1,1,73,0,0.337081," ","integrate((a+b*sec(f*x+e)^2)*sin(f*x+e)^7,x, algorithm=""maxima"")","\frac{5 \, a \cos\left(f x + e\right)^{7} - 7 \, {\left(3 \, a - b\right)} \cos\left(f x + e\right)^{5} + 35 \, {\left(a - b\right)} \cos\left(f x + e\right)^{3} - 35 \, {\left(a - 3 \, b\right)} \cos\left(f x + e\right) + \frac{35 \, b}{\cos\left(f x + e\right)}}{35 \, f}"," ",0,"1/35*(5*a*cos(f*x + e)^7 - 7*(3*a - b)*cos(f*x + e)^5 + 35*(a - b)*cos(f*x + e)^3 - 35*(a - 3*b)*cos(f*x + e) + 35*b/cos(f*x + e))/f","A",0
2,1,58,0,0.333228," ","integrate((a+b*sec(f*x+e)^2)*sin(f*x+e)^5,x, algorithm=""maxima"")","-\frac{3 \, a \cos\left(f x + e\right)^{5} - 5 \, {\left(2 \, a - b\right)} \cos\left(f x + e\right)^{3} + 15 \, {\left(a - 2 \, b\right)} \cos\left(f x + e\right) - \frac{15 \, b}{\cos\left(f x + e\right)}}{15 \, f}"," ",0,"-1/15*(3*a*cos(f*x + e)^5 - 5*(2*a - b)*cos(f*x + e)^3 + 15*(a - 2*b)*cos(f*x + e) - 15*b/cos(f*x + e))/f","A",0
3,1,40,0,0.338621," ","integrate((a+b*sec(f*x+e)^2)*sin(f*x+e)^3,x, algorithm=""maxima"")","\frac{a \cos\left(f x + e\right)^{3} - 3 \, {\left(a - b\right)} \cos\left(f x + e\right) + \frac{3 \, b}{\cos\left(f x + e\right)}}{3 \, f}"," ",0,"1/3*(a*cos(f*x + e)^3 - 3*(a - b)*cos(f*x + e) + 3*b/cos(f*x + e))/f","A",0
4,1,25,0,0.331131," ","integrate((a+b*sec(f*x+e)^2)*sin(f*x+e),x, algorithm=""maxima"")","-\frac{a \cos\left(f x + e\right) - \frac{b}{\cos\left(f x + e\right)}}{f}"," ",0,"-(a*cos(f*x + e) - b/cos(f*x + e))/f","A",0
5,1,44,0,0.334070," ","integrate(csc(f*x+e)*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{{\left(a + b\right)} \log\left(\cos\left(f x + e\right) + 1\right) - {\left(a + b\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, b}{\cos\left(f x + e\right)}}{2 \, f}"," ",0,"-1/2*((a + b)*log(cos(f*x + e) + 1) - (a + b)*log(cos(f*x + e) - 1) - 2*b/cos(f*x + e))/f","A",0
6,1,76,0,0.393310," ","integrate(csc(f*x+e)^3*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{{\left(a + 3 \, b\right)} \log\left(\cos\left(f x + e\right) + 1\right) - {\left(a + 3 \, b\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left({\left(a + 3 \, b\right)} \cos\left(f x + e\right)^{2} - 2 \, b\right)}}{\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)}}{4 \, f}"," ",0,"-1/4*((a + 3*b)*log(cos(f*x + e) + 1) - (a + 3*b)*log(cos(f*x + e) - 1) - 2*((a + 3*b)*cos(f*x + e)^2 - 2*b)/(cos(f*x + e)^3 - cos(f*x + e)))/f","A",0
7,1,101,0,0.330887," ","integrate(csc(f*x+e)^5*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{3 \, {\left(a + 5 \, b\right)} \log\left(\cos\left(f x + e\right) + 1\right) - 3 \, {\left(a + 5 \, b\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(a + 5 \, b\right)} \cos\left(f x + e\right)^{4} - 5 \, {\left(a + 5 \, b\right)} \cos\left(f x + e\right)^{2} + 8 \, b\right)}}{\cos\left(f x + e\right)^{5} - 2 \, \cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)}}{16 \, f}"," ",0,"-1/16*(3*(a + 5*b)*log(cos(f*x + e) + 1) - 3*(a + 5*b)*log(cos(f*x + e) - 1) - 2*(3*(a + 5*b)*cos(f*x + e)^4 - 5*(a + 5*b)*cos(f*x + e)^2 + 8*b)/(cos(f*x + e)^5 - 2*cos(f*x + e)^3 + cos(f*x + e)))/f","A",0
8,1,111,0,0.447018," ","integrate((a+b*sec(f*x+e)^2)*sin(f*x+e)^6,x, algorithm=""maxima"")","\frac{15 \, {\left(f x + e\right)} {\left(a - 6 \, b\right)} + 48 \, b \tan\left(f x + e\right) - \frac{3 \, {\left(11 \, a - 18 \, b\right)} \tan\left(f x + e\right)^{5} + 8 \, {\left(5 \, a - 12 \, b\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(5 \, a - 14 \, b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{6} + 3 \, \tan\left(f x + e\right)^{4} + 3 \, \tan\left(f x + e\right)^{2} + 1}}{48 \, f}"," ",0,"1/48*(15*(f*x + e)*(a - 6*b) + 48*b*tan(f*x + e) - (3*(11*a - 18*b)*tan(f*x + e)^5 + 8*(5*a - 12*b)*tan(f*x + e)^3 + 3*(5*a - 14*b)*tan(f*x + e))/(tan(f*x + e)^6 + 3*tan(f*x + e)^4 + 3*tan(f*x + e)^2 + 1))/f","A",0
