1,1,334,0,0.345444," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","\frac{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^{2} c^{5} - 800 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c^{5} + 480 \, {\left(f x + e\right)} a^{2} c^{5} + 5 \, 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)} + 30 \, 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)} - 600 \, 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)} - 1440 \, a^{2} c^{5} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 480 \, a^{2} c^{5} \tan\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(96*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^2*c^5 - 800*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c^5 + 480*(f*x + e)*a^2*c^5 + 5*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)) + 30*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)) - 600*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)) - 1440*a^2*c^5*log(sec(f*x + e) + tan(f*x + e)) + 480*a^2*c^5*tan(f*x + e))/f","A",0
2,1,240,0,0.341044," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^4,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^{2} c^{4} - 40 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c^{4} + 120 \, {\left(f x + e\right)} a^{2} c^{4} + 15 \, 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)} - 240 \, a^{2} c^{4} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 120 \, a^{2} c^{4} \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^2*c^4 - 40*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c^4 + 120*(f*x + e)*a^2*c^4 + 15*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)) - 240*a^2*c^4*log(sec(f*x + e) + tan(f*x + e)) - 120*a^2*c^4*tan(f*x + e))/f","A",0
3,1,203,0,0.333275," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^3,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} + 48 \, {\left(f x + e\right)} a^{2} c^{3} + 3 \, 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)} - 24 \, 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)} - 48 \, a^{2} c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 96 \, a^{2} c^{3} \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 + 48*(f*x + e)*a^2*c^3 + 3*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)) - 24*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)) - 48*a^2*c^3*log(sec(f*x + e) + tan(f*x + e)) - 96*a^2*c^3*tan(f*x + e))/f","B",0
4,1,57,0,0.321123," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{{\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{2} c^{2} + 3 \, {\left(f x + e\right)} a^{2} c^{2} - 6 \, a^{2} c^{2} \tan\left(f x + e\right)}{3 \, f}"," ",0,"1/3*((tan(f*x + e)^3 + 3*tan(f*x + e))*a^2*c^2 + 3*(f*x + e)*a^2*c^2 - 6*a^2*c^2*tan(f*x + e))/f","A",0
5,1,95,0,0.326027," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a^{2} c + 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)} + 4 \, a^{2} c \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 4 \, a^{2} c \tan\left(f x + e\right)}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a^2*c + 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)) + 4*a^2*c*log(sec(f*x + e) + tan(f*x + e)) - 4*a^2*c*tan(f*x + e))/f","A",0
6,1,153,0,0.430600," ","integrate((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} + \frac{\cos\left(f x + e\right) + 1}{c \sin\left(f x + e\right)}\right)} - 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{2 \, a^{2} {\left(\cos\left(f x + e\right) + 1\right)}}{c \sin\left(f x + e\right)}}{f}"," ",0,"(a^2*(2*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c + (cos(f*x + e) + 1)/(c*sin(f*x + e))) - 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))) + 2*a^2*(cos(f*x + e) + 1)/(c*sin(f*x + e)))/f","B",0
7,1,174,0,0.442858," ","integrate((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 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{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{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}}}{6 \, f}"," ",0,"1/6*(a^2*(12*arctan(sin(f*x + e)/(cos(f*x + e) + 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)) - 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) + 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))/f","B",0
8,1,215,0,0.445400," ","integrate((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{120 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 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{2 \, 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{3 \, 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*(120*arctan(sin(f*x + e)/(cos(f*x + e) + 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)) - 2*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) - 3*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
9,1,294,0,0.435073," ","integrate((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{5 \, a^{2} {\left(\frac{336 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{4}} + \frac{{\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{77 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \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}}{c^{4} \sin\left(f x + e\right)^{7}}\right)} + \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}} + \frac{6 \, 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}}}{840 \, f}"," ",0,"1/840*(5*a^2*(336*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^4 + (21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 77*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 3)*(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) + 6*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))/f","B",0
10,1,335,0,0.446165," ","integrate((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{10080 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{5}} - \frac{{\left(\frac{270 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{1008 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{2730 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{9765 \, \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}}\right)} - \frac{2 \, 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{5 \, 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}}}{5040 \, f}"," ",0,"1/5040*(a^2*(10080*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^5 - (270*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1008*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 2730*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 9765*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)) - 2*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) - 5*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))/f","B",0
11,1,356,0,0.337567," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","-\frac{48 \, {\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} - 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^{3} c^{5} - 1680 \, {\left(f x + e\right)} a^{3} c^{5} + 35 \, 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)} - 630 \, a^{3} 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)} + 2520 \, 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)} + 3360 \, a^{3} c^{5} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 3360 \, a^{3} c^{5} \tan\left(f x + e\right)}{1680 \, f}"," ",0,"-1/1680*(48*(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 - 224*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*c^5 - 1680*(f*x + e)*a^3*c^5 + 35*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)) - 630*a^3*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)) + 2520*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)) + 3360*a^3*c^5*log(sec(f*x + e) + tan(f*x + e)) + 3360*a^3*c^5*tan(f*x + e))/f","B",0
12,1,334,0,0.337959," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","-\frac{32 \, {\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} - 480 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c^{4} - 480 \, {\left(f x + e\right)} a^{3} c^{4} + 5 \, 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)} - 90 \, 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)} + 360 \, 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)} + 480 \, a^{3} c^{4} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + 1440 \, a^{3} c^{4} \tan\left(f x + e\right)}{480 \, f}"," ",0,"-1/480*(32*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*c^4 - 480*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c^4 - 480*(f*x + e)*a^3*c^4 + 5*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)) - 90*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)) + 360*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)) + 480*a^3*c^4*log(sec(f*x + e) + tan(f*x + e)) + 1440*a^3*c^4*tan(f*x + e))/f","B",0
13,1,94,0,0.323019," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{{\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^{3} - 15 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c^{3} - 15 \, {\left(f x + e\right)} a^{3} c^{3} + 45 \, a^{3} c^{3} \tan\left(f x + e\right)}{15 \, f}"," ",0,"-1/15*((3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*a^3*c^3 - 15*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c^3 - 15*(f*x + e)*a^3*c^3 + 45*a^3*c^3*tan(f*x + e))/f","A",0
14,1,203,0,0.337178," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c^{2} + 48 \, {\left(f x + e\right)} a^{3} c^{2} - 3 \, 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)} + 24 \, 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)} + 48 \, a^{3} c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - 96 \, a^{3} c^{2} \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^2 + 48*(f*x + e)*a^3*c^2 - 3*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)) + 24*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)) + 48*a^3*c^2*log(sec(f*x + e) + tan(f*x + e)) - 96*a^3*c^2*tan(f*x + e))/f","B",0
15,1,107,0,0.311769," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a^{3} c - 6 \, {\left(f x + e\right)} a^{3} c - 3 \, 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)} - 12 \, a^{3} c \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{6 \, f}"," ",0,"-1/6*(2*(tan(f*x + e)^3 + 3*tan(f*x + e))*a^3*c - 6*(f*x + e)*a^3*c - 3*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)) - 12*a^3*c*log(sec(f*x + e) + tan(f*x + e)))/f","A",0
16,1,274,0,0.433727," ","integrate((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{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)} - a^{3} {\left(\frac{2 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} + \frac{\cos\left(f x + e\right) + 1}{c \sin\left(f x + e\right)}\right)} + 3 \, 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{3 \, a^{3} {\left(\cos\left(f x + e\right) + 1\right)}}{c \sin\left(f x + e\right)}}{f}"," ",0,"-(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) - a^3*(2*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c + (cos(f*x + e) + 1)/(c*sin(f*x + e))) + 3*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))) - 3*a^3*(cos(f*x + e) + 1)/(c*sin(f*x + e)))/f","B",0
17,1,274,0,0.438530," ","integrate((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{a^{3} {\left(\frac{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 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)} + 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{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}}}{6 \, f}"," ",0,"1/6*(a^3*(12*arctan(sin(f*x + e)/(cos(f*x + e) + 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)) + 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) + 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
18,1,282,0,0.443118," ","integrate((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{a^{3} {\left(\frac{120 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 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{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{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{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*(120*arctan(sin(f*x + e)/(cos(f*x + e) + 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)) + 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) - 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) - 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
19,1,383,0,0.446951," ","integrate((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\frac{5 \, a^{3} {\left(\frac{336 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{4}} + \frac{{\left(\frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{77 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \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}}{c^{4} \sin\left(f x + e\right)^{7}}\right)} + \frac{3 \, 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{9 \, 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}}}{840 \, f}"," ",0,"1/840*(5*a^3*(336*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^4 + (21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 77*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 3)*(cos(f*x + e) + 1)^7/(c^4*sin(f*x + e)^7)) + 3*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) + 9*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
20,1,403,0,0.457698," ","integrate((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","\frac{a^{3} {\left(\frac{10080 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{5}} - \frac{{\left(\frac{270 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{1008 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{2730 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{9765 \, \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}}\right)} - \frac{3 \, 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{7 \, 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*(10080*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^5 - (270*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1008*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 2730*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 9765*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)) - 3*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) - 7*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
21,1,603,0,0.438036," ","integrate((c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{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)} + 5 \, 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)} - 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{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + \frac{10 \, 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{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}}}{6 \, f}"," ",0,"1/6*(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) + 5*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) - 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 - 12*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 10*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 - 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)/f","B",0
22,1,413,0,0.441595," ","integrate((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{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)} + 4 \, 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)} - 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{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + \frac{6 \, 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{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}}}{6 \, f}"," ",0,"1/6*(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))) + 4*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) - 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 - 12*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 6*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 - 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)/f","B",0
23,1,268,0,0.430615," ","integrate((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{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)} - 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{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 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{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}}}{6 \, f}"," ",0,"1/6*(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) - 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 - 12*arctan(sin(f*x + e)/(cos(f*x + e) + 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 - 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)/f","B",0
24,1,170,0,0.427808," ","integrate((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{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \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}} + \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}}}{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 - 12*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/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 + 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
25,1,119,0,0.422213," ","integrate((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{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 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 - 12*arctan(sin(f*x + e)/(cos(f*x + e) + 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
26,1,102,0,0.428315," ","integrate(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{\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}}}{a^{2} c} - \frac{24 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{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*((12*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*c) - 24*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^2*c) - 3*(cos(f*x + e) + 1)/(a^2*c*sin(f*x + e)))/f","A",0
27,1,46,0,0.422202," ","integrate(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(f x + e\right)}}{a^{2} c^{2}} + \frac{3 \, \tan\left(f x + e\right)^{2} - 1}{a^{2} c^{2} \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)/(a^2*c^2) + (3*tan(f*x + e)^2 - 1)/(a^2*c^2*tan(f*x + e)^3))/f","A",0
28,1,147,0,0.425650," ","integrate(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{\frac{5 \, {\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^{3}} - \frac{480 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2} c^{3}} + \frac{3 \, {\left(\frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{80 \, \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^{2} c^{3} \sin\left(f x + e\right)^{5}}}{240 \, f}"," ",0,"-1/240*(5*(18*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*c^3) - 480*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^2*c^3) + 3*(10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 80*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1)*(cos(f*x + e) + 1)^5/(a^2*c^3*sin(f*x + e)^5))/f","A",0
29,1,167,0,0.427988," ","integrate(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","-\frac{\frac{35 \, {\left(\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}}\right)}}{a^{2} c^{4}} - \frac{6720 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2} c^{4}} - \frac{{\left(\frac{147 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{770 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{4410 \, \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}}{a^{2} c^{4} \sin\left(f x + e\right)^{7}}}{3360 \, f}"," ",0,"-1/3360*(35*(21*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*c^4) - 6720*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^2*c^4) - (147*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 770*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4410*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 15)*(cos(f*x + e) + 1)^7/(a^2*c^4*sin(f*x + e)^7))/f","A",0
30,1,186,0,0.429401," ","integrate(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","-\frac{\frac{105 \, {\left(\frac{24 \, \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{40320 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2} c^{5}} + \frac{{\left(\frac{360 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{1827 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{6720 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{31185 \, \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}}{a^{2} c^{5} \sin\left(f x + e\right)^{9}}}{20160 \, f}"," ",0,"-1/20160*(105*(24*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*c^5) - 40320*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^2*c^5) + (360*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1827*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 6720*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 31185*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 35)*(cos(f*x + e) + 1)^9/(a^2*c^5*sin(f*x + e)^9))/f","A",0
31,1,562,0,0.435291," ","integrate((c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{3 \, 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)} + 5 \, 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)} + 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{120 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 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{5 \, 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{30 \, 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*(3*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) + 5*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) + 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 - 120*arctan(sin(f*x + e)/(cos(f*x + e) + 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 + 5*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 - 30*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
32,1,396,0,0.435008," ","integrate((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{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)} + 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{120 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + \frac{4 \, 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{4 \, 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{18 \, 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*(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) + 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 - 120*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 4*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 + 4*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 - 18*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
33,1,277,0,0.432222," ","integrate((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{120 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + \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{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{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 - 120*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/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 + 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
34,1,211,0,0.434926," ","integrate((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{c^{2} {\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{120 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + \frac{2 \, 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{3 \, 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*((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 - 120*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 2*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 - 3*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
35,1,159,0,0.429589," ","integrate((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","-\frac{c {\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{120 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + \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}}}{60 \, f}"," ",0,"-1/60*(c*((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 - 120*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 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)/f","A",0
36,1,122,0,0.424706," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{\frac{165 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{25 \, \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} - \frac{240 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3} c} - \frac{15 \, {\left(\cos\left(f x + e\right) + 1\right)}}{a^{3} c \sin\left(f x + e\right)}}{120 \, f}"," ",0,"-1/120*((165*sin(f*x + e)/(cos(f*x + e) + 1) - 25*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) - 240*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^3*c) - 15*(cos(f*x + e) + 1)/(a^3*c*sin(f*x + e)))/f","A",0
37,1,146,0,0.425453," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(\frac{80 \, \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^{2}} - \frac{480 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3} c^{2}} - \frac{5 \, {\left(\frac{18 \, \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*(3*(80*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^2) - 480*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^3*c^2) - 5*(18*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
38,1,56,0,0.427229," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(f x + e\right)}}{a^{3} c^{3}} + \frac{15 \, \tan\left(f x + e\right)^{4} - 5 \, \tan\left(f x + e\right)^{2} + 3}{a^{3} c^{3} \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"1/15*(15*(f*x + e)/(a^3*c^3) + (15*tan(f*x + e)^4 - 5*tan(f*x + e)^2 + 3)/(a^3*c^3*tan(f*x + e)^5))/f","A",0
39,1,187,0,0.439927," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","-\frac{\frac{7 \, {\left(\frac{435 \, \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^{4}} - \frac{13440 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3} c^{4}} - \frac{{\left(\frac{168 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{1015 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{6720 \, \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}}{a^{3} c^{4} \sin\left(f x + e\right)^{7}}}{6720 \, f}"," ",0,"-1/6720*(7*(435*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^4) - 13440*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^3*c^4) - (168*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1015*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 6720*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 15)*(cos(f*x + e) + 1)^7/(a^3*c^4*sin(f*x + e)^7))/f","A",0
40,1,205,0,0.443713," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","-\frac{\frac{63 \, {\left(\frac{185 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{15 \, \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^{5}} - \frac{80640 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3} c^{5}} + \frac{{\left(\frac{405 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2331 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9765 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{51345 \, \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}}{a^{3} c^{5} \sin\left(f x + e\right)^{9}}}{40320 \, f}"," ",0,"-1/40320*(63*(185*sin(f*x + e)/(cos(f*x + e) + 1) - 15*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) - 80640*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^3*c^5) + (405*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2331*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9765*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 51345*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 35)*(cos(f*x + e) + 1)^9/(a^3*c^5*sin(f*x + e)^9))/f","A",0
41,1,227,0,0.448534," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^6,x, algorithm=""maxima"")","-\frac{\frac{231 \, {\left(\frac{690 \, \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}}\right)}}{a^{3} c^{6}} - \frac{1774080 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3} c^{6}} - \frac{5 \, {\left(\frac{770 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{4554 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{18018 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{59136 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{264726 \, \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}}{a^{3} c^{6} \sin\left(f x + e\right)^{11}}}{887040 \, f}"," ",0,"-1/887040*(231*(690*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*c^6) - 1774080*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^3*c^6) - 5*(770*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4554*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 18018*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 59136*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 264726*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 63)*(cos(f*x + e) + 1)^11/(a^3*c^6*sin(f*x + e)^11))/f","A",0
42,-1,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^4*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,-1,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^3*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,-1,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^2*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,1,147,0,0.835335," ","integrate((c-c*sec(f*x+e))*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} c \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \sin\left(f x + e\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \cos\left(f x + e\right)\right)}{f}"," ",0,"sqrt(a)*c*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + sin(f*x + e), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + cos(f*x + e))/f","B",0
46,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\int \frac{\sqrt{a \sec\left(f x + e\right) + a}}{c \sec\left(f x + e\right) - c}\,{d x}"," ",0,"-integrate(sqrt(a*sec(f*x + e) + a)/(c*sec(f*x + e) - c), x)","F",0
47,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a \sec\left(f x + e\right) + a}}{{\left(c \sec\left(f x + e\right) - c\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)/(c*sec(f*x + e) - c)^2, x)","F",0
48,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,1,998,0,0.818372," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","\frac{{\left({\left(a \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\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) \sin\left(\frac{1}{2} \, \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) + 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)}, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \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) + \sin\left(\frac{1}{2} \, \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)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\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) \sin\left(\frac{1}{2} \, \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) + 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)}, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \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) + \sin\left(\frac{1}{2} \, \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)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\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) + 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) - {\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) - 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) + 1\right)\right)\right)} \sqrt{a}\right)} c}{2 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} f}"," ",0,"1/2*((a*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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) + 1)) - cos(1/2*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)))), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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))) + sin(1/2*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)))) + 1) - a*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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) + 1)) - cos(1/2*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)))), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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))) + sin(1/2*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)))) - 1) - a*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1) + a*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 1))*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*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))) - (a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - a)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))*sqrt(a))*c/((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*f)","B",0
53,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{c \sec\left(f x + e\right) - c}\,{d x}"," ",0,"-integrate((a*sec(f*x + e) + a)^(3/2)/(c*sec(f*x + e) - c), x)","F",0
54,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,1,1396,0,1.145596," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(30 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, 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) \sin\left(2 \, f x + 2 \, e\right) - 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 4 \, 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)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, f x + 2 \, e\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 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 4 \, 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)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\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) \sin\left(\frac{1}{2} \, \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) + 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)}, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \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) + \sin\left(\frac{1}{2} \, \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)} + 1\right) - {\left(a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\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) \sin\left(\frac{1}{2} \, \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) + 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)}, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \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) + \sin\left(\frac{1}{2} \, \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)} - 1\right) - {\left(a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} c}{6 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"1/6*(30*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 2*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(2*f*x + 2*e) - 3*a^2*sin(2*f*x + 2*e) - 4*(3*a^2*cos(2*f*x + 2*e) + 4*a^2)*sin(3/2*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) + 1)) + (12*a^2*sin(2*f*x + 2*e)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*a^2*cos(2*f*x + 2*e) - a^2 + 4*(3*a^2*cos(2*f*x + 2*e) + 4*a^2)*cos(3/2*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) + 1)))*sqrt(a) + 3*((a^2*cos(2*f*x + 2*e)^2 + a^2*sin(2*f*x + 2*e)^2 + 2*a^2*cos(2*f*x + 2*e) + a^2)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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) + 1)) - cos(1/2*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)))), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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))) + sin(1/2*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)))) + 1) - (a^2*cos(2*f*x + 2*e)^2 + a^2*sin(2*f*x + 2*e)^2 + 2*a^2*cos(2*f*x + 2*e) + a^2)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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) + 1)) - cos(1/2*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)))), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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))) + sin(1/2*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)))) - 1) - (a^2*cos(2*f*x + 2*e)^2 + a^2*sin(2*f*x + 2*e)^2 + 2*a^2*cos(2*f*x + 2*e) + a^2)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1) + (a^2*cos(2*f*x + 2*e)^2 + a^2*sin(2*f*x + 2*e)^2 + 2*a^2*cos(2*f*x + 2*e) + a^2)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 1))*sqrt(a))*c/((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*f)","B",0
