)^{2} + a \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, a \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} f}"," ",0,"2*(c^2*cos(2*f*x + 2*e)*sin(4*f*x + 4*e) - c^2*cos(4*f*x + 4*e)*sin(2*f*x + 2*e) - c^2*sin(2*f*x + 2*e) + 2*(c^2*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e)^2 + c^2*sin(4*f*x + 4*e)^2 + 4*c^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*c^2*sin(2*f*x + 2*e)^2 + 4*c^2*cos(2*f*x + 2*e) + c^2 + 2*(2*c^2*cos(2*f*x + 2*e) + c^2)*cos(4*f*x + 4*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*(c^2*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e)^2 + c^2*sin(4*f*x + 4*e)^2 + 4*c^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*c^2*sin(2*f*x + 2*e)^2 + 4*c^2*cos(2*f*x + 2*e) + c^2 + 2*(2*c^2*cos(2*f*x + 2*e) + c^2)*cos(4*f*x + 4*e))*arctan2(sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 3*(c^2*sin(4*f*x + 4*e) + 2*c^2*sin(2*f*x + 2*e))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3*(c^2*sin(4*f*x + 4*e) + 2*c^2*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*(c^2*cos(4*f*x + 4*e) + 2*c^2*cos(2*f*x + 2*e) + c^2)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*(c^2*cos(4*f*x + 4*e) + 2*c^2*cos(2*f*x + 2*e) + c^2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((a*cos(4*f*x + 4*e)^2 + 4*a*cos(2*f*x + 2*e)^2 + a*sin(4*f*x + 4*e)^2 + 4*a*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*a*sin(2*f*x + 2*e)^2 + 2*(2*a*cos(2*f*x + 2*e) + a)*cos(4*f*x + 4*e) + 4*a*cos(2*f*x + 2*e) + a)*f)","B",0
134,1,276,0,0.584708," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) \sin\left(2 \, f x + 2 \, e\right) - {\left(c \cos\left(2 \, f x + 2 \, e\right)^{2} + c \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + c\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) + 2 \, {\left(c \cos\left(2 \, f x + 2 \, e\right)^{2} + c \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + c\right)} \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(c \cos\left(2 \, f x + 2 \, e\right) + c\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(a \cos\left(2 \, f x + 2 \, e\right)^{2} + a \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} f}"," ",0,"-2*(c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(2*f*x + 2*e) - (c*cos(2*f*x + 2*e)^2 + c*sin(2*f*x + 2*e)^2 + 2*c*cos(2*f*x + 2*e) + c)*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 2*(c*cos(2*f*x + 2*e)^2 + c*sin(2*f*x + 2*e)^2 + 2*c*cos(2*f*x + 2*e) + c)*arctan2(sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (c*cos(2*f*x + 2*e) + c)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((a*cos(2*f*x + 2*e)^2 + a*sin(2*f*x + 2*e)^2 + 2*a*cos(2*f*x + 2*e) + a)*f)","B",0
135,1,64,0,0.454483," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\sqrt{c} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{\sqrt{-a}} + \frac{\sqrt{c} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{\sqrt{-a}}}{f}"," ",0,"-(sqrt(c)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/sqrt(-a) + sqrt(c)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/sqrt(-a))/f","A",0
136,1,44,0,0.554021," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right)}{\sqrt{a} \sqrt{c} f}"," ",0,"-(arctan2(sin(f*x + e), cos(f*x + e) + 1) - arctan2(sin(f*x + e), cos(f*x + e) - 1))/(sqrt(a)*sqrt(c)*f)","A",0
137,1,406,0,0.592000," ","integrate(sec(f*x+e)/(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{{\left({\left(2 \, {\left(2 \, \cos\left(f x + e\right) - 1\right)} \cos\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)^{2} - 4 \, \cos\left(f x + e\right)^{2} - \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 4 \, \sin\left(f x + e\right)^{2} + 4 \, \cos\left(f x + e\right) - 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(f x + e\right) - 1\right)} \cos\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)^{2} - 4 \, \cos\left(f x + e\right)^{2} - \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 4 \, \sin\left(f x + e\right)^{2} + 4 \, \cos\left(f x + e\right) - 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) + 2 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 2 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 2 \, \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{2 \, {\left(a c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a c^{2} \cos\left(f x + e\right)^{2} + a c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} - 4 \, a c^{2} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, a c^{2} \sin\left(f x + e\right)^{2} - 4 \, a c^{2} \cos\left(f x + e\right) + a c^{2} - 2 \, {\left(2 \, a c^{2} \cos\left(f x + e\right) - a c^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} f}"," ",0,"1/2*((2*(2*cos(f*x + e) - 1)*cos(2*f*x + 2*e) - cos(2*f*x + 2*e)^2 - 4*cos(f*x + e)^2 - sin(2*f*x + 2*e)^2 + 4*sin(2*f*x + 2*e)*sin(f*x + e) - 4*sin(f*x + e)^2 + 4*cos(f*x + e) - 1)*arctan2(sin(f*x + e), cos(f*x + e) + 1) - (2*(2*cos(f*x + e) - 1)*cos(2*f*x + 2*e) - cos(2*f*x + 2*e)^2 - 4*cos(f*x + e)^2 - sin(2*f*x + 2*e)^2 + 4*sin(2*f*x + 2*e)*sin(f*x + e) - 4*sin(f*x + e)^2 + 4*cos(f*x + e) - 1)*arctan2(sin(f*x + e), cos(f*x + e) - 1) + 2*cos(f*x + e)*sin(2*f*x + 2*e) - 2*cos(2*f*x + 2*e)*sin(f*x + e) - 2*sin(f*x + e))*sqrt(a)*sqrt(c)/((a*c^2*cos(2*f*x + 2*e)^2 + 4*a*c^2*cos(f*x + e)^2 + a*c^2*sin(2*f*x + 2*e)^2 - 4*a*c^2*sin(2*f*x + 2*e)*sin(f*x + e) + 4*a*c^2*sin(f*x + e)^2 - 4*a*c^2*cos(f*x + e) + a*c^2 - 2*(2*a*c^2*cos(f*x + e) - a*c^2)*cos(2*f*x + 2*e))*f)","B",0
138,1,1201,0,0.658680," ","integrate(sec(f*x+e)/(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{{\left({\left(2 \, {\left(4 \, \cos\left(3 \, f x + 3 \, e\right) - 6 \, \cos\left(2 \, f x + 2 \, e\right) + 4 \, \cos\left(f x + e\right) - 1\right)} \cos\left(4 \, f x + 4 \, e\right) - \cos\left(4 \, f x + 4 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(2 \, f x + 2 \, e\right) - 4 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) - 16 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(f x + e\right) - 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 36 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 16 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(2 \, \sin\left(3 \, f x + 3 \, e\right) - 3 \, \sin\left(2 \, f x + 2 \, e\right) + 2 \, \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(2 \, f x + 2 \, e\right) - 2 \, \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 16 \, \sin\left(3 \, f x + 3 \, e\right)^{2} - 36 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 48 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 16 \, \sin\left(f x + e\right)^{2} + 8 \, \cos\left(f x + e\right) - 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - {\left(2 \, {\left(4 \, \cos\left(3 \, f x + 3 \, e\right) - 6 \, \cos\left(2 \, f x + 2 \, e\right) + 4 \, \cos\left(f x + e\right) - 1\right)} \cos\left(4 \, f x + 4 \, e\right) - \cos\left(4 \, f x + 4 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(2 \, f x + 2 \, e\right) - 4 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) - 16 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(f x + e\right) - 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 36 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 16 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(2 \, \sin\left(3 \, f x + 3 \, e\right) - 3 \, \sin\left(2 \, f x + 2 \, e\right) + 2 \, \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(2 \, f x + 2 \, e\right) - 2 \, \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 16 \, \sin\left(3 \, f x + 3 \, e\right)^{2} - 36 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 48 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 16 \, \sin\left(f x + e\right)^{2} + 8 \, \cos\left(f x + e\right) - 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) - 2 \, {\left(3 \, \sin\left(3 \, f x + 3 \, e\right) - 4 \, \sin\left(2 \, f x + 2 \, e\right) + 3 \, \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(3 \, \cos\left(3 \, f x + 3 \, e\right) - 4 \, \cos\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) + 3\right)} \sin\left(3 \, f x + 3 \, e\right) + 4 \, {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(2 \, f x + 2 \, e\right) + 4 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 4 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 6 \, \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{4 \, {\left(a c^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, a c^{3} \cos\left(3 \, f x + 3 \, e\right)^{2} + 36 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, a c^{3} \cos\left(f x + e\right)^{2} + a c^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, a c^{3} \sin\left(3 \, f x + 3 \, e\right)^{2} + 36 \, a c^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} - 48 \, a c^{3} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 16 \, a c^{3} \sin\left(f x + e\right)^{2} - 8 \, a c^{3} \cos\left(f x + e\right) + a c^{3} - 2 \, {\left(4 \, a c^{3} \cos\left(3 \, f x + 3 \, e\right) - 6 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right) + 4 \, a c^{3} \cos\left(f x + e\right) - a c^{3}\right)} \cos\left(4 \, f x + 4 \, e\right) - 8 \, {\left(6 \, a c^{3} \cos\left(2 \, f x + 2 \, e\right) - 4 \, a c^{3} \cos\left(f x + e\right) + a c^{3}\right)} \cos\left(3 \, f x + 3 \, e\right) - 12 \, {\left(4 \, a c^{3} \cos\left(f x + e\right) - a c^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(2 \, a c^{3} \sin\left(3 \, f x + 3 \, e\right) - 3 \, a c^{3} \sin\left(2 \, f x + 2 \, e\right) + 2 \, a c^{3} \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 16 \, {\left(3 \, a c^{3} \sin\left(2 \, f x + 2 \, e\right) - 2 \, a c^{3} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} f}"," ",0,"1/4*((2*(4*cos(3*f*x + 3*e) - 6*cos(2*f*x + 2*e) + 4*cos(f*x + e) - 1)*cos(4*f*x + 4*e) - cos(4*f*x + 4*e)^2 + 8*(6*cos(2*f*x + 2*e) - 4*cos(f*x + e) + 1)*cos(3*f*x + 3*e) - 16*cos(3*f*x + 3*e)^2 + 12*(4*cos(f*x + e) - 1)*cos(2*f*x + 2*e) - 36*cos(2*f*x + 2*e)^2 - 16*cos(f*x + e)^2 + 4*(2*sin(3*f*x + 3*e) - 3*sin(2*f*x + 2*e) + 2*sin(f*x + e))*sin(4*f*x + 4*e) - sin(4*f*x + 4*e)^2 + 16*(3*sin(2*f*x + 2*e) - 2*sin(f*x + e))*sin(3*f*x + 3*e) - 16*sin(3*f*x + 3*e)^2 - 36*sin(2*f*x + 2*e)^2 + 48*sin(2*f*x + 2*e)*sin(f*x + e) - 16*sin(f*x + e)^2 + 8*cos(f*x + e) - 1)*arctan2(sin(f*x + e), cos(f*x + e) + 1) - (2*(4*cos(3*f*x + 3*e) - 6*cos(2*f*x + 2*e) + 4*cos(f*x + e) - 1)*cos(4*f*x + 4*e) - cos(4*f*x + 4*e)^2 + 8*(6*cos(2*f*x + 2*e) - 4*cos(f*x + e) + 1)*cos(3*f*x + 3*e) - 16*cos(3*f*x + 3*e)^2 + 12*(4*cos(f*x + e) - 1)*cos(2*f*x + 2*e) - 36*cos(2*f*x + 2*e)^2 - 16*cos(f*x + e)^2 + 4*(2*sin(3*f*x + 3*e) - 3*sin(2*f*x + 2*e) + 2*sin(f*x + e))*sin(4*f*x + 4*e) - sin(4*f*x + 4*e)^2 + 16*(3*sin(2*f*x + 2*e) - 2*sin(f*x + e))*sin(3*f*x + 3*e) - 16*sin(3*f*x + 3*e)^2 - 36*sin(2*f*x + 2*e)^2 + 48*sin(2*f*x + 2*e)*sin(f*x + e) - 16*sin(f*x + e)^2 + 8*cos(f*x + e) - 1)*arctan2(sin(f*x + e), cos(f*x + e) - 1) - 2*(3*sin(3*f*x + 3*e) - 4*sin(2*f*x + 2*e) + 3*sin(f*x + e))*cos(4*f*x + 4*e) + 2*(3*cos(3*f*x + 3*e) - 4*cos(2*f*x + 2*e) + 3*cos(f*x + e))*sin(4*f*x + 4*e) - 2*(2*cos(2*f*x + 2*e) + 3)*sin(3*f*x + 3*e) + 4*(cos(f*x + e) + 2)*sin(2*f*x + 2*e) + 4*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 4*cos(2*f*x + 2*e)*sin(f*x + e) - 6*sin(f*x + e))*sqrt(a)*sqrt(c)/((a*c^3*cos(4*f*x + 4*e)^2 + 16*a*c^3*cos(3*f*x + 3*e)^2 + 36*a*c^3*cos(2*f*x + 2*e)^2 + 16*a*c^3*cos(f*x + e)^2 + a*c^3*sin(4*f*x + 4*e)^2 + 16*a*c^3*sin(3*f*x + 3*e)^2 + 36*a*c^3*sin(2*f*x + 2*e)^2 - 48*a*c^3*sin(2*f*x + 2*e)*sin(f*x + e) + 16*a*c^3*sin(f*x + e)^2 - 8*a*c^3*cos(f*x + e) + a*c^3 - 2*(4*a*c^3*cos(3*f*x + 3*e) - 6*a*c^3*cos(2*f*x + 2*e) + 4*a*c^3*cos(f*x + e) - a*c^3)*cos(4*f*x + 4*e) - 8*(6*a*c^3*cos(2*f*x + 2*e) - 4*a*c^3*cos(f*x + e) + a*c^3)*cos(3*f*x + 3*e) - 12*(4*a*c^3*cos(f*x + e) - a*c^3)*cos(2*f*x + 2*e) - 4*(2*a*c^3*sin(3*f*x + 3*e) - 3*a*c^3*sin(2*f*x + 2*e) + 2*a*c^3*sin(f*x + e))*sin(4*f*x + 4*e) - 16*(3*a*c^3*sin(2*f*x + 2*e) - 2*a*c^3*sin(f*x + e))*sin(3*f*x + 3*e))*f)","B",0