9,1,82,0,0.446494," ","integrate((a+b*sec(f*x+e)^2)*sin(f*x+e)^4,x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} {\left(a - 4 \, b\right)} + 8 \, b \tan\left(f x + e\right) - \frac{{\left(5 \, a - 4 \, b\right)} \tan\left(f x + e\right)^{3} + {\left(3 \, a - 4 \, b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{2} + 1}}{8 \, f}"," ",0,"1/8*(3*(f*x + e)*(a - 4*b) + 8*b*tan(f*x + e) - ((5*a - 4*b)*tan(f*x + e)^3 + (3*a - 4*b)*tan(f*x + e))/(tan(f*x + e)^4 + 2*tan(f*x + e)^2 + 1))/f","A",0
10,1,47,0,0.453912," ","integrate((a+b*sec(f*x+e)^2)*sin(f*x+e)^2,x, algorithm=""maxima"")","\frac{{\left(f x + e\right)} {\left(a - 2 \, b\right)} + 2 \, b \tan\left(f x + e\right) - \frac{a \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}}{2 \, f}"," ",0,"1/2*((f*x + e)*(a - 2*b) + 2*b*tan(f*x + e) - a*tan(f*x + e)/(tan(f*x + e)^2 + 1))/f","A",0
11,1,15,0,0.346012," ","integrate(a+b*sec(f*x+e)^2,x, algorithm=""maxima"")","a x + \frac{b \tan\left(f x + e\right)}{f}"," ",0,"a*x + b*tan(f*x + e)/f","A",0
12,1,26,0,0.343981," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{b \tan\left(f x + e\right) - \frac{a + b}{\tan\left(f x + e\right)}}{f}"," ",0,"(b*tan(f*x + e) - (a + b)/tan(f*x + e))/f","A",0
13,1,43,0,0.331139," ","integrate(csc(f*x+e)^4*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, b \tan\left(f x + e\right) - \frac{3 \, {\left(a + 2 \, b\right)} \tan\left(f x + e\right)^{2} + a + b}{\tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(3*b*tan(f*x + e) - (3*(a + 2*b)*tan(f*x + e)^2 + a + b)/tan(f*x + e)^3)/f","A",0
14,1,64,0,0.341701," ","integrate(csc(f*x+e)^6*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{15 \, b \tan\left(f x + e\right) - \frac{15 \, {\left(a + 3 \, b\right)} \tan\left(f x + e\right)^{4} + 5 \, {\left(2 \, a + 3 \, b\right)} \tan\left(f x + e\right)^{2} + 3 \, a + 3 \, b}{\tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"1/15*(15*b*tan(f*x + e) - (15*(a + 3*b)*tan(f*x + e)^4 + 5*(2*a + 3*b)*tan(f*x + e)^2 + 3*a + 3*b)/tan(f*x + e)^5)/f","A",0
15,1,89,0,0.324224," ","integrate((a+b*sec(f*x+e)^2)^2*sin(f*x+e)^5,x, algorithm=""maxima"")","-\frac{3 \, a^{2} \cos\left(f x + e\right)^{5} - 10 \, {\left(a^{2} - a b\right)} \cos\left(f x + e\right)^{3} + 15 \, {\left(a^{2} - 4 \, a b + b^{2}\right)} \cos\left(f x + e\right) - \frac{5 \, {\left(6 \, {\left(a b - b^{2}\right)} \cos\left(f x + e\right)^{2} + b^{2}\right)}}{\cos\left(f x + e\right)^{3}}}{15 \, f}"," ",0,"-1/15*(3*a^2*cos(f*x + e)^5 - 10*(a^2 - a*b)*cos(f*x + e)^3 + 15*(a^2 - 4*a*b + b^2)*cos(f*x + e) - 5*(6*(a*b - b^2)*cos(f*x + e)^2 + b^2)/cos(f*x + e)^3)/f","A",0
16,1,67,0,0.323918," ","integrate((a+b*sec(f*x+e)^2)^2*sin(f*x+e)^3,x, algorithm=""maxima"")","\frac{a^{2} \cos\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b\right)} \cos\left(f x + e\right) + \frac{3 \, {\left(2 \, a b - b^{2}\right)} \cos\left(f x + e\right)^{2} + b^{2}}{\cos\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(a^2*cos(f*x + e)^3 - 3*(a^2 - 2*a*b)*cos(f*x + e) + (3*(2*a*b - b^2)*cos(f*x + e)^2 + b^2)/cos(f*x + e)^3)/f","A",0
17,1,42,0,0.324949," ","integrate((a+b*sec(f*x+e)^2)^2*sin(f*x+e),x, algorithm=""maxima"")","-\frac{3 \, a^{2} \cos\left(f x + e\right) - \frac{6 \, a b}{\cos\left(f x + e\right)} - \frac{b^{2}}{\cos\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*a^2*cos(f*x + e) - 6*a*b/cos(f*x + e) - b^2/cos(f*x + e)^3)/f","A",0
18,1,82,0,0.359020," ","integrate(csc(f*x+e)*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(\cos\left(f x + e\right) + 1\right) - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(2 \, a b + b^{2}\right)} \cos\left(f x + e\right)^{2} + b^{2}\right)}}{\cos\left(f x + e\right)^{3}}}{6 \, f}"," ",0,"-1/6*(3*(a^2 + 2*a*b + b^2)*log(cos(f*x + e) + 1) - 3*(a^2 + 2*a*b + b^2)*log(cos(f*x + e) - 1) - 2*(3*(2*a*b + b^2)*cos(f*x + e)^2 + b^2)/cos(f*x + e)^3)/f","A",0
19,1,126,0,0.328543," ","integrate(csc(f*x+e)^3*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \log\left(\cos\left(f x + e\right) + 1\right) - 3 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(6 \, a b + 5 \, b^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, b^{2}\right)}}{\cos\left(f x + e\right)^{5} - \cos\left(f x + e\right)^{3}}}{12 \, f}"," ",0,"-1/12*(3*(a^2 + 6*a*b + 5*b^2)*log(cos(f*x + e) + 1) - 3*(a^2 + 6*a*b + 5*b^2)*log(cos(f*x + e) - 1) - 2*(3*(a^2 + 6*a*b + 5*b^2)*cos(f*x + e)^4 - 2*(6*a*b + 5*b^2)*cos(f*x + e)^2 - 2*b^2)/(cos(f*x + e)^5 - cos(f*x + e)^3))/f","A",0