60,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{c \sec\left(f x + e\right) - c}\,{d x}"," ",0,"-integrate((a*sec(f*x + e) + a)^(5/2)/(c*sec(f*x + e) - c), x)","F",0
61,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-2,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^(1/2),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
66,-2,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),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
67,-2,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),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
68,-2,0,0,0.000000," ","integrate((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),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
69,0,0,0,0.000000," ","integrate(1/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\int \frac{1}{\sqrt{a \sec\left(f x + e\right) + a} {\left(c \sec\left(f x + e\right) - c\right)}}\,{d x}"," ",0,"-integrate(1/(sqrt(a*sec(f*x + e) + a)*(c*sec(f*x + e) - c)), x)","F",0
70,0,0,0,0.000000," ","integrate(1/(c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sec\left(f x + e\right) + a} {\left(c \sec\left(f x + e\right) - c\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(f*x + e) + a)*(c*sec(f*x + e) - c)^2), x)","F",0
71,0,0,0,0.000000," ","integrate(1/(c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\int \frac{1}{\sqrt{a \sec\left(f x + e\right) + a} {\left(c \sec\left(f x + e\right) - c\right)}^{3}}\,{d x}"," ",0,"-integrate(1/(sqrt(a*sec(f*x + e) + a)*(c*sec(f*x + e) - c)^3), x)","F",0
72,-1,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,0,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(c \sec\left(f x + e\right) - c\right)}^{3}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((c*sec(f*x + e) - c)^3/(a*sec(f*x + e) + a)^(3/2), x)","F",0
74,0,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c \sec\left(f x + e\right) - c\right)}^{2}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*sec(f*x + e) - c)^2/(a*sec(f*x + e) + a)^(3/2), x)","F",0
75,0,0,0,0.000000," ","integrate((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\int \frac{c \sec\left(f x + e\right) - c}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((c*sec(f*x + e) - c)/(a*sec(f*x + e) + a)^(3/2), x)","F",0
76,0,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\int \frac{1}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(c \sec\left(f x + e\right) - c\right)}}\,{d x}"," ",0,"-integrate(1/((a*sec(f*x + e) + a)^(3/2)*(c*sec(f*x + e) - c)), x)","F",0
77,0,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(c \sec\left(f x + e\right) - c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((a*sec(f*x + e) + a)^(3/2)*(c*sec(f*x + e) - c)^2), x)","F",0
78,0,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^3,x, algorithm=""maxima"")","-\int \frac{1}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(c \sec\left(f x + e\right) - c\right)}^{3}}\,{d x}"," ",0,"-integrate(1/((a*sec(f*x + e) + a)^(3/2)*(c*sec(f*x + e) - c)^3), x)","F",0
79,-1,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^4/(a+a*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((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,0,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(c \sec\left(f x + e\right) - c\right)}^{2}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*sec(f*x + e) - c)^2/(a*sec(f*x + e) + a)^(5/2), x)","F",0
83,0,0,0,0.000000," ","integrate((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\int \frac{c \sec\left(f x + e\right) - c}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-integrate((c*sec(f*x + e) - c)/(a*sec(f*x + e) + a)^(5/2), x)","F",0
84,0,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e)),x, algorithm=""maxima"")","-\int \frac{1}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(c \sec\left(f x + e\right) - c\right)}}\,{d x}"," ",0,"-integrate(1/((a*sec(f*x + e) + a)^(5/2)*(c*sec(f*x + e) - c)), x)","F",0
85,0,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(c \sec\left(f x + e\right) - c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((a*sec(f*x + e) + a)^(5/2)*(c*sec(f*x + e) - c)^2), x)","F",0
86,1,1289,0,0.886657," ","integrate((c-c*sec(f*x+e))^(7/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(3 \, {\left(f x + e\right)} c^{3} \cos\left(6 \, f x + 6 \, e\right)^{2} + 27 \, {\left(f x + e\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 27 \, {\left(f x + e\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(f x + e\right)} c^{3} \sin\left(6 \, f x + 6 \, e\right)^{2} + 27 \, {\left(f x + e\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} + 27 \, {\left(f x + e\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(f x + e\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(f x + e\right)} c^{3} + 18 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) - 3 \, {\left(c^{3} \cos\left(6 \, f x + 6 \, e\right)^{2} + 9 \, c^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 9 \, c^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + c^{3} \sin\left(6 \, f x + 6 \, e\right)^{2} + 9 \, c^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} + 18 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, c^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 6 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3} + 2 \, {\left(3 \, c^{3} \cos\left(4 \, f x + 4 \, e\right) + 3 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\right)} \cos\left(6 \, f x + 6 \, e\right) + 6 \, {\left(3 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\right)} \cos\left(4 \, f x + 4 \, e\right) + 6 \, {\left(c^{3} \sin\left(4 \, f x + 4 \, e\right) + c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) + 6 \, {\left(3 \, {\left(f x + e\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 3 \, {\left(f x + e\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} c^{3} + 3 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) + 3 \, c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 18 \, {\left(3 \, {\left(f x + e\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} c^{3}\right)} \cos\left(4 \, f x + 4 \, e\right) + 18 \, {\left(c^{3} \sin\left(6 \, f x + 6 \, e\right) + 3 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) + 3 \, c^{3} \sin\left(2 \, f x + 2 \, e\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) + 44 \, {\left(c^{3} \sin\left(6 \, f x + 6 \, e\right) + 3 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) + 3 \, c^{3} \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) + 18 \, {\left(c^{3} \sin\left(6 \, f x + 6 \, e\right) + 3 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) + 3 \, c^{3} \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) + 18 \, {\left({\left(f x + e\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right) + {\left(f x + e\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) - c^{3} \cos\left(4 \, f x + 4 \, e\right) - c^{3} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 18 \, {\left(3 \, {\left(f x + e\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) + c^{3}\right)} \sin\left(4 \, f x + 4 \, e\right) - 18 \, {\left(c^{3} \cos\left(6 \, f x + 6 \, e\right) + 3 \, c^{3} \cos\left(4 \, f x + 4 \, e\right) + 3 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\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) - 44 \, {\left(c^{3} \cos\left(6 \, f x + 6 \, e\right) + 3 \, c^{3} \cos\left(4 \, f x + 4 \, e\right) + 3 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\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) - 18 \, {\left(c^{3} \cos\left(6 \, f x + 6 \, e\right) + 3 \, c^{3} \cos\left(4 \, f x + 4 \, e\right) + 3 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\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(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,"-1/3*(3*(f*x + e)*c^3*cos(6*f*x + 6*e)^2 + 27*(f*x + e)*c^3*cos(4*f*x + 4*e)^2 + 27*(f*x + e)*c^3*cos(2*f*x + 2*e)^2 + 3*(f*x + e)*c^3*sin(6*f*x + 6*e)^2 + 27*(f*x + e)*c^3*sin(4*f*x + 4*e)^2 + 27*(f*x + e)*c^3*sin(2*f*x + 2*e)^2 + 18*(f*x + e)*c^3*cos(2*f*x + 2*e) + 3*(f*x + e)*c^3 + 18*c^3*sin(2*f*x + 2*e) - 3*(c^3*cos(6*f*x + 6*e)^2 + 9*c^3*cos(4*f*x + 4*e)^2 + 9*c^3*cos(2*f*x + 2*e)^2 + c^3*sin(6*f*x + 6*e)^2 + 9*c^3*sin(4*f*x + 4*e)^2 + 18*c^3*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 9*c^3*sin(2*f*x + 2*e)^2 + 6*c^3*cos(2*f*x + 2*e) + c^3 + 2*(3*c^3*cos(4*f*x + 4*e) + 3*c^3*cos(2*f*x + 2*e) + c^3)*cos(6*f*x + 6*e) + 6*(3*c^3*cos(2*f*x + 2*e) + c^3)*cos(4*f*x + 4*e) + 6*(c^3*sin(4*f*x + 4*e) + c^3*sin(2*f*x + 2*e))*sin(6*f*x + 6*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 6*(3*(f*x + e)*c^3*cos(4*f*x + 4*e) + 3*(f*x + e)*c^3*cos(2*f*x + 2*e) + (f*x + e)*c^3 + 3*c^3*sin(4*f*x + 4*e) + 3*c^3*sin(2*f*x + 2*e))*cos(6*f*x + 6*e) + 18*(3*(f*x + e)*c^3*cos(2*f*x + 2*e) + (f*x + e)*c^3)*cos(4*f*x + 4*e) + 18*(c^3*sin(6*f*x + 6*e) + 3*c^3*sin(4*f*x + 4*e) + 3*c^3*sin(2*f*x + 2*e))*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 44*(c^3*sin(6*f*x + 6*e) + 3*c^3*sin(4*f*x + 4*e) + 3*c^3*sin(2*f*x + 2*e))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 18*(c^3*sin(6*f*x + 6*e) + 3*c^3*sin(4*f*x + 4*e) + 3*c^3*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 18*((f*x + e)*c^3*sin(4*f*x + 4*e) + (f*x + e)*c^3*sin(2*f*x + 2*e) - c^3*cos(4*f*x + 4*e) - c^3*cos(2*f*x + 2*e))*sin(6*f*x + 6*e) + 18*(3*(f*x + e)*c^3*sin(2*f*x + 2*e) + c^3)*sin(4*f*x + 4*e) - 18*(c^3*cos(6*f*x + 6*e) + 3*c^3*cos(4*f*x + 4*e) + 3*c^3*cos(2*f*x + 2*e) + c^3)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 44*(c^3*cos(6*f*x + 6*e) + 3*c^3*cos(4*f*x + 4*e) + 3*c^3*cos(2*f*x + 2*e) + c^3)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 18*(c^3*cos(6*f*x + 6*e) + 3*c^3*cos(4*f*x + 4*e) + 3*c^3*cos(2*f*x + 2*e) + c^3)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(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
87,1,710,0,1.041107," ","integrate((c-c*sec(f*x+e))^(5/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(f x + e\right)} c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(f x + e\right)} c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(f x + e\right)} c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(f x + e\right)} c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} c^{2} + 2 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) - {\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) + 2 \, {\left(2 \, {\left(f x + e\right)} c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} c^{2} + c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\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)} \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} \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) + 2 \, {\left(2 \, {\left(f x + e\right)} c^{2} \sin\left(2 \, f x + 2 \, e\right) - c^{2} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\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) + 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) - 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)} \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(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,"-((f*x + e)*c^2*cos(4*f*x + 4*e)^2 + 4*(f*x + e)*c^2*cos(2*f*x + 2*e)^2 + (f*x + e)*c^2*sin(4*f*x + 4*e)^2 + 4*(f*x + e)*c^2*sin(2*f*x + 2*e)^2 + 4*(f*x + e)*c^2*cos(2*f*x + 2*e) + (f*x + e)*c^2 + 2*c^2*sin(2*f*x + 2*e) - (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) + 2*(2*(f*x + e)*c^2*cos(2*f*x + 2*e) + (f*x + e)*c^2 + c^2*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(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))) + 4*(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))) + 2*(2*(f*x + e)*c^2*sin(2*f*x + 2*e) - c^2*cos(2*f*x + 2*e))*sin(4*f*x + 4*e) - 4*(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))) - 4*(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)/((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
88,1,243,0,0.774439," ","integrate((c-c*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} c \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(f x + e\right)} c \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(f x + e\right)} c \cos\left(2 \, f x + 2 \, e\right) + 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) \sin\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} 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)} \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) + 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(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"-((f*x + e)*c*cos(2*f*x + 2*e)^2 + (f*x + e)*c*sin(2*f*x + 2*e)^2 + 2*(f*x + e)*c*cos(2*f*x + 2*e) + 2*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(2*f*x + 2*e) + (f*x + e)*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)*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*(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)/((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*f)","B",0
89,1,39,0,0.813072," ","integrate((c-c*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(f x + e - \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)} \sqrt{a} \sqrt{c}}{f}"," ",0,"-(f*x + e - arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*sqrt(a)*sqrt(c)/f","A",0
90,1,65,0,0.592795," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{-a} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{\sqrt{c}} - \frac{\sqrt{-a} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{\sqrt{c}}}{f}"," ",0,"(2*sqrt(-a)*log(sin(f*x + e)/(cos(f*x + e) + 1))/sqrt(c) - sqrt(-a)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/sqrt(c))/f","A",0
91,1,399,0,1.027784," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(f x + e\right)} \cos\left(f x + e\right)^{2} + {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(f x + e\right)} \sin\left(f x + e\right)^{2} + f x + 2 \, {\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 \, {\left(f x - 2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e + \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(f x + e\right)} \cos\left(f x + e\right) - 2 \, {\left(2 \, {\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) + e + 2 \, \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{{\left(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(2 \, f x + 2 \, e\right)^{2} - 4 \, 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(f x + e\right) - c^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} f}"," ",0,"-((f*x + e)*cos(2*f*x + 2*e)^2 + 4*(f*x + e)*cos(f*x + e)^2 + (f*x + e)*sin(2*f*x + 2*e)^2 + 4*(f*x + e)*sin(f*x + e)^2 + f*x + 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*(f*x - 2*(f*x + e)*cos(f*x + e) + e + sin(f*x + e))*cos(2*f*x + 2*e) - 4*(f*x + e)*cos(f*x + e) - 2*(2*(f*x + e)*sin(f*x + e) + cos(f*x + e))*sin(2*f*x + 2*e) + e + 2*sin(f*x + e))*sqrt(a)*sqrt(c)/((c^2*cos(2*f*x + 2*e)^2 + 4*c^2*cos(f*x + e)^2 + c^2*sin(2*f*x + 2*e)^2 - 4*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(f*x + e) - c^2)*cos(2*f*x + 2*e))*f)","B",0
92,1,1173,0,1.097029," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 36 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \cos\left(f x + e\right)^{2} + {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 36 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \sin\left(f x + e\right)^{2} + f x + 2 \, {\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(f x - 4 \, {\left(f x + e\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e + 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)} \cos\left(4 \, f x + 4 \, e\right) - 8 \, {\left(f x + 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e\right)} \cos\left(3 \, f x + 3 \, e\right) + 12 \, {\left(f x - 4 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 8 \, {\left(f x + e\right)} \cos\left(f x + e\right) - 2 \, {\left(4 \, {\left(f x + e\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(f x + e\right)} \sin\left(f x + e\right) + 2 \, \cos\left(3 \, f x + 3 \, e\right) - 3 \, \cos\left(2 \, f x + 2 \, e\right) + 2 \, \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 4 \, {\left(12 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 8 \, {\left(f x + e\right)} \sin\left(f x + e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(8 \, {\left(f x + e\right)} \sin\left(f x + e\right) + 1\right)} \sin\left(2 \, f x + 2 \, e\right) + e + 4 \, \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,"-((f*x + e)*cos(4*f*x + 4*e)^2 + 16*(f*x + e)*cos(3*f*x + 3*e)^2 + 36*(f*x + e)*cos(2*f*x + 2*e)^2 + 16*(f*x + e)*cos(f*x + e)^2 + (f*x + e)*sin(4*f*x + 4*e)^2 + 16*(f*x + e)*sin(3*f*x + 3*e)^2 + 36*(f*x + e)*sin(2*f*x + 2*e)^2 + 16*(f*x + e)*sin(f*x + e)^2 + f*x + 2*(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*(f*x - 4*(f*x + e)*cos(3*f*x + 3*e) + 6*(f*x + e)*cos(2*f*x + 2*e) - 4*(f*x + e)*cos(f*x + e) + e + 2*sin(3*f*x + 3*e) - 3*sin(2*f*x + 2*e) + 2*sin(f*x + e))*cos(4*f*x + 4*e) - 8*(f*x + 6*(f*x + e)*cos(2*f*x + 2*e) - 4*(f*x + e)*cos(f*x + e) + e)*cos(3*f*x + 3*e) + 12*(f*x - 4*(f*x + e)*cos(f*x + e) + e)*cos(2*f*x + 2*e) - 8*(f*x + e)*cos(f*x + e) - 2*(4*(f*x + e)*sin(3*f*x + 3*e) - 6*(f*x + e)*sin(2*f*x + 2*e) + 4*(f*x + e)*sin(f*x + e) + 2*cos(3*f*x + 3*e) - 3*cos(2*f*x + 2*e) + 2*cos(f*x + e))*sin(4*f*x + 4*e) - 4*(12*(f*x + e)*sin(2*f*x + 2*e) - 8*(f*x + e)*sin(f*x + e) - 1)*sin(3*f*x + 3*e) - 6*(8*(f*x + e)*sin(f*x + e) + 1)*sin(2*f*x + 2*e) + e + 4*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
93,1,2444,0,4.634473," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(3 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right)^{2} + 108 \, {\left(f x + e\right)} \cos\left(5 \, f x + 5 \, e\right)^{2} + 675 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 1200 \, {\left(f x + e\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 675 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 108 \, {\left(f x + e\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right)^{2} + 108 \, {\left(f x + e\right)} \sin\left(5 \, f x + 5 \, e\right)^{2} + 675 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 1200 \, {\left(f x + e\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 675 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 108 \, {\left(f x + e\right)} \sin\left(f x + e\right)^{2} + 3 \, f x + 6 \, {\left(2 \, {\left(6 \, \cos\left(5 \, f x + 5 \, e\right) - 15 \, \cos\left(4 \, f x + 4 \, e\right) + 20 \, \cos\left(3 \, f x + 3 \, e\right) - 15 \, \cos\left(2 \, f x + 2 \, e\right) + 6 \, \cos\left(f x + e\right) - 1\right)} \cos\left(6 \, f x + 6 \, e\right) - \cos\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(15 \, \cos\left(4 \, f x + 4 \, e\right) - 20 \, \cos\left(3 \, f x + 3 \, e\right) + 15 \, \cos\left(2 \, f x + 2 \, e\right) - 6 \, \cos\left(f x + e\right) + 1\right)} \cos\left(5 \, f x + 5 \, e\right) - 36 \, \cos\left(5 \, f x + 5 \, e\right)^{2} + 30 \, {\left(20 \, \cos\left(3 \, f x + 3 \, e\right) - 15 \, \cos\left(2 \, f x + 2 \, e\right) + 6 \, \cos\left(f x + e\right) - 1\right)} \cos\left(4 \, f x + 4 \, e\right) - 225 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 40 \, {\left(15 \, \cos\left(2 \, f x + 2 \, e\right) - 6 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) - 400 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 30 \, {\left(6 \, \cos\left(f x + e\right) - 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 225 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 36 \, \cos\left(f x + e\right)^{2} + 2 \, {\left(6 \, \sin\left(5 \, f x + 5 \, e\right) - 15 \, \sin\left(4 \, f x + 4 \, e\right) + 20 \, \sin\left(3 \, f x + 3 \, e\right) - 15 \, \sin\left(2 \, f x + 2 \, e\right) + 6 \, \sin\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - \sin\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(15 \, \sin\left(4 \, f x + 4 \, e\right) - 20 \, \sin\left(3 \, f x + 3 \, e\right) + 15 \, \sin\left(2 \, f x + 2 \, e\right) - 6 \, \sin\left(f x + e\right)\right)} \sin\left(5 \, f x + 5 \, e\right) - 36 \, \sin\left(5 \, f x + 5 \, e\right)^{2} + 30 \, {\left(20 \, \sin\left(3 \, f x + 3 \, e\right) - 15 \, \sin\left(2 \, f x + 2 \, e\right) + 6 \, \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 225 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 120 \, {\left(5 \, \sin\left(2 \, f x + 2 \, e\right) - 2 \, \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 400 \, \sin\left(3 \, f x + 3 \, e\right)^{2} - 225 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 180 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 36 \, \sin\left(f x + e\right)^{2} + 12 \, \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 \, f x - 18 \, {\left(f x + e\right)} \cos\left(5 \, f x + 5 \, e\right) + 45 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 60 \, {\left(f x + e\right)} \cos\left(3 \, f x + 3 \, e\right) + 45 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 18 \, {\left(f x + e\right)} \cos\left(f x + e\right) + 3 \, e + 9 \, \sin\left(5 \, f x + 5 \, e\right) - 27 \, \sin\left(4 \, f x + 4 \, e\right) + 40 \, \sin\left(3 \, f x + 3 \, e\right) - 27 \, \sin\left(2 \, f x + 2 \, e\right) + 9 \, \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) - 6 \, {\left(6 \, f x + 90 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 120 \, {\left(f x + e\right)} \cos\left(3 \, f x + 3 \, e\right) + 90 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 36 \, {\left(f x + e\right)} \cos\left(f x + e\right) + 6 \, e - 9 \, \sin\left(4 \, f x + 4 \, e\right) + 20 \, \sin\left(3 \, f x + 3 \, e\right) - 9 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + 6 \, {\left(15 \, f x - 300 \, {\left(f x + e\right)} \cos\left(3 \, f x + 3 \, e\right) + 225 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 90 \, {\left(f x + e\right)} \cos\left(f x + e\right) + 15 \, e + 20 \, \sin\left(3 \, f x + 3 \, e\right) - 9 \, \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 120 \, {\left(f x + 15 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 6 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e + \sin\left(2 \, f x + 2 \, e\right) - \sin\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 18 \, {\left(5 \, f x - 30 \, {\left(f x + e\right)} \cos\left(f x + e\right) + 5 \, e - 3 \, \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - 36 \, {\left(f x + e\right)} \cos\left(f x + e\right) - 2 \, {\left(18 \, {\left(f x + e\right)} \sin\left(5 \, f x + 5 \, e\right) - 45 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) + 60 \, {\left(f x + e\right)} \sin\left(3 \, f x + 3 \, e\right) - 45 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 18 \, {\left(f x + e\right)} \sin\left(f x + e\right) + 9 \, \cos\left(5 \, f x + 5 \, e\right) - 27 \, \cos\left(4 \, f x + 4 \, e\right) + 40 \, \cos\left(3 \, f x + 3 \, e\right) - 27 \, \cos\left(2 \, f x + 2 \, e\right) + 9 \, \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 6 \, {\left(90 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) - 120 \, {\left(f x + e\right)} \sin\left(3 \, f x + 3 \, e\right) + 90 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 36 \, {\left(f x + e\right)} \sin\left(f x + e\right) + 9 \, \cos\left(4 \, f x + 4 \, e\right) - 20 \, \cos\left(3 \, f x + 3 \, e\right) + 9 \, \cos\left(2 \, f x + 2 \, e\right) - 3\right)} \sin\left(5 \, f x + 5 \, e\right) - 6 \, {\left(300 \, {\left(f x + e\right)} \sin\left(3 \, f x + 3 \, e\right) - 225 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 90 \, {\left(f x + e\right)} \sin\left(f x + e\right) + 20 \, \cos\left(3 \, f x + 3 \, e\right) - 9 \, \cos\left(f x + e\right) + 9\right)} \sin\left(4 \, f x + 4 \, e\right) - 40 \, {\left(45 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 18 \, {\left(f x + e\right)} \sin\left(f x + e\right) - 3 \, \cos\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(f x + e\right) - 2\right)} \sin\left(3 \, f x + 3 \, e\right) - 54 \, {\left(10 \, {\left(f x + e\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) + 1\right)} \sin\left(2 \, f x + 2 \, e\right) + 3 \, e + 18 \, \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{3 \, {\left(c^{4} \cos\left(6 \, f x + 6 \, e\right)^{2} + 36 \, c^{4} \cos\left(5 \, f x + 5 \, e\right)^{2} + 225 \, c^{4} \cos\left(4 \, f x + 4 \, e\right)^{2} + 400 \, c^{4} \cos\left(3 \, f x + 3 \, e\right)^{2} + 225 \, 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(6 \, f x + 6 \, e\right)^{2} + 36 \, c^{4} \sin\left(5 \, f x + 5 \, e\right)^{2} + 225 \, c^{4} \sin\left(4 \, f x + 4 \, e\right)^{2} + 400 \, c^{4} \sin\left(3 \, f x + 3 \, e\right)^{2} + 225 \, c^{4} \sin\left(2 \, f x + 2 \, e\right)^{2} - 180 \, 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(5 \, f x + 5 \, e\right) - 15 \, c^{4} \cos\left(4 \, f x + 4 \, e\right) + 20 \, c^{4} \cos\left(3 \, f x + 3 \, e\right) - 15 \, 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) - 12 \, {\left(15 \, c^{4} \cos\left(4 \, f x + 4 \, e\right) - 20 \, c^{4} \cos\left(3 \, f x + 3 \, e\right) + 15 \, 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) - 30 \, {\left(20 \, c^{4} \cos\left(3 \, f x + 3 \, e\right) - 15 \, 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) - 40 \, {\left(15 \, 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) - 30 \, {\left(6 \, c^{4} \cos\left(f x + e\right) - c^{4}\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(6 \, c^{4} \sin\left(5 \, f x + 5 \, e\right) - 15 \, c^{4} \sin\left(4 \, f x + 4 \, e\right) + 20 \, c^{4} \sin\left(3 \, f x + 3 \, e\right) - 15 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) + 6 \, c^{4} \sin\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 12 \, {\left(15 \, c^{4} \sin\left(4 \, f x + 4 \, e\right) - 20 \, c^{4} \sin\left(3 \, f x + 3 \, e\right) + 15 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) - 6 \, c^{4} \sin\left(f x + e\right)\right)} \sin\left(5 \, f x + 5 \, e\right) - 30 \, {\left(20 \, c^{4} \sin\left(3 \, f x + 3 \, e\right) - 15 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) + 6 \, c^{4} \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 120 \, {\left(5 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) - 2 \, c^{4} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} f}"," ",0,"-1/3*(3*(f*x + e)*cos(6*f*x + 6*e)^2 + 108*(f*x + e)*cos(5*f*x + 5*e)^2 + 675*(f*x + e)*cos(4*f*x + 4*e)^2 + 1200*(f*x + e)*cos(3*f*x + 3*e)^2 + 675*(f*x + e)*cos(2*f*x + 2*e)^2 + 108*(f*x + e)*cos(f*x + e)^2 + 3*(f*x + e)*sin(6*f*x + 6*e)^2 + 108*(f*x + e)*sin(5*f*x + 5*e)^2 + 675*(f*x + e)*sin(4*f*x + 4*e)^2 + 1200*(f*x + e)*sin(3*f*x + 3*e)^2 + 675*(f*x + e)*sin(2*f*x + 2*e)^2 + 108*(f*x + e)*sin(f*x + e)^2 + 3*f*x + 6*(2*(6*cos(5*f*x + 5*e) - 15*cos(4*f*x + 4*e) + 20*cos(3*f*x + 3*e) - 15*cos(2*f*x + 2*e) + 6*cos(f*x + e) - 1)*cos(6*f*x + 6*e) - cos(6*f*x + 6*e)^2 + 12*(15*cos(4*f*x + 4*e) - 20*cos(3*f*x + 3*e) + 15*cos(2*f*x + 2*e) - 6*cos(f*x + e) + 1)*cos(5*f*x + 5*e) - 36*cos(5*f*x + 5*e)^2 + 30*(20*cos(3*f*x + 3*e) - 15*cos(2*f*x + 2*e) + 6*cos(f*x + e) - 1)*cos(4*f*x + 4*e) - 225*cos(4*f*x + 4*e)^2 + 40*(15*cos(2*f*x + 2*e) - 6*cos(f*x + e) + 1)*cos(3*f*x + 3*e) - 400*cos(3*f*x + 3*e)^2 + 30*(6*cos(f*x + e) - 1)*cos(2*f*x + 2*e) - 225*cos(2*f*x + 2*e)^2 - 36*cos(f*x + e)^2 + 2*(6*sin(5*f*x + 5*e) - 15*sin(4*f*x + 4*e) + 20*sin(3*f*x + 3*e) - 15*sin(2*f*x + 2*e) + 6*sin(f*x + e))*sin(6*f*x + 6*e) - sin(6*f*x + 6*e)^2 + 12*(15*sin(4*f*x + 4*e) - 20*sin(3*f*x + 3*e) + 15*sin(2*f*x + 2*e) - 6*sin(f*x + e))*sin(5*f*x + 5*e) - 36*sin(5*f*x + 5*e)^2 + 30*(20*sin(3*f*x + 3*e) - 15*sin(2*f*x + 2*e) + 6*sin(f*x + e))*sin(4*f*x + 4*e) - 225*sin(4*f*x + 4*e)^2 + 120*(5*sin(2*f*x + 2*e) - 2*sin(f*x + e))*sin(3*f*x + 3*e) - 400*sin(3*f*x + 3*e)^2 - 225*sin(2*f*x + 2*e)^2 + 180*sin(2*f*x + 2*e)*sin(f*x + e) - 36*sin(f*x + e)^2 + 12*cos(f*x + e) - 1)*arctan2(sin(f*x + e), cos(f*x + e) - 1) + 2*(3*f*x - 18*(f*x + e)*cos(5*f*x + 5*e) + 45*(f*x + e)*cos(4*f*x + 4*e) - 60*(f*x + e)*cos(3*f*x + 3*e) + 45*(f*x + e)*cos(2*f*x + 2*e) - 18*(f*x + e)*cos(f*x + e) + 3*e + 9*sin(5*f*x + 5*e) - 27*sin(4*f*x + 4*e) + 40*sin(3*f*x + 3*e) - 27*sin(2*f*x + 2*e) + 9*sin(f*x + e))*cos(6*f*x + 6*e) - 6*(6*f*x + 90*(f*x + e)*cos(4*f*x + 4*e) - 120*(f*x + e)*cos(3*f*x + 3*e) + 90*(f*x + e)*cos(2*f*x + 2*e) - 36*(f*x + e)*cos(f*x + e) + 6*e - 9*sin(4*f*x + 4*e) + 20*sin(3*f*x + 3*e) - 9*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) + 6*(15*f*x - 300*(f*x + e)*cos(3*f*x + 3*e) + 225*(f*x + e)*cos(2*f*x + 2*e) - 90*(f*x + e)*cos(f*x + e) + 15*e + 20*sin(3*f*x + 3*e) - 9*sin(f*x + e))*cos(4*f*x + 4*e) - 120*(f*x + 15*(f*x + e)*cos(2*f*x + 2*e) - 6*(f*x + e)*cos(f*x + e) + e + sin(2*f*x + 2*e) - sin(f*x + e))*cos(3*f*x + 3*e) + 18*(5*f*x - 30*(f*x + e)*cos(f*x + e) + 5*e - 3*sin(f*x + e))*cos(2*f*x + 2*e) - 36*(f*x + e)*cos(f*x + e) - 2*(18*(f*x + e)*sin(5*f*x + 5*e) - 45*(f*x + e)*sin(4*f*x + 4*e) + 60*(f*x + e)*sin(3*f*x + 3*e) - 45*(f*x + e)*sin(2*f*x + 2*e) + 18*(f*x + e)*sin(f*x + e) + 9*cos(5*f*x + 5*e) - 27*cos(4*f*x + 4*e) + 40*cos(3*f*x + 3*e) - 27*cos(2*f*x + 2*e) + 9*cos(f*x + e))*sin(6*f*x + 6*e) - 6*(90*(f*x + e)*sin(4*f*x + 4*e) - 120*(f*x + e)*sin(3*f*x + 3*e) + 90*(f*x + e)*sin(2*f*x + 2*e) - 36*(f*x + e)*sin(f*x + e) + 9*cos(4*f*x + 4*e) - 20*cos(3*f*x + 3*e) + 9*cos(2*f*x + 2*e) - 3)*sin(5*f*x + 5*e) - 6*(300*(f*x + e)*sin(3*f*x + 3*e) - 225*(f*x + e)*sin(2*f*x + 2*e) + 90*(f*x + e)*sin(f*x + e) + 20*cos(3*f*x + 3*e) - 9*cos(f*x + e) + 9)*sin(4*f*x + 4*e) - 40*(45*(f*x + e)*sin(2*f*x + 2*e) - 18*(f*x + e)*sin(f*x + e) - 3*cos(2*f*x + 2*e) + 3*cos(f*x + e) - 2)*sin(3*f*x + 3*e) - 54*(10*(f*x + e)*sin(f*x + e) - cos(f*x + e) + 1)*sin(2*f*x + 2*e) + 3*e + 18*sin(f*x + e))*sqrt(a)*sqrt(c)/((c^4*cos(6*f*x + 6*e)^2 + 36*c^4*cos(5*f*x + 5*e)^2 + 225*c^4*cos(4*f*x + 4*e)^2 + 400*c^4*cos(3*f*x + 3*e)^2 + 225*c^4*cos(2*f*x + 2*e)^2 + 36*c^4*cos(f*x + e)^2 + c^4*sin(6*f*x + 6*e)^2 + 36*c^4*sin(5*f*x + 5*e)^2 + 225*c^4*sin(4*f*x + 4*e)^2 + 400*c^4*sin(3*f*x + 3*e)^2 + 225*c^4*sin(2*f*x + 2*e)^2 - 180*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(5*f*x + 5*e) - 15*c^4*cos(4*f*x + 4*e) + 20*c^4*cos(3*f*x + 3*e) - 15*c^4*cos(2*f*x + 2*e) + 6*c^4*cos(f*x + e) - c^4)*cos(6*f*x + 6*e) - 12*(15*c^4*cos(4*f*x + 4*e) - 20*c^4*cos(3*f*x + 3*e) + 15*c^4*cos(2*f*x + 2*e) - 6*c^4*cos(f*x + e) + c^4)*cos(5*f*x + 5*e) - 30*(20*c^4*cos(3*f*x + 3*e) - 15*c^4*cos(2*f*x + 2*e) + 6*c^4*cos(f*x + e) - c^4)*cos(4*f*x + 4*e) - 40*(15*c^4*cos(2*f*x + 2*e) - 6*c^4*cos(f*x + e) + c^4)*cos(3*f*x + 3*e) - 30*(6*c^4*cos(f*x + e) - c^4)*cos(2*f*x + 2*e) - 2*(6*c^4*sin(5*f*x + 5*e) - 15*c^4*sin(4*f*x + 4*e) + 20*c^4*sin(3*f*x + 3*e) - 15*c^4*sin(2*f*x + 2*e) + 6*c^4*sin(f*x + e))*sin(6*f*x + 6*e) - 12*(15*c^4*sin(4*f*x + 4*e) - 20*c^4*sin(3*f*x + 3*e) + 15*c^4*sin(2*f*x + 2*e) - 6*c^4*sin(f*x + e))*sin(5*f*x + 5*e) - 30*(20*c^4*sin(3*f*x + 3*e) - 15*c^4*sin(2*f*x + 2*e) + 6*c^4*sin(f*x + e))*sin(4*f*x + 4*e) - 120*(5*c^4*sin(2*f*x + 2*e) - 2*c^4*sin(f*x + e))*sin(3*f*x + 3*e))*f)","B",0
94,1,1356,0,1.052152," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(3 \, {\left(f x + e\right)} a c^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 27 \, {\left(f x + e\right)} a c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 27 \, {\left(f x + e\right)} a c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(f x + e\right)} a c^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 27 \, {\left(f x + e\right)} a c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 27 \, {\left(f x + e\right)} a c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(f x + e\right)} a c^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(f x + e\right)} a c^{2} - 6 \, a c^{2} \sin\left(2 \, f x + 2 \, e\right) - 3 \, {\left(a c^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 9 \, a c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 9 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a c^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 9 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 18 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, a c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 6 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a c^{2} + 2 \, {\left(3 \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 3 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a c^{2}\right)} \cos\left(6 \, f x + 6 \, e\right) + 6 \, {\left(3 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 6 \, {\left(a c^{2} \sin\left(4 \, f x + 4 \, e\right) + a c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) + 6 \, {\left(3 \, {\left(f x + e\right)} a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 3 \, {\left(f x + e\right)} a c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a c^{2} - a c^{2} \sin\left(4 \, f x + 4 \, e\right) - a c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 18 \, {\left(3 \, {\left(f x + e\right)} a c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 6 \, {\left(a c^{2} \sin\left(6 \, f x + 6 \, e\right) + 3 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, a c^{2} \sin\left(2 \, f x + 2 \, e\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(a c^{2} \sin\left(6 \, f x + 6 \, e\right) + 3 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, a 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) + 6 \, {\left(a c^{2} \sin\left(6 \, f x + 6 \, e\right) + 3 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, a 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) + 6 \, {\left(3 \, {\left(f x + e\right)} a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, {\left(f x + e\right)} a c^{2} \sin\left(2 \, f x + 2 \, e\right) + a c^{2} \cos\left(4 \, f x + 4 \, e\right) + a c^{2} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 6 \, {\left(9 \, {\left(f x + e\right)} a c^{2} \sin\left(2 \, f x + 2 \, e\right) - a c^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) - 6 \, {\left(a c^{2} \cos\left(6 \, f x + 6 \, e\right) + 3 \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 3 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a c^{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) - 4 \, {\left(a c^{2} \cos\left(6 \, f x + 6 \, e\right) + 3 \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 3 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a 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) - 6 \, {\left(a c^{2} \cos\left(6 \, f x + 6 \, e\right) + 3 \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 3 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a 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}}{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,"-1/3*(3*(f*x + e)*a*c^2*cos(6*f*x + 6*e)^2 + 27*(f*x + e)*a*c^2*cos(4*f*x + 4*e)^2 + 27*(f*x + e)*a*c^2*cos(2*f*x + 2*e)^2 + 3*(f*x + e)*a*c^2*sin(6*f*x + 6*e)^2 + 27*(f*x + e)*a*c^2*sin(4*f*x + 4*e)^2 + 27*(f*x + e)*a*c^2*sin(2*f*x + 2*e)^2 + 18*(f*x + e)*a*c^2*cos(2*f*x + 2*e) + 3*(f*x + e)*a*c^2 - 6*a*c^2*sin(2*f*x + 2*e) - 3*(a*c^2*cos(6*f*x + 6*e)^2 + 9*a*c^2*cos(4*f*x + 4*e)^2 + 9*a*c^2*cos(2*f*x + 2*e)^2 + a*c^2*sin(6*f*x + 6*e)^2 + 9*a*c^2*sin(4*f*x + 4*e)^2 + 18*a*c^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 9*a*c^2*sin(2*f*x + 2*e)^2 + 6*a*c^2*cos(2*f*x + 2*e) + a*c^2 + 2*(3*a*c^2*cos(4*f*x + 4*e) + 3*a*c^2*cos(2*f*x + 2*e) + a*c^2)*cos(6*f*x + 6*e) + 6*(3*a*c^2*cos(2*f*x + 2*e) + a*c^2)*cos(4*f*x + 4*e) + 6*(a*c^2*sin(4*f*x + 4*e) + a*c^2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 6*(3*(f*x + e)*a*c^2*cos(4*f*x + 4*e) + 3*(f*x + e)*a*c^2*cos(2*f*x + 2*e) + (f*x + e)*a*c^2 - a*c^2*sin(4*f*x + 4*e) - a*c^2*sin(2*f*x + 2*e))*cos(6*f*x + 6*e) + 18*(3*(f*x + e)*a*c^2*cos(2*f*x + 2*e) + (f*x + e)*a*c^2)*cos(4*f*x + 4*e) + 6*(a*c^2*sin(6*f*x + 6*e) + 3*a*c^2*sin(4*f*x + 4*e) + 3*a*c^2*sin(2*f*x + 2*e))*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(a*c^2*sin(6*f*x + 6*e) + 3*a*c^2*sin(4*f*x + 4*e) + 3*a*c^2*sin(2*f*x + 2*e))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 6*(a*c^2*sin(6*f*x + 6*e) + 3*a*c^2*sin(4*f*x + 4*e) + 3*a*c^2*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 6*(3*(f*x + e)*a*c^2*sin(4*f*x + 4*e) + 3*(f*x + e)*a*c^2*sin(2*f*x + 2*e) + a*c^2*cos(4*f*x + 4*e) + a*c^2*cos(2*f*x + 2*e))*sin(6*f*x + 6*e) + 6*(9*(f*x + e)*a*c^2*sin(2*f*x + 2*e) - a*c^2)*sin(4*f*x + 4*e) - 6*(a*c^2*cos(6*f*x + 6*e) + 3*a*c^2*cos(4*f*x + 4*e) + 3*a*c^2*cos(2*f*x + 2*e) + a*c^2)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(a*c^2*cos(6*f*x + 6*e) + 3*a*c^2*cos(4*f*x + 4*e) + 3*a*c^2*cos(2*f*x + 2*e) + a*c^2)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*(a*c^2*cos(6*f*x + 6*e) + 3*a*c^2*cos(4*f*x + 4*e) + 3*a*c^2*cos(2*f*x + 2*e) + a*c^2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(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