139,1,2035,0,0.748988," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(8 \, c^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 8 \, c^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 8 \, c^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 8 \, c^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \cos\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 2 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, c^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, c^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 2 \, c^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 \, {\left(c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) + 2 \, c^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 \, {\left(c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(16 \, c^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 5 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) - 6 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) + 8 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(5 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) + 6 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) - 8 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(16 \, c^{2} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 5 \, c^{2} \cos\left(4 \, f x + 4 \, e\right) + 6 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 5 \, c^{2} + 8 \, {\left(c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(5 \, c^{2} \cos\left(4 \, f x + 4 \, e\right) + 6 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 5 \, c^{2} + 8 \, {\left(c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} + 2 \, {\left(2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 2 \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 2 \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} f}"," ",0,"-2*(8*c^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*c^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*c^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*c^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*c^2*cos(2*f*x + 2*e)*sin(4*f*x + 4*e) + 2*c^2*cos(4*f*x + 4*e)*sin(2*f*x + 2*e) + 2*c^2*sin(2*f*x + 2*e) + 2*(c^2*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e)^2 + c^2*sin(4*f*x + 4*e)^2 + 4*c^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*c^2*sin(2*f*x + 2*e)^2 + 4*c^2*cos(2*f*x + 2*e) + c^2 + 2*(2*c^2*cos(2*f*x + 2*e) + c^2)*cos(4*f*x + 4*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*(c^2*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c^2*sin(4*f*x + 4*e)^2 + 4*c^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*c^2*sin(2*f*x + 2*e)^2 + 4*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*c^2*cos(2*f*x + 2*e) + c^2 + 2*(2*c^2*cos(2*f*x + 2*e) + c^2)*cos(4*f*x + 4*e) + 4*(c^2*cos(4*f*x + 4*e) + 2*c^2*cos(2*f*x + 2*e) + 2*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c^2)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(c^2*cos(4*f*x + 4*e) + 2*c^2*cos(2*f*x + 2*e) + c^2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(c^2*sin(4*f*x + 4*e) + 2*c^2*sin(2*f*x + 2*e) + 2*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(c^2*sin(4*f*x + 4*e) + 2*c^2*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*arctan2(sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (16*c^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*c^2*sin(4*f*x + 4*e) - 6*c^2*sin(2*f*x + 2*e) + 8*(c^2*cos(4*f*x + 4*e) + 2*c^2*cos(2*f*x + 2*e) + c^2)*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (5*c^2*sin(4*f*x + 4*e) + 6*c^2*sin(2*f*x + 2*e) - 8*(c^2*cos(4*f*x + 4*e) + 2*c^2*cos(2*f*x + 2*e) + c^2)*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (16*c^2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 5*c^2*cos(4*f*x + 4*e) + 6*c^2*cos(2*f*x + 2*e) + 5*c^2 + 8*(c^2*sin(4*f*x + 4*e) + 2*c^2*sin(2*f*x + 2*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (5*c^2*cos(4*f*x + 4*e) + 6*c^2*cos(2*f*x + 2*e) + 5*c^2 + 8*(c^2*sin(4*f*x + 4*e) + 2*c^2*sin(2*f*x + 2*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((a^2*cos(4*f*x + 4*e)^2 + 4*a^2*cos(2*f*x + 2*e)^2 + 4*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a^2*sin(4*f*x + 4*e)^2 + 4*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*a^2*sin(2*f*x + 2*e)^2 + 4*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a^2*cos(2*f*x + 2*e) + a^2 + 2*(2*a^2*cos(2*f*x + 2*e) + a^2)*cos(4*f*x + 4*e) + 4*(a^2*cos(4*f*x + 4*e) + 2*a^2*cos(2*f*x + 2*e) + 2*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^2)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(a^2*cos(4*f*x + 4*e) + 2*a^2*cos(2*f*x + 2*e) + a^2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(a^2*sin(4*f*x + 4*e) + 2*a^2*sin(2*f*x + 2*e) + 2*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(a^2*sin(4*f*x + 4*e) + 2*a^2*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
140,1,99,0,0.468087," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{\frac{c^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{\sqrt{-a} a} + \frac{c^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{\sqrt{-a} a} + \frac{c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{\sqrt{-a} a {\left(\cos\left(f x + e\right) + 1\right)}^{2}}}{f}"," ",0,"(c^(3/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(sqrt(-a)*a) + c^(3/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(sqrt(-a)*a) + c^(3/2)*sin(f*x + e)^2/(sqrt(-a)*a*(cos(f*x + e) + 1)^2))/f","A",0
141,1,54,0,0.466431," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{c} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}{2 \, \sqrt{-a} a f}"," ",0,"1/2*sqrt(c)*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(sqrt(-a)*a*f)","A",0
142,1,397,0,0.578289," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(2 \, {\left(2 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(f x + e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, \sin\left(f x + e\right)^{2} + 4 \, \cos\left(f x + e\right) + 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(f x + e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, \sin\left(f x + e\right)^{2} + 4 \, \cos\left(f x + e\right) + 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) - 2 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 2 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{2 \, {\left(a^{2} c \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} c \cos\left(f x + e\right)^{2} + a^{2} c \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} c \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, a^{2} c \sin\left(f x + e\right)^{2} + 4 \, a^{2} c \cos\left(f x + e\right) + a^{2} c + 2 \, {\left(2 \, a^{2} c \cos\left(f x + e\right) + a^{2} c\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} f}"," ",0,"-1/2*((2*(2*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + cos(2*f*x + 2*e)^2 + 4*cos(f*x + e)^2 + sin(2*f*x + 2*e)^2 + 4*sin(2*f*x + 2*e)*sin(f*x + e) + 4*sin(f*x + e)^2 + 4*cos(f*x + e) + 1)*arctan2(sin(f*x + e), cos(f*x + e) + 1) - (2*(2*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + cos(2*f*x + 2*e)^2 + 4*cos(f*x + e)^2 + sin(2*f*x + 2*e)^2 + 4*sin(2*f*x + 2*e)*sin(f*x + e) + 4*sin(f*x + e)^2 + 4*cos(f*x + e) + 1)*arctan2(sin(f*x + e), cos(f*x + e) - 1) - 2*cos(f*x + e)*sin(2*f*x + 2*e) + 2*cos(2*f*x + 2*e)*sin(f*x + e) + 2*sin(f*x + e))*sqrt(a)*sqrt(c)/((a^2*c*cos(2*f*x + 2*e)^2 + 4*a^2*c*cos(f*x + e)^2 + a^2*c*sin(2*f*x + 2*e)^2 + 4*a^2*c*sin(2*f*x + 2*e)*sin(f*x + e) + 4*a^2*c*sin(f*x + e)^2 + 4*a^2*c*cos(f*x + e) + a^2*c + 2*(2*a^2*c*cos(f*x + e) + a^2*c)*cos(2*f*x + 2*e))*f)","B",0
143,1,567,0,0.583637," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{{\left({\left(2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \cos\left(4 \, f x + 4 \, e\right) - \cos\left(4 \, f x + 4 \, e\right)^{2} - 4 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 4 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \cos\left(4 \, f x + 4 \, e\right) - \cos\left(4 \, f x + 4 \, e\right)^{2} - 4 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 4 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) - 2 \, {\left(\sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(\cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) - 4 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 4 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 2 \, \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{2 \, {\left(a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} - 4 \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} - 4 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{2} - 2 \, {\left(2 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) - a^{2} c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)\right)} f}"," ",0,"1/2*((2*(2*cos(2*f*x + 2*e) - 1)*cos(4*f*x + 4*e) - cos(4*f*x + 4*e)^2 - 4*cos(2*f*x + 2*e)^2 - sin(4*f*x + 4*e)^2 + 4*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) - 4*sin(2*f*x + 2*e)^2 + 4*cos(2*f*x + 2*e) - 1)*arctan2(sin(f*x + e), cos(f*x + e) + 1) - (2*(2*cos(2*f*x + 2*e) - 1)*cos(4*f*x + 4*e) - cos(4*f*x + 4*e)^2 - 4*cos(2*f*x + 2*e)^2 - sin(4*f*x + 4*e)^2 + 4*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) - 4*sin(2*f*x + 2*e)^2 + 4*cos(2*f*x + 2*e) - 1)*arctan2(sin(f*x + e), cos(f*x + e) - 1) - 2*(sin(3*f*x + 3*e) + sin(f*x + e))*cos(4*f*x + 4*e) + 2*(cos(3*f*x + 3*e) + cos(f*x + e))*sin(4*f*x + 4*e) + 2*(2*cos(2*f*x + 2*e) - 1)*sin(3*f*x + 3*e) - 4*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 4*cos(f*x + e)*sin(2*f*x + 2*e) + 4*cos(2*f*x + 2*e)*sin(f*x + e) - 2*sin(f*x + e))*sqrt(a)*sqrt(c)/((a^2*c^2*cos(4*f*x + 4*e)^2 + 4*a^2*c^2*cos(2*f*x + 2*e)^2 + a^2*c^2*sin(4*f*x + 4*e)^2 - 4*a^2*c^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*a^2*c^2*sin(2*f*x + 2*e)^2 - 4*a^2*c^2*cos(2*f*x + 2*e) + a^2*c^2 - 2*(2*a^2*c^2*cos(2*f*x + 2*e) - a^2*c^2)*cos(4*f*x + 4*e))*f)","B",0
144,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
145,1,133,0,0.468376," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, c^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{\sqrt{-a} a^{2}} + \frac{2 \, c^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{\sqrt{-a} a^{2}} - \frac{\frac{2 \, \sqrt{-a} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sqrt{-a} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}}{a^{3}}}{2 \, f}"," ",0,"-1/2*(2*c^(5/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(sqrt(-a)*a^2) + 2*c^(5/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(sqrt(-a)*a^2) - (2*sqrt(-a)*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sqrt(-a)*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)/a^3)/f","A",0
146,1,98,0,0.472359," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{\sqrt{-a} c^{\frac{3}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)} \sin\left(f x + e\right)^{4}}{4 \, {\left(a^{3} - \frac{a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} f {\left(\cos\left(f x + e\right) + 1\right)}^{4}}"," ",0,"-1/4*sqrt(-a)*c^(3/2)*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)*sin(f*x + e)^4/((a^3 - a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*f*(cos(f*x + e) + 1)^4)","B",0
147,1,58,0,0.459579," ","integrate(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{\sqrt{c} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{2} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{2}}{8 \, \sqrt{-a} a^{2} f}"," ",0,"-1/8*sqrt(c)*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^2*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^2/(sqrt(-a)*a^2*f)","A",0