20,1,165,0,0.350122," ","integrate(csc(f*x+e)^5*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(3 \, a^{2} + 30 \, a b + 35 \, b^{2}\right)} \log\left(\cos\left(f x + e\right) + 1\right) - 3 \, {\left(3 \, a^{2} + 30 \, a b + 35 \, b^{2}\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(3 \, a^{2} + 30 \, a b + 35 \, b^{2}\right)} \cos\left(f x + e\right)^{6} - 5 \, {\left(3 \, a^{2} + 30 \, a b + 35 \, b^{2}\right)} \cos\left(f x + e\right)^{4} + 8 \, {\left(6 \, a b + 7 \, b^{2}\right)} \cos\left(f x + e\right)^{2} + 8 \, b^{2}\right)}}{\cos\left(f x + e\right)^{7} - 2 \, \cos\left(f x + e\right)^{5} + \cos\left(f x + e\right)^{3}}}{48 \, f}"," ",0,"-1/48*(3*(3*a^2 + 30*a*b + 35*b^2)*log(cos(f*x + e) + 1) - 3*(3*a^2 + 30*a*b + 35*b^2)*log(cos(f*x + e) - 1) - 2*(3*(3*a^2 + 30*a*b + 35*b^2)*cos(f*x + e)^6 - 5*(3*a^2 + 30*a*b + 35*b^2)*cos(f*x + e)^4 + 8*(6*a*b + 7*b^2)*cos(f*x + e)^2 + 8*b^2)/(cos(f*x + e)^7 - 2*cos(f*x + e)^5 + cos(f*x + e)^3))/f","A",0
21,1,164,0,0.445173," ","integrate((a+b*sec(f*x+e)^2)^2*sin(f*x+e)^6,x, algorithm=""maxima"")","\frac{16 \, b^{2} \tan\left(f x + e\right)^{3} + 15 \, {\left(a^{2} - 12 \, a b + 8 \, b^{2}\right)} {\left(f x + e\right)} + 96 \, {\left(a b - b^{2}\right)} \tan\left(f x + e\right) - \frac{3 \, {\left(11 \, a^{2} - 36 \, a b + 8 \, b^{2}\right)} \tan\left(f x + e\right)^{5} + 8 \, {\left(5 \, a^{2} - 24 \, a b + 6 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(5 \, a^{2} - 28 \, a b + 8 \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{6} + 3 \, \tan\left(f x + e\right)^{4} + 3 \, \tan\left(f x + e\right)^{2} + 1}}{48 \, f}"," ",0,"1/48*(16*b^2*tan(f*x + e)^3 + 15*(a^2 - 12*a*b + 8*b^2)*(f*x + e) + 96*(a*b - b^2)*tan(f*x + e) - (3*(11*a^2 - 36*a*b + 8*b^2)*tan(f*x + e)^5 + 8*(5*a^2 - 24*a*b + 6*b^2)*tan(f*x + e)^3 + 3*(5*a^2 - 28*a*b + 8*b^2)*tan(f*x + e))/(tan(f*x + e)^6 + 3*tan(f*x + e)^4 + 3*tan(f*x + e)^2 + 1))/f","A",0
22,1,120,0,0.450611," ","integrate((a+b*sec(f*x+e)^2)^2*sin(f*x+e)^4,x, algorithm=""maxima"")","\frac{8 \, b^{2} \tan\left(f x + e\right)^{3} + 3 \, {\left(3 \, a^{2} - 24 \, a b + 8 \, b^{2}\right)} {\left(f x + e\right)} + 24 \, {\left(2 \, a b - b^{2}\right)} \tan\left(f x + e\right) - \frac{3 \, {\left({\left(5 \, a^{2} - 8 \, a b\right)} \tan\left(f x + e\right)^{3} + {\left(3 \, a^{2} - 8 \, a b\right)} \tan\left(f x + e\right)\right)}}{\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{2} + 1}}{24 \, f}"," ",0,"1/24*(8*b^2*tan(f*x + e)^3 + 3*(3*a^2 - 24*a*b + 8*b^2)*(f*x + e) + 24*(2*a*b - b^2)*tan(f*x + e) - 3*((5*a^2 - 8*a*b)*tan(f*x + e)^3 + (3*a^2 - 8*a*b)*tan(f*x + e))/(tan(f*x + e)^4 + 2*tan(f*x + e)^2 + 1))/f","A",0
23,1,67,0,0.435159," ","integrate((a+b*sec(f*x+e)^2)^2*sin(f*x+e)^2,x, algorithm=""maxima"")","\frac{2 \, b^{2} \tan\left(f x + e\right)^{3} + 12 \, a b \tan\left(f x + e\right) + 3 \, {\left(a^{2} - 4 \, a b\right)} {\left(f x + e\right)} - \frac{3 \, a^{2} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}}{6 \, f}"," ",0,"1/6*(2*b^2*tan(f*x + e)^3 + 12*a*b*tan(f*x + e) + 3*(a^2 - 4*a*b)*(f*x + e) - 3*a^2*tan(f*x + e)/(tan(f*x + e)^2 + 1))/f","A",0
24,1,44,0,0.341764," ","integrate((a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} b^{2}}{3 \, f} + \frac{2 \, a b \tan\left(f x + e\right)}{f}"," ",0,"a^2*x + 1/3*(tan(f*x + e)^3 + 3*tan(f*x + e))*b^2/f + 2*a*b*tan(f*x + e)/f","A",0
25,1,54,0,0.355605," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{b^{2} \tan\left(f x + e\right)^{3} + 6 \, {\left(a b + b^{2}\right)} \tan\left(f x + e\right) - \frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}}{\tan\left(f x + e\right)}}{3 \, f}"," ",0,"1/3*(b^2*tan(f*x + e)^3 + 6*(a*b + b^2)*tan(f*x + e) - 3*(a^2 + 2*a*b + b^2)/tan(f*x + e))/f","A",0