95,1,477,0,0.886793," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} a c \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(f x + e\right)} a c \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(f x + e\right)} a c \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(f x + e\right)} a c \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(f x + e\right)} a c \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a c - 2 \, a c \sin\left(2 \, f x + 2 \, e\right) - {\left(a c \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a c \cos\left(2 \, f x + 2 \, e\right)^{2} + a c \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a c \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, a c \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a c \cos\left(2 \, f x + 2 \, e\right) + a c + 2 \, {\left(2 \, a c \cos\left(2 \, f x + 2 \, e\right) + a c\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) + 2 \, {\left(2 \, {\left(f x + e\right)} a c \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a c - a c \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(2 \, {\left(f x + e\right)} a c \sin\left(2 \, f x + 2 \, e\right) + a c \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(4 \, f x + 4 \, 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,"-((f*x + e)*a*c*cos(4*f*x + 4*e)^2 + 4*(f*x + e)*a*c*cos(2*f*x + 2*e)^2 + (f*x + e)*a*c*sin(4*f*x + 4*e)^2 + 4*(f*x + e)*a*c*sin(2*f*x + 2*e)^2 + 4*(f*x + e)*a*c*cos(2*f*x + 2*e) + (f*x + e)*a*c - 2*a*c*sin(2*f*x + 2*e) - (a*c*cos(4*f*x + 4*e)^2 + 4*a*c*cos(2*f*x + 2*e)^2 + a*c*sin(4*f*x + 4*e)^2 + 4*a*c*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*a*c*sin(2*f*x + 2*e)^2 + 4*a*c*cos(2*f*x + 2*e) + a*c + 2*(2*a*c*cos(2*f*x + 2*e) + a*c)*cos(4*f*x + 4*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 2*(2*(f*x + e)*a*c*cos(2*f*x + 2*e) + (f*x + e)*a*c - a*c*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) + 2*(2*(f*x + e)*a*c*sin(2*f*x + 2*e) + a*c*cos(2*f*x + 2*e))*sin(4*f*x + 4*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
96,1,243,0,0.990617," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(f x + e\right)} 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) \sin\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a - {\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) + 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(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"-((f*x + e)*a*cos(2*f*x + 2*e)^2 + (f*x + e)*a*sin(2*f*x + 2*e)^2 + 2*(f*x + e)*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)))*sin(2*f*x + 2*e) + (f*x + e)*a - (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) + a)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*f)","B",0
97,1,60,0,0.556367," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} a + a \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, a \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right)\right)} \sqrt{a}}{\sqrt{c} f}"," ",0,"-((f*x + e)*a + a*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*a*arctan2(sin(f*x + e), cos(f*x + e) - 1))*sqrt(a)/(sqrt(c)*f)","A",0
98,1,95,0,0.723420," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{\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 \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 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,"(2*sqrt(-a)*a*log(sin(f*x + e)/(cos(f*x + e) + 1))/c^(3/2) - sqrt(-a)*a*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(3/2) + sqrt(-a)*a*(cos(f*x + e) + 1)^2/(c^(3/2)*sin(f*x + e)^2))/f","A",0
99,1,1786,0,1.213265," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} a \cos\left(4 \, f x + 4 \, e\right)^{2} + 36 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, {\left(f x + e\right)} 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)^{2} + 16 \, {\left(f x + e\right)} 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} + {\left(f x + e\right)} a \sin\left(4 \, f x + 4 \, e\right)^{2} + 36 \, {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right)^{2} + 16 \, {\left(f x + e\right)} 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)^{2} + 16 \, {\left(f x + e\right)} 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)^{2} + 12 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a - 2 \, {\left(a \cos\left(4 \, f x + 4 \, e\right)^{2} + 36 \, a \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, 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)^{2} + 16 \, 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 \sin\left(4 \, f x + 4 \, e\right)^{2} + 12 \, a \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 36 \, a \sin\left(2 \, f x + 2 \, e\right)^{2} + 16 \, 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)^{2} + 16 \, 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)^{2} + 2 \, {\left(6 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \cos\left(4 \, f x + 4 \, e\right) + 12 \, a \cos\left(2 \, f x + 2 \, e\right) - 8 \, {\left(a \cos\left(4 \, f x + 4 \, e\right) + 6 \, a \cos\left(2 \, f x + 2 \, e\right) - 4 \, 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)} \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(a \cos\left(4 \, f x + 4 \, e\right) + 6 \, a \cos\left(2 \, f x + 2 \, e\right) + a\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(a \sin\left(4 \, f x + 4 \, e\right) + 6 \, a \sin\left(2 \, f x + 2 \, e\right) - 4 \, 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)} \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(a \sin\left(4 \, f x + 4 \, e\right) + 6 \, a \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) + 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) + 2 \, {\left(6 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a - 4 \, a \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 2 \, {\left(4 \, {\left(f x + e\right)} a \cos\left(4 \, f x + 4 \, e\right) + 24 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right) - 16 \, {\left(f x + e\right)} 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) + 4 \, {\left(f x + e\right)} a + 3 \, a \sin\left(4 \, f x + 4 \, e\right) + 2 \, a \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) - 2 \, {\left(4 \, {\left(f x + e\right)} a \cos\left(4 \, f x + 4 \, e\right) + 24 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(f x + e\right)} a + 3 \, a \sin\left(4 \, f x + 4 \, e\right) + 2 \, 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) + 4 \, {\left(3 \, {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right) + 2 \, a \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 8 \, a \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(4 \, {\left(f x + e\right)} a \sin\left(4 \, f x + 4 \, e\right) + 24 \, {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right) - 16 \, {\left(f x + e\right)} 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) - 3 \, a \cos\left(4 \, f x + 4 \, e\right) - 2 \, a \cos\left(2 \, f x + 2 \, e\right) - 3 \, 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) - 2 \, {\left(4 \, {\left(f x + e\right)} a \sin\left(4 \, f x + 4 \, e\right) + 24 \, {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right) - 3 \, a \cos\left(4 \, f x + 4 \, e\right) - 2 \, 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}}{{\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,"-((f*x + e)*a*cos(4*f*x + 4*e)^2 + 36*(f*x + e)*a*cos(2*f*x + 2*e)^2 + 16*(f*x + e)*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*(f*x + e)*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + (f*x + e)*a*sin(4*f*x + 4*e)^2 + 36*(f*x + e)*a*sin(2*f*x + 2*e)^2 + 16*(f*x + e)*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*(f*x + e)*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 12*(f*x + e)*a*cos(2*f*x + 2*e) + (f*x + e)*a - 2*(a*cos(4*f*x + 4*e)^2 + 36*a*cos(2*f*x + 2*e)^2 + 16*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a*sin(4*f*x + 4*e)^2 + 12*a*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*a*sin(2*f*x + 2*e)^2 + 16*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*(6*a*cos(2*f*x + 2*e) + a)*cos(4*f*x + 4*e) + 12*a*cos(2*f*x + 2*e) - 8*(a*cos(4*f*x + 4*e) + 6*a*cos(2*f*x + 2*e) - 4*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*(a*cos(4*f*x + 4*e) + 6*a*cos(2*f*x + 2*e) + a)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*(a*sin(4*f*x + 4*e) + 6*a*sin(2*f*x + 2*e) - 4*a*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*(a*sin(4*f*x + 4*e) + 6*a*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), 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) + 2*(6*(f*x + e)*a*cos(2*f*x + 2*e) + (f*x + e)*a - 4*a*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) - 2*(4*(f*x + e)*a*cos(4*f*x + 4*e) + 24*(f*x + e)*a*cos(2*f*x + 2*e) - 16*(f*x + e)*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(f*x + e)*a + 3*a*sin(4*f*x + 4*e) + 2*a*sin(2*f*x + 2*e))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*(4*(f*x + e)*a*cos(4*f*x + 4*e) + 24*(f*x + e)*a*cos(2*f*x + 2*e) + 4*(f*x + e)*a + 3*a*sin(4*f*x + 4*e) + 2*a*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(3*(f*x + e)*a*sin(2*f*x + 2*e) + 2*a*cos(2*f*x + 2*e))*sin(4*f*x + 4*e) - 8*a*sin(2*f*x + 2*e) - 2*(4*(f*x + e)*a*sin(4*f*x + 4*e) + 24*(f*x + e)*a*sin(2*f*x + 2*e) - 16*(f*x + e)*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3*a*cos(4*f*x + 4*e) - 2*a*cos(2*f*x + 2*e) - 3*a)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*(4*(f*x + e)*a*sin(4*f*x + 4*e) + 24*(f*x + e)*a*sin(2*f*x + 2*e) - 3*a*cos(4*f*x + 4*e) - 2*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^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
100,1,3480,0,3.656191," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(3 \, {\left(f x + e\right)} a \cos\left(6 \, f x + 6 \, e\right)^{2} + 675 \, {\left(f x + e\right)} a \cos\left(4 \, f x + 4 \, e\right)^{2} + 675 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right)^{2} + 108 \, {\left(f x + e\right)} 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)^{2} + 1200 \, {\left(f x + e\right)} 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)^{2} + 108 \, {\left(f x + e\right)} 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} + 3 \, {\left(f x + e\right)} a \sin\left(6 \, f x + 6 \, e\right)^{2} + 675 \, {\left(f x + e\right)} a \sin\left(4 \, f x + 4 \, e\right)^{2} + 675 \, {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right)^{2} + 108 \, {\left(f x + e\right)} 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)^{2} + 1200 \, {\left(f x + e\right)} 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)^{2} + 108 \, {\left(f x + e\right)} 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)^{2} + 90 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(f x + e\right)} a - 6 \, {\left(a \cos\left(6 \, f x + 6 \, e\right)^{2} + 225 \, a \cos\left(4 \, f x + 4 \, e\right)^{2} + 225 \, a \cos\left(2 \, f x + 2 \, e\right)^{2} + 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)^{2} + 400 \, 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)^{2} + 36 \, 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 \sin\left(6 \, f x + 6 \, e\right)^{2} + 225 \, a \sin\left(4 \, f x + 4 \, e\right)^{2} + 450 \, a \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 225 \, a \sin\left(2 \, f x + 2 \, e\right)^{2} + 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)^{2} + 400 \, 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)^{2} + 36 \, 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)^{2} + 2 \, {\left(15 \, a \cos\left(4 \, f x + 4 \, e\right) + 15 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \cos\left(6 \, f x + 6 \, e\right) + 30 \, {\left(15 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \cos\left(4 \, f x + 4 \, e\right) + 30 \, a \cos\left(2 \, f x + 2 \, e\right) - 12 \, {\left(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) - 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) - 6 \, 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)} \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(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) - 6 \, 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)} \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(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) + a\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(a \sin\left(4 \, f x + 4 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 12 \, {\left(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) - 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) - 6 \, 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)} \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(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) - 6 \, 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)} \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(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)\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) + 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) + 6 \, {\left(15 \, {\left(f x + e\right)} a \cos\left(4 \, f x + 4 \, e\right) + 15 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a - 11 \, a \sin\left(4 \, f x + 4 \, e\right) - 11 \, a \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 90 \, {\left(15 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a\right)} \cos\left(4 \, f x + 4 \, e\right) - 12 \, {\left(3 \, {\left(f x + e\right)} a \cos\left(6 \, f x + 6 \, e\right) + 45 \, {\left(f x + e\right)} a \cos\left(4 \, f x + 4 \, e\right) + 45 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right) - 60 \, {\left(f x + e\right)} 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) - 18 \, {\left(f x + e\right)} 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) + 3 \, {\left(f x + e\right)} a + 2 \, a \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) + 10 \, 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) - 20 \, {\left(6 \, {\left(f x + e\right)} a \cos\left(6 \, f x + 6 \, e\right) + 90 \, {\left(f x + e\right)} a \cos\left(4 \, f x + 4 \, e\right) + 90 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right) - 36 \, {\left(f x + e\right)} 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) + 6 \, {\left(f x + e\right)} a + 5 \, 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) - 6 \, 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) - 12 \, {\left(3 \, {\left(f x + e\right)} a \cos\left(6 \, f x + 6 \, e\right) + 45 \, {\left(f x + e\right)} a \cos\left(4 \, f x + 4 \, e\right) + 45 \, {\left(f x + e\right)} a \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(f x + e\right)} a + 2 \, a \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)\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) + 6 \, {\left(15 \, {\left(f x + e\right)} a \sin\left(4 \, f x + 4 \, e\right) + 15 \, {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right) + 11 \, a \cos\left(4 \, f x + 4 \, e\right) + 11 \, a \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 6 \, {\left(225 \, {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right) - 11 \, a\right)} \sin\left(4 \, f x + 4 \, e\right) - 66 \, a \sin\left(2 \, f x + 2 \, e\right) - 12 \, {\left(3 \, {\left(f x + e\right)} a \sin\left(6 \, f x + 6 \, e\right) + 45 \, {\left(f x + e\right)} a \sin\left(4 \, f x + 4 \, e\right) + 45 \, {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right) - 60 \, {\left(f x + e\right)} 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) - 18 \, {\left(f x + e\right)} 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) - 2 \, a \cos\left(6 \, f x + 6 \, e\right) + 3 \, a \cos\left(4 \, f x + 4 \, e\right) + 3 \, a \cos\left(2 \, f x + 2 \, e\right) - 10 \, 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) - 2 \, 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) - 20 \, {\left(6 \, {\left(f x + e\right)} a \sin\left(6 \, f x + 6 \, e\right) + 90 \, {\left(f x + e\right)} a \sin\left(4 \, f x + 4 \, e\right) + 90 \, {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right) - 36 \, {\left(f x + e\right)} 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) - 5 \, 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) + 6 \, 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{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12 \, {\left(3 \, {\left(f x + e\right)} a \sin\left(6 \, f x + 6 \, e\right) + 45 \, {\left(f x + e\right)} a \sin\left(4 \, f x + 4 \, e\right) + 45 \, {\left(f x + e\right)} a \sin\left(2 \, f x + 2 \, e\right) - 2 \, a \cos\left(6 \, f x + 6 \, e\right) + 3 \, a \cos\left(4 \, f x + 4 \, e\right) + 3 \, a \cos\left(2 \, f x + 2 \, e\right) - 2 \, 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,"-1/3*(3*(f*x + e)*a*cos(6*f*x + 6*e)^2 + 675*(f*x + e)*a*cos(4*f*x + 4*e)^2 + 675*(f*x + e)*a*cos(2*f*x + 2*e)^2 + 108*(f*x + e)*a*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 1200*(f*x + e)*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 108*(f*x + e)*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3*(f*x + e)*a*sin(6*f*x + 6*e)^2 + 675*(f*x + e)*a*sin(4*f*x + 4*e)^2 + 675*(f*x + e)*a*sin(2*f*x + 2*e)^2 + 108*(f*x + e)*a*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 1200*(f*x + e)*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 108*(f*x + e)*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 90*(f*x + e)*a*cos(2*f*x + 2*e) + 3*(f*x + e)*a - 6*(a*cos(6*f*x + 6*e)^2 + 225*a*cos(4*f*x + 4*e)^2 + 225*a*cos(2*f*x + 2*e)^2 + 36*a*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 400*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 36*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a*sin(6*f*x + 6*e)^2 + 225*a*sin(4*f*x + 4*e)^2 + 450*a*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 225*a*sin(2*f*x + 2*e)^2 + 36*a*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 400*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 36*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*(15*a*cos(4*f*x + 4*e) + 15*a*cos(2*f*x + 2*e) + a)*cos(6*f*x + 6*e) + 30*(15*a*cos(2*f*x + 2*e) + a)*cos(4*f*x + 4*e) + 30*a*cos(2*f*x + 2*e) - 12*(a*cos(6*f*x + 6*e) + 15*a*cos(4*f*x + 4*e) + 15*a*cos(2*f*x + 2*e) - 20*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 40*(a*cos(6*f*x + 6*e) + 15*a*cos(4*f*x + 4*e) + 15*a*cos(2*f*x + 2*e) - 6*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*(a*cos(6*f*x + 6*e) + 15*a*cos(4*f*x + 4*e) + 15*a*cos(2*f*x + 2*e) + a)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 30*(a*sin(4*f*x + 4*e) + a*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 12*(a*sin(6*f*x + 6*e) + 15*a*sin(4*f*x + 4*e) + 15*a*sin(2*f*x + 2*e) - 20*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*a*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*(a*sin(6*f*x + 6*e) + 15*a*sin(4*f*x + 4*e) + 15*a*sin(2*f*x + 2*e) - 6*a*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*(a*sin(6*f*x + 6*e) + 15*a*sin(4*f*x + 4*e) + 15*a*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), 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) + 6*(15*(f*x + e)*a*cos(4*f*x + 4*e) + 15*(f*x + e)*a*cos(2*f*x + 2*e) + (f*x + e)*a - 11*a*sin(4*f*x + 4*e) - 11*a*sin(2*f*x + 2*e))*cos(6*f*x + 6*e) + 90*(15*(f*x + e)*a*cos(2*f*x + 2*e) + (f*x + e)*a)*cos(4*f*x + 4*e) - 12*(3*(f*x + e)*a*cos(6*f*x + 6*e) + 45*(f*x + e)*a*cos(4*f*x + 4*e) + 45*(f*x + e)*a*cos(2*f*x + 2*e) - 60*(f*x + e)*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 18*(f*x + e)*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*(f*x + e)*a + 2*a*sin(6*f*x + 6*e) - 3*a*sin(4*f*x + 4*e) - 3*a*sin(2*f*x + 2*e) + 10*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))) - 20*(6*(f*x + e)*a*cos(6*f*x + 6*e) + 90*(f*x + e)*a*cos(4*f*x + 4*e) + 90*(f*x + e)*a*cos(2*f*x + 2*e) - 36*(f*x + e)*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 6*(f*x + e)*a + 5*a*sin(6*f*x + 6*e) + 9*a*sin(4*f*x + 4*e) + 9*a*sin(2*f*x + 2*e) - 6*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))) - 12*(3*(f*x + e)*a*cos(6*f*x + 6*e) + 45*(f*x + e)*a*cos(4*f*x + 4*e) + 45*(f*x + e)*a*cos(2*f*x + 2*e) + 3*(f*x + e)*a + 2*a*sin(6*f*x + 6*e) - 3*a*sin(4*f*x + 4*e) - 3*a*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 6*(15*(f*x + e)*a*sin(4*f*x + 4*e) + 15*(f*x + e)*a*sin(2*f*x + 2*e) + 11*a*cos(4*f*x + 4*e) + 11*a*cos(2*f*x + 2*e))*sin(6*f*x + 6*e) + 6*(225*(f*x + e)*a*sin(2*f*x + 2*e) - 11*a)*sin(4*f*x + 4*e) - 66*a*sin(2*f*x + 2*e) - 12*(3*(f*x + e)*a*sin(6*f*x + 6*e) + 45*(f*x + e)*a*sin(4*f*x + 4*e) + 45*(f*x + e)*a*sin(2*f*x + 2*e) - 60*(f*x + e)*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 18*(f*x + e)*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*a*cos(6*f*x + 6*e) + 3*a*cos(4*f*x + 4*e) + 3*a*cos(2*f*x + 2*e) - 10*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*a)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*(6*(f*x + e)*a*sin(6*f*x + 6*e) + 90*(f*x + e)*a*sin(4*f*x + 4*e) + 90*(f*x + e)*a*sin(2*f*x + 2*e) - 36*(f*x + e)*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*a*cos(6*f*x + 6*e) - 9*a*cos(4*f*x + 4*e) - 9*a*cos(2*f*x + 2*e) + 6*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*a)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*(3*(f*x + e)*a*sin(6*f*x + 6*e) + 45*(f*x + e)*a*sin(4*f*x + 4*e) + 45*(f*x + e)*a*sin(2*f*x + 2*e) - 2*a*cos(6*f*x + 6*e) + 3*a*cos(4*f*x + 4*e) + 3*a*cos(2*f*x + 2*e) - 2*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
101,1,1619,0,1.180691," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(f x + e\right)} a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 36 \, {\left(f x + e\right)} a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(f x + e\right)} a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(f x + e\right)} a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(f x + e\right)} a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, {\left(f x + e\right)} a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(f x + e\right)} a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, {\left(f x + e\right)} a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2} c^{2} - 4 \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) - {\left(a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right)^{2} + 16 \, a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 36 \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{2} + 2 \, {\left(4 \, a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 6 \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 4 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{2}\right)} \cos\left(8 \, f x + 8 \, e\right) + 8 \, {\left(6 \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 4 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} c^{2}\right)} \cos\left(6 \, f x + 6 \, e\right) + 12 \, {\left(4 \, 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) + 4 \, {\left(2 \, a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 16 \, {\left(3 \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) + 2 \, {\left(4 \, {\left(f x + e\right)} a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 6 \, {\left(f x + e\right)} a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(f x + e\right)} a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2} c^{2} - 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) - 2 \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + 8 \, {\left(6 \, {\left(f x + e\right)} a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(f x + e\right)} a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2} c^{2} + a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 4 \, {\left(12 \, {\left(f x + e\right)} a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(f x + e\right)} a^{2} c^{2} - 2 \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(2 \, {\left(f x + e\right)} a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 3 \, {\left(f x + e\right)} a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(f x + e\right)} a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) + a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 4 \, {\left(12 \, {\left(f x + e\right)} a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 8 \, {\left(f x + e\right)} a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) - 2 \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) - a^{2} c^{2}\right)} \sin\left(6 \, f x + 6 \, e\right) + 4 \, {\left(12 \, {\left(f x + e\right)} a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 2 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) - a^{2} c^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)\right)} \sqrt{a} \sqrt{c}}{{\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,"-((f*x + e)*a^2*c^2*cos(8*f*x + 8*e)^2 + 16*(f*x + e)*a^2*c^2*cos(6*f*x + 6*e)^2 + 36*(f*x + e)*a^2*c^2*cos(4*f*x + 4*e)^2 + 16*(f*x + e)*a^2*c^2*cos(2*f*x + 2*e)^2 + (f*x + e)*a^2*c^2*sin(8*f*x + 8*e)^2 + 16*(f*x + e)*a^2*c^2*sin(6*f*x + 6*e)^2 + 36*(f*x + e)*a^2*c^2*sin(4*f*x + 4*e)^2 + 16*(f*x + e)*a^2*c^2*sin(2*f*x + 2*e)^2 + 8*(f*x + e)*a^2*c^2*cos(2*f*x + 2*e) + (f*x + e)*a^2*c^2 - 4*a^2*c^2*sin(2*f*x + 2*e) - (a^2*c^2*cos(8*f*x + 8*e)^2 + 16*a^2*c^2*cos(6*f*x + 6*e)^2 + 36*a^2*c^2*cos(4*f*x + 4*e)^2 + 16*a^2*c^2*cos(2*f*x + 2*e)^2 + a^2*c^2*sin(8*f*x + 8*e)^2 + 16*a^2*c^2*sin(6*f*x + 6*e)^2 + 36*a^2*c^2*sin(4*f*x + 4*e)^2 + 48*a^2*c^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 16*a^2*c^2*sin(2*f*x + 2*e)^2 + 8*a^2*c^2*cos(2*f*x + 2*e) + a^2*c^2 + 2*(4*a^2*c^2*cos(6*f*x + 6*e) + 6*a^2*c^2*cos(4*f*x + 4*e) + 4*a^2*c^2*cos(2*f*x + 2*e) + a^2*c^2)*cos(8*f*x + 8*e) + 8*(6*a^2*c^2*cos(4*f*x + 4*e) + 4*a^2*c^2*cos(2*f*x + 2*e) + a^2*c^2)*cos(6*f*x + 6*e) + 12*(4*a^2*c^2*cos(2*f*x + 2*e) + a^2*c^2)*cos(4*f*x + 4*e) + 4*(2*a^2*c^2*sin(6*f*x + 6*e) + 3*a^2*c^2*sin(4*f*x + 4*e) + 2*a^2*c^2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 16*(3*a^2*c^2*sin(4*f*x + 4*e) + 2*a^2*c^2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 2*(4*(f*x + e)*a^2*c^2*cos(6*f*x + 6*e) + 6*(f*x + e)*a^2*c^2*cos(4*f*x + 4*e) + 4*(f*x + e)*a^2*c^2*cos(2*f*x + 2*e) + (f*x + e)*a^2*c^2 - 2*a^2*c^2*sin(6*f*x + 6*e) - 2*a^2*c^2*sin(4*f*x + 4*e) - 2*a^2*c^2*sin(2*f*x + 2*e))*cos(8*f*x + 8*e) + 8*(6*(f*x + e)*a^2*c^2*cos(4*f*x + 4*e) + 4*(f*x + e)*a^2*c^2*cos(2*f*x + 2*e) + (f*x + e)*a^2*c^2 + a^2*c^2*sin(4*f*x + 4*e))*cos(6*f*x + 6*e) + 4*(12*(f*x + e)*a^2*c^2*cos(2*f*x + 2*e) + 3*(f*x + e)*a^2*c^2 - 2*a^2*c^2*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(2*(f*x + e)*a^2*c^2*sin(6*f*x + 6*e) + 3*(f*x + e)*a^2*c^2*sin(4*f*x + 4*e) + 2*(f*x + e)*a^2*c^2*sin(2*f*x + 2*e) + a^2*c^2*cos(6*f*x + 6*e) + a^2*c^2*cos(4*f*x + 4*e) + a^2*c^2*cos(2*f*x + 2*e))*sin(8*f*x + 8*e) + 4*(12*(f*x + e)*a^2*c^2*sin(4*f*x + 4*e) + 8*(f*x + e)*a^2*c^2*sin(2*f*x + 2*e) - 2*a^2*c^2*cos(4*f*x + 4*e) - a^2*c^2)*sin(6*f*x + 6*e) + 4*(12*(f*x + e)*a^2*c^2*sin(2*f*x + 2*e) + 2*a^2*c^2*cos(2*f*x + 2*e) - a^2*c^2)*sin(4*f*x + 4*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
102,1,1356,0,1.114137," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(3 \, {\left(f x + e\right)} a^{2} c \cos\left(6 \, f x + 6 \, e\right)^{2} + 27 \, {\left(f x + e\right)} a^{2} c \cos\left(4 \, f x + 4 \, e\right)^{2} + 27 \, {\left(f x + e\right)} a^{2} c \cos\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(f x + e\right)} a^{2} c \sin\left(6 \, f x + 6 \, e\right)^{2} + 27 \, {\left(f x + e\right)} a^{2} c \sin\left(4 \, f x + 4 \, e\right)^{2} + 27 \, {\left(f x + e\right)} a^{2} c \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(f x + e\right)} a^{2} c \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(f x + e\right)} a^{2} c - 6 \, a^{2} c \sin\left(2 \, f x + 2 \, e\right) - 3 \, {\left(a^{2} c \cos\left(6 \, f x + 6 \, e\right)^{2} + 9 \, a^{2} c \cos\left(4 \, f x + 4 \, e\right)^{2} + 9 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} c \sin\left(6 \, f x + 6 \, e\right)^{2} + 9 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right)^{2} + 18 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, a^{2} c \sin\left(2 \, f x + 2 \, e\right)^{2} + 6 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} c + 2 \, {\left(3 \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} c\right)} \cos\left(6 \, f x + 6 \, e\right) + 6 \, {\left(3 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} c\right)} \cos\left(4 \, f x + 4 \, e\right) + 6 \, {\left(a^{2} c \sin\left(4 \, f x + 4 \, e\right) + a^{2} c \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) + 6 \, {\left(3 \, {\left(f x + e\right)} a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 3 \, {\left(f x + e\right)} a^{2} c \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2} c - a^{2} c \sin\left(4 \, f x + 4 \, e\right) - a^{2} c \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 18 \, {\left(3 \, {\left(f x + e\right)} a^{2} c \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2} c\right)} \cos\left(4 \, f x + 4 \, e\right) - 6 \, {\left(a^{2} c \sin\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} c \sin\left(2 \, f x + 2 \, e\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(a^{2} c \sin\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} c \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) - 6 \, {\left(a^{2} c \sin\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} c \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) + 6 \, {\left(3 \, {\left(f x + e\right)} a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 3 \, {\left(f x + e\right)} a^{2} c \sin\left(2 \, f x + 2 \, e\right) + a^{2} c \cos\left(4 \, f x + 4 \, e\right) + a^{2} c \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 6 \, {\left(9 \, {\left(f x + e\right)} a^{2} c \sin\left(2 \, f x + 2 \, e\right) - a^{2} c\right)} \sin\left(4 \, f x + 4 \, e\right) + 6 \, {\left(a^{2} c \cos\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} c\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(a^{2} c \cos\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} c\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) + 6 \, {\left(a^{2} c \cos\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} 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}}{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,"-1/3*(3*(f*x + e)*a^2*c*cos(6*f*x + 6*e)^2 + 27*(f*x + e)*a^2*c*cos(4*f*x + 4*e)^2 + 27*(f*x + e)*a^2*c*cos(2*f*x + 2*e)^2 + 3*(f*x + e)*a^2*c*sin(6*f*x + 6*e)^2 + 27*(f*x + e)*a^2*c*sin(4*f*x + 4*e)^2 + 27*(f*x + e)*a^2*c*sin(2*f*x + 2*e)^2 + 18*(f*x + e)*a^2*c*cos(2*f*x + 2*e) + 3*(f*x + e)*a^2*c - 6*a^2*c*sin(2*f*x + 2*e) - 3*(a^2*c*cos(6*f*x + 6*e)^2 + 9*a^2*c*cos(4*f*x + 4*e)^2 + 9*a^2*c*cos(2*f*x + 2*e)^2 + a^2*c*sin(6*f*x + 6*e)^2 + 9*a^2*c*sin(4*f*x + 4*e)^2 + 18*a^2*c*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 9*a^2*c*sin(2*f*x + 2*e)^2 + 6*a^2*c*cos(2*f*x + 2*e) + a^2*c + 2*(3*a^2*c*cos(4*f*x + 4*e) + 3*a^2*c*cos(2*f*x + 2*e) + a^2*c)*cos(6*f*x + 6*e) + 6*(3*a^2*c*cos(2*f*x + 2*e) + a^2*c)*cos(4*f*x + 4*e) + 6*(a^2*c*sin(4*f*x + 4*e) + a^2*c*sin(2*f*x + 2*e))*sin(6*f*x + 6*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 6*(3*(f*x + e)*a^2*c*cos(4*f*x + 4*e) + 3*(f*x + e)*a^2*c*cos(2*f*x + 2*e) + (f*x + e)*a^2*c - a^2*c*sin(4*f*x + 4*e) - a^2*c*sin(2*f*x + 2*e))*cos(6*f*x + 6*e) + 18*(3*(f*x + e)*a^2*c*cos(2*f*x + 2*e) + (f*x + e)*a^2*c)*cos(4*f*x + 4*e) - 6*(a^2*c*sin(6*f*x + 6*e) + 3*a^2*c*sin(4*f*x + 4*e) + 3*a^2*c*sin(2*f*x + 2*e))*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(a^2*c*sin(6*f*x + 6*e) + 3*a^2*c*sin(4*f*x + 4*e) + 3*a^2*c*sin(2*f*x + 2*e))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*(a^2*c*sin(6*f*x + 6*e) + 3*a^2*c*sin(4*f*x + 4*e) + 3*a^2*c*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 6*(3*(f*x + e)*a^2*c*sin(4*f*x + 4*e) + 3*(f*x + e)*a^2*c*sin(2*f*x + 2*e) + a^2*c*cos(4*f*x + 4*e) + a^2*c*cos(2*f*x + 2*e))*sin(6*f*x + 6*e) + 6*(9*(f*x + e)*a^2*c*sin(2*f*x + 2*e) - a^2*c)*sin(4*f*x + 4*e) + 6*(a^2*c*cos(6*f*x + 6*e) + 3*a^2*c*cos(4*f*x + 4*e) + 3*a^2*c*cos(2*f*x + 2*e) + a^2*c)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(a^2*c*cos(6*f*x + 6*e) + 3*a^2*c*cos(4*f*x + 4*e) + 3*a^2*c*cos(2*f*x + 2*e) + a^2*c)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 6*(a^2*c*cos(6*f*x + 6*e) + 3*a^2*c*cos(4*f*x + 4*e) + 3*a^2*c*cos(2*f*x + 2*e) + a^2*c)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(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