148,1,1191,0,0.640284," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(2 \, {\left(4 \, \cos\left(3 \, f x + 3 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\right) + 4 \, \cos\left(f x + e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + \cos\left(4 \, f x + 4 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(2 \, f x + 2 \, e\right) + 4 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) + 16 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 36 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(2 \, \sin\left(3 \, f x + 3 \, e\right) + 3 \, \sin\left(2 \, f x + 2 \, e\right) + 2 \, \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(2 \, f x + 2 \, e\right) + 2 \, \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + 16 \, \sin\left(3 \, f x + 3 \, e\right)^{2} + 36 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 48 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 16 \, \sin\left(f x + e\right)^{2} + 8 \, \cos\left(f x + e\right) + 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - {\left(2 \, {\left(4 \, \cos\left(3 \, f x + 3 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\right) + 4 \, \cos\left(f x + e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + \cos\left(4 \, f x + 4 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(2 \, f x + 2 \, e\right) + 4 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) + 16 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 36 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(2 \, \sin\left(3 \, f x + 3 \, e\right) + 3 \, \sin\left(2 \, f x + 2 \, e\right) + 2 \, \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(2 \, f x + 2 \, e\right) + 2 \, \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + 16 \, \sin\left(3 \, f x + 3 \, e\right)^{2} + 36 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 48 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 16 \, \sin\left(f x + e\right)^{2} + 8 \, \cos\left(f x + e\right) + 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) + 2 \, {\left(3 \, \sin\left(3 \, f x + 3 \, e\right) + 4 \, \sin\left(2 \, f x + 2 \, e\right) + 3 \, \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 2 \, {\left(3 \, \cos\left(3 \, f x + 3 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) + 3\right)} \sin\left(3 \, f x + 3 \, e\right) - 4 \, {\left(\cos\left(f x + e\right) - 2\right)} \sin\left(2 \, f x + 2 \, e\right) - 4 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 6 \, \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{4 \, {\left(a^{3} c \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, a^{3} c \cos\left(3 \, f x + 3 \, e\right)^{2} + 36 \, a^{3} c \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, a^{3} c \cos\left(f x + e\right)^{2} + a^{3} c \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, a^{3} c \sin\left(3 \, f x + 3 \, e\right)^{2} + 36 \, a^{3} c \sin\left(2 \, f x + 2 \, e\right)^{2} + 48 \, a^{3} c \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 16 \, a^{3} c \sin\left(f x + e\right)^{2} + 8 \, a^{3} c \cos\left(f x + e\right) + a^{3} c + 2 \, {\left(4 \, a^{3} c \cos\left(3 \, f x + 3 \, e\right) + 6 \, a^{3} c \cos\left(2 \, f x + 2 \, e\right) + 4 \, a^{3} c \cos\left(f x + e\right) + a^{3} c\right)} \cos\left(4 \, f x + 4 \, e\right) + 8 \, {\left(6 \, a^{3} c \cos\left(2 \, f x + 2 \, e\right) + 4 \, a^{3} c \cos\left(f x + e\right) + a^{3} c\right)} \cos\left(3 \, f x + 3 \, e\right) + 12 \, {\left(4 \, a^{3} c \cos\left(f x + e\right) + a^{3} c\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(2 \, a^{3} c \sin\left(3 \, f x + 3 \, e\right) + 3 \, a^{3} c \sin\left(2 \, f x + 2 \, e\right) + 2 \, a^{3} c \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 16 \, {\left(3 \, a^{3} c \sin\left(2 \, f x + 2 \, e\right) + 2 \, a^{3} c \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} f}"," ",0,"-1/4*((2*(4*cos(3*f*x + 3*e) + 6*cos(2*f*x + 2*e) + 4*cos(f*x + e) + 1)*cos(4*f*x + 4*e) + cos(4*f*x + 4*e)^2 + 8*(6*cos(2*f*x + 2*e) + 4*cos(f*x + e) + 1)*cos(3*f*x + 3*e) + 16*cos(3*f*x + 3*e)^2 + 12*(4*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 36*cos(2*f*x + 2*e)^2 + 16*cos(f*x + e)^2 + 4*(2*sin(3*f*x + 3*e) + 3*sin(2*f*x + 2*e) + 2*sin(f*x + e))*sin(4*f*x + 4*e) + sin(4*f*x + 4*e)^2 + 16*(3*sin(2*f*x + 2*e) + 2*sin(f*x + e))*sin(3*f*x + 3*e) + 16*sin(3*f*x + 3*e)^2 + 36*sin(2*f*x + 2*e)^2 + 48*sin(2*f*x + 2*e)*sin(f*x + e) + 16*sin(f*x + e)^2 + 8*cos(f*x + e) + 1)*arctan2(sin(f*x + e), cos(f*x + e) + 1) - (2*(4*cos(3*f*x + 3*e) + 6*cos(2*f*x + 2*e) + 4*cos(f*x + e) + 1)*cos(4*f*x + 4*e) + cos(4*f*x + 4*e)^2 + 8*(6*cos(2*f*x + 2*e) + 4*cos(f*x + e) + 1)*cos(3*f*x + 3*e) + 16*cos(3*f*x + 3*e)^2 + 12*(4*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 36*cos(2*f*x + 2*e)^2 + 16*cos(f*x + e)^2 + 4*(2*sin(3*f*x + 3*e) + 3*sin(2*f*x + 2*e) + 2*sin(f*x + e))*sin(4*f*x + 4*e) + sin(4*f*x + 4*e)^2 + 16*(3*sin(2*f*x + 2*e) + 2*sin(f*x + e))*sin(3*f*x + 3*e) + 16*sin(3*f*x + 3*e)^2 + 36*sin(2*f*x + 2*e)^2 + 48*sin(2*f*x + 2*e)*sin(f*x + e) + 16*sin(f*x + e)^2 + 8*cos(f*x + e) + 1)*arctan2(sin(f*x + e), cos(f*x + e) - 1) + 2*(3*sin(3*f*x + 3*e) + 4*sin(2*f*x + 2*e) + 3*sin(f*x + e))*cos(4*f*x + 4*e) - 2*(3*cos(3*f*x + 3*e) + 4*cos(2*f*x + 2*e) + 3*cos(f*x + e))*sin(4*f*x + 4*e) + 2*(2*cos(2*f*x + 2*e) + 3)*sin(3*f*x + 3*e) - 4*(cos(f*x + e) - 2)*sin(2*f*x + 2*e) - 4*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) + 4*cos(2*f*x + 2*e)*sin(f*x + e) + 6*sin(f*x + e))*sqrt(a)*sqrt(c)/((a^3*c*cos(4*f*x + 4*e)^2 + 16*a^3*c*cos(3*f*x + 3*e)^2 + 36*a^3*c*cos(2*f*x + 2*e)^2 + 16*a^3*c*cos(f*x + e)^2 + a^3*c*sin(4*f*x + 4*e)^2 + 16*a^3*c*sin(3*f*x + 3*e)^2 + 36*a^3*c*sin(2*f*x + 2*e)^2 + 48*a^3*c*sin(2*f*x + 2*e)*sin(f*x + e) + 16*a^3*c*sin(f*x + e)^2 + 8*a^3*c*cos(f*x + e) + a^3*c + 2*(4*a^3*c*cos(3*f*x + 3*e) + 6*a^3*c*cos(2*f*x + 2*e) + 4*a^3*c*cos(f*x + e) + a^3*c)*cos(4*f*x + 4*e) + 8*(6*a^3*c*cos(2*f*x + 2*e) + 4*a^3*c*cos(f*x + e) + a^3*c)*cos(3*f*x + 3*e) + 12*(4*a^3*c*cos(f*x + e) + a^3*c)*cos(2*f*x + 2*e) + 4*(2*a^3*c*sin(3*f*x + 3*e) + 3*a^3*c*sin(2*f*x + 2*e) + 2*a^3*c*sin(f*x + e))*sin(4*f*x + 4*e) + 16*(3*a^3*c*sin(2*f*x + 2*e) + 2*a^3*c*sin(f*x + e))*sin(3*f*x + 3*e))*f)","B",0
149,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
150,1,1659,0,0.821691," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left(3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) - 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \cos\left(8 \, f x + 8 \, e\right) - \cos\left(8 \, f x + 8 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) - 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) - 16 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \cos\left(4 \, f x + 4 \, e\right) - 36 \, \cos\left(4 \, f x + 4 \, e\right)^{2} - 16 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) - 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) - 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, \sin\left(6 \, f x + 6 \, e\right)^{2} - 36 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 16 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) - 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \cos\left(8 \, f x + 8 \, e\right) - \cos\left(8 \, f x + 8 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) - 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) - 16 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \cos\left(4 \, f x + 4 \, e\right) - 36 \, \cos\left(4 \, f x + 4 \, e\right)^{2} - 16 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) - 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) - 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, \sin\left(6 \, f x + 6 \, e\right)^{2} - 36 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 16 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) - 2 \, {\left(5 \, \sin\left(7 \, f x + 7 \, e\right) + 3 \, \sin\left(5 \, f x + 5 \, e\right) + 3 \, \sin\left(3 \, f x + 3 \, e\right) + 5 \, \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) - 20 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) - 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) + 8 \, {\left(3 \, \sin\left(5 \, f x + 5 \, e\right) + 3 \, \sin\left(3 \, f x + 3 \, e\right) + 5 \, \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 12 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) - 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - 12 \, {\left(3 \, \sin\left(3 \, f x + 3 \, e\right) + 5 \, \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(5 \, \cos\left(7 \, f x + 7 \, e\right) + 3 \, \cos\left(5 \, f x + 5 \, e\right) + 3 \, \cos\left(3 \, f x + 3 \, e\right) + 5 \, \cos\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 10 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) - 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(7 \, f x + 7 \, e\right) - 8 \, {\left(3 \, \cos\left(5 \, f x + 5 \, e\right) + 3 \, \cos\left(3 \, f x + 3 \, e\right) + 5 \, \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 6 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) - 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(5 \, f x + 5 \, e\right) + 12 \, {\left(3 \, \cos\left(3 \, f x + 3 \, e\right) + 5 \, \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 6 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) - 24 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 40 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 40 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 10 \, \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{8 \, {\left(a^{3} c^{3} \cos\left(8 \, f x + 8 \, e\right)^{2} + 16 \, a^{3} c^{3} \cos\left(6 \, f x + 6 \, e\right)^{2} + 36 \, a^{3} c^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, a^{3} c^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{3} c^{3} \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, a^{3} c^{3} \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, a^{3} c^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} - 48 \, a^{3} c^{3} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, a^{3} c^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} - 8 \, a^{3} c^{3} \cos\left(2 \, f x + 2 \, e\right) + a^{3} c^{3} - 2 \, {\left(4 \, a^{3} c^{3} \cos\left(6 \, f x + 6 \, e\right) - 6 \, a^{3} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 4 \, a^{3} c^{3} \cos\left(2 \, f x + 2 \, e\right) - a^{3} c^{3}\right)} \cos\left(8 \, f x + 8 \, e\right) - 8 \, {\left(6 \, a^{3} c^{3} \cos\left(4 \, f x + 4 \, e\right) - 4 \, a^{3} c^{3} \cos\left(2 \, f x + 2 \, e\right) + a^{3} c^{3}\right)} \cos\left(6 \, f x + 6 \, e\right) - 12 \, {\left(4 \, a^{3} c^{3} \cos\left(2 \, f x + 2 \, e\right) - a^{3} c^{3}\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(2 \, a^{3} c^{3} \sin\left(6 \, f x + 6 \, e\right) - 3 \, a^{3} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{3} c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 16 \, {\left(3 \, a^{3} c^{3} \sin\left(4 \, f x + 4 \, e\right) - 2 \, a^{3} c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right)\right)} f}"," ",0,"1/8*(3*(2*(4*cos(6*f*x + 6*e) - 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) - 1)*cos(8*f*x + 8*e) - cos(8*f*x + 8*e)^2 + 8*(6*cos(4*f*x + 4*e) - 4*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) - 16*cos(6*f*x + 6*e)^2 + 12*(4*cos(2*f*x + 2*e) - 1)*cos(4*f*x + 4*e) - 36*cos(4*f*x + 4*e)^2 - 16*cos(2*f*x + 2*e)^2 + 4*(2*sin(6*f*x + 6*e) - 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) - sin(8*f*x + 8*e)^2 + 16*(3*sin(4*f*x + 4*e) - 2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 16*sin(6*f*x + 6*e)^2 - 36*sin(4*f*x + 4*e)^2 + 48*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) - 16*sin(2*f*x + 2*e)^2 + 8*cos(2*f*x + 2*e) - 1)*arctan2(sin(f*x + e), cos(f*x + e) + 1) - 3*(2*(4*cos(6*f*x + 6*e) - 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) - 1)*cos(8*f*x + 8*e) - cos(8*f*x + 8*e)^2 + 8*(6*cos(4*f*x + 4*e) - 4*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) - 16*cos(6*f*x + 6*e)^2 + 12*(4*cos(2*f*x + 2*e) - 1)*cos(4*f*x + 4*e) - 36*cos(4*f*x + 4*e)^2 - 16*cos(2*f*x + 2*e)^2 + 4*(2*sin(6*f*x + 6*e) - 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) - sin(8*f*x + 8*e)^2 + 16*(3*sin(4*f*x + 4*e) - 2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 16*sin(6*f*x + 6*e)^2 - 36*sin(4*f*x + 4*e)^2 + 48*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) - 16*sin(2*f*x + 2*e)^2 + 8*cos(2*f*x + 2*e) - 1)*arctan2(sin(f*x + e), cos(f*x + e) - 1) - 2*(5*sin(7*f*x + 7*e) + 3*sin(5*f*x + 5*e) + 3*sin(3*f*x + 3*e) + 5*sin(f*x + e))*cos(8*f*x + 8*e) - 20*(2*sin(6*f*x + 6*e) - 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*cos(7*f*x + 7*e) + 8*(3*sin(5*f*x + 5*e) + 3*sin(3*f*x + 3*e) + 5*sin(f*x + e))*cos(6*f*x + 6*e) + 12*(3*sin(4*f*x + 4*e) - 2*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - 12*(3*sin(3*f*x + 3*e) + 5*sin(f*x + e))*cos(4*f*x + 4*e) + 2*(5*cos(7*f*x + 7*e) + 3*cos(5*f*x + 5*e) + 3*cos(3*f*x + 3*e) + 5*cos(f*x + e))*sin(8*f*x + 8*e) + 10*(4*cos(6*f*x + 6*e) - 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) - 1)*sin(7*f*x + 7*e) - 8*(3*cos(5*f*x + 5*e) + 3*cos(3*f*x + 3*e) + 5*cos(f*x + e))*sin(6*f*x + 6*e) - 6*(6*cos(4*f*x + 4*e) - 4*cos(2*f*x + 2*e) + 1)*sin(5*f*x + 5*e) + 12*(3*cos(3*f*x + 3*e) + 5*cos(f*x + e))*sin(4*f*x + 4*e) + 6*(4*cos(2*f*x + 2*e) - 1)*sin(3*f*x + 3*e) - 24*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 40*cos(f*x + e)*sin(2*f*x + 2*e) + 40*cos(2*f*x + 2*e)*sin(f*x + e) - 10*sin(f*x + e))*sqrt(a)*sqrt(c)/((a^3*c^3*cos(8*f*x + 8*e)^2 + 16*a^3*c^3*cos(6*f*x + 6*e)^2 + 36*a^3*c^3*cos(4*f*x + 4*e)^2 + 16*a^3*c^3*cos(2*f*x + 2*e)^2 + a^3*c^3*sin(8*f*x + 8*e)^2 + 16*a^3*c^3*sin(6*f*x + 6*e)^2 + 36*a^3*c^3*sin(4*f*x + 4*e)^2 - 48*a^3*c^3*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 16*a^3*c^3*sin(2*f*x + 2*e)^2 - 8*a^3*c^3*cos(2*f*x + 2*e) + a^3*c^3 - 2*(4*a^3*c^3*cos(6*f*x + 6*e) - 6*a^3*c^3*cos(4*f*x + 4*e) + 4*a^3*c^3*cos(2*f*x + 2*e) - a^3*c^3)*cos(8*f*x + 8*e) - 8*(6*a^3*c^3*cos(4*f*x + 4*e) - 4*a^3*c^3*cos(2*f*x + 2*e) + a^3*c^3)*cos(6*f*x + 6*e) - 12*(4*a^3*c^3*cos(2*f*x + 2*e) - a^3*c^3)*cos(4*f*x + 4*e) - 4*(2*a^3*c^3*sin(6*f*x + 6*e) - 3*a^3*c^3*sin(4*f*x + 4*e) + 2*a^3*c^3*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) - 16*(3*a^3*c^3*sin(4*f*x + 4*e) - 2*a^3*c^3*sin(2*f*x + 2*e))*sin(6*f*x + 6*e))*f)","B",0