26,1,80,0,0.341630," ","integrate(csc(f*x+e)^4*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{b^{2} \tan\left(f x + e\right)^{3} + 3 \, {\left(2 \, a b + 3 \, b^{2}\right)} \tan\left(f x + e\right) - \frac{3 \, {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + 2 \, a b + b^{2}}{\tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(b^2*tan(f*x + e)^3 + 3*(2*a*b + 3*b^2)*tan(f*x + e) - (3*(a^2 + 4*a*b + 3*b^2)*tan(f*x + e)^2 + a^2 + 2*a*b + b^2)/tan(f*x + e)^3)/f","A",0
27,1,107,0,0.337419," ","integrate(csc(f*x+e)^6*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{5 \, b^{2} \tan\left(f x + e\right)^{3} + 30 \, {\left(a b + 2 \, b^{2}\right)} \tan\left(f x + e\right) - \frac{15 \, {\left(a^{2} + 6 \, a b + 6 \, b^{2}\right)} \tan\left(f x + e\right)^{4} + 10 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \tan\left(f x + e\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}}{\tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"1/15*(5*b^2*tan(f*x + e)^3 + 30*(a*b + 2*b^2)*tan(f*x + e) - (15*(a^2 + 6*a*b + 6*b^2)*tan(f*x + e)^4 + 10*(a^2 + 3*a*b + 2*b^2)*tan(f*x + e)^2 + 3*a^2 + 6*a*b + 3*b^2)/tan(f*x + e)^5)/f","A",0
28,1,102,0,0.430213," ","integrate(sin(f*x+e)^5/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} - \frac{3 \, a^{2} \cos\left(f x + e\right)^{5} - 5 \, {\left(2 \, a^{2} + a b\right)} \cos\left(f x + e\right)^{3} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cos\left(f x + e\right)}{a^{3}}}{15 \, f}"," ",0,"1/15*(15*(a^2*b + 2*a*b^2 + b^3)*arctan(a*cos(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^3) - (3*a^2*cos(f*x + e)^5 - 5*(2*a^2 + a*b)*cos(f*x + e)^3 + 15*(a^2 + 2*a*b + b^2)*cos(f*x + e))/a^3)/f","A",0
29,1,63,0,0.437663," ","integrate(sin(f*x+e)^3/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a b + b^{2}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{a \cos\left(f x + e\right)^{3} - 3 \, {\left(a + b\right)} \cos\left(f x + e\right)}{a^{2}}}{3 \, f}"," ",0,"1/3*(3*(a*b + b^2)*arctan(a*cos(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^2) + (a*cos(f*x + e)^3 - 3*(a + b)*cos(f*x + e))/a^2)/f","A",0
30,1,40,0,0.422484," ","integrate(sin(f*x+e)/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{b \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{\cos\left(f x + e\right)}{a}}{f}"," ",0,"(b*arctan(a*cos(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a) - cos(f*x + e)/a)/f","A",0
31,1,64,0,0.442755," ","integrate(csc(f*x+e)/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{2 \, b \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(a + b\right)}} - \frac{\log\left(\cos\left(f x + e\right) + 1\right)}{a + b} + \frac{\log\left(\cos\left(f x + e\right) - 1\right)}{a + b}}{2 \, f}"," ",0,"1/2*(2*b*arctan(a*cos(f*x + e)/sqrt(a*b))/(sqrt(a*b)*(a + b)) - log(cos(f*x + e) + 1)/(a + b) + log(cos(f*x + e) - 1)/(a + b))/f","A",0
32,1,128,0,0.448382," ","integrate(csc(f*x+e)^3/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{4 \, a b \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b}} - \frac{{\left(a - b\right)} \log\left(\cos\left(f x + e\right) + 1\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{{\left(a - b\right)} \log\left(\cos\left(f x + e\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, \cos\left(f x + e\right)}{{\left(a + b\right)} \cos\left(f x + e\right)^{2} - a - b}}{4 \, f}"," ",0,"1/4*(4*a*b*arctan(a*cos(f*x + e)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)) - (a - b)*log(cos(f*x + e) + 1)/(a^2 + 2*a*b + b^2) + (a - b)*log(cos(f*x + e) - 1)/(a^2 + 2*a*b + b^2) + 2*cos(f*x + e)/((a + b)*cos(f*x + e)^2 - a - b))/f","A",0