103,1,710,0,1.051440," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2} + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - {\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) + 2 \, {\left(2 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\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)} \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} \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) + 2 \, {\left(2 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - a^{2} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\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) + 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) + 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)} \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(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,"-((f*x + e)*a^2*cos(4*f*x + 4*e)^2 + 4*(f*x + e)*a^2*cos(2*f*x + 2*e)^2 + (f*x + e)*a^2*sin(4*f*x + 4*e)^2 + 4*(f*x + e)*a^2*sin(2*f*x + 2*e)^2 + 4*(f*x + e)*a^2*cos(2*f*x + 2*e) + (f*x + e)*a^2 + 2*a^2*sin(2*f*x + 2*e) - (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) + 2*(2*(f*x + e)*a^2*cos(2*f*x + 2*e) + (f*x + e)*a^2 + a^2*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) - 4*(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))) - 4*(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))) + 2*(2*(f*x + e)*a^2*sin(2*f*x + 2*e) - a^2*cos(2*f*x + 2*e))*sin(4*f*x + 4*e) + 4*(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))) + 4*(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)/((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
104,-2,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
105,-2,0,0,0.000000," ","integrate((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
106,1,139,0,0.567071," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{\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{2 \, \sqrt{-a} a^{2} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 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*(4*sqrt(-a)*a^2*log(sin(f*x + e)/(cos(f*x + e) + 1))/c^(5/2) - 2*sqrt(-a)*a^2*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 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
107,1,3738,0,4.395832," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(3 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 675 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 675 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 108 \, {\left(f x + e\right)} 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)^{2} + 1200 \, {\left(f x + e\right)} 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} + 108 \, {\left(f x + e\right)} 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} + 3 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 675 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 675 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 108 \, {\left(f x + e\right)} 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)^{2} + 1200 \, {\left(f x + e\right)} 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} + 108 \, {\left(f x + e\right)} 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} + 90 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(f x + e\right)} a^{2} - 72 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 6 \, {\left(a^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 225 \, a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 225 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 36 \, 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)^{2} + 400 \, 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} + 36 \, 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(6 \, f x + 6 \, e\right)^{2} + 225 \, a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 450 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 225 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 36 \, 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)^{2} + 400 \, 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} + 36 \, 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} + 30 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} + 2 \, {\left(15 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 15 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(6 \, f x + 6 \, e\right) + 30 \, {\left(15 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 12 \, {\left(a^{2} \cos\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 15 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 20 \, 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) - 6 \, 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{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 40 \, {\left(a^{2} \cos\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 15 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 6 \, 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) - 12 \, {\left(a^{2} \cos\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 15 \, 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) + 30 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) + a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 12 \, {\left(a^{2} \sin\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 15 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 20 \, 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) - 6 \, 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{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 40 \, {\left(a^{2} \sin\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 15 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 6 \, 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) - 12 \, {\left(a^{2} \sin\left(6 \, f x + 6 \, e\right) + 15 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 15 \, 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) + 6 \, {\left(15 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 15 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2} - 12 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - 12 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 90 \, {\left(15 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 6 \, {\left(6 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 90 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 90 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 120 \, {\left(f x + e\right)} 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) - 36 \, {\left(f x + e\right)} 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) + 6 \, {\left(f x + e\right)} a^{2} + 5 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 16 \, 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{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, {\left(30 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 450 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 450 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 180 \, {\left(f x + e\right)} 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) + 30 \, {\left(f x + e\right)} a^{2} + 29 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 75 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 75 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 24 \, 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) - 6 \, {\left(6 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 90 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 90 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(f x + e\right)} a^{2} + 5 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, 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) + 18 \, {\left(5 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 5 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 4 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 18 \, {\left(75 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 4 \, a^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) - 6 \, {\left(6 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 90 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 90 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 120 \, {\left(f x + e\right)} 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) - 36 \, {\left(f x + e\right)} 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) - 5 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) - 3 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 3 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 16 \, 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) - 5 \, 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) - 4 \, {\left(30 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 450 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 450 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 180 \, {\left(f x + e\right)} 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) - 29 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) - 75 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 75 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 24 \, 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) - 29 \, 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) - 6 \, {\left(6 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 90 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 90 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 5 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) - 3 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 3 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 5 \, 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^{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,"-1/3*(3*(f*x + e)*a^2*cos(6*f*x + 6*e)^2 + 675*(f*x + e)*a^2*cos(4*f*x + 4*e)^2 + 675*(f*x + e)*a^2*cos(2*f*x + 2*e)^2 + 108*(f*x + e)*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 1200*(f*x + e)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 108*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3*(f*x + e)*a^2*sin(6*f*x + 6*e)^2 + 675*(f*x + e)*a^2*sin(4*f*x + 4*e)^2 + 675*(f*x + e)*a^2*sin(2*f*x + 2*e)^2 + 108*(f*x + e)*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 1200*(f*x + e)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 108*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 90*(f*x + e)*a^2*cos(2*f*x + 2*e) + 3*(f*x + e)*a^2 - 72*a^2*sin(2*f*x + 2*e) - 6*(a^2*cos(6*f*x + 6*e)^2 + 225*a^2*cos(4*f*x + 4*e)^2 + 225*a^2*cos(2*f*x + 2*e)^2 + 36*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 400*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 36*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a^2*sin(6*f*x + 6*e)^2 + 225*a^2*sin(4*f*x + 4*e)^2 + 450*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 225*a^2*sin(2*f*x + 2*e)^2 + 36*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 400*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 36*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 30*a^2*cos(2*f*x + 2*e) + a^2 + 2*(15*a^2*cos(4*f*x + 4*e) + 15*a^2*cos(2*f*x + 2*e) + a^2)*cos(6*f*x + 6*e) + 30*(15*a^2*cos(2*f*x + 2*e) + a^2)*cos(4*f*x + 4*e) - 12*(a^2*cos(6*f*x + 6*e) + 15*a^2*cos(4*f*x + 4*e) + 15*a^2*cos(2*f*x + 2*e) - 20*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^2)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 40*(a^2*cos(6*f*x + 6*e) + 15*a^2*cos(4*f*x + 4*e) + 15*a^2*cos(2*f*x + 2*e) - 6*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))) - 12*(a^2*cos(6*f*x + 6*e) + 15*a^2*cos(4*f*x + 4*e) + 15*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))) + 30*(a^2*sin(4*f*x + 4*e) + a^2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 12*(a^2*sin(6*f*x + 6*e) + 15*a^2*sin(4*f*x + 4*e) + 15*a^2*sin(2*f*x + 2*e) - 20*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*a^2*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*(a^2*sin(6*f*x + 6*e) + 15*a^2*sin(4*f*x + 4*e) + 15*a^2*sin(2*f*x + 2*e) - 6*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))) - 12*(a^2*sin(6*f*x + 6*e) + 15*a^2*sin(4*f*x + 4*e) + 15*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) + 6*(15*(f*x + e)*a^2*cos(4*f*x + 4*e) + 15*(f*x + e)*a^2*cos(2*f*x + 2*e) + (f*x + e)*a^2 - 12*a^2*sin(4*f*x + 4*e) - 12*a^2*sin(2*f*x + 2*e))*cos(6*f*x + 6*e) + 90*(15*(f*x + e)*a^2*cos(2*f*x + 2*e) + (f*x + e)*a^2)*cos(4*f*x + 4*e) - 6*(6*(f*x + e)*a^2*cos(6*f*x + 6*e) + 90*(f*x + e)*a^2*cos(4*f*x + 4*e) + 90*(f*x + e)*a^2*cos(2*f*x + 2*e) - 120*(f*x + e)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 36*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 6*(f*x + e)*a^2 + 5*a^2*sin(6*f*x + 6*e) + 3*a^2*sin(4*f*x + 4*e) + 3*a^2*sin(2*f*x + 2*e) + 16*a^2*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*(30*(f*x + e)*a^2*cos(6*f*x + 6*e) + 450*(f*x + e)*a^2*cos(4*f*x + 4*e) + 450*(f*x + e)*a^2*cos(2*f*x + 2*e) - 180*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 30*(f*x + e)*a^2 + 29*a^2*sin(6*f*x + 6*e) + 75*a^2*sin(4*f*x + 4*e) + 75*a^2*sin(2*f*x + 2*e) - 24*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))) - 6*(6*(f*x + e)*a^2*cos(6*f*x + 6*e) + 90*(f*x + e)*a^2*cos(4*f*x + 4*e) + 90*(f*x + e)*a^2*cos(2*f*x + 2*e) + 6*(f*x + e)*a^2 + 5*a^2*sin(6*f*x + 6*e) + 3*a^2*sin(4*f*x + 4*e) + 3*a^2*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 18*(5*(f*x + e)*a^2*sin(4*f*x + 4*e) + 5*(f*x + e)*a^2*sin(2*f*x + 2*e) + 4*a^2*cos(4*f*x + 4*e) + 4*a^2*cos(2*f*x + 2*e))*sin(6*f*x + 6*e) + 18*(75*(f*x + e)*a^2*sin(2*f*x + 2*e) - 4*a^2)*sin(4*f*x + 4*e) - 6*(6*(f*x + e)*a^2*sin(6*f*x + 6*e) + 90*(f*x + e)*a^2*sin(4*f*x + 4*e) + 90*(f*x + e)*a^2*sin(2*f*x + 2*e) - 120*(f*x + e)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 36*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*a^2*cos(6*f*x + 6*e) - 3*a^2*cos(4*f*x + 4*e) - 3*a^2*cos(2*f*x + 2*e) - 16*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*a^2)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(30*(f*x + e)*a^2*sin(6*f*x + 6*e) + 450*(f*x + e)*a^2*sin(4*f*x + 4*e) + 450*(f*x + e)*a^2*sin(2*f*x + 2*e) - 180*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 29*a^2*cos(6*f*x + 6*e) - 75*a^2*cos(4*f*x + 4*e) - 75*a^2*cos(2*f*x + 2*e) + 24*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 29*a^2)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6*(6*(f*x + e)*a^2*sin(6*f*x + 6*e) + 90*(f*x + e)*a^2*sin(4*f*x + 4*e) + 90*(f*x + e)*a^2*sin(2*f*x + 2*e) - 5*a^2*cos(6*f*x + 6*e) - 3*a^2*cos(4*f*x + 4*e) - 3*a^2*cos(2*f*x + 2*e) - 5*a^2)*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
108,1,6134,0,24.801129," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(9/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right)^{2} + 784 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 4900 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 784 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 64 \, {\left(f x + e\right)} 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)^{2} + 3136 \, {\left(f x + e\right)} 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)^{2} + 3136 \, {\left(f x + e\right)} 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} + 64 \, {\left(f x + e\right)} 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} + {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right)^{2} + 784 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 4900 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 784 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 64 \, {\left(f x + e\right)} 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)^{2} + 3136 \, {\left(f x + e\right)} 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)^{2} + 3136 \, {\left(f x + e\right)} 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} + 64 \, {\left(f x + e\right)} 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} + 56 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2} - 46 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} \cos\left(8 \, f x + 8 \, e\right)^{2} + 784 \, a^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 4900 \, a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 784 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 64 \, 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)^{2} + 3136 \, 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)^{2} + 3136 \, 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} + 64 \, 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(8 \, f x + 8 \, e\right)^{2} + 784 \, a^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 4900 \, a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 3920 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 784 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 64 \, 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)^{2} + 3136 \, 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)^{2} + 3136 \, 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} + 64 \, 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} + 56 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} + 2 \, {\left(28 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 70 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 28 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(8 \, f x + 8 \, e\right) + 56 \, {\left(70 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 28 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(6 \, f x + 6 \, e\right) + 140 \, {\left(28 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(a^{2} \cos\left(8 \, f x + 8 \, e\right) + 28 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 70 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 28 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 56 \, 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) - 56 \, 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) - 8 \, 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{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(a^{2} \cos\left(8 \, f x + 8 \, e\right) + 28 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 70 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 28 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 56 \, 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) - 8 \, 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{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(a^{2} \cos\left(8 \, f x + 8 \, e\right) + 28 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 70 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 28 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 8 \, 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) - 16 \, {\left(a^{2} \cos\left(8 \, f x + 8 \, e\right) + 28 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 70 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 28 \, 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) + 28 \, {\left(2 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 5 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 784 \, {\left(5 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, {\left(a^{2} \sin\left(8 \, f x + 8 \, e\right) + 28 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 70 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 28 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 56 \, 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) - 56 \, 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) - 8 \, 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{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(a^{2} \sin\left(8 \, f x + 8 \, e\right) + 28 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 70 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 28 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 56 \, 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) - 8 \, 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{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 112 \, {\left(a^{2} \sin\left(8 \, f x + 8 \, e\right) + 28 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 70 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 28 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 8 \, 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) - 16 \, {\left(a^{2} \sin\left(8 \, f x + 8 \, e\right) + 28 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 70 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 28 \, 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) + 2 \, {\left(28 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 70 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 28 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} a^{2} - 23 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 66 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - 23 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + 28 \, {\left(140 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 56 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(f x + e\right)} a^{2} - 17 \, a^{2} \sin\left(4 \, f x + 4 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 28 \, {\left(140 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 5 \, {\left(f x + e\right)} a^{2} + 17 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(4 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right) + 112 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 280 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 112 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 224 \, {\left(f x + e\right)} 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) - 224 \, {\left(f x + e\right)} 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) - 32 \, {\left(f x + e\right)} 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) + 4 \, {\left(f x + e\right)} a^{2} + 3 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) - 8 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 54 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - 8 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 48 \, 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) + 48 \, 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) - 4 \, {\left(28 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right) + 784 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 1960 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 784 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 1568 \, {\left(f x + e\right)} 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) - 224 \, {\left(f x + e\right)} 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) + 28 \, {\left(f x + e\right)} a^{2} + 27 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 112 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 42 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 112 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 48 \, 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) - 4 \, {\left(28 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right) + 784 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 1960 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 784 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 224 \, {\left(f x + e\right)} 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) + 28 \, {\left(f x + e\right)} a^{2} + 27 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 112 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 42 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 112 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 48 \, 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) - 4 \, {\left(4 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right) + 112 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 280 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 112 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(f x + e\right)} a^{2} + 3 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) - 8 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 54 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - 8 \, 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) + 2 \, {\left(28 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 70 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 28 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 23 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 66 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 23 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 2 \, {\left(1960 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 784 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 238 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 23 \, a^{2}\right)} \sin\left(6 \, f x + 6 \, e\right) + 4 \, {\left(980 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 119 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 33 \, a^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) - 4 \, {\left(4 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right) + 112 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 280 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 112 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 224 \, {\left(f x + e\right)} 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) - 224 \, {\left(f x + e\right)} 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) - 32 \, {\left(f x + e\right)} 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) - 3 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 8 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 54 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 8 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 48 \, 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) - 48 \, 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) - 4 \, {\left(28 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right) + 784 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 1960 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 784 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 1568 \, {\left(f x + e\right)} 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) - 224 \, {\left(f x + e\right)} 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) - 27 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) - 112 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) - 42 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 112 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 48 \, 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) - 27 \, 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) - 4 \, {\left(28 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right) + 784 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 1960 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 784 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 224 \, {\left(f x + e\right)} 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) - 27 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) - 112 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) - 42 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 112 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 48 \, 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) - 27 \, 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) - 4 \, {\left(4 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right) + 112 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 280 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 112 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 3 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 8 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 54 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 8 \, 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}}{{\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,"-((f*x + e)*a^2*cos(8*f*x + 8*e)^2 + 784*(f*x + e)*a^2*cos(6*f*x + 6*e)^2 + 4900*(f*x + e)*a^2*cos(4*f*x + 4*e)^2 + 784*(f*x + e)*a^2*cos(2*f*x + 2*e)^2 + 64*(f*x + e)*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*(f*x + e)*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*(f*x + e)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + (f*x + e)*a^2*sin(8*f*x + 8*e)^2 + 784*(f*x + e)*a^2*sin(6*f*x + 6*e)^2 + 4900*(f*x + e)*a^2*sin(4*f*x + 4*e)^2 + 784*(f*x + e)*a^2*sin(2*f*x + 2*e)^2 + 64*(f*x + e)*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*(f*x + e)*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*(f*x + e)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 56*(f*x + e)*a^2*cos(2*f*x + 2*e) + (f*x + e)*a^2 - 46*a^2*sin(2*f*x + 2*e) - 2*(a^2*cos(8*f*x + 8*e)^2 + 784*a^2*cos(6*f*x + 6*e)^2 + 4900*a^2*cos(4*f*x + 4*e)^2 + 784*a^2*cos(2*f*x + 2*e)^2 + 64*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a^2*sin(8*f*x + 8*e)^2 + 784*a^2*sin(6*f*x + 6*e)^2 + 4900*a^2*sin(4*f*x + 4*e)^2 + 3920*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 784*a^2*sin(2*f*x + 2*e)^2 + 64*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 3136*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 56*a^2*cos(2*f*x + 2*e) + a^2 + 2*(28*a^2*cos(6*f*x + 6*e) + 70*a^2*cos(4*f*x + 4*e) + 28*a^2*cos(2*f*x + 2*e) + a^2)*cos(8*f*x + 8*e) + 56*(70*a^2*cos(4*f*x + 4*e) + 28*a^2*cos(2*f*x + 2*e) + a^2)*cos(6*f*x + 6*e) + 140*(28*a^2*cos(2*f*x + 2*e) + a^2)*cos(4*f*x + 4*e) - 16*(a^2*cos(8*f*x + 8*e) + 28*a^2*cos(6*f*x + 6*e) + 70*a^2*cos(4*f*x + 4*e) + 28*a^2*cos(2*f*x + 2*e) - 56*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 56*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^2)*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 112*(a^2*cos(8*f*x + 8*e) + 28*a^2*cos(6*f*x + 6*e) + 70*a^2*cos(4*f*x + 4*e) + 28*a^2*cos(2*f*x + 2*e) - 56*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^2)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 112*(a^2*cos(8*f*x + 8*e) + 28*a^2*cos(6*f*x + 6*e) + 70*a^2*cos(4*f*x + 4*e) + 28*a^2*cos(2*f*x + 2*e) - 8*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))) - 16*(a^2*cos(8*f*x + 8*e) + 28*a^2*cos(6*f*x + 6*e) + 70*a^2*cos(4*f*x + 4*e) + 28*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))) + 28*(2*a^2*sin(6*f*x + 6*e) + 5*a^2*sin(4*f*x + 4*e) + 2*a^2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 784*(5*a^2*sin(4*f*x + 4*e) + 2*a^2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 16*(a^2*sin(8*f*x + 8*e) + 28*a^2*sin(6*f*x + 6*e) + 70*a^2*sin(4*f*x + 4*e) + 28*a^2*sin(2*f*x + 2*e) - 56*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 56*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*a^2*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*(a^2*sin(8*f*x + 8*e) + 28*a^2*sin(6*f*x + 6*e) + 70*a^2*sin(4*f*x + 4*e) + 28*a^2*sin(2*f*x + 2*e) - 56*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*a^2*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*(a^2*sin(8*f*x + 8*e) + 28*a^2*sin(6*f*x + 6*e) + 70*a^2*sin(4*f*x + 4*e) + 28*a^2*sin(2*f*x + 2*e) - 8*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))) - 16*(a^2*sin(8*f*x + 8*e) + 28*a^2*sin(6*f*x + 6*e) + 70*a^2*sin(4*f*x + 4*e) + 28*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) + 2*(28*(f*x + e)*a^2*cos(6*f*x + 6*e) + 70*(f*x + e)*a^2*cos(4*f*x + 4*e) + 28*(f*x + e)*a^2*cos(2*f*x + 2*e) + (f*x + e)*a^2 - 23*a^2*sin(6*f*x + 6*e) - 66*a^2*sin(4*f*x + 4*e) - 23*a^2*sin(2*f*x + 2*e))*cos(8*f*x + 8*e) + 28*(140*(f*x + e)*a^2*cos(4*f*x + 4*e) + 56*(f*x + e)*a^2*cos(2*f*x + 2*e) + 2*(f*x + e)*a^2 - 17*a^2*sin(4*f*x + 4*e))*cos(6*f*x + 6*e) + 28*(140*(f*x + e)*a^2*cos(2*f*x + 2*e) + 5*(f*x + e)*a^2 + 17*a^2*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) - 4*(4*(f*x + e)*a^2*cos(8*f*x + 8*e) + 112*(f*x + e)*a^2*cos(6*f*x + 6*e) + 280*(f*x + e)*a^2*cos(4*f*x + 4*e) + 112*(f*x + e)*a^2*cos(2*f*x + 2*e) - 224*(f*x + e)*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 224*(f*x + e)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(f*x + e)*a^2 + 3*a^2*sin(8*f*x + 8*e) - 8*a^2*sin(6*f*x + 6*e) - 54*a^2*sin(4*f*x + 4*e) - 8*a^2*sin(2*f*x + 2*e) + 48*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 48*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))) - 4*(28*(f*x + e)*a^2*cos(8*f*x + 8*e) + 784*(f*x + e)*a^2*cos(6*f*x + 6*e) + 1960*(f*x + e)*a^2*cos(4*f*x + 4*e) + 784*(f*x + e)*a^2*cos(2*f*x + 2*e) - 1568*(f*x + e)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 224*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 28*(f*x + e)*a^2 + 27*a^2*sin(8*f*x + 8*e) + 112*a^2*sin(6*f*x + 6*e) + 42*a^2*sin(4*f*x + 4*e) + 112*a^2*sin(2*f*x + 2*e) - 48*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))) - 4*(28*(f*x + e)*a^2*cos(8*f*x + 8*e) + 784*(f*x + e)*a^2*cos(6*f*x + 6*e) + 1960*(f*x + e)*a^2*cos(4*f*x + 4*e) + 784*(f*x + e)*a^2*cos(2*f*x + 2*e) - 224*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 28*(f*x + e)*a^2 + 27*a^2*sin(8*f*x + 8*e) + 112*a^2*sin(6*f*x + 6*e) + 42*a^2*sin(4*f*x + 4*e) + 112*a^2*sin(2*f*x + 2*e) - 48*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))) - 4*(4*(f*x + e)*a^2*cos(8*f*x + 8*e) + 112*(f*x + e)*a^2*cos(6*f*x + 6*e) + 280*(f*x + e)*a^2*cos(4*f*x + 4*e) + 112*(f*x + e)*a^2*cos(2*f*x + 2*e) + 4*(f*x + e)*a^2 + 3*a^2*sin(8*f*x + 8*e) - 8*a^2*sin(6*f*x + 6*e) - 54*a^2*sin(4*f*x + 4*e) - 8*a^2*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*(28*(f*x + e)*a^2*sin(6*f*x + 6*e) + 70*(f*x + e)*a^2*sin(4*f*x + 4*e) + 28*(f*x + e)*a^2*sin(2*f*x + 2*e) + 23*a^2*cos(6*f*x + 6*e) + 66*a^2*cos(4*f*x + 4*e) + 23*a^2*cos(2*f*x + 2*e))*sin(8*f*x + 8*e) + 2*(1960*(f*x + e)*a^2*sin(4*f*x + 4*e) + 784*(f*x + e)*a^2*sin(2*f*x + 2*e) + 238*a^2*cos(4*f*x + 4*e) - 23*a^2)*sin(6*f*x + 6*e) + 4*(980*(f*x + e)*a^2*sin(2*f*x + 2*e) - 119*a^2*cos(2*f*x + 2*e) - 33*a^2)*sin(4*f*x + 4*e) - 4*(4*(f*x + e)*a^2*sin(8*f*x + 8*e) + 112*(f*x + e)*a^2*sin(6*f*x + 6*e) + 280*(f*x + e)*a^2*sin(4*f*x + 4*e) + 112*(f*x + e)*a^2*sin(2*f*x + 2*e) - 224*(f*x + e)*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 224*(f*x + e)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3*a^2*cos(8*f*x + 8*e) + 8*a^2*cos(6*f*x + 6*e) + 54*a^2*cos(4*f*x + 4*e) + 8*a^2*cos(2*f*x + 2*e) - 48*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 48*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))) - 4*(28*(f*x + e)*a^2*sin(8*f*x + 8*e) + 784*(f*x + e)*a^2*sin(6*f*x + 6*e) + 1960*(f*x + e)*a^2*sin(4*f*x + 4*e) + 784*(f*x + e)*a^2*sin(2*f*x + 2*e) - 1568*(f*x + e)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 224*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 27*a^2*cos(8*f*x + 8*e) - 112*a^2*cos(6*f*x + 6*e) - 42*a^2*cos(4*f*x + 4*e) - 112*a^2*cos(2*f*x + 2*e) + 48*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 27*a^2)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(28*(f*x + e)*a^2*sin(8*f*x + 8*e) + 784*(f*x + e)*a^2*sin(6*f*x + 6*e) + 1960*(f*x + e)*a^2*sin(4*f*x + 4*e) + 784*(f*x + e)*a^2*sin(2*f*x + 2*e) - 224*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 27*a^2*cos(8*f*x + 8*e) - 112*a^2*cos(6*f*x + 6*e) - 42*a^2*cos(4*f*x + 4*e) - 112*a^2*cos(2*f*x + 2*e) + 48*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 27*a^2)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(4*(f*x + e)*a^2*sin(8*f*x + 8*e) + 112*(f*x + e)*a^2*sin(6*f*x + 6*e) + 280*(f*x + e)*a^2*sin(4*f*x + 4*e) + 112*(f*x + e)*a^2*sin(2*f*x + 2*e) - 3*a^2*cos(8*f*x + 8*e) + 8*a^2*cos(6*f*x + 6*e) + 54*a^2*cos(4*f*x + 4*e) + 8*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