151,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x, algorithm=""maxima"")","\int {\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)\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*(-c*sec(f*x + e) + c)^n*sec(f*x + e), x)","F",0
152,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(c \sec\left(f x + e\right) - c\right)}^{2} {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((c*sec(f*x + e) - c)^2*(a*sec(f*x + e) + a)^m*sec(f*x + e), x)","F",0
153,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\int {\left(c \sec\left(f x + e\right) - c\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)\,{d x}"," ",0,"-integrate((c*sec(f*x + e) - c)*(a*sec(f*x + e) + a)^m*sec(f*x + e), x)","F",0
154,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\int \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}\,{d x}"," ",0,"-integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)/(c*sec(f*x + e) - c), x)","F",0
155,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\int \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)}^{2}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)/(c*sec(f*x + e) - c)^2, x)","F",0
156,1,228,0,0.476739," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\sqrt{2} {\left(2^{m + 5} m + 5 \cdot 2^{m + 4}\right)} \left(-a\right)^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{\sqrt{2} {\left(2^{m + 4} m^{2} + 2^{m + 6} m + 15 \cdot 2^{m + 2}\right)} \left(-a\right)^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 2^{m + \frac{11}{2}} \left(-a\right)^{m} c^{\frac{5}{2}}\right)} e^{\left(-m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)\right)}}{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{5}{2}}}"," ",0,"-2*(sqrt(2)*(2^(m + 5)*m + 5*2^(m + 4))*(-a)^m*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - sqrt(2)*(2^(m + 4)*m^2 + 2^(m + 6)*m + 15*2^(m + 2))*(-a)^m*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2^(m + 11/2)*(-a)^m*c^(5/2))*e^(-m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1))/((8*m^3 + 36*m^2 + 46*m + 15)*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(5/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(5/2))","A",0
157,1,171,0,0.465426," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{2} 2^{m + 2} \left(-a\right)^{m} c^{\frac{3}{2}} - \frac{\sqrt{2} {\left(2^{m + 2} m + 3 \cdot 2^{m + 1}\right)} \left(-a\right)^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} e^{\left(-m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)\right)}}{{\left(4 \, m^{2} + 8 \, m + 3\right)} f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}^{\frac{3}{2}}}"," ",0,"-2*(sqrt(2)*2^(m + 2)*(-a)^m*c^(3/2) - sqrt(2)*(2^(m + 2)*m + 3*2^(m + 1))*(-a)^m*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*e^(-m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1))/((4*m^2 + 8*m + 3)*f*(sin(f*x + e)/(cos(f*x + e) + 1) + 1)^(3/2)*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)^(3/2))","A",0
158,1,114,0,0.462173," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{2^{m + \frac{3}{2}} \left(-a\right)^{m} \sqrt{c} e^{\left(-m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)\right)}}{f {\left(2 \, m + 1\right)} \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1} \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1}}"," ",0,"2^(m + 3/2)*(-a)^m*sqrt(c)*e^(-m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1))/(f*(2*m + 1)*sqrt(sin(f*x + e)/(cos(f*x + e) + 1) + 1)*sqrt(sin(f*x + e)/(cos(f*x + e) + 1) - 1))","B",0
159,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)}{\sqrt{-c \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)/sqrt(-c*sec(f*x + e) + c), x)","F",0
160,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \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)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)/(-c*sec(f*x + e) + c)^(3/2), x)","F",0
161,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \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)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)/(-c*sec(f*x + e) + c)^(5/2), x)","F",0
162,1,156,0,0.660539," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-3-m),x, algorithm=""maxima"")","\frac{{\left({\left(4 \, m^{2} + 8 \, m + 3\right)} \left(-a\right)^{m} - \frac{2 \, {\left(4 \, m^{2} + 12 \, m + 5\right)} \left(-a\right)^{m} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(4 \, m^{2} + 16 \, m + 15\right)} \left(-a\right)^{m} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} c^{-m - 3} {\left(\cos\left(f x + e\right) + 1\right)}^{5}}{4 \, {\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} f \left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)^{2 \, m} \sin\left(f x + e\right)^{5}}"," ",0,"1/4*((4*m^2 + 8*m + 3)*(-a)^m - 2*(4*m^2 + 12*m + 5)*(-a)^m*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (4*m^2 + 16*m + 15)*(-a)^m*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*c^(-m - 3)*(cos(f*x + e) + 1)^5/((8*m^3 + 36*m^2 + 46*m + 15)*f*(sin(f*x + e)/(cos(f*x + e) + 1))^(2*m)*sin(f*x + e)^5)","A",0
163,1,107,0,0.834185," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-2-m),x, algorithm=""maxima"")","-\frac{{\left(\left(-a\right)^{m} {\left(2 \, m + 1\right)} - \frac{\left(-a\right)^{m} {\left(2 \, m + 3\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} c^{-m - 2} {\left(\cos\left(f x + e\right) + 1\right)}^{3}}{2 \, {\left(4 \, m^{2} + 8 \, m + 3\right)} f \left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)^{2 \, m} \sin\left(f x + e\right)^{3}}"," ",0,"-1/2*((-a)^m*(2*m + 1) - (-a)^m*(2*m + 3)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*c^(-m - 2)*(cos(f*x + e) + 1)^3/((4*m^2 + 8*m + 3)*f*(sin(f*x + e)/(cos(f*x + e) + 1))^(2*m)*sin(f*x + e)^3)","A",0
164,1,62,0,0.596854," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-1-m),x, algorithm=""maxima"")","\frac{\left(-a\right)^{m} c^{-m - 1} {\left(\cos\left(f x + e\right) + 1\right)}}{f {\left(2 \, m + 1\right)} \left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)^{2 \, m} \sin\left(f x + e\right)}"," ",0,"(-a)^m*c^(-m - 1)*(cos(f*x + e) + 1)/(f*(2*m + 1)*(sin(f*x + e)/(cos(f*x + e) + 1))^(2*m)*sin(f*x + e))","A",0
165,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m/((c-c*sec(f*x+e))^m),x, algorithm=""maxima"")","\int \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}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)/(-c*sec(f*x + e) + c)^m, x)","F",0
166,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(1-m),x, algorithm=""maxima"")","\int {\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)\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*(-c*sec(f*x + e) + c)^(-m + 1)*sec(f*x + e), x)","F",0
167,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(2-m),x, algorithm=""maxima"")","\int {\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)\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*(-c*sec(f*x + e) + c)^(-m + 2)*sec(f*x + e), x)","F",0
168,1,172,0,0.459396," ","integrate(sec(f*x+e)^2*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{8 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{3} c - 15 \, a^{3} c {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 60 \, a^{3} c {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 120 \, a^{3} c \tan\left(f x + e\right)}{120 \, f}"," ",0,"-1/120*(8*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*c - 15*a^3*c*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) + 60*a^3*c*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 120*a^3*c*tan(f*x + e))/f","A",0
169,1,160,0,0.476484," ","integrate(sec(f*x+e)^2*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{16 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c - 3 \, a^{2} c {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 12 \, a^{2} c {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 48 \, a^{2} c \tan\left(f x + e\right)}{48 \, f}"," ",0,"-1/48*(16*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c - 3*a^2*c*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) + 12*a^2*c*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 48*a^2*c*tan(f*x + e))/f","B",0
170,1,36,0,0.555480," ","integrate(sec(f*x+e)^2*(a+a*sec(f*x+e))*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{{\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a c - 3 \, a c \tan\left(f x + e\right)}{3 \, f}"," ",0,"-1/3*((tan(f*x + e)^3 + 3*tan(f*x + e))*a*c - 3*a*c*tan(f*x + e))/f","B",0
171,1,194,0,0.412969," ","integrate(sec(f*x+e)^2*(c-c*sec(f*x+e))/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{c {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(f x + e\right)}{{\left(a - \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + c {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)}}{f}"," ",0,"(c*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - 2*sin(f*x + e)/((a - a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) - sin(f*x + e)/(a*(cos(f*x + e) + 1))) + c*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))))/f","B",0
172,1,144,0,0.606846," ","integrate(sec(f*x+e)^2*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{c {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + \frac{c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"1/6*(c*((9*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","B",0
173,1,115,0,0.512210," ","integrate(sec(f*x+e)^2*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{\frac{c {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{3 \, c {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"-1/60*(c*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 3*c*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","A",0
174,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\int {\left(a \sec\left(f x + e\right) + a\right)}^{2} {\left(c \sec\left(f x + e\right) - c\right)} \left(g \sec\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"-integrate((a*sec(f*x + e) + a)^2*(c*sec(f*x + e) - c)*(g*sec(f*x + e))^p, x)","F",0
175,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p*(a+a*sec(f*x+e))*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\int {\left(a \sec\left(f x + e\right) + a\right)} {\left(c \sec\left(f x + e\right) - c\right)} \left(g \sec\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"-integrate((a*sec(f*x + e) + a)*(c*sec(f*x + e) - c)*(g*sec(f*x + e))^p, x)","F",0
176,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p*(c-c*sec(f*x+e))/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","-\int \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}\,{d x}"," ",0,"-integrate((c*sec(f*x + e) - c)*(g*sec(f*x + e))^p/(a*sec(f*x + e) + a), x)","F",0
177,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\int \frac{{\left(c \sec\left(f x + e\right) - c\right)} \left(g \sec\left(f x + e\right)\right)^{p}}{{\left(a \sec\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"-integrate((c*sec(f*x + e) - c)*(g*sec(f*x + e))^p/(a*sec(f*x + e) + a)^2, x)","F",0
178,1,979,0,1.223852," ","integrate((g*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(4 \, \sqrt{2} g \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, \sqrt{2} g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 \, \sqrt{2} g \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + g \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + g\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) + {\left(g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + g \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + g\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) - {\left(g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + g \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + g\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) + {\left(g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + g \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + g\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right)\right)} \sqrt{a} \sqrt{g}}{2 \, {\left(c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + c \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + c\right)} f}"," ",0,"1/2*(4*sqrt(2)*g*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*sqrt(2)*g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*sqrt(2)*g*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + g*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + g)*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) + (g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + g*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + g)*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) - (g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + g*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + g)*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) + (g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + g*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + g)*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2))*sqrt(a)*sqrt(g)/((c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c)*f)","B",0