33,1,231,0,0.457983," ","integrate(csc(f*x+e)^5/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{16 \, a^{2} b \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a b}} - \frac{{\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \log\left(\cos\left(f x + e\right) + 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{{\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \log\left(\cos\left(f x + e\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left({\left(3 \, a - b\right)} \cos\left(f x + e\right)^{3} - {\left(5 \, a + b\right)} \cos\left(f x + e\right)\right)}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cos\left(f x + e\right)^{2} + a^{2} + 2 \, a b + b^{2}}}{16 \, f}"," ",0,"1/16*(16*a^2*b*arctan(a*cos(f*x + e)/sqrt(a*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a*b)) - (3*a^2 - 6*a*b - b^2)*log(cos(f*x + e) + 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + (3*a^2 - 6*a*b - b^2)*log(cos(f*x + e) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*((3*a - b)*cos(f*x + e)^3 - (5*a + b)*cos(f*x + e))/((a^2 + 2*a*b + b^2)*cos(f*x + e)^4 - 2*(a^2 + 2*a*b + b^2)*cos(f*x + e)^2 + a^2 + 2*a*b + b^2))/f","B",0
34,1,209,0,0.426037," ","integrate(sin(f*x+e)^6/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(11 \, a^{2} + 18 \, a b + 8 \, b^{2}\right)} \tan\left(f x + e\right)^{5} + 8 \, {\left(5 \, a^{2} + 12 \, a b + 6 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(5 \, a^{2} + 14 \, a b + 8 \, b^{2}\right)} \tan\left(f x + e\right)}{a^{3} \tan\left(f x + e\right)^{6} + 3 \, a^{3} \tan\left(f x + e\right)^{4} + 3 \, a^{3} \tan\left(f x + e\right)^{2} + a^{3}} - \frac{3 \, {\left(5 \, a^{3} + 30 \, a^{2} b + 40 \, a b^{2} + 16 \, b^{3}\right)} {\left(f x + e\right)}}{a^{4}} + \frac{48 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{4}}}{48 \, f}"," ",0,"-1/48*((3*(11*a^2 + 18*a*b + 8*b^2)*tan(f*x + e)^5 + 8*(5*a^2 + 12*a*b + 6*b^2)*tan(f*x + e)^3 + 3*(5*a^2 + 14*a*b + 8*b^2)*tan(f*x + e))/(a^3*tan(f*x + e)^6 + 3*a^3*tan(f*x + e)^4 + 3*a^3*tan(f*x + e)^2 + a^3) - 3*(5*a^3 + 30*a^2*b + 40*a*b^2 + 16*b^3)*(f*x + e)/a^4 + 48*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^4))/f","A",0
35,1,137,0,0.443930," ","integrate(sin(f*x+e)^4/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{{\left(5 \, a + 4 \, b\right)} \tan\left(f x + e\right)^{3} + {\left(3 \, a + 4 \, b\right)} \tan\left(f x + e\right)}{a^{2} \tan\left(f x + e\right)^{4} + 2 \, a^{2} \tan\left(f x + e\right)^{2} + a^{2}} - \frac{{\left(3 \, a^{2} + 12 \, a b + 8 \, b^{2}\right)} {\left(f x + e\right)}}{a^{3}} + \frac{8 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{3}}}{8 \, f}"," ",0,"-1/8*(((5*a + 4*b)*tan(f*x + e)^3 + (3*a + 4*b)*tan(f*x + e))/(a^2*tan(f*x + e)^4 + 2*a^2*tan(f*x + e)^2 + a^2) - (3*a^2 + 12*a*b + 8*b^2)*(f*x + e)/a^3 + 8*(a^2*b + 2*a*b^2 + b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^3))/f","A",0
36,1,77,0,0.448361," ","integrate(sin(f*x+e)^2/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{{\left(f x + e\right)} {\left(a + 2 \, b\right)}}{a^{2}} - \frac{\tan\left(f x + e\right)}{a \tan\left(f x + e\right)^{2} + a} - \frac{2 \, {\left(a b + b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{2}}}{2 \, f}"," ",0,"1/2*((f*x + e)*(a + 2*b)/a^2 - tan(f*x + e)/(a*tan(f*x + e)^2 + a) - 2*(a*b + b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^2))/f","A",0
37,1,44,0,0.448298," ","integrate(1/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a} - \frac{f x + e}{a}}{f}"," ",0,"-(b*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a) - (f*x + e)/a)/f","A",0
38,1,50,0,0.436538," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} {\left(a + b\right)}} + \frac{1}{{\left(a + b\right)} \tan\left(f x + e\right)}}{f}"," ",0,"-(b*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*(a + b)) + 1/((a + b)*tan(f*x + e)))/f","A",0
39,1,82,0,0.424554," ","integrate(csc(f*x+e)^4/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{3 \, a b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{3 \, a \tan\left(f x + e\right)^{2} + a + b}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*a*b*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)) + (3*a*tan(f*x + e)^2 + a + b)/((a^2 + 2*a*b + b^2)*tan(f*x + e)^3))/f","A",0
40,1,137,0,0.438673," ","integrate(csc(f*x+e)^6/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{15 \, a^{2} b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{15 \, a^{2} \tan\left(f x + e\right)^{4} + 5 \, {\left(2 \, a^{2} + 3 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(15*a^2*b*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*b)) + (15*a^2*tan(f*x + e)^4 + 5*(2*a^2 + 3*a*b + b^2)*tan(f*x + e)^2 + 3*a^2 + 6*a*b + 3*b^2)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*tan(f*x + e)^5))/f","A",0