109,1,9150,0,146.306140," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(11/2),x, algorithm=""maxima"")","-\frac{{\left(15 \, {\left(f x + e\right)} a^{2} \cos\left(10 \, f x + 10 \, e\right)^{2} + 30375 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right)^{2} + 661500 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 661500 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 30375 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 1500 \, {\left(f x + e\right)} a^{2} \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} + 216000 \, {\left(f x + e\right)} 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)^{2} + 952560 \, {\left(f x + e\right)} 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)^{2} + 216000 \, {\left(f x + e\right)} 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} + 1500 \, {\left(f x + e\right)} 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} + 15 \, {\left(f x + e\right)} a^{2} \sin\left(10 \, f x + 10 \, e\right)^{2} + 30375 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right)^{2} + 661500 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 661500 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 30375 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 1500 \, {\left(f x + e\right)} a^{2} \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} + 216000 \, {\left(f x + e\right)} 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)^{2} + 952560 \, {\left(f x + e\right)} 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)^{2} + 216000 \, {\left(f x + e\right)} 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} + 1500 \, {\left(f x + e\right)} 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} + 1350 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 15 \, {\left(f x + e\right)} a^{2} - 1110 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 30 \, {\left(a^{2} \cos\left(10 \, f x + 10 \, e\right)^{2} + 2025 \, a^{2} \cos\left(8 \, f x + 8 \, e\right)^{2} + 44100 \, a^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 44100 \, a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 2025 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 100 \, a^{2} \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 \, 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)^{2} + 63504 \, 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)^{2} + 14400 \, 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} + 100 \, 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(10 \, f x + 10 \, e\right)^{2} + 2025 \, a^{2} \sin\left(8 \, f x + 8 \, e\right)^{2} + 44100 \, a^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 44100 \, a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 18900 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 2025 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 100 \, a^{2} \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 \, 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)^{2} + 63504 \, 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)^{2} + 14400 \, 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} + 100 \, 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} + 90 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} + 2 \, {\left(45 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(10 \, f x + 10 \, e\right) + 90 \, {\left(210 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(8 \, f x + 8 \, e\right) + 420 \, {\left(210 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(6 \, f x + 6 \, e\right) + 420 \, {\left(45 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 20 \, {\left(a^{2} \cos\left(10 \, f x + 10 \, e\right) + 45 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 120 \, 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) - 252 \, 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) - 120 \, 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) - 10 \, 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{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(a^{2} \cos\left(10 \, f x + 10 \, e\right) + 45 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 252 \, 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) - 120 \, 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) - 10 \, 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{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 504 \, {\left(a^{2} \cos\left(10 \, f x + 10 \, e\right) + 45 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 120 \, 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) - 10 \, 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{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(a^{2} \cos\left(10 \, f x + 10 \, e\right) + 45 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 10 \, 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) - 20 \, {\left(a^{2} \cos\left(10 \, f x + 10 \, e\right) + 45 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 45 \, 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) + 30 \, {\left(3 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 14 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 14 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + 1350 \, {\left(14 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 14 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 6300 \, {\left(14 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 20 \, {\left(a^{2} \sin\left(10 \, f x + 10 \, e\right) + 45 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 120 \, 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) - 252 \, 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) - 120 \, 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) - 10 \, 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{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(a^{2} \sin\left(10 \, f x + 10 \, e\right) + 45 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 252 \, 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) - 120 \, 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) - 10 \, 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{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 504 \, {\left(a^{2} \sin\left(10 \, f x + 10 \, e\right) + 45 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 120 \, 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) - 10 \, 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{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 240 \, {\left(a^{2} \sin\left(10 \, f x + 10 \, e\right) + 45 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 45 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 10 \, 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) - 20 \, {\left(a^{2} \sin\left(10 \, f x + 10 \, e\right) + 45 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 210 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 210 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 45 \, 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) + 10 \, {\left(135 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right) + 630 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 630 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 135 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(f x + e\right)} a^{2} - 111 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) - 625 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 625 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - 111 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(10 \, f x + 10 \, e\right) + 450 \, {\left(630 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 630 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 135 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(f x + e\right)} a^{2} - 107 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 107 \, a^{2} \sin\left(4 \, f x + 4 \, e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + 450 \, {\left(2940 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 630 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 14 \, {\left(f x + e\right)} a^{2} + 107 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 450 \, {\left(630 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 14 \, {\left(f x + e\right)} a^{2} + 107 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 10 \, {\left(30 \, {\left(f x + e\right)} a^{2} \cos\left(10 \, f x + 10 \, e\right) + 1350 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right) + 6300 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 6300 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 1350 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 3600 \, {\left(f x + e\right)} 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) - 7560 \, {\left(f x + e\right)} 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) - 3600 \, {\left(f x + e\right)} 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) - 300 \, {\left(f x + e\right)} 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) + 30 \, {\left(f x + e\right)} a^{2} + 21 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) - 165 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) - 1840 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 1840 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - 165 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 940 \, 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) + 2472 \, 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) + 940 \, 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(180 \, {\left(f x + e\right)} a^{2} \cos\left(10 \, f x + 10 \, e\right) + 8100 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right) + 37800 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 37800 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 8100 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 45360 \, {\left(f x + e\right)} 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) - 21600 \, {\left(f x + e\right)} 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) - 1800 \, {\left(f x + e\right)} 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) + 180 \, {\left(f x + e\right)} a^{2} + 173 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) + 1125 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) - 1170 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 1170 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 1125 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 2988 \, 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) - 470 \, 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) - 12 \, {\left(630 \, {\left(f x + e\right)} a^{2} \cos\left(10 \, f x + 10 \, e\right) + 28350 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right) + 132300 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 132300 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 28350 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 75600 \, {\left(f x + e\right)} 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) - 6300 \, {\left(f x + e\right)} 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) + 630 \, {\left(f x + e\right)} a^{2} + 647 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) + 5805 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 4620 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 4620 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 5805 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 4980 \, 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) - 2060 \, 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(180 \, {\left(f x + e\right)} a^{2} \cos\left(10 \, f x + 10 \, e\right) + 8100 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right) + 37800 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 37800 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 8100 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 1800 \, {\left(f x + e\right)} 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) + 180 \, {\left(f x + e\right)} a^{2} + 173 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) + 1125 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) - 1170 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 1170 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 1125 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 470 \, 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) - 10 \, {\left(30 \, {\left(f x + e\right)} a^{2} \cos\left(10 \, f x + 10 \, e\right) + 1350 \, {\left(f x + e\right)} a^{2} \cos\left(8 \, f x + 8 \, e\right) + 6300 \, {\left(f x + e\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 6300 \, {\left(f x + e\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 1350 \, {\left(f x + e\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 30 \, {\left(f x + e\right)} a^{2} + 21 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) - 165 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) - 1840 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 1840 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - 165 \, 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(135 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right) + 630 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 630 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 135 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 111 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 625 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 625 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 111 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + 30 \, {\left(9450 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 9450 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 2025 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 1605 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 1605 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 37 \, a^{2}\right)} \sin\left(8 \, f x + 8 \, e\right) + 50 \, {\left(26460 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 5670 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 963 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 125 \, a^{2}\right)} \sin\left(6 \, f x + 6 \, e\right) + 50 \, {\left(5670 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 963 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 125 \, a^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) - 10 \, {\left(30 \, {\left(f x + e\right)} a^{2} \sin\left(10 \, f x + 10 \, e\right) + 1350 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right) + 6300 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 6300 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 1350 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 3600 \, {\left(f x + e\right)} 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) - 7560 \, {\left(f x + e\right)} 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) - 3600 \, {\left(f x + e\right)} 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) - 300 \, {\left(f x + e\right)} 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) - 21 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) + 165 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 1840 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 1840 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 165 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 940 \, 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) - 2472 \, 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) - 940 \, 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) - 21 \, 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(180 \, {\left(f x + e\right)} a^{2} \sin\left(10 \, f x + 10 \, e\right) + 8100 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right) + 37800 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 37800 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 8100 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 45360 \, {\left(f x + e\right)} 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) - 21600 \, {\left(f x + e\right)} 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) - 1800 \, {\left(f x + e\right)} 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) - 173 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) - 1125 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 1170 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 1170 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 1125 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 2988 \, 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) + 470 \, 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) - 173 \, 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) - 12 \, {\left(630 \, {\left(f x + e\right)} a^{2} \sin\left(10 \, f x + 10 \, e\right) + 28350 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right) + 132300 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 132300 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 28350 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 75600 \, {\left(f x + e\right)} 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) - 6300 \, {\left(f x + e\right)} 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) - 647 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) - 5805 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) - 4620 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) - 4620 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 5805 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 4980 \, 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) + 2060 \, 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) - 647 \, 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(180 \, {\left(f x + e\right)} a^{2} \sin\left(10 \, f x + 10 \, e\right) + 8100 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right) + 37800 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 37800 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 8100 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 1800 \, {\left(f x + e\right)} 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) - 173 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) - 1125 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 1170 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 1170 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 1125 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 470 \, 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) - 173 \, 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) - 10 \, {\left(30 \, {\left(f x + e\right)} a^{2} \sin\left(10 \, f x + 10 \, e\right) + 1350 \, {\left(f x + e\right)} a^{2} \sin\left(8 \, f x + 8 \, e\right) + 6300 \, {\left(f x + e\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 6300 \, {\left(f x + e\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 1350 \, {\left(f x + e\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) - 21 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) + 165 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 1840 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 1840 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 165 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 21 \, 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,"-1/15*(15*(f*x + e)*a^2*cos(10*f*x + 10*e)^2 + 30375*(f*x + e)*a^2*cos(8*f*x + 8*e)^2 + 661500*(f*x + e)*a^2*cos(6*f*x + 6*e)^2 + 661500*(f*x + e)*a^2*cos(4*f*x + 4*e)^2 + 30375*(f*x + e)*a^2*cos(2*f*x + 2*e)^2 + 1500*(f*x + e)*a^2*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 216000*(f*x + e)*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 952560*(f*x + e)*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 216000*(f*x + e)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 1500*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 15*(f*x + e)*a^2*sin(10*f*x + 10*e)^2 + 30375*(f*x + e)*a^2*sin(8*f*x + 8*e)^2 + 661500*(f*x + e)*a^2*sin(6*f*x + 6*e)^2 + 661500*(f*x + e)*a^2*sin(4*f*x + 4*e)^2 + 30375*(f*x + e)*a^2*sin(2*f*x + 2*e)^2 + 1500*(f*x + e)*a^2*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 216000*(f*x + e)*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 952560*(f*x + e)*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 216000*(f*x + e)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 1500*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 1350*(f*x + e)*a^2*cos(2*f*x + 2*e) + 15*(f*x + e)*a^2 - 1110*a^2*sin(2*f*x + 2*e) - 30*(a^2*cos(10*f*x + 10*e)^2 + 2025*a^2*cos(8*f*x + 8*e)^2 + 44100*a^2*cos(6*f*x + 6*e)^2 + 44100*a^2*cos(4*f*x + 4*e)^2 + 2025*a^2*cos(2*f*x + 2*e)^2 + 100*a^2*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 63504*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 100*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a^2*sin(10*f*x + 10*e)^2 + 2025*a^2*sin(8*f*x + 8*e)^2 + 44100*a^2*sin(6*f*x + 6*e)^2 + 44100*a^2*sin(4*f*x + 4*e)^2 + 18900*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 2025*a^2*sin(2*f*x + 2*e)^2 + 100*a^2*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 63504*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 14400*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 100*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 90*a^2*cos(2*f*x + 2*e) + a^2 + 2*(45*a^2*cos(8*f*x + 8*e) + 210*a^2*cos(6*f*x + 6*e) + 210*a^2*cos(4*f*x + 4*e) + 45*a^2*cos(2*f*x + 2*e) + a^2)*cos(10*f*x + 10*e) + 90*(210*a^2*cos(6*f*x + 6*e) + 210*a^2*cos(4*f*x + 4*e) + 45*a^2*cos(2*f*x + 2*e) + a^2)*cos(8*f*x + 8*e) + 420*(210*a^2*cos(4*f*x + 4*e) + 45*a^2*cos(2*f*x + 2*e) + a^2)*cos(6*f*x + 6*e) + 420*(45*a^2*cos(2*f*x + 2*e) + a^2)*cos(4*f*x + 4*e) - 20*(a^2*cos(10*f*x + 10*e) + 45*a^2*cos(8*f*x + 8*e) + 210*a^2*cos(6*f*x + 6*e) + 210*a^2*cos(4*f*x + 4*e) + 45*a^2*cos(2*f*x + 2*e) - 120*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 252*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^2)*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 240*(a^2*cos(10*f*x + 10*e) + 45*a^2*cos(8*f*x + 8*e) + 210*a^2*cos(6*f*x + 6*e) + 210*a^2*cos(4*f*x + 4*e) + 45*a^2*cos(2*f*x + 2*e) - 252*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^2)*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 504*(a^2*cos(10*f*x + 10*e) + 45*a^2*cos(8*f*x + 8*e) + 210*a^2*cos(6*f*x + 6*e) + 210*a^2*cos(4*f*x + 4*e) + 45*a^2*cos(2*f*x + 2*e) - 120*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^2)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 240*(a^2*cos(10*f*x + 10*e) + 45*a^2*cos(8*f*x + 8*e) + 210*a^2*cos(6*f*x + 6*e) + 210*a^2*cos(4*f*x + 4*e) + 45*a^2*cos(2*f*x + 2*e) - 10*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))) - 20*(a^2*cos(10*f*x + 10*e) + 45*a^2*cos(8*f*x + 8*e) + 210*a^2*cos(6*f*x + 6*e) + 210*a^2*cos(4*f*x + 4*e) + 45*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))) + 30*(3*a^2*sin(8*f*x + 8*e) + 14*a^2*sin(6*f*x + 6*e) + 14*a^2*sin(4*f*x + 4*e) + 3*a^2*sin(2*f*x + 2*e))*sin(10*f*x + 10*e) + 1350*(14*a^2*sin(6*f*x + 6*e) + 14*a^2*sin(4*f*x + 4*e) + 3*a^2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 6300*(14*a^2*sin(4*f*x + 4*e) + 3*a^2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 20*(a^2*sin(10*f*x + 10*e) + 45*a^2*sin(8*f*x + 8*e) + 210*a^2*sin(6*f*x + 6*e) + 210*a^2*sin(4*f*x + 4*e) + 45*a^2*sin(2*f*x + 2*e) - 120*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 252*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*a^2*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*(a^2*sin(10*f*x + 10*e) + 45*a^2*sin(8*f*x + 8*e) + 210*a^2*sin(6*f*x + 6*e) + 210*a^2*sin(4*f*x + 4*e) + 45*a^2*sin(2*f*x + 2*e) - 252*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 120*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*a^2*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*(a^2*sin(10*f*x + 10*e) + 45*a^2*sin(8*f*x + 8*e) + 210*a^2*sin(6*f*x + 6*e) + 210*a^2*sin(4*f*x + 4*e) + 45*a^2*sin(2*f*x + 2*e) - 120*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*a^2*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*(a^2*sin(10*f*x + 10*e) + 45*a^2*sin(8*f*x + 8*e) + 210*a^2*sin(6*f*x + 6*e) + 210*a^2*sin(4*f*x + 4*e) + 45*a^2*sin(2*f*x + 2*e) - 10*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))) - 20*(a^2*sin(10*f*x + 10*e) + 45*a^2*sin(8*f*x + 8*e) + 210*a^2*sin(6*f*x + 6*e) + 210*a^2*sin(4*f*x + 4*e) + 45*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) + 10*(135*(f*x + e)*a^2*cos(8*f*x + 8*e) + 630*(f*x + e)*a^2*cos(6*f*x + 6*e) + 630*(f*x + e)*a^2*cos(4*f*x + 4*e) + 135*(f*x + e)*a^2*cos(2*f*x + 2*e) + 3*(f*x + e)*a^2 - 111*a^2*sin(8*f*x + 8*e) - 625*a^2*sin(6*f*x + 6*e) - 625*a^2*sin(4*f*x + 4*e) - 111*a^2*sin(2*f*x + 2*e))*cos(10*f*x + 10*e) + 450*(630*(f*x + e)*a^2*cos(6*f*x + 6*e) + 630*(f*x + e)*a^2*cos(4*f*x + 4*e) + 135*(f*x + e)*a^2*cos(2*f*x + 2*e) + 3*(f*x + e)*a^2 - 107*a^2*sin(6*f*x + 6*e) - 107*a^2*sin(4*f*x + 4*e))*cos(8*f*x + 8*e) + 450*(2940*(f*x + e)*a^2*cos(4*f*x + 4*e) + 630*(f*x + e)*a^2*cos(2*f*x + 2*e) + 14*(f*x + e)*a^2 + 107*a^2*sin(2*f*x + 2*e))*cos(6*f*x + 6*e) + 450*(630*(f*x + e)*a^2*cos(2*f*x + 2*e) + 14*(f*x + e)*a^2 + 107*a^2*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) - 10*(30*(f*x + e)*a^2*cos(10*f*x + 10*e) + 1350*(f*x + e)*a^2*cos(8*f*x + 8*e) + 6300*(f*x + e)*a^2*cos(6*f*x + 6*e) + 6300*(f*x + e)*a^2*cos(4*f*x + 4*e) + 1350*(f*x + e)*a^2*cos(2*f*x + 2*e) - 3600*(f*x + e)*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 7560*(f*x + e)*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3600*(f*x + e)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 300*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 30*(f*x + e)*a^2 + 21*a^2*sin(10*f*x + 10*e) - 165*a^2*sin(8*f*x + 8*e) - 1840*a^2*sin(6*f*x + 6*e) - 1840*a^2*sin(4*f*x + 4*e) - 165*a^2*sin(2*f*x + 2*e) + 940*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2472*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 940*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*(180*(f*x + e)*a^2*cos(10*f*x + 10*e) + 8100*(f*x + e)*a^2*cos(8*f*x + 8*e) + 37800*(f*x + e)*a^2*cos(6*f*x + 6*e) + 37800*(f*x + e)*a^2*cos(4*f*x + 4*e) + 8100*(f*x + e)*a^2*cos(2*f*x + 2*e) - 45360*(f*x + e)*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 21600*(f*x + e)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1800*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 180*(f*x + e)*a^2 + 173*a^2*sin(10*f*x + 10*e) + 1125*a^2*sin(8*f*x + 8*e) - 1170*a^2*sin(6*f*x + 6*e) - 1170*a^2*sin(4*f*x + 4*e) + 1125*a^2*sin(2*f*x + 2*e) + 2988*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 470*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))) - 12*(630*(f*x + e)*a^2*cos(10*f*x + 10*e) + 28350*(f*x + e)*a^2*cos(8*f*x + 8*e) + 132300*(f*x + e)*a^2*cos(6*f*x + 6*e) + 132300*(f*x + e)*a^2*cos(4*f*x + 4*e) + 28350*(f*x + e)*a^2*cos(2*f*x + 2*e) - 75600*(f*x + e)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6300*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 630*(f*x + e)*a^2 + 647*a^2*sin(10*f*x + 10*e) + 5805*a^2*sin(8*f*x + 8*e) + 4620*a^2*sin(6*f*x + 6*e) + 4620*a^2*sin(4*f*x + 4*e) + 5805*a^2*sin(2*f*x + 2*e) - 4980*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2060*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*(180*(f*x + e)*a^2*cos(10*f*x + 10*e) + 8100*(f*x + e)*a^2*cos(8*f*x + 8*e) + 37800*(f*x + e)*a^2*cos(6*f*x + 6*e) + 37800*(f*x + e)*a^2*cos(4*f*x + 4*e) + 8100*(f*x + e)*a^2*cos(2*f*x + 2*e) - 1800*(f*x + e)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 180*(f*x + e)*a^2 + 173*a^2*sin(10*f*x + 10*e) + 1125*a^2*sin(8*f*x + 8*e) - 1170*a^2*sin(6*f*x + 6*e) - 1170*a^2*sin(4*f*x + 4*e) + 1125*a^2*sin(2*f*x + 2*e) - 470*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))) - 10*(30*(f*x + e)*a^2*cos(10*f*x + 10*e) + 1350*(f*x + e)*a^2*cos(8*f*x + 8*e) + 6300*(f*x + e)*a^2*cos(6*f*x + 6*e) + 6300*(f*x + e)*a^2*cos(4*f*x + 4*e) + 1350*(f*x + e)*a^2*cos(2*f*x + 2*e) + 30*(f*x + e)*a^2 + 21*a^2*sin(10*f*x + 10*e) - 165*a^2*sin(8*f*x + 8*e) - 1840*a^2*sin(6*f*x + 6*e) - 1840*a^2*sin(4*f*x + 4*e) - 165*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*(135*(f*x + e)*a^2*sin(8*f*x + 8*e) + 630*(f*x + e)*a^2*sin(6*f*x + 6*e) + 630*(f*x + e)*a^2*sin(4*f*x + 4*e) + 135*(f*x + e)*a^2*sin(2*f*x + 2*e) + 111*a^2*cos(8*f*x + 8*e) + 625*a^2*cos(6*f*x + 6*e) + 625*a^2*cos(4*f*x + 4*e) + 111*a^2*cos(2*f*x + 2*e))*sin(10*f*x + 10*e) + 30*(9450*(f*x + e)*a^2*sin(6*f*x + 6*e) + 9450*(f*x + e)*a^2*sin(4*f*x + 4*e) + 2025*(f*x + e)*a^2*sin(2*f*x + 2*e) + 1605*a^2*cos(6*f*x + 6*e) + 1605*a^2*cos(4*f*x + 4*e) - 37*a^2)*sin(8*f*x + 8*e) + 50*(26460*(f*x + e)*a^2*sin(4*f*x + 4*e) + 5670*(f*x + e)*a^2*sin(2*f*x + 2*e) - 963*a^2*cos(2*f*x + 2*e) - 125*a^2)*sin(6*f*x + 6*e) + 50*(5670*(f*x + e)*a^2*sin(2*f*x + 2*e) - 963*a^2*cos(2*f*x + 2*e) - 125*a^2)*sin(4*f*x + 4*e) - 10*(30*(f*x + e)*a^2*sin(10*f*x + 10*e) + 1350*(f*x + e)*a^2*sin(8*f*x + 8*e) + 6300*(f*x + e)*a^2*sin(6*f*x + 6*e) + 6300*(f*x + e)*a^2*sin(4*f*x + 4*e) + 1350*(f*x + e)*a^2*sin(2*f*x + 2*e) - 3600*(f*x + e)*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 7560*(f*x + e)*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3600*(f*x + e)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 300*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 21*a^2*cos(10*f*x + 10*e) + 165*a^2*cos(8*f*x + 8*e) + 1840*a^2*cos(6*f*x + 6*e) + 1840*a^2*cos(4*f*x + 4*e) + 165*a^2*cos(2*f*x + 2*e) - 940*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2472*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 940*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 21*a^2)*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*(180*(f*x + e)*a^2*sin(10*f*x + 10*e) + 8100*(f*x + e)*a^2*sin(8*f*x + 8*e) + 37800*(f*x + e)*a^2*sin(6*f*x + 6*e) + 37800*(f*x + e)*a^2*sin(4*f*x + 4*e) + 8100*(f*x + e)*a^2*sin(2*f*x + 2*e) - 45360*(f*x + e)*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 21600*(f*x + e)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1800*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 173*a^2*cos(10*f*x + 10*e) - 1125*a^2*cos(8*f*x + 8*e) + 1170*a^2*cos(6*f*x + 6*e) + 1170*a^2*cos(4*f*x + 4*e) - 1125*a^2*cos(2*f*x + 2*e) - 2988*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 470*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 173*a^2)*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*(630*(f*x + e)*a^2*sin(10*f*x + 10*e) + 28350*(f*x + e)*a^2*sin(8*f*x + 8*e) + 132300*(f*x + e)*a^2*sin(6*f*x + 6*e) + 132300*(f*x + e)*a^2*sin(4*f*x + 4*e) + 28350*(f*x + e)*a^2*sin(2*f*x + 2*e) - 75600*(f*x + e)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6300*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 647*a^2*cos(10*f*x + 10*e) - 5805*a^2*cos(8*f*x + 8*e) - 4620*a^2*cos(6*f*x + 6*e) - 4620*a^2*cos(4*f*x + 4*e) - 5805*a^2*cos(2*f*x + 2*e) + 4980*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2060*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 647*a^2)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*(180*(f*x + e)*a^2*sin(10*f*x + 10*e) + 8100*(f*x + e)*a^2*sin(8*f*x + 8*e) + 37800*(f*x + e)*a^2*sin(6*f*x + 6*e) + 37800*(f*x + e)*a^2*sin(4*f*x + 4*e) + 8100*(f*x + e)*a^2*sin(2*f*x + 2*e) - 1800*(f*x + e)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 173*a^2*cos(10*f*x + 10*e) - 1125*a^2*cos(8*f*x + 8*e) + 1170*a^2*cos(6*f*x + 6*e) + 1170*a^2*cos(4*f*x + 4*e) - 1125*a^2*cos(2*f*x + 2*e) + 470*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 173*a^2)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10*(30*(f*x + e)*a^2*sin(10*f*x + 10*e) + 1350*(f*x + e)*a^2*sin(8*f*x + 8*e) + 6300*(f*x + e)*a^2*sin(6*f*x + 6*e) + 6300*(f*x + e)*a^2*sin(4*f*x + 4*e) + 1350*(f*x + e)*a^2*sin(2*f*x + 2*e) - 21*a^2*cos(10*f*x + 10*e) + 165*a^2*cos(8*f*x + 8*e) + 1840*a^2*cos(6*f*x + 6*e) + 1840*a^2*cos(4*f*x + 4*e) + 165*a^2*cos(2*f*x + 2*e) - 21*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
110,-2,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
111,-2,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
112,1,60,0,0.835292," ","integrate((c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} c + c \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, c \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right)\right)} \sqrt{c}}{\sqrt{a} f}"," ",0,"-((f*x + e)*c + c*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*c*arctan2(sin(f*x + e), cos(f*x + e) + 1))*sqrt(c)/(sqrt(a)*f)","A",0
113,1,34,0,0.729287," ","integrate((c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{\sqrt{-a} f}"," ",0,"sqrt(c)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(sqrt(-a)*f)","A",0
114,1,39,0,0.837874," ","integrate(1/(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{f x + e - \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,"-(f*x + e - arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) - 1))/(sqrt(a)*sqrt(c)*f)","A",0
115,1,818,0,0.950131," ","integrate(1/(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 8 \, {\left(f x + e\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} + 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, {\left(f x + e\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 \, f x - {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} - 4 \, {\left(\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) + 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} + \sin\left(2 \, f x + 2 \, e\right)^{2} - 4 \, \sin\left(2 \, f x + 2 \, e\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 \, \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(2 \, f x + 2 \, e\right) + 1\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(\cos\left(2 \, f x + 2 \, e\right)^{2} - 4 \, {\left(\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) + 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} + \sin\left(2 \, f x + 2 \, e\right)^{2} - 4 \, \sin\left(2 \, f x + 2 \, e\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 \, \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(2 \, f x + 2 \, e\right) + 1\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) + 4 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(4 \, f x + 4 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, e + \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(4 \, {\left(f x + e\right)} \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 \, e}{2 \, {\left(c \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, 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(2 \, f x + 2 \, e\right)^{2} - 4 \, c \sin\left(2 \, f x + 2 \, e\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 \, 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(2 \, f x + 2 \, e\right) - 4 \, {\left(c \cos\left(2 \, f x + 2 \, e\right) + c\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) + c\right)} \sqrt{a} \sqrt{c} f}"," ",0,"-1/2*(2*(f*x + e)*cos(2*f*x + 2*e)^2 + 8*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*(f*x + e)*sin(2*f*x + 2*e)^2 + 8*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*f*x - (cos(2*f*x + 2*e)^2 - 4*(cos(2*f*x + 2*e) + 1)*cos(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)))^2 + sin(2*f*x + 2*e)^2 - 4*sin(2*f*x + 2*e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*cos(2*f*x + 2*e) + 1)*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*(cos(2*f*x + 2*e)^2 - 4*(cos(2*f*x + 2*e) + 1)*cos(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)))^2 + sin(2*f*x + 2*e)^2 - 4*sin(2*f*x + 2*e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*cos(2*f*x + 2*e) + 1)*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) + 4*(f*x + e)*cos(2*f*x + 2*e) - 2*(4*f*x + 4*(f*x + e)*cos(2*f*x + 2*e) + 4*e + sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*(4*(f*x + e)*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*e)/((c*cos(2*f*x + 2*e)^2 + 4*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c*sin(2*f*x + 2*e)^2 - 4*c*sin(2*f*x + 2*e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*c*cos(2*f*x + 2*e) - 4*(c*cos(2*f*x + 2*e) + c)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c)*sqrt(a)*sqrt(c)*f)","B",0