179,0,0,0,0.000000," ","integrate(sec(f*x+e)^2/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\int \frac{\sec\left(f x + e\right)^{2}}{\sqrt{a \sec\left(f x + e\right) + a} {\left(c \sec\left(f x + e\right) - c\right)}}\,{d x}"," ",0,"-integrate(sec(f*x + e)^2/(sqrt(a*sec(f*x + e) + a)*(c*sec(f*x + e) - c)), x)","F",0
180,1,1310,0,1.058424," ","integrate(sec(f*x+e)^(5/2)/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) + {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) - {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 4 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)}{2 \, {\left(\sqrt{2} c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} c \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2} c\right)} \sqrt{a} f}"," ",0,"-1/2*((sqrt(2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) - (sqrt(2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) + (sqrt(2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) - (sqrt(2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) - (cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1)*log(cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1)*log(cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 4*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))/((sqrt(2)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2)*c)*sqrt(a)*f)","B",0
181,1,536,0,1.093625," ","integrate((g*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{{\left(4 \, g \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + g \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + g\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + g \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, g \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + g\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + 4 \, g \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{g}}{2 \, {\left(\sqrt{2} c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} c \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2} c\right)} \sqrt{a} f}"," ",0,"1/2*(4*g*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + g*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + g)*log(cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + g*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*g*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + g)*log(cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + 4*g*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(g)/((sqrt(2)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2)*c)*sqrt(a)*f)","B",0
182,1,1400,0,1.215793," ","integrate((g*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{{\left(4 \, g^{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 \, g^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(\sqrt{2} g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} g^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2} g^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) + {\left(\sqrt{2} g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} g^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2} g^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) - {\left(\sqrt{2} g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} g^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2} g^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) + {\left(\sqrt{2} g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} g^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2} g^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2\right) + {\left(g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + g^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + g^{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + g^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, g^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + g^{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right)\right)} \sqrt{g}}{2 \, {\left(\sqrt{2} c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sqrt{2} c \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sqrt{2} c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + \sqrt{2} c\right)} \sqrt{a} f}"," ",0,"1/2*(4*g^2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*g^2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (sqrt(2)*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*g^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2)*g^2)*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) + (sqrt(2)*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*g^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2)*g^2)*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) - (sqrt(2)*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*g^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2)*g^2)*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) + (sqrt(2)*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*g^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2)*g^2)*log(2*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2) + (g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + g^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + g^2)*log(cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + g^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*g^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + g^2)*log(cos(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/4*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1))*sqrt(g)/((sqrt(2)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sqrt(2)*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sqrt(2)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + sqrt(2)*c)*sqrt(a)*f)","B",0
183,1,56,0,1.090276," ","integrate(sec(f*x+e)^2/(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) - 1\right)}{\sqrt{a} \sqrt{c} f}"," ",0,"-(arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) - 1))/(sqrt(a)*sqrt(c)*f)","A",0
184,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c-d*sec(f*x+e)),x, algorithm=""maxima"")","-\int \frac{\sqrt{a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)}{d \sec\left(f x + e\right) - c}\,{d x}"," ",0,"-integrate(sqrt(a*sec(f*x + e) + a)*sec(f*x + e)/(d*sec(f*x + e) - c), x)","F",0
185,1,379,0,0.381778," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{480 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a c^{2} d^{2} + 320 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a c d^{3} + 16 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a d^{4} - 60 \, a c d^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 15 \, a d^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 240 \, a c^{3} d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 360 \, a c^{2} d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 240 \, a c^{4} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 240 \, a c^{4} \tan\left(f x + e\right) + 960 \, a c^{3} d \tan\left(f x + e\right)}{240 \, f}"," ",0,"1/240*(480*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*c^2*d^2 + 320*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*c*d^3 + 16*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a*d^4 - 60*a*c*d^3*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 15*a*d^4*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 240*a*c^3*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 360*a*c^2*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 240*a*c^4*log(sec(f*x + e) + tan(f*x + e)) + 240*a*c^4*tan(f*x + e) + 960*a*c^3*d*tan(f*x + e))/f","A",0
186,1,266,0,0.620392," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{48 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a c d^{2} + 16 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a d^{3} - 3 \, a d^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 36 \, a c^{2} d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 36 \, a c d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 48 \, a c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 48 \, a c^{3} \tan\left(f x + e\right) + 144 \, a c^{2} d \tan\left(f x + e\right)}{48 \, f}"," ",0,"1/48*(48*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*c*d^2 + 16*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*d^3 - 3*a*d^3*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 36*a*c^2*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 36*a*c*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 48*a*c^3*log(sec(f*x + e) + tan(f*x + e)) + 48*a*c^3*tan(f*x + e) + 144*a*c^2*d*tan(f*x + e))/f","A",0
187,1,165,0,0.469999," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a d^{2} - 6 \, a c d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 3 \, a d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 12 \, a c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 12 \, a c^{2} \tan\left(f x + e\right) + 24 \, a c d \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(4*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*d^2 - 6*a*c*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 3*a*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 12*a*c^2*log(sec(f*x + e) + tan(f*x + e)) + 12*a*c^2*tan(f*x + e) + 24*a*c*d*tan(f*x + e))/f","A",0
188,1,88,0,0.384760," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{a d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 4 \, a c \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 4 \, a c \tan\left(f x + e\right) - 4 \, a d \tan\left(f x + e\right)}{4 \, f}"," ",0,"-1/4*(a*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 4*a*c*log(sec(f*x + e) + tan(f*x + e)) - 4*a*c*tan(f*x + e) - 4*a*d*tan(f*x + e))/f","A",0
189,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
190,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
191,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
192,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
193,1,683,0,0.475369," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{640 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c^{3} d + 1920 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c^{2} d^{2} + 128 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{2} c d^{3} + 640 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c d^{3} + 64 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{2} d^{4} - 5 \, a^{2} d^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(f x + e\right)^{5} - 40 \, \sin\left(f x + e\right)^{3} + 33 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1} - 15 \, \log\left(\sin\left(f x + e\right) + 1\right) + 15 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 180 \, a^{2} c^{2} d^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 240 \, a^{2} c d^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 30 \, a^{2} d^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 120 \, a^{2} c^{4} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 960 \, a^{2} c^{3} d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 720 \, a^{2} c^{2} d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 480 \, a^{2} c^{4} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 960 \, a^{2} c^{4} \tan\left(f x + e\right) + 1920 \, a^{2} c^{3} d \tan\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(640*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c^3*d + 1920*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c^2*d^2 + 128*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^2*c*d^3 + 640*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c*d^3 + 64*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^2*d^4 - 5*a^2*d^4*(2*(15*sin(f*x + e)^5 - 40*sin(f*x + e)^3 + 33*sin(f*x + e))/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1) - 15*log(sin(f*x + e) + 1) + 15*log(sin(f*x + e) - 1)) - 180*a^2*c^2*d^2*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 240*a^2*c*d^3*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 30*a^2*d^4*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 120*a^2*c^4*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 960*a^2*c^3*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 720*a^2*c^2*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 480*a^2*c^4*log(sec(f*x + e) + tan(f*x + e)) + 960*a^2*c^4*tan(f*x + e) + 1920*a^2*c^3*d*tan(f*x + e))/f","B",0