41,1,148,0,0.530931," ","integrate(sin(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cos\left(f x + e\right)}{a^{5} \cos\left(f x + e\right)^{2} + a^{4} b} - \frac{15 \, {\left(3 \, a^{2} b + 10 \, a b^{2} + 7 \, b^{3}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}} + \frac{2 \, {\left(3 \, a^{2} \cos\left(f x + e\right)^{5} - 10 \, {\left(a^{2} + a b\right)} \cos\left(f x + e\right)^{3} + 15 \, {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cos\left(f x + e\right)\right)}}{a^{4}}}{30 \, f}"," ",0,"-1/30*(15*(a^2*b + 2*a*b^2 + b^3)*cos(f*x + e)/(a^5*cos(f*x + e)^2 + a^4*b) - 15*(3*a^2*b + 10*a*b^2 + 7*b^3)*arctan(a*cos(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^4) + 2*(3*a^2*cos(f*x + e)^5 - 10*(a^2 + a*b)*cos(f*x + e)^3 + 15*(a^2 + 4*a*b + 3*b^2)*cos(f*x + e))/a^4)/f","A",0
42,1,104,0,0.428351," ","integrate(sin(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a b + b^{2}\right)} \cos\left(f x + e\right)}{a^{4} \cos\left(f x + e\right)^{2} + a^{3} b} - \frac{3 \, {\left(3 \, a b + 5 \, b^{2}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} - \frac{2 \, {\left(a \cos\left(f x + e\right)^{3} - 3 \, {\left(a + 2 \, b\right)} \cos\left(f x + e\right)\right)}}{a^{3}}}{6 \, f}"," ",0,"-1/6*(3*(a*b + b^2)*cos(f*x + e)/(a^4*cos(f*x + e)^2 + a^3*b) - 3*(3*a*b + 5*b^2)*arctan(a*cos(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^3) - 2*(a*cos(f*x + e)^3 - 3*(a + 2*b)*cos(f*x + e))/a^3)/f","A",0
43,1,70,0,0.445354," ","integrate(sin(f*x+e)/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{b \cos\left(f x + e\right)}{a^{3} \cos\left(f x + e\right)^{2} + a^{2} b} - \frac{3 \, b \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{2 \, \cos\left(f x + e\right)}{a^{2}}}{2 \, f}"," ",0,"-1/2*(b*cos(f*x + e)/(a^3*cos(f*x + e)^2 + a^2*b) - 3*b*arctan(a*cos(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^2) + 2*cos(f*x + e)/a^2)/f","A",0
44,1,138,0,0.428839," ","integrate(csc(f*x+e)/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{b \cos\left(f x + e\right)}{a^{2} b + a b^{2} + {\left(a^{3} + a^{2} b\right)} \cos\left(f x + e\right)^{2}} - \frac{{\left(3 \, a b + b^{2}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b}} + \frac{\log\left(\cos\left(f x + e\right) + 1\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{\log\left(\cos\left(f x + e\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}}}{2 \, f}"," ",0,"-1/2*(b*cos(f*x + e)/(a^2*b + a*b^2 + (a^3 + a^2*b)*cos(f*x + e)^2) - (3*a*b + b^2)*arctan(a*cos(f*x + e)/sqrt(a*b))/((a^3 + 2*a^2*b + a*b^2)*sqrt(a*b)) + log(cos(f*x + e) + 1)/(a^2 + 2*a*b + b^2) - log(cos(f*x + e) - 1)/(a^2 + 2*a*b + b^2))/f","A",0
45,1,231,0,0.445985," ","integrate(csc(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{{\left(a - 3 \, b\right)} \log\left(\cos\left(f x + e\right) + 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{{\left(a - 3 \, b\right)} \log\left(\cos\left(f x + e\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left(3 \, a b - b^{2}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a b}} - \frac{2 \, {\left({\left(a - b\right)} \cos\left(f x + e\right)^{3} + 2 \, b \cos\left(f x + e\right)\right)}}{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cos\left(f x + e\right)^{4} - a^{2} b - 2 \, a b^{2} - b^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cos\left(f x + e\right)^{2}}}{4 \, f}"," ",0,"-1/4*((a - 3*b)*log(cos(f*x + e) + 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (a - 3*b)*log(cos(f*x + e) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*(3*a*b - b^2)*arctan(a*cos(f*x + e)/sqrt(a*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a*b)) - 2*((a - b)*cos(f*x + e)^3 + 2*b*cos(f*x + e))/((a^3 + 2*a^2*b + a*b^2)*cos(f*x + e)^4 - a^2*b - 2*a*b^2 - b^3 - (a^3 + a^2*b - a*b^2 - b^3)*cos(f*x + e)^2))/f","A",0