116,1,2206,0,1.279125," ","integrate(1/(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 144 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 64 \, {\left(f x + e\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} + 64 \, {\left(f x + e\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} + 4 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 144 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 64 \, {\left(f x + e\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} + 64 \, {\left(f x + e\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} + 4 \, f x - {\left(2 \, {\left(6 \, \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} + 36 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 8 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\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) + 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) + 16 \, \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 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + 6 \, \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) + 16 \, \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(4 \, f x + 4 \, e\right)^{2} + 12 \, \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} - 8 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + 6 \, \sin\left(2 \, f x + 2 \, e\right) - 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) + 16 \, \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 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + 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) + 16 \, \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 \, \cos\left(2 \, f x + 2 \, e\right) + 1\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) - 7 \, {\left(2 \, {\left(6 \, \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} + 36 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 8 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\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) + 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) + 16 \, \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 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + 6 \, \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) + 16 \, \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(4 \, f x + 4 \, e\right)^{2} + 12 \, \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} - 8 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + 6 \, \sin\left(2 \, f x + 2 \, e\right) - 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) + 16 \, \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 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + 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) + 16 \, \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 \, \cos\left(2 \, f x + 2 \, e\right) + 1\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) + 8 \, {\left(f x + 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + e - 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 48 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(16 \, f x + 16 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) + 96 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 64 \, {\left(f x + e\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) + 16 \, e + 5 \, \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) - 2 \, {\left(16 \, f x + 16 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) + 96 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 16 \, e + 5 \, \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) + 16 \, {\left(3 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 2 \, {\left(16 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) + 96 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 64 \, {\left(f x + e\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 \, \cos\left(4 \, f x + 4 \, e\right) + 2 \, \cos\left(2 \, f x + 2 \, e\right) - 5\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 \, {\left(16 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) + 96 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 5 \, \cos\left(4 \, f x + 4 \, e\right) + 2 \, \cos\left(2 \, f x + 2 \, e\right) - 5\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 \, e - 16 \, \sin\left(2 \, f x + 2 \, e\right)}{4 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 36 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, 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} + 16 \, 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} + 12 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 36 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 16 \, 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} + 16 \, 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} + 12 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2} + 2 \, {\left(6 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 8 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right) + 6 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 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) + 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) - 8 \, {\left(c^{2} \cos\left(4 \, f x + 4 \, e\right) + 6 \, 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) - 8 \, {\left(c^{2} \sin\left(4 \, f x + 4 \, e\right) + 6 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) - 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)\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^{2} \sin\left(4 \, f x + 4 \, e\right) + 6 \, 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)} \sqrt{a} \sqrt{c} f}"," ",0,"-1/4*(4*(f*x + e)*cos(4*f*x + 4*e)^2 + 144*(f*x + e)*cos(2*f*x + 2*e)^2 + 64*(f*x + e)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*(f*x + e)*sin(4*f*x + 4*e)^2 + 144*(f*x + e)*sin(2*f*x + 2*e)^2 + 64*(f*x + e)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*f*x - (2*(6*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + cos(4*f*x + 4*e)^2 + 36*cos(2*f*x + 2*e)^2 - 8*(cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) - 4*cos(1/2*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))) + 16*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 8*(cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) + 1)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(4*f*x + 4*e)^2 + 12*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*sin(2*f*x + 2*e)^2 - 8*(sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e) - 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))) + 16*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 8*(sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 12*cos(2*f*x + 2*e) + 1)*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) - 7*(2*(6*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + cos(4*f*x + 4*e)^2 + 36*cos(2*f*x + 2*e)^2 - 8*(cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) - 4*cos(1/2*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))) + 16*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 8*(cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) + 1)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(4*f*x + 4*e)^2 + 12*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*sin(2*f*x + 2*e)^2 - 8*(sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e) - 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))) + 16*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 8*(sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 12*cos(2*f*x + 2*e) + 1)*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) + 8*(f*x + 6*(f*x + e)*cos(2*f*x + 2*e) + e - 2*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) + 48*(f*x + e)*cos(2*f*x + 2*e) - 2*(16*f*x + 16*(f*x + e)*cos(4*f*x + 4*e) + 96*(f*x + e)*cos(2*f*x + 2*e) - 64*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*e + 5*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))) - 2*(16*f*x + 16*(f*x + e)*cos(4*f*x + 4*e) + 96*(f*x + e)*cos(2*f*x + 2*e) + 16*e + 5*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))) + 16*(3*(f*x + e)*sin(2*f*x + 2*e) + cos(2*f*x + 2*e))*sin(4*f*x + 4*e) - 2*(16*(f*x + e)*sin(4*f*x + 4*e) + 96*(f*x + e)*sin(2*f*x + 2*e) - 64*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*cos(4*f*x + 4*e) + 2*cos(2*f*x + 2*e) - 5)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*(16*(f*x + e)*sin(4*f*x + 4*e) + 96*(f*x + e)*sin(2*f*x + 2*e) - 5*cos(4*f*x + 4*e) + 2*cos(2*f*x + 2*e) - 5)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*e - 16*sin(2*f*x + 2*e))/((c^2*cos(4*f*x + 4*e)^2 + 36*c^2*cos(2*f*x + 2*e)^2 + 16*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*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 + 12*c^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*c^2*sin(2*f*x + 2*e)^2 + 16*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 12*c^2*cos(2*f*x + 2*e) + c^2 + 2*(6*c^2*cos(2*f*x + 2*e) + c^2)*cos(4*f*x + 4*e) - 8*(c^2*cos(4*f*x + 4*e) + 6*c^2*cos(2*f*x + 2*e) - 4*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))) - 8*(c^2*cos(4*f*x + 4*e) + 6*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))) - 8*(c^2*sin(4*f*x + 4*e) + 6*c^2*sin(2*f*x + 2*e) - 4*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))) - 8*(c^2*sin(4*f*x + 4*e) + 6*c^2*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)*f)","B",0
117,1,2393,0,1.484122," ","integrate((c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(f x + e\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(f x + e\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(f x + e\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(f x + e\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} c^{3} - 4 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(f x + e\right)} c^{3} - 5 \, c^{3} \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)^{2} + 4 \, {\left({\left(f x + e\right)} c^{3} - 5 \, c^{3} \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)^{2} + 4 \, {\left({\left(f x + e\right)} c^{3} - 5 \, c^{3} \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)^{2} + 4 \, {\left({\left(f x + e\right)} c^{3} - 5 \, c^{3} \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)^{2} - 5 \, {\left(c^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + c^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, c^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3} + 2 \, {\left(2 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\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) + 8 \, {\left(c^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, 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} + 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)^{2} + c^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, c^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, 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} + 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)^{2} + 4 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3} + 2 \, {\left(2 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c^{3} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + 2 \, 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) + 4 \, {\left(c^{3} \cos\left(4 \, f x + 4 \, e\right) + 2 \, 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) + 4 \, {\left(c^{3} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) + 2 \, 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) + 4 \, {\left(c^{3} \sin\left(4 \, f x + 4 \, e\right) + 2 \, 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)} \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) + 2 \, {\left(2 \, {\left(f x + e\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} c^{3} - 2 \, c^{3} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(2 \, {\left(f x + e\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(f x + e\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(f x + e\right)} c^{3} + 9 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) + 14 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) - 10 \, {\left(c^{3} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) + 4 \, {\left({\left(f x + e\right)} c^{3} - 5 \, c^{3} \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)\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 \, {\left(2 \, {\left(f x + e\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(f x + e\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(f x + e\right)} c^{3} + 9 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) + 14 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) - 10 \, {\left(c^{3} \cos\left(4 \, f x + 4 \, e\right) + 2 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + c^{3}\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) + 4 \, {\left({\left(f x + e\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) + c^{3} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(2 \, {\left(f x + e\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 4 \, {\left(f x + e\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) - 9 \, c^{3} \cos\left(4 \, f x + 4 \, e\right) - 14 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) - 9 \, c^{3} - 10 \, {\left(c^{3} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{3} \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) + 4 \, {\left({\left(f x + e\right)} c^{3} - 5 \, c^{3} \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)} \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 \, {\left(2 \, {\left(f x + e\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 4 \, {\left(f x + e\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) - 9 \, c^{3} \cos\left(4 \, f x + 4 \, e\right) - 14 \, c^{3} \cos\left(2 \, f x + 2 \, e\right) - 9 \, c^{3} - 10 \, {\left(c^{3} \sin\left(4 \, f x + 4 \, e\right) + 2 \, c^{3} \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{c}}{{\left(a \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, a \cos\left(2 \, f x + 2 \, e\right)^{2} + 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)^{2} + 4 \, 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 \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} + 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)^{2} + 4 \, 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)^{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) + 4 \, {\left(a \cos\left(4 \, f x + 4 \, e\right) + 2 \, 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)} \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 \cos\left(4 \, f x + 4 \, e\right) + 2 \, a \cos\left(2 \, f x + 2 \, e\right) + a\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 \sin\left(4 \, f x + 4 \, e\right) + 2 \, 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)} \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 \sin\left(4 \, f x + 4 \, e\right) + 2 \, a \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) + a\right)} \sqrt{a} f}"," ",0,"-((f*x + e)*c^3*cos(4*f*x + 4*e)^2 + 4*(f*x + e)*c^3*cos(2*f*x + 2*e)^2 + (f*x + e)*c^3*sin(4*f*x + 4*e)^2 + 4*(f*x + e)*c^3*sin(2*f*x + 2*e)^2 + 4*(f*x + e)*c^3*cos(2*f*x + 2*e) + (f*x + e)*c^3 - 4*c^3*sin(2*f*x + 2*e) + 4*((f*x + e)*c^3 - 5*c^3*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 + 4*((f*x + e)*c^3 - 5*c^3*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 + 4*((f*x + e)*c^3 - 5*c^3*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 + 4*((f*x + e)*c^3 - 5*c^3*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 - 5*(c^3*cos(4*f*x + 4*e)^2 + 4*c^3*cos(2*f*x + 2*e)^2 + c^3*sin(4*f*x + 4*e)^2 + 4*c^3*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*c^3*sin(2*f*x + 2*e)^2 + 4*c^3*cos(2*f*x + 2*e) + c^3 + 2*(2*c^3*cos(2*f*x + 2*e) + c^3)*cos(4*f*x + 4*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 8*(c^3*cos(4*f*x + 4*e)^2 + 4*c^3*cos(2*f*x + 2*e)^2 + 4*c^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*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 + 4*c^3*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*c^3*sin(2*f*x + 2*e)^2 + 4*c^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*c^3*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*c^3*cos(2*f*x + 2*e) + c^3 + 2*(2*c^3*cos(2*f*x + 2*e) + c^3)*cos(4*f*x + 4*e) + 4*(c^3*cos(4*f*x + 4*e) + 2*c^3*cos(2*f*x + 2*e) + 2*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))) + 4*(c^3*cos(4*f*x + 4*e) + 2*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))) + 4*(c^3*sin(4*f*x + 4*e) + 2*c^3*sin(2*f*x + 2*e) + 2*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))) + 4*(c^3*sin(4*f*x + 4*e) + 2*c^3*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) + 2*(2*(f*x + e)*c^3*cos(2*f*x + 2*e) + (f*x + e)*c^3 - 2*c^3*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) + 2*(2*(f*x + e)*c^3*cos(4*f*x + 4*e) + 4*(f*x + e)*c^3*cos(2*f*x + 2*e) + 2*(f*x + e)*c^3 + 9*c^3*sin(4*f*x + 4*e) + 14*c^3*sin(2*f*x + 2*e) - 10*(c^3*cos(4*f*x + 4*e) + 2*c^3*cos(2*f*x + 2*e) + c^3)*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 4*((f*x + e)*c^3 - 5*c^3*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))))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*(2*(f*x + e)*c^3*cos(4*f*x + 4*e) + 4*(f*x + e)*c^3*cos(2*f*x + 2*e) + 2*(f*x + e)*c^3 + 9*c^3*sin(4*f*x + 4*e) + 14*c^3*sin(2*f*x + 2*e) - 10*(c^3*cos(4*f*x + 4*e) + 2*c^3*cos(2*f*x + 2*e) + c^3)*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))) + 4*((f*x + e)*c^3*sin(2*f*x + 2*e) + c^3*cos(2*f*x + 2*e))*sin(4*f*x + 4*e) + 2*(2*(f*x + e)*c^3*sin(4*f*x + 4*e) + 4*(f*x + e)*c^3*sin(2*f*x + 2*e) - 9*c^3*cos(4*f*x + 4*e) - 14*c^3*cos(2*f*x + 2*e) - 9*c^3 - 10*(c^3*sin(4*f*x + 4*e) + 2*c^3*sin(2*f*x + 2*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 4*((f*x + e)*c^3 - 5*c^3*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))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*(2*(f*x + e)*c^3*sin(4*f*x + 4*e) + 4*(f*x + e)*c^3*sin(2*f*x + 2*e) - 9*c^3*cos(4*f*x + 4*e) - 14*c^3*cos(2*f*x + 2*e) - 9*c^3 - 10*(c^3*sin(4*f*x + 4*e) + 2*c^3*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(c)/((a*cos(4*f*x + 4*e)^2 + 4*a*cos(2*f*x + 2*e)^2 + 4*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a*cos(1/2*arctan2(sin(2*f*x + 2*e), 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 + 4*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(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) + 4*(a*cos(4*f*x + 4*e) + 2*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)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(a*cos(4*f*x + 4*e) + 2*a*cos(2*f*x + 2*e) + a)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(a*sin(4*f*x + 4*e) + 2*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))))*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(a*sin(4*f*x + 4*e) + 2*a*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a)*sqrt(a)*f)","B",0
118,-2,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^(5/2)/(a+a*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
119,1,70,0,0.726472," ","integrate((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)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 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)^2/(cos(f*x + e) + 1)^2 + 1)/(sqrt(-a)*a) - c^(3/2)*sin(f*x + e)^2/(sqrt(-a)*a*(cos(f*x + e) + 1)^2))/f","A",0
120,1,395,0,0.957031," ","integrate((c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(f x + e\right)} \cos\left(f x + e\right)^{2} + {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(f x + e\right)} \sin\left(f x + e\right)^{2} + f x - 2 \, {\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 \, {\left(f x + 2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e - \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(f x + e\right)} \cos\left(f x + e\right) + 2 \, {\left(2 \, {\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) + e - 2 \, \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{{\left(a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \cos\left(f x + e\right)^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, a^{2} \sin\left(f x + e\right)^{2} + 4 \, a^{2} \cos\left(f x + e\right) + a^{2} + 2 \, {\left(2 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} f}"," ",0,"-((f*x + e)*cos(2*f*x + 2*e)^2 + 4*(f*x + e)*cos(f*x + e)^2 + (f*x + e)*sin(2*f*x + 2*e)^2 + 4*(f*x + e)*sin(f*x + e)^2 + f*x - 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*(f*x + 2*(f*x + e)*cos(f*x + e) + e - sin(f*x + e))*cos(2*f*x + 2*e) + 4*(f*x + e)*cos(f*x + e) + 2*(2*(f*x + e)*sin(f*x + e) + cos(f*x + e))*sin(2*f*x + 2*e) + e - 2*sin(f*x + e))*sqrt(a)*sqrt(c)/((a^2*cos(2*f*x + 2*e)^2 + 4*a^2*cos(f*x + e)^2 + a^2*sin(2*f*x + 2*e)^2 + 4*a^2*sin(2*f*x + 2*e)*sin(f*x + e) + 4*a^2*sin(f*x + e)^2 + 4*a^2*cos(f*x + e) + a^2 + 2*(2*a^2*cos(f*x + e) + a^2)*cos(2*f*x + 2*e))*f)","B",0
121,1,818,0,0.958212," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 8 \, {\left(f x + e\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} + 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, {\left(f x + e\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 \, f x - 3 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(\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) + 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} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \sin\left(2 \, f x + 2 \, e\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 \, \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(2 \, f x + 2 \, e\right) + 1\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(\cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(\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) + 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} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \sin\left(2 \, f x + 2 \, e\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 \, \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(2 \, f x + 2 \, e\right) + 1\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) + 4 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(4 \, f x + 4 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, e + \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(4 \, {\left(f x + e\right)} \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 \, e}{2 \, {\left(a \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, 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 \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a \sin\left(2 \, f x + 2 \, e\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 \, 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)^{2} + 2 \, a \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a \cos\left(2 \, f x + 2 \, e\right) + a\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) + a\right)} \sqrt{a} \sqrt{c} f}"," ",0,"-1/2*(2*(f*x + e)*cos(2*f*x + 2*e)^2 + 8*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*(f*x + e)*sin(2*f*x + 2*e)^2 + 8*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*f*x - 3*(cos(2*f*x + 2*e)^2 + 4*(cos(2*f*x + 2*e) + 1)*cos(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)))^2 + sin(2*f*x + 2*e)^2 + 4*sin(2*f*x + 2*e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*cos(2*f*x + 2*e) + 1)*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) - (cos(2*f*x + 2*e)^2 + 4*(cos(2*f*x + 2*e) + 1)*cos(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)))^2 + sin(2*f*x + 2*e)^2 + 4*sin(2*f*x + 2*e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*cos(2*f*x + 2*e) + 1)*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) + 4*(f*x + e)*cos(2*f*x + 2*e) + 2*(4*f*x + 4*(f*x + e)*cos(2*f*x + 2*e) + 4*e + sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*(4*(f*x + e)*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*e)/((a*cos(2*f*x + 2*e)^2 + 4*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a*sin(2*f*x + 2*e)^2 + 4*a*sin(2*f*x + 2*e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*a*cos(2*f*x + 2*e) + 4*(a*cos(2*f*x + 2*e) + a)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a)*sqrt(a)*sqrt(c)*f)","B",0
122,1,486,0,0.879654," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + f x + {\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(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) - 1\right) + 2 \, {\left(f x - 2 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + e + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + e + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a} \sqrt{c}}{{\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,"-((f*x + e)*cos(4*f*x + 4*e)^2 + 4*(f*x + e)*cos(2*f*x + 2*e)^2 + (f*x + e)*sin(4*f*x + 4*e)^2 + 4*(f*x + e)*sin(2*f*x + 2*e)^2 + f*x + (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(2*f*x + 2*e), cos(2*f*x + 2*e) - 1) + 2*(f*x - 2*(f*x + e)*cos(2*f*x + 2*e) + e + sin(2*f*x + 2*e))*cos(4*f*x + 4*e) - 4*(f*x + e)*cos(2*f*x + 2*e) - 2*(2*(f*x + e)*sin(2*f*x + 2*e) + cos(2*f*x + 2*e))*sin(4*f*x + 4*e) + e + 2*sin(2*f*x + 2*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
123,1,4272,0,4.182893," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{8 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right)^{2} + 8 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 8 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 32 \, {\left(f x + e\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)^{2} + 128 \, {\left(f x + e\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} + 32 \, {\left(f x + e\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 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right)^{2} + 8 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 8 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 32 \, {\left(f x + e\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)^{2} + 128 \, {\left(f x + e\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} + 32 \, {\left(f x + e\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} + 8 \, f x + 5 \, {\left(2 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + \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} - 2 \, {\left(\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} - \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, e\right) - \cos\left(2 \, f x + 2 \, e\right) + 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 \, \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)} \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 \, \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} - 8 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, e\right) - \cos\left(2 \, f x + 2 \, e\right) - 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)} \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 \, \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 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, 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) - 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} + 2 \, {\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} - \sin\left(4 \, f x + 4 \, e\right)^{2} - 2 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right) + 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 \, \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) - 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} - 8 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\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)\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 \, \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 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \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) - 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} + 2 \, \cos\left(2 \, f x + 2 \, e\right) - 1\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) + 11 \, {\left(2 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + \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} - 2 \, {\left(\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} - \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, e\right) - \cos\left(2 \, f x + 2 \, e\right) + 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 \, \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)} \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 \, \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} - 8 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, e\right) - \cos\left(2 \, f x + 2 \, e\right) - 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)} \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 \, \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 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, 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) - 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} + 2 \, {\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} - \sin\left(4 \, f x + 4 \, e\right)^{2} - 2 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right) + 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 \, \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) - 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} - 8 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\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)\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 \, \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 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \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) - 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} + 2 \, \cos\left(2 \, f x + 2 \, e\right) - 1\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) + 4 \, {\left(4 \, f x - 4 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, e + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 3 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x - {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(16 \, f x + 16 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 64 \, {\left(f x + e\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) - 32 \, {\left(f x + e\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) + 16 \, e + 5 \, \sin\left(6 \, f x + 6 \, e\right) + 7 \, \sin\left(4 \, f x + 4 \, e\right) + 7 \, \sin\left(2 \, f x + 2 \, e\right) - 8 \, \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(16 \, f x + 16 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 32 \, {\left(f x + e\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) + 16 \, e + 7 \, \sin\left(6 \, f x + 6 \, e\right) + 5 \, \sin\left(4 \, f x + 4 \, e\right) + 5 \, \sin\left(2 \, f x + 2 \, e\right) - 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)} \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 \, {\left(16 \, f x + 16 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 16 \, e + 5 \, \sin\left(6 \, f x + 6 \, e\right) + 7 \, \sin\left(4 \, f x + 4 \, e\right) + 7 \, \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) - 4 \, {\left(4 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) + 4 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(4 \, f x + 4 \, e\right) + 3 \, \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 4 \, {\left(4 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 3\right)} \sin\left(4 \, f x + 4 \, e\right) - 2 \, {\left(16 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 64 \, {\left(f x + e\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) - 32 \, {\left(f x + e\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 \, \cos\left(6 \, f x + 6 \, e\right) - 7 \, \cos\left(4 \, f x + 4 \, e\right) - 7 \, \cos\left(2 \, f x + 2 \, e\right) + 8 \, \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\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(16 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 32 \, {\left(f x + e\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) - 7 \, \cos\left(6 \, f x + 6 \, e\right) - 5 \, \cos\left(4 \, f x + 4 \, e\right) - 5 \, \cos\left(2 \, f x + 2 \, e\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) - 7\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 \, {\left(16 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 5 \, \cos\left(6 \, f x + 6 \, e\right) - 7 \, \cos\left(4 \, f x + 4 \, e\right) - 7 \, \cos\left(2 \, f x + 2 \, e\right) - 5\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) + 8 \, e + 12 \, \sin\left(2 \, f x + 2 \, e\right)}{8 \, {\left(a c^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + a c^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a c^{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)^{2} + 16 \, a 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 \, a 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} + a c^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + a c^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 2 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + a c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a c^{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)^{2} + 16 \, a 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 \, a 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} - 2 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a c^{2} - 2 \, {\left(a c^{2} \cos\left(4 \, f x + 4 \, e\right) + a c^{2} \cos\left(2 \, f x + 2 \, e\right) - a c^{2}\right)} \cos\left(6 \, f x + 6 \, e\right) + 2 \, {\left(a c^{2} \cos\left(2 \, f x + 2 \, e\right) - a c^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(a c^{2} \cos\left(6 \, f x + 6 \, e\right) - a c^{2} \cos\left(4 \, f x + 4 \, e\right) - a c^{2} \cos\left(2 \, f x + 2 \, e\right) + 4 \, a 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 \, a 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) + a c^{2}\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) + 8 \, {\left(a c^{2} \cos\left(6 \, f x + 6 \, e\right) - a c^{2} \cos\left(4 \, f x + 4 \, e\right) - a c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, a 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) + a 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(a c^{2} \cos\left(6 \, f x + 6 \, e\right) - a c^{2} \cos\left(4 \, f x + 4 \, e\right) - a c^{2} \cos\left(2 \, f x + 2 \, e\right) + a 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) - 2 \, {\left(a c^{2} \sin\left(4 \, f x + 4 \, e\right) + a c^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 4 \, {\left(a c^{2} \sin\left(6 \, f x + 6 \, e\right) - a c^{2} \sin\left(4 \, f x + 4 \, e\right) - a c^{2} \sin\left(2 \, f x + 2 \, e\right) + 4 \, a 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 \, a 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{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 8 \, {\left(a c^{2} \sin\left(6 \, f x + 6 \, e\right) - a c^{2} \sin\left(4 \, f x + 4 \, e\right) - a c^{2} \sin\left(2 \, f x + 2 \, e\right) - 2 \, a 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(a c^{2} \sin\left(6 \, f x + 6 \, e\right) - a c^{2} \sin\left(4 \, f x + 4 \, e\right) - a 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)} \sqrt{a} \sqrt{c} f}"," ",0,"-1/8*(8*(f*x + e)*cos(6*f*x + 6*e)^2 + 8*(f*x + e)*cos(4*f*x + 4*e)^2 + 8*(f*x + e)*cos(2*f*x + 2*e)^2 + 32*(f*x + e)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 128*(f*x + e)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 32*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*(f*x + e)*sin(6*f*x + 6*e)^2 + 8*(f*x + e)*sin(4*f*x + 4*e)^2 + 8*(f*x + e)*sin(2*f*x + 2*e)^2 + 32*(f*x + e)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 128*(f*x + e)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 32*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*f*x + 5*(2*(cos(4*f*x + 4*e) + cos(2*f*x + 2*e) - 1)*cos(6*f*x + 6*e) - cos(6*f*x + 6*e)^2 - 2*(cos(2*f*x + 2*e) - 1)*cos(4*f*x + 4*e) - cos(4*f*x + 4*e)^2 - cos(2*f*x + 2*e)^2 + 4*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) + 4*cos(3/2*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))) + 1)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 8*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) - 2*cos(1/2*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))) - 16*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) + 1)*cos(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)))^2 + 2*(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 - sin(4*f*x + 4*e)^2 - 2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) - sin(2*f*x + 2*e)^2 + 4*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e) + 4*sin(3/2*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))))*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 8*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e) - 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))) - 16*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*cos(2*f*x + 2*e) - 1)*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) + 11*(2*(cos(4*f*x + 4*e) + cos(2*f*x + 2*e) - 1)*cos(6*f*x + 6*e) - cos(6*f*x + 6*e)^2 - 2*(cos(2*f*x + 2*e) - 1)*cos(4*f*x + 4*e) - cos(4*f*x + 4*e)^2 - cos(2*f*x + 2*e)^2 + 4*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) + 4*cos(3/2*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))) + 1)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 8*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) - 2*cos(1/2*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))) - 16*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) + 1)*cos(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)))^2 + 2*(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 - sin(4*f*x + 4*e)^2 - 2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) - sin(2*f*x + 2*e)^2 + 4*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e) + 4*sin(3/2*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))))*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 8*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e) - 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))) - 16*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*cos(2*f*x + 2*e) - 1)*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) + 4*(4*f*x - 4*(f*x + e)*cos(4*f*x + 4*e) - 4*(f*x + e)*cos(2*f*x + 2*e) + 4*e + 3*sin(4*f*x + 4*e) + 3*sin(2*f*x + 2*e))*cos(6*f*x + 6*e) - 16*(f*x - (f*x + e)*cos(2*f*x + 2*e) + e)*cos(4*f*x + 4*e) - 16*(f*x + e)*cos(2*f*x + 2*e) - 2*(16*f*x + 16*(f*x + e)*cos(6*f*x + 6*e) - 16*(f*x + e)*cos(4*f*x + 4*e) - 16*(f*x + e)*cos(2*f*x + 2*e) + 64*(f*x + e)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*e + 5*sin(6*f*x + 6*e) + 7*sin(4*f*x + 4*e) + 7*sin(2*f*x + 2*e) - 8*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*(16*f*x + 16*(f*x + e)*cos(6*f*x + 6*e) - 16*(f*x + e)*cos(4*f*x + 4*e) - 16*(f*x + e)*cos(2*f*x + 2*e) - 32*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*e + 7*sin(6*f*x + 6*e) + 5*sin(4*f*x + 4*e) + 5*sin(2*f*x + 2*e) - 4*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))) - 2*(16*f*x + 16*(f*x + e)*cos(6*f*x + 6*e) - 16*(f*x + e)*cos(4*f*x + 4*e) - 16*(f*x + e)*cos(2*f*x + 2*e) + 16*e + 5*sin(6*f*x + 6*e) + 7*sin(4*f*x + 4*e) + 7*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(4*(f*x + e)*sin(4*f*x + 4*e) + 4*(f*x + e)*sin(2*f*x + 2*e) + 3*cos(4*f*x + 4*e) + 3*cos(2*f*x + 2*e))*sin(6*f*x + 6*e) + 4*(4*(f*x + e)*sin(2*f*x + 2*e) + 3)*sin(4*f*x + 4*e) - 2*(16*(f*x + e)*sin(6*f*x + 6*e) - 16*(f*x + e)*sin(4*f*x + 4*e) - 16*(f*x + e)*sin(2*f*x + 2*e) + 64*(f*x + e)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*cos(6*f*x + 6*e) - 7*cos(4*f*x + 4*e) - 7*cos(2*f*x + 2*e) + 8*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(16*(f*x + e)*sin(6*f*x + 6*e) - 16*(f*x + e)*sin(4*f*x + 4*e) - 16*(f*x + e)*sin(2*f*x + 2*e) - 32*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 7*cos(6*f*x + 6*e) - 5*cos(4*f*x + 4*e) - 5*cos(2*f*x + 2*e) + 4*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 7)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*(16*(f*x + e)*sin(6*f*x + 6*e) - 16*(f*x + e)*sin(4*f*x + 4*e) - 16*(f*x + e)*sin(2*f*x + 2*e) - 5*cos(6*f*x + 6*e) - 7*cos(4*f*x + 4*e) - 7*cos(2*f*x + 2*e) - 5)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 8*e + 12*sin(2*f*x + 2*e))/((a*c^2*cos(6*f*x + 6*e)^2 + a*c^2*cos(4*f*x + 4*e)^2 + a*c^2*cos(2*f*x + 2*e)^2 + 4*a*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*a*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a*c^2*sin(6*f*x + 6*e)^2 + a*c^2*sin(4*f*x + 4*e)^2 + 2*a*c^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + a*c^2*sin(2*f*x + 2*e)^2 + 4*a*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*a*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*a*c^2*cos(2*f*x + 2*e) + a*c^2 - 2*(a*c^2*cos(4*f*x + 4*e) + a*c^2*cos(2*f*x + 2*e) - a*c^2)*cos(6*f*x + 6*e) + 2*(a*c^2*cos(2*f*x + 2*e) - a*c^2)*cos(4*f*x + 4*e) - 4*(a*c^2*cos(6*f*x + 6*e) - a*c^2*cos(4*f*x + 4*e) - a*c^2*cos(2*f*x + 2*e) + 4*a*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*a*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a*c^2)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 8*(a*c^2*cos(6*f*x + 6*e) - a*c^2*cos(4*f*x + 4*e) - a*c^2*cos(2*f*x + 2*e) - 2*a*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a*c^2)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(a*c^2*cos(6*f*x + 6*e) - a*c^2*cos(4*f*x + 4*e) - a*c^2*cos(2*f*x + 2*e) + a*c^2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*(a*c^2*sin(4*f*x + 4*e) + a*c^2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) - 4*(a*c^2*sin(6*f*x + 6*e) - a*c^2*sin(4*f*x + 4*e) - a*c^2*sin(2*f*x + 2*e) + 4*a*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*a*c^2*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))) + 8*(a*c^2*sin(6*f*x + 6*e) - a*c^2*sin(4*f*x + 4*e) - a*c^2*sin(2*f*x + 2*e) - 2*a*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*(a*c^2*sin(6*f*x + 6*e) - a*c^2*sin(4*f*x + 4*e) - a*c^2*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)*f)","B",0
124,-2,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^(7/2)/(a+a*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
125,1,102,0,0.713751," ","integrate((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)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 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)^2/(cos(f*x + e) + 1)^2 + 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
126,1,1786,0,1.146050," ","integrate((c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} c \cos\left(4 \, f x + 4 \, e\right)^{2} + 36 \, {\left(f x + e\right)} c \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, {\left(f x + e\right)} c \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 \, {\left(f x + e\right)} 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} + {\left(f x + e\right)} c \sin\left(4 \, f x + 4 \, e\right)^{2} + 36 \, {\left(f x + e\right)} c \sin\left(2 \, f x + 2 \, e\right)^{2} + 16 \, {\left(f x + e\right)} c \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 \, {\left(f x + e\right)} 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} + 12 \, {\left(f x + e\right)} c \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} c - 2 \, {\left(c \cos\left(4 \, f x + 4 \, e\right)^{2} + 36 \, c \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, c \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 \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(4 \, f x + 4 \, e\right)^{2} + 12 \, c \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 36 \, c \sin\left(2 \, f x + 2 \, e\right)^{2} + 16 \, c \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 \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 \, {\left(6 \, c \cos\left(2 \, f x + 2 \, e\right) + c\right)} \cos\left(4 \, f x + 4 \, e\right) + 12 \, c \cos\left(2 \, f x + 2 \, e\right) + 8 \, {\left(c \cos\left(4 \, f x + 4 \, e\right) + 6 \, c \cos\left(2 \, f x + 2 \, e\right) + 4 \, 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)} \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 \cos\left(4 \, f x + 4 \, e\right) + 6 \, c \cos\left(2 \, f x + 2 \, e\right) + c\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 \sin\left(4 \, f x + 4 \, e\right) + 6 \, c \sin\left(2 \, f x + 2 \, e\right) + 4 \, 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)\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 \sin\left(4 \, f x + 4 \, e\right) + 6 \, c \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) + 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) + 2 \, {\left(6 \, {\left(f x + e\right)} c \cos\left(2 \, f x + 2 \, e\right) + {\left(f x + e\right)} c - 4 \, c \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(4 \, {\left(f x + e\right)} c \cos\left(4 \, f x + 4 \, e\right) + 24 \, {\left(f x + e\right)} c \cos\left(2 \, f x + 2 \, e\right) + 16 \, {\left(f x + e\right)} 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) + 4 \, {\left(f x + e\right)} c + 3 \, c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \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) + 2 \, {\left(4 \, {\left(f x + e\right)} c \cos\left(4 \, f x + 4 \, e\right) + 24 \, {\left(f x + e\right)} c \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(f x + e\right)} c + 3 \, c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \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) + 4 \, {\left(3 \, {\left(f x + e\right)} c \sin\left(2 \, f x + 2 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 8 \, c \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(4 \, {\left(f x + e\right)} c \sin\left(4 \, f x + 4 \, e\right) + 24 \, {\left(f x + e\right)} c \sin\left(2 \, f x + 2 \, e\right) + 16 \, {\left(f x + e\right)} 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) - 3 \, c \cos\left(4 \, f x + 4 \, e\right) - 2 \, c \cos\left(2 \, f x + 2 \, e\right) - 3 \, c\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 \, {\left(4 \, {\left(f x + e\right)} c \sin\left(4 \, f x + 4 \, e\right) + 24 \, {\left(f x + e\right)} c \sin\left(2 \, f x + 2 \, e\right) - 3 \, c \cos\left(4 \, f x + 4 \, e\right) - 2 \, c \cos\left(2 \, f x + 2 \, e\right) - 3 \, 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^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 36 \, a^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, a^{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 \, a^{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} + a^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} + 12 \, a^{3} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 36 \, a^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 16 \, a^{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 \, a^{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 \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + a^{3} + 2 \, {\left(6 \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + a^{3}\right)} \cos\left(4 \, f x + 4 \, e\right) + 8 \, {\left(a^{3} \cos\left(4 \, f x + 4 \, e\right) + 6 \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + 4 \, a^{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) + a^{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(a^{3} \cos\left(4 \, f x + 4 \, e\right) + 6 \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + a^{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(a^{3} \sin\left(4 \, f x + 4 \, e\right) + 6 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 4 \, a^{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(a^{3} \sin\left(4 \, f x + 4 \, e\right) + 6 \, a^{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,"-((f*x + e)*c*cos(4*f*x + 4*e)^2 + 36*(f*x + e)*c*cos(2*f*x + 2*e)^2 + 16*(f*x + e)*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*(f*x + e)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + (f*x + e)*c*sin(4*f*x + 4*e)^2 + 36*(f*x + e)*c*sin(2*f*x + 2*e)^2 + 16*(f*x + e)*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*(f*x + e)*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 12*(f*x + e)*c*cos(2*f*x + 2*e) + (f*x + e)*c - 2*(c*cos(4*f*x + 4*e)^2 + 36*c*cos(2*f*x + 2*e)^2 + 16*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + c*sin(4*f*x + 4*e)^2 + 12*c*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*c*sin(2*f*x + 2*e)^2 + 16*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*(6*c*cos(2*f*x + 2*e) + c)*cos(4*f*x + 4*e) + 12*c*cos(2*f*x + 2*e) + 8*(c*cos(4*f*x + 4*e) + 6*c*cos(2*f*x + 2*e) + 4*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + c)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 8*(c*cos(4*f*x + 4*e) + 6*c*cos(2*f*x + 2*e) + c)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 8*(c*sin(4*f*x + 4*e) + 6*c*sin(2*f*x + 2*e) + 4*c*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*sin(4*f*x + 4*e) + 6*c*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), 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) + 2*(6*(f*x + e)*c*cos(2*f*x + 2*e) + (f*x + e)*c - 4*c*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) + 2*(4*(f*x + e)*c*cos(4*f*x + 4*e) + 24*(f*x + e)*c*cos(2*f*x + 2*e) + 16*(f*x + e)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(f*x + e)*c + 3*c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e))*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*(4*(f*x + e)*c*cos(4*f*x + 4*e) + 24*(f*x + e)*c*cos(2*f*x + 2*e) + 4*(f*x + e)*c + 3*c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(3*(f*x + e)*c*sin(2*f*x + 2*e) + 2*c*cos(2*f*x + 2*e))*sin(4*f*x + 4*e) - 8*c*sin(2*f*x + 2*e) + 2*(4*(f*x + e)*c*sin(4*f*x + 4*e) + 24*(f*x + e)*c*sin(2*f*x + 2*e) + 16*(f*x + e)*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3*c*cos(4*f*x + 4*e) - 2*c*cos(2*f*x + 2*e) - 3*c)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*(4*(f*x + e)*c*sin(4*f*x + 4*e) + 24*(f*x + e)*c*sin(2*f*x + 2*e) - 3*c*cos(4*f*x + 4*e) - 2*c*cos(2*f*x + 2*e) - 3*c)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((a^3*cos(4*f*x + 4*e)^2 + 36*a^3*cos(2*f*x + 2*e)^2 + 16*a^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*a^3*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a^3*sin(4*f*x + 4*e)^2 + 12*a^3*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*a^3*sin(2*f*x + 2*e)^2 + 16*a^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*a^3*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 12*a^3*cos(2*f*x + 2*e) + a^3 + 2*(6*a^3*cos(2*f*x + 2*e) + a^3)*cos(4*f*x + 4*e) + 8*(a^3*cos(4*f*x + 4*e) + 6*a^3*cos(2*f*x + 2*e) + 4*a^3*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^3)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 8*(a^3*cos(4*f*x + 4*e) + 6*a^3*cos(2*f*x + 2*e) + a^3)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 8*(a^3*sin(4*f*x + 4*e) + 6*a^3*sin(2*f*x + 2*e) + 4*a^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*(a^3*sin(4*f*x + 4*e) + 6*a^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
127,1,1165,0,1.397284," ","integrate((c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 36 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \cos\left(f x + e\right)^{2} + {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 36 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \sin\left(f x + e\right)^{2} + f x - 2 \, {\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(f x + 4 \, {\left(f x + e\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e - 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)} \cos\left(4 \, f x + 4 \, e\right) + 8 \, {\left(f x + 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e\right)} \cos\left(3 \, f x + 3 \, e\right) + 12 \, {\left(f x + 4 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 8 \, {\left(f x + e\right)} \cos\left(f x + e\right) + 2 \, {\left(4 \, {\left(f x + e\right)} \sin\left(3 \, f x + 3 \, e\right) + 6 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(f x + e\right)} \sin\left(f x + e\right) + 2 \, \cos\left(3 \, f x + 3 \, e\right) + 3 \, \cos\left(2 \, f x + 2 \, e\right) + 2 \, \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 4 \, {\left(12 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 8 \, {\left(f x + e\right)} \sin\left(f x + e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) + 6 \, {\left(8 \, {\left(f x + e\right)} \sin\left(f x + e\right) - 1\right)} \sin\left(2 \, f x + 2 \, e\right) + e - 4 \, \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{{\left(a^{3} \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, a^{3} \cos\left(3 \, f x + 3 \, e\right)^{2} + 36 \, a^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, a^{3} \cos\left(f x + e\right)^{2} + a^{3} \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, a^{3} \sin\left(3 \, f x + 3 \, e\right)^{2} + 36 \, a^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 48 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 16 \, a^{3} \sin\left(f x + e\right)^{2} + 8 \, a^{3} \cos\left(f x + e\right) + a^{3} + 2 \, {\left(4 \, a^{3} \cos\left(3 \, f x + 3 \, e\right) + 6 \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + 4 \, a^{3} \cos\left(f x + e\right) + a^{3}\right)} \cos\left(4 \, f x + 4 \, e\right) + 8 \, {\left(6 \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + 4 \, a^{3} \cos\left(f x + e\right) + a^{3}\right)} \cos\left(3 \, f x + 3 \, e\right) + 12 \, {\left(4 \, a^{3} \cos\left(f x + e\right) + a^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(2 \, a^{3} \sin\left(3 \, f x + 3 \, e\right) + 3 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 2 \, a^{3} \sin\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 16 \, {\left(3 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 2 \, a^{3} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} f}"," ",0,"-((f*x + e)*cos(4*f*x + 4*e)^2 + 16*(f*x + e)*cos(3*f*x + 3*e)^2 + 36*(f*x + e)*cos(2*f*x + 2*e)^2 + 16*(f*x + e)*cos(f*x + e)^2 + (f*x + e)*sin(4*f*x + 4*e)^2 + 16*(f*x + e)*sin(3*f*x + 3*e)^2 + 36*(f*x + e)*sin(2*f*x + 2*e)^2 + 16*(f*x + e)*sin(f*x + e)^2 + f*x - 2*(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*(f*x + 4*(f*x + e)*cos(3*f*x + 3*e) + 6*(f*x + e)*cos(2*f*x + 2*e) + 4*(f*x + e)*cos(f*x + e) + e - 2*sin(3*f*x + 3*e) - 3*sin(2*f*x + 2*e) - 2*sin(f*x + e))*cos(4*f*x + 4*e) + 8*(f*x + 6*(f*x + e)*cos(2*f*x + 2*e) + 4*(f*x + e)*cos(f*x + e) + e)*cos(3*f*x + 3*e) + 12*(f*x + 4*(f*x + e)*cos(f*x + e) + e)*cos(2*f*x + 2*e) + 8*(f*x + e)*cos(f*x + e) + 2*(4*(f*x + e)*sin(3*f*x + 3*e) + 6*(f*x + e)*sin(2*f*x + 2*e) + 4*(f*x + e)*sin(f*x + e) + 2*cos(3*f*x + 3*e) + 3*cos(2*f*x + 2*e) + 2*cos(f*x + e))*sin(4*f*x + 4*e) + 4*(12*(f*x + e)*sin(2*f*x + 2*e) + 8*(f*x + e)*sin(f*x + e) - 1)*sin(3*f*x + 3*e) + 6*(8*(f*x + e)*sin(f*x + e) - 1)*sin(2*f*x + 2*e) + e - 4*sin(f*x + e))*sqrt(a)*sqrt(c)/((a^3*cos(4*f*x + 4*e)^2 + 16*a^3*cos(3*f*x + 3*e)^2 + 36*a^3*cos(2*f*x + 2*e)^2 + 16*a^3*cos(f*x + e)^2 + a^3*sin(4*f*x + 4*e)^2 + 16*a^3*sin(3*f*x + 3*e)^2 + 36*a^3*sin(2*f*x + 2*e)^2 + 48*a^3*sin(2*f*x + 2*e)*sin(f*x + e) + 16*a^3*sin(f*x + e)^2 + 8*a^3*cos(f*x + e) + a^3 + 2*(4*a^3*cos(3*f*x + 3*e) + 6*a^3*cos(2*f*x + 2*e) + 4*a^3*cos(f*x + e) + a^3)*cos(4*f*x + 4*e) + 8*(6*a^3*cos(2*f*x + 2*e) + 4*a^3*cos(f*x + e) + a^3)*cos(3*f*x + 3*e) + 12*(4*a^3*cos(f*x + e) + a^3)*cos(2*f*x + 2*e) + 4*(2*a^3*sin(3*f*x + 3*e) + 3*a^3*sin(2*f*x + 2*e) + 2*a^3*sin(f*x + e))*sin(4*f*x + 4*e) + 16*(3*a^3*sin(2*f*x + 2*e) + 2*a^3*sin(f*x + e))*sin(3*f*x + 3*e))*f)","B",0
128,1,2206,0,1.143986," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 144 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 64 \, {\left(f x + e\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} + 64 \, {\left(f x + e\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} + 4 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 144 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 64 \, {\left(f x + e\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} + 64 \, {\left(f x + e\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} + 4 \, f x - 7 \, {\left(2 \, {\left(6 \, \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} + 36 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 8 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\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) + 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) + 16 \, \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 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + 6 \, \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) + 16 \, \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(4 \, f x + 4 \, e\right)^{2} + 12 \, \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} + 8 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + 6 \, \sin\left(2 \, f x + 2 \, e\right) + 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) + 16 \, \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 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + 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) + 16 \, \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 \, \cos\left(2 \, f x + 2 \, e\right) + 1\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(2 \, {\left(6 \, \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} + 36 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 8 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\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) + 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) + 16 \, \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 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + 6 \, \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) + 16 \, \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(4 \, f x + 4 \, e\right)^{2} + 12 \, \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} + 8 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + 6 \, \sin\left(2 \, f x + 2 \, e\right) + 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) + 16 \, \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 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + 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) + 16 \, \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 \, \cos\left(2 \, f x + 2 \, e\right) + 1\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) + 8 \, {\left(f x + 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + e - 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 48 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(16 \, f x + 16 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) + 96 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 64 \, {\left(f x + e\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) + 16 \, e + 5 \, \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) + 2 \, {\left(16 \, f x + 16 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) + 96 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 16 \, e + 5 \, \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) + 16 \, {\left(3 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(16 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) + 96 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 64 \, {\left(f x + e\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 \, \cos\left(4 \, f x + 4 \, e\right) + 2 \, \cos\left(2 \, f x + 2 \, e\right) - 5\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 \, {\left(16 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) + 96 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 5 \, \cos\left(4 \, f x + 4 \, e\right) + 2 \, \cos\left(2 \, f x + 2 \, e\right) - 5\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 \, e - 16 \, \sin\left(2 \, f x + 2 \, e\right)}{4 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 36 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 16 \, 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} + 16 \, 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} + 12 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 36 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 16 \, 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} + 16 \, 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} + 12 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} + 2 \, {\left(6 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 8 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 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) + 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) + 8 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right) + 6 \, 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) + 8 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 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)\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(a^{2} \sin\left(4 \, f x + 4 \, e\right) + 6 \, 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)} \sqrt{a} \sqrt{c} f}"," ",0,"-1/4*(4*(f*x + e)*cos(4*f*x + 4*e)^2 + 144*(f*x + e)*cos(2*f*x + 2*e)^2 + 64*(f*x + e)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*(f*x + e)*sin(4*f*x + 4*e)^2 + 144*(f*x + e)*sin(2*f*x + 2*e)^2 + 64*(f*x + e)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 64*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*f*x - 7*(2*(6*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + cos(4*f*x + 4*e)^2 + 36*cos(2*f*x + 2*e)^2 + 8*(cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) + 4*cos(1/2*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))) + 16*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*(cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) + 1)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(4*f*x + 4*e)^2 + 12*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*sin(2*f*x + 2*e)^2 + 8*(sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e) + 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))) + 16*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*(sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 12*cos(2*f*x + 2*e) + 1)*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) - (2*(6*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + cos(4*f*x + 4*e)^2 + 36*cos(2*f*x + 2*e)^2 + 8*(cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) + 4*cos(1/2*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))) + 16*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*(cos(4*f*x + 4*e) + 6*cos(2*f*x + 2*e) + 1)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(4*f*x + 4*e)^2 + 12*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*sin(2*f*x + 2*e)^2 + 8*(sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e) + 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))) + 16*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*(sin(4*f*x + 4*e) + 6*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 12*cos(2*f*x + 2*e) + 1)*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) + 8*(f*x + 6*(f*x + e)*cos(2*f*x + 2*e) + e - 2*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) + 48*(f*x + e)*cos(2*f*x + 2*e) + 2*(16*f*x + 16*(f*x + e)*cos(4*f*x + 4*e) + 96*(f*x + e)*cos(2*f*x + 2*e) + 64*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*e + 5*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))) + 2*(16*f*x + 16*(f*x + e)*cos(4*f*x + 4*e) + 96*(f*x + e)*cos(2*f*x + 2*e) + 16*e + 5*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))) + 16*(3*(f*x + e)*sin(2*f*x + 2*e) + cos(2*f*x + 2*e))*sin(4*f*x + 4*e) + 2*(16*(f*x + e)*sin(4*f*x + 4*e) + 96*(f*x + e)*sin(2*f*x + 2*e) + 64*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*cos(4*f*x + 4*e) + 2*cos(2*f*x + 2*e) - 5)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*(16*(f*x + e)*sin(4*f*x + 4*e) + 96*(f*x + e)*sin(2*f*x + 2*e) - 5*cos(4*f*x + 4*e) + 2*cos(2*f*x + 2*e) - 5)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*e - 16*sin(2*f*x + 2*e))/((a^2*cos(4*f*x + 4*e)^2 + 36*a^2*cos(2*f*x + 2*e)^2 + 16*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*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 + 12*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 36*a^2*sin(2*f*x + 2*e)^2 + 16*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 12*a^2*cos(2*f*x + 2*e) + a^2 + 2*(6*a^2*cos(2*f*x + 2*e) + a^2)*cos(4*f*x + 4*e) + 8*(a^2*cos(4*f*x + 4*e) + 6*a^2*cos(2*f*x + 2*e) + 4*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))) + 8*(a^2*cos(4*f*x + 4*e) + 6*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))) + 8*(a^2*sin(4*f*x + 4*e) + 6*a^2*sin(2*f*x + 2*e) + 4*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))) + 8*(a^2*sin(4*f*x + 4*e) + 6*a^2*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)*f)","B",0
129,1,4272,0,4.632193," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{8 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right)^{2} + 8 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 8 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 32 \, {\left(f x + e\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)^{2} + 128 \, {\left(f x + e\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} + 32 \, {\left(f x + e\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 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right)^{2} + 8 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 8 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 32 \, {\left(f x + e\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)^{2} + 128 \, {\left(f x + e\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} + 32 \, {\left(f x + e\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} + 8 \, f x + 11 \, {\left(2 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + \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} - 2 \, {\left(\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} - \cos\left(2 \, f x + 2 \, e\right)^{2} - 4 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, e\right) - \cos\left(2 \, f x + 2 \, e\right) - 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 \, \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)} \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 \, \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} + 8 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, e\right) - \cos\left(2 \, f x + 2 \, e\right) + 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)} \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 \, \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 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, 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) - 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} + 2 \, {\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} - \sin\left(4 \, f x + 4 \, e\right)^{2} - 2 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)^{2} - 4 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right) - 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 \, \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) - 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} + 8 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\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)\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 \, \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 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \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) - 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} + 2 \, \cos\left(2 \, f x + 2 \, e\right) - 1\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) + 5 \, {\left(2 \, {\left(\cos\left(4 \, f x + 4 \, e\right) + \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} - 2 \, {\left(\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} - \cos\left(2 \, f x + 2 \, e\right)^{2} - 4 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, e\right) - \cos\left(2 \, f x + 2 \, e\right) - 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 \, \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)} \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 \, \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} + 8 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, e\right) - \cos\left(2 \, f x + 2 \, e\right) + 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)} \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 \, \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 \, {\left(\cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, 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) - 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} + 2 \, {\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} - \sin\left(4 \, f x + 4 \, e\right)^{2} - 2 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)^{2} - 4 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right) - 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 \, \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) - 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} + 8 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\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)\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 \, \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 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - \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) - 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} + 2 \, \cos\left(2 \, f x + 2 \, e\right) - 1\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) + 4 \, {\left(4 \, f x - 4 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, e + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 3 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x - {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(16 \, f x + 16 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 64 \, {\left(f x + e\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) + 32 \, {\left(f x + e\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) + 16 \, e + 5 \, \sin\left(6 \, f x + 6 \, e\right) + 7 \, \sin\left(4 \, f x + 4 \, e\right) + 7 \, \sin\left(2 \, f x + 2 \, e\right) + 8 \, \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(16 \, f x + 16 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 32 \, {\left(f x + e\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) + 16 \, e + 7 \, \sin\left(6 \, f x + 6 \, e\right) + 5 \, \sin\left(4 \, f x + 4 \, e\right) + 5 \, \sin\left(2 \, f x + 2 \, e\right) + 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)} \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 \, {\left(16 \, f x + 16 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 16 \, e + 5 \, \sin\left(6 \, f x + 6 \, e\right) + 7 \, \sin\left(4 \, f x + 4 \, e\right) + 7 \, \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) - 4 \, {\left(4 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) + 4 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(4 \, f x + 4 \, e\right) + 3 \, \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 4 \, {\left(4 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 3\right)} \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(16 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 64 \, {\left(f x + e\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) + 32 \, {\left(f x + e\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 \, \cos\left(6 \, f x + 6 \, e\right) - 7 \, \cos\left(4 \, f x + 4 \, e\right) - 7 \, \cos\left(2 \, f x + 2 \, e\right) - 8 \, \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\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(16 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 32 \, {\left(f x + e\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) - 7 \, \cos\left(6 \, f x + 6 \, e\right) - 5 \, \cos\left(4 \, f x + 4 \, e\right) - 5 \, \cos\left(2 \, f x + 2 \, e\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) - 7\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 \, {\left(16 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) - 16 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 5 \, \cos\left(6 \, f x + 6 \, e\right) - 7 \, \cos\left(4 \, f x + 4 \, e\right) - 7 \, \cos\left(2 \, f x + 2 \, e\right) - 5\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) + 8 \, e + 12 \, \sin\left(2 \, f x + 2 \, e\right)}{8 \, {\left(a^{2} c \cos\left(6 \, f x + 6 \, e\right)^{2} + a^{2} c \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} c \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} c \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} + 16 \, a^{2} c \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} 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} + a^{2} c \sin\left(6 \, f x + 6 \, e\right)^{2} + a^{2} c \sin\left(4 \, f x + 4 \, e\right)^{2} + 2 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + a^{2} c \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} c \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} + 16 \, a^{2} c \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} 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 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} c - 2 \, {\left(a^{2} c \cos\left(4 \, f x + 4 \, e\right) + a^{2} c \cos\left(2 \, f x + 2 \, e\right) - a^{2} c\right)} \cos\left(6 \, f x + 6 \, e\right) + 2 \, {\left(a^{2} c \cos\left(2 \, f x + 2 \, e\right) - a^{2} c\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} c \cos\left(6 \, f x + 6 \, e\right) - a^{2} c \cos\left(4 \, f x + 4 \, e\right) - a^{2} c \cos\left(2 \, f x + 2 \, e\right) - 4 \, a^{2} c \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 \, a^{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) + a^{2} c\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) - 8 \, {\left(a^{2} c \cos\left(6 \, f x + 6 \, e\right) - a^{2} c \cos\left(4 \, f x + 4 \, e\right) - a^{2} c \cos\left(2 \, f x + 2 \, e\right) + 2 \, a^{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) + a^{2} c\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} c \cos\left(6 \, f x + 6 \, e\right) - a^{2} c \cos\left(4 \, f x + 4 \, e\right) - a^{2} c \cos\left(2 \, f x + 2 \, e\right) + a^{2} c\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(a^{2} c \sin\left(4 \, f x + 4 \, e\right) + a^{2} c \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 4 \, {\left(a^{2} c \sin\left(6 \, f x + 6 \, e\right) - a^{2} c \sin\left(4 \, f x + 4 \, e\right) - a^{2} c \sin\left(2 \, f x + 2 \, e\right) - 4 \, a^{2} c \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 \, a^{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)\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) - 8 \, {\left(a^{2} c \sin\left(6 \, f x + 6 \, e\right) - a^{2} c \sin\left(4 \, f x + 4 \, e\right) - a^{2} c \sin\left(2 \, f x + 2 \, e\right) + 2 \, a^{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)\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} c \sin\left(6 \, f x + 6 \, e\right) - a^{2} c \sin\left(4 \, f x + 4 \, e\right) - a^{2} c \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)} \sqrt{a} \sqrt{c} f}"," ",0,"-1/8*(8*(f*x + e)*cos(6*f*x + 6*e)^2 + 8*(f*x + e)*cos(4*f*x + 4*e)^2 + 8*(f*x + e)*cos(2*f*x + 2*e)^2 + 32*(f*x + e)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 128*(f*x + e)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 32*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*(f*x + e)*sin(6*f*x + 6*e)^2 + 8*(f*x + e)*sin(4*f*x + 4*e)^2 + 8*(f*x + e)*sin(2*f*x + 2*e)^2 + 32*(f*x + e)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 128*(f*x + e)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 32*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*f*x + 11*(2*(cos(4*f*x + 4*e) + cos(2*f*x + 2*e) - 1)*cos(6*f*x + 6*e) - cos(6*f*x + 6*e)^2 - 2*(cos(2*f*x + 2*e) - 1)*cos(4*f*x + 4*e) - cos(4*f*x + 4*e)^2 - cos(2*f*x + 2*e)^2 - 4*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) - 4*cos(3/2*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))) + 1)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) + 2*cos(1/2*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))) - 16*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 4*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) + 1)*cos(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)))^2 + 2*(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 - sin(4*f*x + 4*e)^2 - 2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) - sin(2*f*x + 2*e)^2 - 4*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e) - 4*sin(3/2*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))))*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e) + 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))) - 16*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 4*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*cos(2*f*x + 2*e) - 1)*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) + 5*(2*(cos(4*f*x + 4*e) + cos(2*f*x + 2*e) - 1)*cos(6*f*x + 6*e) - cos(6*f*x + 6*e)^2 - 2*(cos(2*f*x + 2*e) - 1)*cos(4*f*x + 4*e) - cos(4*f*x + 4*e)^2 - cos(2*f*x + 2*e)^2 - 4*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) - 4*cos(3/2*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))) + 1)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) + 2*cos(1/2*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))) - 16*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 4*(cos(6*f*x + 6*e) - cos(4*f*x + 4*e) - cos(2*f*x + 2*e) + 1)*cos(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)))^2 + 2*(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 - sin(4*f*x + 4*e)^2 - 2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) - sin(2*f*x + 2*e)^2 - 4*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e) - 4*sin(3/2*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))))*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 8*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e) + 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))) - 16*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 4*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*cos(2*f*x + 2*e) - 1)*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) + 4*(4*f*x - 4*(f*x + e)*cos(4*f*x + 4*e) - 4*(f*x + e)*cos(2*f*x + 2*e) + 4*e + 3*sin(4*f*x + 4*e) + 3*sin(2*f*x + 2*e))*cos(6*f*x + 6*e) - 16*(f*x - (f*x + e)*cos(2*f*x + 2*e) + e)*cos(4*f*x + 4*e) - 16*(f*x + e)*cos(2*f*x + 2*e) + 2*(16*f*x + 16*(f*x + e)*cos(6*f*x + 6*e) - 16*(f*x + e)*cos(4*f*x + 4*e) - 16*(f*x + e)*cos(2*f*x + 2*e) - 64*(f*x + e)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 32*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*e + 5*sin(6*f*x + 6*e) + 7*sin(4*f*x + 4*e) + 7*sin(2*f*x + 2*e) + 8*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*(16*f*x + 16*(f*x + e)*cos(6*f*x + 6*e) - 16*(f*x + e)*cos(4*f*x + 4*e) - 16*(f*x + e)*cos(2*f*x + 2*e) + 32*(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*e + 7*sin(6*f*x + 6*e) + 5*sin(4*f*x + 4*e) + 5*sin(2*f*x + 2*e) + 4*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))) + 2*(16*f*x + 16*(f*x + e)*cos(6*f*x + 6*e) - 16*(f*x + e)*cos(4*f*x + 4*e) - 16*(f*x + e)*cos(2*f*x + 2*e) + 16*e + 5*sin(6*f*x + 6*e) + 7*sin(4*f*x + 4*e) + 7*sin(2*f*x + 2*e))*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(4*(f*x + e)*sin(4*f*x + 4*e) + 4*(f*x + e)*sin(2*f*x + 2*e) + 3*cos(4*f*x + 4*e) + 3*cos(2*f*x + 2*e))*sin(6*f*x + 6*e) + 4*(4*(f*x + e)*sin(2*f*x + 2*e) + 3)*sin(4*f*x + 4*e) + 2*(16*(f*x + e)*sin(6*f*x + 6*e) - 16*(f*x + e)*sin(4*f*x + 4*e) - 16*(f*x + e)*sin(2*f*x + 2*e) - 64*(f*x + e)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 32*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*cos(6*f*x + 6*e) - 7*cos(4*f*x + 4*e) - 7*cos(2*f*x + 2*e) - 8*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*(16*(f*x + e)*sin(6*f*x + 6*e) - 16*(f*x + e)*sin(4*f*x + 4*e) - 16*(f*x + e)*sin(2*f*x + 2*e) + 32*(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 7*cos(6*f*x + 6*e) - 5*cos(4*f*x + 4*e) - 5*cos(2*f*x + 2*e) - 4*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 7)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*(16*(f*x + e)*sin(6*f*x + 6*e) - 16*(f*x + e)*sin(4*f*x + 4*e) - 16*(f*x + e)*sin(2*f*x + 2*e) - 5*cos(6*f*x + 6*e) - 7*cos(4*f*x + 4*e) - 7*cos(2*f*x + 2*e) - 5)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 8*e + 12*sin(2*f*x + 2*e))/((a^2*c*cos(6*f*x + 6*e)^2 + a^2*c*cos(4*f*x + 4*e)^2 + a^2*c*cos(2*f*x + 2*e)^2 + 4*a^2*c*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*a^2*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a^2*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + a^2*c*sin(6*f*x + 6*e)^2 + a^2*c*sin(4*f*x + 4*e)^2 + 2*a^2*c*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + a^2*c*sin(2*f*x + 2*e)^2 + 4*a^2*c*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 16*a^2*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 4*a^2*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*a^2*c*cos(2*f*x + 2*e) + a^2*c - 2*(a^2*c*cos(4*f*x + 4*e) + a^2*c*cos(2*f*x + 2*e) - a^2*c)*cos(6*f*x + 6*e) + 2*(a^2*c*cos(2*f*x + 2*e) - a^2*c)*cos(4*f*x + 4*e) + 4*(a^2*c*cos(6*f*x + 6*e) - a^2*c*cos(4*f*x + 4*e) - a^2*c*cos(2*f*x + 2*e) - 4*a^2*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*a^2*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^2*c)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 8*(a^2*c*cos(6*f*x + 6*e) - a^2*c*cos(4*f*x + 4*e) - a^2*c*cos(2*f*x + 2*e) + 2*a^2*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a^2*c)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*(a^2*c*cos(6*f*x + 6*e) - a^2*c*cos(4*f*x + 4*e) - a^2*c*cos(2*f*x + 2*e) + a^2*c)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*(a^2*c*sin(4*f*x + 4*e) + a^2*c*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 4*(a^2*c*sin(6*f*x + 6*e) - a^2*c*sin(4*f*x + 4*e) - a^2*c*sin(2*f*x + 2*e) - 4*a^2*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*a^2*c*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))) - 8*(a^2*c*sin(6*f*x + 6*e) - a^2*c*sin(4*f*x + 4*e) - a^2*c*sin(2*f*x + 2*e) + 2*a^2*c*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*c*sin(6*f*x + 6*e) - a^2*c*sin(4*f*x + 4*e) - a^2*c*sin(2*f*x + 2*e))*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)*f)","B",0
130,1,1386,0,1.338048," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(f x + e\right)} \cos\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right)^{2} + 36 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(f x + e\right)} \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 16 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + f x + {\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(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) - 1\right) + 2 \, {\left(f x - 4 \, {\left(f x + e\right)} \cos\left(6 \, f x + 6 \, e\right) + 6 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + e + 2 \, \sin\left(6 \, f x + 6 \, e\right) - 2 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) - 8 \, {\left(f x + 6 \, {\left(f x + e\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + e + \sin\left(4 \, f x + 4 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 4 \, {\left(3 \, f x - 12 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, e + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 8 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(2 \, {\left(f x + e\right)} \sin\left(6 \, f x + 6 \, e\right) - 3 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + \cos\left(6 \, f x + 6 \, e\right) - \cos\left(4 \, f x + 4 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 4 \, {\left(12 \, {\left(f x + e\right)} \sin\left(4 \, f x + 4 \, e\right) - 8 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - 2 \, \cos\left(4 \, f x + 4 \, e\right) - 1\right)} \sin\left(6 \, f x + 6 \, e\right) - 4 \, {\left(12 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(4 \, f x + 4 \, e\right) + e + 4 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a} \sqrt{c}}{{\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,"-((f*x + e)*cos(8*f*x + 8*e)^2 + 16*(f*x + e)*cos(6*f*x + 6*e)^2 + 36*(f*x + e)*cos(4*f*x + 4*e)^2 + 16*(f*x + e)*cos(2*f*x + 2*e)^2 + (f*x + e)*sin(8*f*x + 8*e)^2 + 16*(f*x + e)*sin(6*f*x + 6*e)^2 + 36*(f*x + e)*sin(4*f*x + 4*e)^2 + 16*(f*x + e)*sin(2*f*x + 2*e)^2 + f*x + (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(2*f*x + 2*e), cos(2*f*x + 2*e) - 1) + 2*(f*x - 4*(f*x + e)*cos(6*f*x + 6*e) + 6*(f*x + e)*cos(4*f*x + 4*e) - 4*(f*x + e)*cos(2*f*x + 2*e) + e + 2*sin(6*f*x + 6*e) - 2*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*cos(8*f*x + 8*e) - 8*(f*x + 6*(f*x + e)*cos(4*f*x + 4*e) - 4*(f*x + e)*cos(2*f*x + 2*e) + e + sin(4*f*x + 4*e))*cos(6*f*x + 6*e) + 4*(3*f*x - 12*(f*x + e)*cos(2*f*x + 2*e) + 3*e + 2*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) - 8*(f*x + e)*cos(2*f*x + 2*e) - 4*(2*(f*x + e)*sin(6*f*x + 6*e) - 3*(f*x + e)*sin(4*f*x + 4*e) + 2*(f*x + e)*sin(2*f*x + 2*e) + cos(6*f*x + 6*e) - cos(4*f*x + 4*e) + cos(2*f*x + 2*e))*sin(8*f*x + 8*e) - 4*(12*(f*x + e)*sin(4*f*x + 4*e) - 8*(f*x + e)*sin(2*f*x + 2*e) - 2*cos(4*f*x + 4*e) - 1)*sin(6*f*x + 6*e) - 4*(12*(f*x + e)*sin(2*f*x + 2*e) + 2*cos(2*f*x + 2*e) + 1)*sin(4*f*x + 4*e) + e + 4*sin(2*f*x + 2*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
131,0,0,0,0.000000," ","integrate((1+sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(-c \sec\left(f x + e\right) + c\right)}^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((-c*sec(f*x + e) + c)^n*(sec(f*x + e) + 1)^m, x)","F",0
132,0,0,0,0.000000," ","integrate((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}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*(-c*sec(f*x + e) + c)^n, x)","F",0
133,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{3} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^3*(-c*sec(f*x + e) + c)^n, x)","F",0
134,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^n,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)}^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^2*(-c*sec(f*x + e) + c)^n, x)","F",0
135,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))*(c-c*sec(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)*(-c*sec(f*x + e) + c)^n, x)","F",0
136,0,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(-c \sec\left(f x + e\right) + c\right)}^{n}}{a \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((-c*sec(f*x + e) + c)^n/(a*sec(f*x + e) + a), x)","F",0
137,0,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(-c \sec\left(f x + e\right) + c\right)}^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((-c*sec(f*x + e) + c)^n/(a*sec(f*x + e) + a)^2, x)","F",0
138,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(5/2)*(-c*sec(f*x + e) + c)^n, x)","F",0
139,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(3/2)*(-c*sec(f*x + e) + c)^n, x)","F",0
140,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(1/2)*(c-c*sec(f*x+e))^n,x, algorithm=""maxima"")","\int \sqrt{a \sec\left(f x + e\right) + a} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*(-c*sec(f*x + e) + c)^n, x)","F",0
141,0,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sec\left(f x + e\right) + c\right)}^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-c*sec(f*x + e) + c)^n/sqrt(a*sec(f*x + e) + a), x)","F",0
142,0,0,0,0.000000," ","integrate((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sec\left(f x + e\right) + c\right)}^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-c*sec(f*x + e) + c)^n/(a*sec(f*x + e) + a)^(3/2), x)","F",0
143,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+c*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sec\left(f x + e\right) + a}}{c \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)/(c*sec(f*x + e) + c), x)","F",0
144,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{a \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e) + c)^(3/2)/(a*sec(f*x + e) + a), x)","F",0
145,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sec\left(f x + e\right) + c}}{a \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e) + c)/(a*sec(f*x + e) + a), x)","F",0
146,0,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(f x + e\right) + a\right)} \sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)), x)","F",0
147,-1,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^4*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^3*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^2*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,1,147,0,0.591731," ","integrate((c+d*sec(f*x+e))*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} c \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \sin\left(f x + e\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \cos\left(f x + e\right)\right)}{f}"," ",0,"sqrt(a)*c*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + sin(f*x + e), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + cos(f*x + e))/f","B",0
151,0,0,0,0.000000," ","integrate((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}}{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)/(d*sec(f*x + e) + c), x)","F",0
152,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a \sec\left(f x + e\right) + a}}{{\left(d \sec\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)/(d*sec(f*x + e) + c)^2, x)","F",0
153,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,1,998,0,1.400423," ","integrate((a+a*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\frac{{\left({\left(a \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\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) \sin\left(\frac{1}{2} \, \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) + 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)}, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \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) + \sin\left(\frac{1}{2} \, \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)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\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) \sin\left(\frac{1}{2} \, \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) + 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)}, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \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) + \sin\left(\frac{1}{2} \, \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)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\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) + 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) - {\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) - 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) + 1\right)\right)\right)} \sqrt{a}\right)} c}{2 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} f}"," ",0,"1/2*((a*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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) + 1)) - cos(1/2*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)))), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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))) + sin(1/2*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)))) + 1) - a*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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) + 1)) - cos(1/2*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)))), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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))) + sin(1/2*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)))) - 1) - a*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1) + a*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 1))*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*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))) - (a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - a)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))*sqrt(a))*c/((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*f)","B",0
157,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(3/2)/(d*sec(f*x + e) + c), x)","F",0
158,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,1,1396,0,0.798541," ","integrate((a+a*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(30 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, 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) \sin\left(2 \, f x + 2 \, e\right) - 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 4 \, 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)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, f x + 2 \, e\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 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 4 \, 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)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\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) \sin\left(\frac{1}{2} \, \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) + 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)}, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \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) + \sin\left(\frac{1}{2} \, \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)} + 1\right) - {\left(a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\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) \sin\left(\frac{1}{2} \, \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) + 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)}, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \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) + \sin\left(\frac{1}{2} \, \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)} - 1\right) - {\left(a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} c}{6 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} f}"," ",0,"1/6*(30*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 2*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))*sin(2*f*x + 2*e) - 3*a^2*sin(2*f*x + 2*e) - 4*(3*a^2*cos(2*f*x + 2*e) + 4*a^2)*sin(3/2*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) + 1)) + (12*a^2*sin(2*f*x + 2*e)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*a^2*cos(2*f*x + 2*e) - a^2 + 4*(3*a^2*cos(2*f*x + 2*e) + 4*a^2)*cos(3/2*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) + 1)))*sqrt(a) + 3*((a^2*cos(2*f*x + 2*e)^2 + a^2*sin(2*f*x + 2*e)^2 + 2*a^2*cos(2*f*x + 2*e) + a^2)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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) + 1)) - cos(1/2*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)))), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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))) + sin(1/2*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)))) + 1) - (a^2*cos(2*f*x + 2*e)^2 + a^2*sin(2*f*x + 2*e)^2 + 2*a^2*cos(2*f*x + 2*e) + a^2)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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) + 1)) - cos(1/2*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)))), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(1/2*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))) + sin(1/2*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)))) - 1) - (a^2*cos(2*f*x + 2*e)^2 + a^2*sin(2*f*x + 2*e)^2 + 2*a^2*cos(2*f*x + 2*e) + a^2)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1) + (a^2*cos(2*f*x + 2*e)^2 + a^2*sin(2*f*x + 2*e)^2 + 2*a^2*cos(2*f*x + 2*e) + a^2)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 1))*sqrt(a))*c/((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*f)","B",0
163,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(5/2)/(d*sec(f*x + e) + c), x)","F",0
164,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-2,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),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
167,-2,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),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
168,-2,0,0,0.000000," ","integrate((c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),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
169,0,0,0,0.000000," ","integrate(1/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(f*x + e) + a)*(d*sec(f*x + e) + c)), x)","F",0
170,0,0,0,0.000000," ","integrate(1/(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(f*x + e) + a)*(d*sec(f*x + e) + c)^2), x)","F",0
171,-1,0,0,0.000000," ","integrate(1/(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sec\left(f x + e\right) + c\right)}^{2}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e) + c)^2/(a*sec(f*x + e) + a)^(3/2), x)","F",0
174,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{d \sec\left(f x + e\right) + c}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e) + c)/(a*sec(f*x + e) + a)^(3/2), x)","F",0
175,0,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(f*x + e) + a)^(3/2)*(d*sec(f*x + e) + c)), x)","F",0
176,-1,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{d \sec\left(f x + e\right) + c}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e) + c)/(a*sec(f*x + e) + a)^(5/2), x)","F",0
181,0,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(f*x + e) + a)^(5/2)*(d*sec(f*x + e) + c)), x)","F",0
182,-1,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(f x + e\right) + a} \sqrt{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c), x)","F",0
185,-2,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),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(d-c>0)', see `assume?` for more details)Is d-c zero or nonzero?","F(-2)",0
186,-2,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(3/2),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(d-c>0)', see `assume?` for more details)Is d-c zero or nonzero?","F(-2)",0
187,-2,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),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(d-c>0)', see `assume?` for more details)Is d-c positive, negative or zero?","F(-2)",0
188,0,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)), x)","F",0
189,-2,0,0,0.000000," ","integrate((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
190,-2,0,0,0.000000," ","integrate((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
191,-2,0,0,0.000000," ","integrate((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
192,-2,0,0,0.000000," ","integrate((a+b*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
193,-2,0,0,0.000000," ","integrate((a+b*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
194,-2,0,0,0.000000," ","integrate((a+b*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
195,-2,0,0,0.000000," ","integrate((a+b*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
196,-2,0,0,0.000000," ","integrate((a+b*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
197,-2,0,0,0.000000," ","integrate((a+b*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
198,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))*(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e) + c), x)","F",0
199,0,0,0,0.000000," ","integrate((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}}{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)/(d*sec(f*x + e) + c), x)","F",0
200,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sec\left(f x + e\right) + c\right)}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2)*(d*sec(f*x + e) + c), x)","F",0
201,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2)/(d*sec(f*x + e) + c), x)","F",0
202,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e)),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sec\left(f x + e\right) + c\right)}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(5/2)*(d*sec(f*x + e) + c), x)","F",0
203,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{d \sec\left(f x + e\right) + c}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sec(f*x + e) + c)/sqrt(b*sec(f*x + e) + a), x)","F",0
204,0,0,0,0.000000," ","integrate(1/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e) + c)), x)","F",0
205,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{d \sec\left(f x + e\right) + c}{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e) + c)/(b*sec(f*x + e) + a)^(3/2), x)","F",0
206,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{d \sec\left(f x + e\right) + c}{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e) + c)/(b*sec(f*x + e) + a)^(5/2), x)","F",0
207,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2)*(c+d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right) + a} \sqrt{d \sec\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c), x)","F",0
208,0,0,0,0.000000," ","integrate((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}}{\sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)/sqrt(d*sec(f*x + e) + c), x)","F",0
209,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(f x + e\right) + a}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)/(d*sec(f*x + e) + c)^(3/2), x)","F",0
210,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(f x + e\right) + a}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)/(d*sec(f*x + e) + c)^(5/2), x)","F",0
211,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2)/(d*sec(f*x + e) + c)^(3/2), x)","F",0
212,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2)/(d*sec(f*x + e) + c)^(5/2), x)","F",0
213,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2)/(d*sec(f*x + e) + c)^(7/2), x)","F",0
214,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(5/2)/(d*sec(f*x + e) + c)^(5/2), x)","F",0
215,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(5/2)/(d*sec(f*x + e) + c)^(7/2), x)","F",0
216,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(5/2)/(d*sec(f*x + e) + c)^(9/2), x)","F",0
217,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^(3/2)/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sec(f*x + e) + c)^(3/2)/sqrt(b*sec(f*x + e) + a), x)","F",0
218,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^(1/2)/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sec\left(f x + e\right) + c}}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e) + c)/sqrt(b*sec(f*x + e) + a), x)","F",0
219,0,0,0,0.000000," ","integrate(1/(c+d*sec(f*x+e))^(1/2)/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(f x + e\right) + a} \sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)), x)","F",0
220,0,0,0,0.000000," ","integrate(1/(c+d*sec(f*x+e))^(3/2)/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e) + c)^(3/2)), x)","F",0
221,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{1}{3}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(1/3)/(d*sec(f*x + e) + c)^(1/3), x)","F",0
222,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{1}{3}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(1/3)/(d*sec(f*x + e) + c)^(4/3), x)","F",0
223,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(7/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{1}{3}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(1/3)/(d*sec(f*x + e) + c)^(7/3), x)","F",0
224,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{2}{3}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(2/3)/(d*sec(f*x + e) + c)^(2/3), x)","F",0
225,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(5/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{2}{3}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(2/3)/(d*sec(f*x + e) + c)^(5/3), x)","F",0
226,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(8/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{2}{3}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{8}{3}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(2/3)/(d*sec(f*x + e) + c)^(8/3), x)","F",0
227,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{4}{3}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(4/3)/(d*sec(f*x + e) + c)^(4/3), x)","F",0
228,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(7/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{4}{3}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(4/3)/(d*sec(f*x + e) + c)^(7/3), x)","F",0
229,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(10/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{4}{3}}}{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{10}{3}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(4/3)/(d*sec(f*x + e) + c)^(10/3), x)","F",0
230,0,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n} {\left(a \sec\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(((d*sec(f*x + e))^p*c)^n*(a*sec(f*x + e) + a)^m, x)","F",0
231,-1,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,0,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{2} \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^2*((d*sec(f*x + e))^p*c)^n, x)","F",0
233,0,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)} \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)*((d*sec(f*x + e))^p*c)^n, x)","F",0
234,0,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}}{a \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(((d*sec(f*x + e))^p*c)^n/(a*sec(f*x + e) + a), x)","F",0
235,-1,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,0,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^m,x, algorithm=""maxima"")","\int \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n} {\left(b \sec\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(((d*sec(f*x + e))^p*c)^n*(b*sec(f*x + e) + a)^m, x)","F",0
237,-1,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,0,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{2} \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^2*((d*sec(f*x + e))^p*c)^n, x)","F",0
239,0,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)} \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)*((d*sec(f*x + e))^p*c)^n, x)","F",0
240,0,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}}{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(((d*sec(f*x + e))^p*c)^n/(b*sec(f*x + e) + a), x)","F",0
241,-1,0,0,0.000000," ","integrate((c*(d*sec(f*x+e))^p)^n/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