194,1,469,0,0.406899," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{240 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c^{2} d + 480 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c d^{2} + 16 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{2} d^{3} + 80 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} d^{3} - 45 \, a^{2} c d^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 30 \, a^{2} d^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 60 \, a^{2} c^{3} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 360 \, a^{2} c^{2} d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 180 \, a^{2} c d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 240 \, a^{2} c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 480 \, a^{2} c^{3} \tan\left(f x + e\right) + 720 \, a^{2} c^{2} d \tan\left(f x + e\right)}{240 \, f}"," ",0,"1/240*(240*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c^2*d + 480*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c*d^2 + 16*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^2*d^3 + 80*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*d^3 - 45*a^2*c*d^2*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 30*a^2*d^3*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 60*a^2*c^3*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 360*a^2*c^2*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 180*a^2*c*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 240*a^2*c^3*log(sec(f*x + e) + tan(f*x + e)) + 480*a^2*c^3*tan(f*x + e) + 720*a^2*c^2*d*tan(f*x + e))/f","B",0
195,1,324,0,0.627986," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c d + 32 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} d^{2} - 3 \, a^{2} d^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 12 \, a^{2} c^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 48 \, a^{2} c d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 12 \, a^{2} d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 48 \, a^{2} c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 96 \, a^{2} c^{2} \tan\left(f x + e\right) + 96 \, a^{2} c d \tan\left(f x + e\right)}{48 \, f}"," ",0,"1/48*(32*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c*d + 32*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*d^2 - 3*a^2*d^2*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 12*a^2*c^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 48*a^2*c*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 12*a^2*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 48*a^2*c^2*log(sec(f*x + e) + tan(f*x + e)) + 96*a^2*c^2*tan(f*x + e) + 96*a^2*c*d*tan(f*x + e))/f","A",0
196,1,167,0,0.530571," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} d - 3 \, a^{2} c {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 6 \, a^{2} d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 12 \, a^{2} c \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 24 \, a^{2} c \tan\left(f x + e\right) + 12 \, a^{2} d \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(4*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*d - 3*a^2*c*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 6*a^2*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 12*a^2*c*log(sec(f*x + e) + tan(f*x + e)) + 24*a^2*c*tan(f*x + e) + 12*a^2*d*tan(f*x + e))/f","A",0
197,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
198,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
199,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
200,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
201,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
202,1,701,0,0.576701," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{160 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c^{3} + 1440 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c^{2} d + 96 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{3} c d^{2} + 1440 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c d^{2} + 96 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{3} d^{3} + 160 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} d^{3} - 5 \, a^{3} d^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(f x + e\right)^{5} - 40 \, \sin\left(f x + e\right)^{3} + 33 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1} - 15 \, \log\left(\sin\left(f x + e\right) + 1\right) + 15 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 90 \, a^{3} c^{2} d {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 270 \, a^{3} c d^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 90 \, a^{3} d^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 360 \, a^{3} c^{3} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 1080 \, a^{3} c^{2} d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 360 \, a^{3} c d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 480 \, a^{3} c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 1440 \, a^{3} c^{3} \tan\left(f x + e\right) + 1440 \, a^{3} c^{2} d \tan\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(160*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c^3 + 1440*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c^2*d + 96*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*c*d^2 + 1440*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c*d^2 + 96*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*d^3 + 160*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*d^3 - 5*a^3*d^3*(2*(15*sin(f*x + e)^5 - 40*sin(f*x + e)^3 + 33*sin(f*x + e))/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1) - 15*log(sin(f*x + e) + 1) + 15*log(sin(f*x + e) - 1)) - 90*a^3*c^2*d*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 270*a^3*c*d^2*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 90*a^3*d^3*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 360*a^3*c^3*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 1080*a^3*c^2*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 360*a^3*c*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 480*a^3*c^3*log(sec(f*x + e) + tan(f*x + e)) + 1440*a^3*c^3*tan(f*x + e) + 1440*a^3*c^2*d*tan(f*x + e))/f","B",0
203,1,459,0,0.433311," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c^{2} + 480 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c d + 16 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} a^{3} d^{2} + 240 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} d^{2} - 30 \, a^{3} c d {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 45 \, a^{3} d^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 180 \, a^{3} c^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 360 \, a^{3} c d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 60 \, a^{3} d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 240 \, a^{3} c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 720 \, a^{3} c^{2} \tan\left(f x + e\right) + 480 \, a^{3} c d \tan\left(f x + e\right)}{240 \, f}"," ",0,"1/240*(80*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c^2 + 480*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c*d + 16*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*d^2 + 240*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*d^2 - 30*a^3*c*d*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 45*a^3*d^2*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 180*a^3*c^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 360*a^3*c*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 60*a^3*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 240*a^3*c^2*log(sec(f*x + e) + tan(f*x + e)) + 720*a^3*c^2*tan(f*x + e) + 480*a^3*c*d*tan(f*x + e))/f","A",0
204,1,262,0,0.416996," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c + 48 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} d - 3 \, a^{3} d {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 36 \, a^{3} c {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 36 \, a^{3} d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 48 \, a^{3} c \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 144 \, a^{3} c \tan\left(f x + e\right) + 48 \, a^{3} d \tan\left(f x + e\right)}{48 \, f}"," ",0,"1/48*(16*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c + 48*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*d - 3*a^3*d*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 36*a^3*c*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 36*a^3*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 48*a^3*c*log(sec(f*x + e) + tan(f*x + e)) + 144*a^3*c*tan(f*x + e) + 48*a^3*d*tan(f*x + e))/f","B",0
205,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
206,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
207,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
208,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
209,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
210,1,596,0,0.462394," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{d^{4} {\left(\frac{2 \, {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{16 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a - \frac{3 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{a \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} - \frac{9 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} + \frac{6 \, \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 12 \, c d^{3} {\left(\frac{2 \, {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 36 \, c^{2} d^{2} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(f x + e\right)}{{\left(a - \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + 24 \, c^{3} d {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + \frac{6 \, c^{4} \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}}{6 \, f}"," ",0,"1/6*(d^4*(2*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 16*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a - 3*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - a*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) - 9*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a + 9*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a + 6*sin(f*x + e)/(a*(cos(f*x + e) + 1))) - 12*c*d^3*(2*(sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a - 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) - 3*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a + 3*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a + 2*sin(f*x + e)/(a*(cos(f*x + e) + 1))) - 36*c^2*d^2*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - 2*sin(f*x + e)/((a - a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) - sin(f*x + e)/(a*(cos(f*x + e) + 1))) + 24*c^3*d*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))) + 6*c^4*sin(f*x + e)/(a*(cos(f*x + e) + 1)))/f","B",0
211,1,388,0,0.529095," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{d^{3} {\left(\frac{2 \, {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + 6 \, c d^{2} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(f x + e\right)}{{\left(a - \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 6 \, c^{2} d {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - \frac{2 \, c^{3} \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}}{2 \, f}"," ",0,"-1/2*(d^3*(2*(sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a - 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) - 3*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a + 3*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a + 2*sin(f*x + e)/(a*(cos(f*x + e) + 1))) + 6*c*d^2*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - 2*sin(f*x + e)/((a - a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) - sin(f*x + e)/(a*(cos(f*x + e) + 1))) - 6*c^2*d*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))) - 2*c^3*sin(f*x + e)/(a*(cos(f*x + e) + 1)))/f","B",0