46,1,369,0,0.433943," ","integrate(csc(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a^{2} - 6 \, a b + b^{2}\right)} \log\left(\cos\left(f x + e\right) + 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{3 \, {\left(a^{2} - 6 \, a b + b^{2}\right)} \log\left(\cos\left(f x + e\right) - 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{24 \, {\left(a^{2} b - a b^{2}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{a b}} - \frac{2 \, {\left(3 \, {\left(a^{2} - 3 \, a b\right)} \cos\left(f x + e\right)^{5} - {\left(5 \, a^{2} - 14 \, a b + 5 \, b^{2}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(3 \, a b - b^{2}\right)} \cos\left(f x + e\right)\right)}}{{\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cos\left(f x + e\right)^{6} - {\left(2 \, a^{4} + 5 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cos\left(f x + e\right)^{4} + a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4} + {\left(a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)} \cos\left(f x + e\right)^{2}}}{16 \, f}"," ",0,"-1/16*(3*(a^2 - 6*a*b + b^2)*log(cos(f*x + e) + 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 3*(a^2 - 6*a*b + b^2)*log(cos(f*x + e) - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 24*(a^2*b - a*b^2)*arctan(a*cos(f*x + e)/sqrt(a*b))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt(a*b)) - 2*(3*(a^2 - 3*a*b)*cos(f*x + e)^5 - (5*a^2 - 14*a*b + 5*b^2)*cos(f*x + e)^3 - 3*(3*a*b - b^2)*cos(f*x + e))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cos(f*x + e)^6 - (2*a^4 + 5*a^3*b + 3*a^2*b^2 - a*b^3 - b^4)*cos(f*x + e)^4 + a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4 + (a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4)*cos(f*x + e)^2))/f","B",0
47,1,302,0,0.460881," ","integrate(sin(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(19 \, a^{2} b + 52 \, a b^{2} + 32 \, b^{3}\right)} \tan\left(f x + e\right)^{7} + {\left(33 \, a^{3} + 253 \, a^{2} b + 516 \, a b^{2} + 288 \, b^{3}\right)} \tan\left(f x + e\right)^{5} + {\left(40 \, a^{3} + 319 \, a^{2} b + 564 \, a b^{2} + 288 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(5 \, a^{3} + 41 \, a^{2} b + 68 \, a b^{2} + 32 \, b^{3}\right)} \tan\left(f x + e\right)}{a^{4} b \tan\left(f x + e\right)^{8} + {\left(a^{5} + 4 \, a^{4} b\right)} \tan\left(f x + e\right)^{6} + a^{5} + a^{4} b + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \tan\left(f x + e\right)^{4} + {\left(3 \, a^{5} + 4 \, a^{4} b\right)} \tan\left(f x + e\right)^{2}} - \frac{3 \, {\left(5 \, a^{3} + 60 \, a^{2} b + 120 \, a b^{2} + 64 \, b^{3}\right)} {\left(f x + e\right)}}{a^{5}} + \frac{24 \, {\left(3 \, a^{3} b + 14 \, a^{2} b^{2} + 19 \, a b^{3} + 8 \, b^{4}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{5}}}{48 \, f}"," ",0,"-1/48*((3*(19*a^2*b + 52*a*b^2 + 32*b^3)*tan(f*x + e)^7 + (33*a^3 + 253*a^2*b + 516*a*b^2 + 288*b^3)*tan(f*x + e)^5 + (40*a^3 + 319*a^2*b + 564*a*b^2 + 288*b^3)*tan(f*x + e)^3 + 3*(5*a^3 + 41*a^2*b + 68*a*b^2 + 32*b^3)*tan(f*x + e))/(a^4*b*tan(f*x + e)^8 + (a^5 + 4*a^4*b)*tan(f*x + e)^6 + a^5 + a^4*b + 3*(a^5 + 2*a^4*b)*tan(f*x + e)^4 + (3*a^5 + 4*a^4*b)*tan(f*x + e)^2) - 3*(5*a^3 + 60*a^2*b + 120*a*b^2 + 64*b^3)*(f*x + e)/a^5 + 24*(3*a^3*b + 14*a^2*b^2 + 19*a*b^3 + 8*b^4)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^5))/f","A",0
48,1,205,0,0.482769," ","integrate(sin(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(3 \, a b + 4 \, b^{2}\right)} \tan\left(f x + e\right)^{5} + {\left(5 \, a^{2} + 24 \, a b + 24 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \tan\left(f x + e\right)}{a^{3} b \tan\left(f x + e\right)^{6} + {\left(a^{4} + 3 \, a^{3} b\right)} \tan\left(f x + e\right)^{4} + a^{4} + a^{3} b + {\left(2 \, a^{4} + 3 \, a^{3} b\right)} \tan\left(f x + e\right)^{2}} - \frac{3 \, {\left(a^{2} + 8 \, a b + 8 \, b^{2}\right)} {\left(f x + e\right)}}{a^{4}} + \frac{12 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{4}}}{8 \, f}"," ",0,"-1/8*((3*(3*a*b + 4*b^2)*tan(f*x + e)^5 + (5*a^2 + 24*a*b + 24*b^2)*tan(f*x + e)^3 + 3*(a^2 + 5*a*b + 4*b^2)*tan(f*x + e))/(a^3*b*tan(f*x + e)^6 + (a^4 + 3*a^3*b)*tan(f*x + e)^4 + a^4 + a^3*b + (2*a^4 + 3*a^3*b)*tan(f*x + e)^2) - 3*(a^2 + 8*a*b + 8*b^2)*(f*x + e)/a^4 + 12*(a^2*b + 3*a*b^2 + 2*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^4))/f","A",0