212,1,223,0,0.444935," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{d^{2} {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(f x + e\right)}{{\left(a - \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 2 \, c d {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - \frac{c^{2} \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}}{f}"," ",0,"-(d^2*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - 2*sin(f*x + e)/((a - a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) - sin(f*x + e)/(a*(cos(f*x + e) + 1))) - 2*c*d*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))) - c^2*sin(f*x + e)/(a*(cos(f*x + e) + 1)))/f","B",0
213,1,99,0,0.382473," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{d {\left(\frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + \frac{c \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}}{f}"," ",0,"(d*(log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a - log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))) + c*sin(f*x + e)/(a*(cos(f*x + e) + 1)))/f","B",0
214,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
215,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
216,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
217,1,772,0,0.363506," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^5/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{d^{5} {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{2} - \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{30 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{30 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} - 5 \, c d^{4} {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + 10 \, c^{2} d^{3} {\left(\frac{\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(f x + e\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 10 \, c^{3} d^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + \frac{5 \, c^{4} d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} + \frac{c^{5} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"1/6*(d^5*(4*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^2 - 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) + (27*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 30*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 30*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) - 5*c*d^4*(6*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2 - 2*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + (21*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 21*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 21*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + 10*c^2*d^3*((15*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 12*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 12*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2 + 12*sin(f*x + e)/((a^2 - a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1))) - 10*c^3*d^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + 5*c^4*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 + c^5*(3*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","B",0
218,1,536,0,0.365084," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{d^{4} {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} - 4 \, c d^{3} {\left(\frac{\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(f x + e\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + 6 \, c^{2} d^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} - \frac{4 \, c^{3} d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{c^{4} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"-1/6*(d^4*(6*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2 - 2*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + (21*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 21*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 21*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) - 4*c*d^3*((15*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 12*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 12*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2 + 12*sin(f*x + e)/((a^2 - a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1))) + 6*c^2*d^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) - 4*c^3*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - c^4*(3*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","B",0
219,1,342,0,0.350436," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{d^{3} {\left(\frac{\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(f x + e\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 3 \, c d^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} + \frac{3 \, c^{2} d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} + \frac{c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"1/6*(d^3*((15*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 12*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 12*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2 + 12*sin(f*x + e)/((a^2 - a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1))) - 3*c*d^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) + 3*c^2*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 + c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","B",0
220,1,195,0,0.341758," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{d^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{2}}\right)} - \frac{2 \, c d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"-1/6*(d^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 6*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^2 + 6*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^2) - 2*c*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","B",0
221,1,93,0,0.349288," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} + \frac{c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, f}"," ",0,"1/6*(d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 + c*(3*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2)/f","A",0
222,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
223,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
224,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
225,1,946,0,0.392593," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^6/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{d^{6} {\left(\frac{20 \, {\left(\frac{33 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{76 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{51 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3} - \frac{3 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} + \frac{\frac{735 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{50 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{690 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{690 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} - 6 \, c d^{5} {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{7 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + 45 \, c^{2} d^{4} {\left(\frac{40 \, \sin\left(f x + e\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} - 20 \, c^{3} d^{3} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{15 \, c^{4} d^{2} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{c^{6} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{18 \, c^{5} d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"1/60*(d^6*(20*(33*sin(f*x + e)/(cos(f*x + e) + 1) - 76*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 51*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^3 - 3*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) + (735*sin(f*x + e)/(cos(f*x + e) + 1) + 50*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 690*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 690*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) - 6*c*d^5*(60*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^3 - 2*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + (465*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 390*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 390*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 45*c^2*d^4*(40*sin(f*x + e)/((a^3 - a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) + (85*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) - 20*c^3*d^3*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 15*c^4*d^2*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + c^6*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + 18*c^5*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","B",0
226,1,689,0,0.370932," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^5/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{d^{5} {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{7 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} - 15 \, c d^{4} {\left(\frac{40 \, \sin\left(f x + e\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + 10 \, c^{2} d^{3} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} - \frac{10 \, c^{3} d^{2} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{c^{5} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{15 \, c^{4} d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"-1/60*(d^5*(60*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^3 - 2*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + (465*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 390*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 390*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) - 15*c*d^4*(40*sin(f*x + e)/((a^3 - a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) + (85*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 10*c^2*d^3*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) - 10*c^3*d^2*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - c^5*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 15*c^4*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","B",0
227,1,475,0,0.364576," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{3 \, d^{4} {\left(\frac{40 \, \sin\left(f x + e\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} - 4 \, c d^{3} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{6 \, c^{2} d^{2} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{c^{4} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{12 \, c^{3} d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"1/60*(3*d^4*(40*sin(f*x + e)/((a^3 - a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)) + (85*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) - 4*c*d^3*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) + 6*c^2*d^2*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + c^4*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + 12*c^3*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","B",0
228,1,307,0,0.344445," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{d^{3} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{a^{3}}\right)} - \frac{3 \, c d^{2} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{c^{3} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{9 \, c^{2} d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"-1/60*(d^3*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 60*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^3 + 60*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/a^3) - 3*c*d^2*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - c^3*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 - 9*c^2*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","B",0
229,1,184,0,0.345771," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{d^{2} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{c^{2} {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{6 \, c d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"1/60*(d^2*(15*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + c^2*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + 6*c*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","A",0
230,1,115,0,0.334274," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{c {\left(\frac{15 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{3 \, d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, f}"," ",0,"1/60*(c*(15*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3 + 3*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/a^3)/f","A",0
231,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
232,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
233,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
234,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)}{\sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*sec(f*x + e)/sqrt(d*sec(f*x + e) + c), x)","F",0
235,0,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sec\left(f x + e\right) + c} \sec\left(f x + e\right)}{\sqrt{a \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e) + c)*sec(f*x + e)/sqrt(a*sec(f*x + e) + a), x)","F",0
236,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sec(f*x + e)/(sqrt(a*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)), x)","F",0
237,0,0,0,0.000000," ","integrate(sec(f*x+e)^2/(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{2}}{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sec(f*x + e)^2/(sqrt(a*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)), x)","F",0
238,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)}{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*sec(f*x + e)/(d*sec(f*x + e) + c), x)","F",0
239,-2,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found %i","F(-2)",0
240,0,0,0,0.000000," ","integrate(sec(f*x+e)/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{\sqrt{a \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(sec(f*x + e)/(sqrt(a*sec(f*x + e) + a)*(d*sec(f*x + e) + c)), x)","F",0
241,0,0,0,0.000000," ","integrate(sec(f*x+e)^2/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{2}}{\sqrt{a \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(sec(f*x + e)^2/(sqrt(a*sec(f*x + e) + a)*(d*sec(f*x + e) + c)), x)","F",0
242,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,1,379,0,0.921315," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{480 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} b c^{2} d^{2} + 320 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a c d^{3} + 16 \, {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} b d^{4} - 60 \, b c d^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 15 \, a d^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 240 \, b c^{3} d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 360 \, a c^{2} d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 240 \, a c^{4} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 240 \, b c^{4} \tan\left(f x + e\right) + 960 \, a c^{3} d \tan\left(f x + e\right)}{240 \, f}"," ",0,"1/240*(480*(tan(f*x + e)^3 + 3*tan(f*x + e))*b*c^2*d^2 + 320*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*c*d^3 + 16*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*b*d^4 - 60*b*c*d^3*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 15*a*d^4*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 240*b*c^3*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 360*a*c^2*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 240*a*c^4*log(sec(f*x + e) + tan(f*x + e)) + 240*b*c^4*tan(f*x + e) + 960*a*c^3*d*tan(f*x + e))/f","A",0
245,1,266,0,0.336466," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{48 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} b c d^{2} + 16 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a d^{3} - 3 \, b d^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(f x + e\right)^{3} - 5 \, \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 36 \, b c^{2} d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 36 \, a c d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 48 \, a c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 48 \, b c^{3} \tan\left(f x + e\right) + 144 \, a c^{2} d \tan\left(f x + e\right)}{48 \, f}"," ",0,"1/48*(48*(tan(f*x + e)^3 + 3*tan(f*x + e))*b*c*d^2 + 16*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*d^3 - 3*b*d^3*(2*(3*sin(f*x + e)^3 - 5*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1) - 3*log(sin(f*x + e) + 1) + 3*log(sin(f*x + e) - 1)) - 36*b*c^2*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 36*a*c*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 48*a*c^3*log(sec(f*x + e) + tan(f*x + e)) + 48*b*c^3*tan(f*x + e) + 144*a*c^2*d*tan(f*x + e))/f","A",0
246,1,165,0,0.333315," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} b d^{2} - 6 \, b c d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 3 \, a d^{2} {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 12 \, a c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 12 \, b c^{2} \tan\left(f x + e\right) + 24 \, a c d \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(4*(tan(f*x + e)^3 + 3*tan(f*x + e))*b*d^2 - 6*b*c*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 3*a*d^2*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) + 12*a*c^2*log(sec(f*x + e) + tan(f*x + e)) + 12*b*c^2*tan(f*x + e) + 24*a*c*d*tan(f*x + e))/f","A",0
247,1,88,0,0.325611," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{b d {\left(\frac{2 \, \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1} - \log\left(\sin\left(f x + e\right) + 1\right) + \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 4 \, a c \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 4 \, b c \tan\left(f x + e\right) - 4 \, a d \tan\left(f x + e\right)}{4 \, f}"," ",0,"-1/4*(b*d*(2*sin(f*x + e)/(sin(f*x + e)^2 - 1) - log(sin(f*x + e) + 1) + log(sin(f*x + e) - 1)) - 4*a*c*log(sec(f*x + e) + tan(f*x + e)) - 4*b*c*tan(f*x + e) - 4*a*d*tan(f*x + e))/f","A",0
248,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
249,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
250,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
251,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
252,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
253,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
254,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
255,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
256,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e))/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
257,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
258,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^5/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
259,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
260,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
261,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
262,-2,0,0,0.000000," ","integrate(sec(f*x+e)*(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
263,-2,0,0,0.000000," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e))^2/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*d^2>0)', see `assume?` for more details)Is 4*c^2-4*d^2 positive or negative?","F(-2)",0
264,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(f x + e\right) + a} \sec\left(f x + e\right)}{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*sec(f*x + e)/(d*sec(f*x + e) + c), x)","F",0
265,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(f x + e\right) + a} \sec\left(f x + e\right)}{\sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*sec(f*x + e)/sqrt(d*sec(f*x + e) + c), x)","F",0
266,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right) + a} \sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sec(f*x + e)/(sqrt(b*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)), x)","F",0
267,0,0,0,0.000000," ","integrate(sec(f*x+e)/(2+3*sec(f*x+e))^(1/2)/(-4+5*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{\sqrt{5 \, \sec\left(f x + e\right) - 4} \sqrt{3 \, \sec\left(f x + e\right) + 2}}\,{d x}"," ",0,"integrate(sec(f*x + e)/(sqrt(5*sec(f*x + e) - 4)*sqrt(3*sec(f*x + e) + 2)), x)","F",0
268,0,0,0,0.000000," ","integrate(sec(f*x+e)/(4-5*sec(f*x+e))^(1/2)/(2+3*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{\sqrt{3 \, \sec\left(f x + e\right) + 2} \sqrt{-5 \, \sec\left(f x + e\right) + 4}}\,{d x}"," ",0,"integrate(sec(f*x + e)/(sqrt(3*sec(f*x + e) + 2)*sqrt(-5*sec(f*x + e) + 4)), x)","F",0
269,0,0,0,0.000000," ","integrate(sec(f*x+e)^2/(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{2}}{\sqrt{b \sec\left(f x + e\right) + a} \sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sec(f*x + e)^2/(sqrt(b*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)), x)","F",0
270,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e))^(1/2)/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sec\left(f x + e\right) + c} \left(g \sec\left(f x + e\right)\right)^{\frac{3}{2}}}{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e) + c)*(g*sec(f*x + e))^(3/2)/(b*sec(f*x + e) + a), x)","F",0
271,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)/(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \sec\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sec\left(f x + e\right) + a\right)} \sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^(3/2)/((b*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)), x)","F",0
272,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^(1/2)*(c+d*sec(f*x+e))^(1/2)/(a+b*cos(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sec\left(f x + e\right) + c} \sqrt{g \sec\left(f x + e\right)}}{b \cos\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e) + c)*sqrt(g*sec(f*x + e))/(b*cos(f*x + e) + a), x)","F",0
273,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^(1/2)/(c+c*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(f x + e\right) + a} \sec\left(f x + e\right)}{c \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*sec(f*x + e)/(c*sec(f*x + e) + c), x)","F",0
274,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)*(a+b*sec(f*x+e))^(1/2)/(c+c*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(f x + e\right) + a} \left(g \sec\left(f x + e\right)\right)^{\frac{3}{2}}}{c \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*(g*sec(f*x + e))^(3/2)/(c*sec(f*x + e) + c), x)","F",0
275,0,0,0,0.000000," ","integrate(sec(f*x+e)/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right) + a} {\left(c \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(sec(f*x + e)/(sqrt(b*sec(f*x + e) + a)*(c*sec(f*x + e) + c)), x)","F",0
276,0,0,0,0.000000," ","integrate(sec(f*x+e)^2/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{2}}{\sqrt{b \sec\left(f x + e\right) + a} {\left(c \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(sec(f*x + e)^2/(sqrt(b*sec(f*x + e) + a)*(c*sec(f*x + e) + c)), x)","F",0
277,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \sec\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(f x + e\right) + a} {\left(c \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^(3/2)/(sqrt(b*sec(f*x + e) + a)*(c*sec(f*x + e) + 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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(f x + e\right) + a} \sec\left(f x + e\right)}{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*sec(f*x + e)/(d*sec(f*x + e) + c), x)","F",0
280,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)*(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(f x + e\right) + a} \left(g \sec\left(f x + e\right)\right)^{\frac{3}{2}}}{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*(g*sec(f*x + e))^(3/2)/(d*sec(f*x + e) + c), x)","F",0
281,0,0,0,0.000000," ","integrate(sec(f*x+e)/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(sec(f*x + e)/(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e) + c)), x)","F",0
282,0,0,0,0.000000," ","integrate(sec(f*x+e)^2/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{2}}{\sqrt{b \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(sec(f*x + e)^2/(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e) + c)), x)","F",0
283,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \sec\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^(3/2)/(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e) + c)), x)","F",0
284,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \sec\left(f x + e\right)\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^(5/2)/(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e) + c)), x)","F",0
285,1,68,0,0.334157," ","integrate(sec(f*x+e)*tan(f*x+e)^4/(c-c*sec(f*x+e))^7,x, algorithm=""maxima"")","-\frac{{\left(\frac{90 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{63 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 35\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{9}}{1260 \, c^{7} f \sin\left(f x + e\right)^{9}}"," ",0,"-1/1260*(90*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 63*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 35)*(cos(f*x + e) + 1)^9/(c^7*f*sin(f*x + e)^9)","A",0
286,1,88,0,0.340979," ","integrate(sec(f*x+e)*tan(f*x+e)^4/(c-c*sec(f*x+e))^8,x, algorithm=""maxima"")","\frac{{\left(\frac{385 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{495 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{231 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 105\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{11}}{9240 \, c^{8} f \sin\left(f x + e\right)^{11}}"," ",0,"1/9240*(385*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 495*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 231*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 105)*(cos(f*x + e) + 1)^11/(c^8*f*sin(f*x + e)^11)","A",0