49,1,126,0,0.600132," ","integrate(sin(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, b \tan\left(f x + e\right)^{3} + {\left(a + 2 \, b\right)} \tan\left(f x + e\right)}{a^{2} b \tan\left(f x + e\right)^{4} + a^{3} + a^{2} b + {\left(a^{3} + 2 \, a^{2} b\right)} \tan\left(f x + e\right)^{2}} - \frac{{\left(f x + e\right)} {\left(a + 4 \, b\right)}}{a^{3}} + \frac{{\left(3 \, a b + 4 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{3}}}{2 \, f}"," ",0,"-1/2*((2*b*tan(f*x + e)^3 + (a + 2*b)*tan(f*x + e))/(a^2*b*tan(f*x + e)^4 + a^3 + a^2*b + (a^3 + 2*a^2*b)*tan(f*x + e)^2) - (f*x + e)*(a + 4*b)/a^3 + (3*a*b + 4*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^3))/f","A",0
50,1,106,0,0.478096," ","integrate(1/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{b \tan\left(f x + e\right)}{a^{3} + 2 \, a^{2} b + a b^{2} + {\left(a^{2} b + a b^{2}\right)} \tan\left(f x + e\right)^{2}} + \frac{{\left(3 \, a b + 2 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b}} - \frac{2 \, {\left(f x + e\right)}}{a^{2}}}{2 \, f}"," ",0,"-1/2*(b*tan(f*x + e)/(a^3 + 2*a^2*b + a*b^2 + (a^2*b + a*b^2)*tan(f*x + e)^2) + (3*a*b + 2*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^3 + a^2*b)*sqrt((a + b)*b)) - 2*(f*x + e)/a^2)/f","A",0
51,1,117,0,0.466573," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{3 \, b \tan\left(f x + e\right)^{2} + 2 \, a + 2 \, b}{{\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"-1/2*(3*b*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)) + (3*b*tan(f*x + e)^2 + 2*a + 2*b)/((a^2*b + 2*a*b^2 + b^3)*tan(f*x + e)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*tan(f*x + e)))/f","A",0
52,1,193,0,0.545716," ","integrate(csc(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(3 \, a b - 2 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{3 \, {\left(3 \, a b - 2 \, b^{2}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \tan\left(f x + e\right)^{2} + 2 \, a^{2} + 4 \, a b + 2 \, b^{2}}{{\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \tan\left(f x + e\right)^{5} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \tan\left(f x + e\right)^{3}}}{6 \, f}"," ",0,"-1/6*(3*(3*a*b - 2*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*b)) + (3*(3*a*b - 2*b^2)*tan(f*x + e)^4 + 2*(3*a^2 + a*b - 2*b^2)*tan(f*x + e)^2 + 2*a^2 + 4*a*b + 2*b^2)/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*tan(f*x + e)^5 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*tan(f*x + e)^3))/f","A",0
53,1,268,0,0.443393," ","integrate(csc(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(3 \, a^{2} b - 4 \, a b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{15 \, {\left(3 \, a^{2} b - 4 \, a b^{2}\right)} \tan\left(f x + e\right)^{6} + 10 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \tan\left(f x + e\right)^{4} + 6 \, a^{3} + 18 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} + 2 \, {\left(10 \, a^{3} + 23 \, a^{2} b + 16 \, a b^{2} + 3 \, b^{3}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{4} b + 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 4 \, a b^{4} + b^{5}\right)} \tan\left(f x + e\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \tan\left(f x + e\right)^{5}}}{30 \, f}"," ",0,"-1/30*(15*(3*a^2*b - 4*a*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt((a + b)*b)) + (15*(3*a^2*b - 4*a*b^2)*tan(f*x + e)^6 + 10*(3*a^3 - a^2*b - 4*a*b^2)*tan(f*x + e)^4 + 6*a^3 + 18*a^2*b + 18*a*b^2 + 6*b^3 + 2*(10*a^3 + 23*a^2*b + 16*a*b^2 + 3*b^3)*tan(f*x + e)^2)/((a^4*b + 4*a^3*b^2 + 6*a^2*b^3 + 4*a*b^4 + b^5)*tan(f*x + e)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*tan(f*x + e)^5))/f","A",0
54,1,204,0,0.432907," ","integrate(sin(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left({\left(9 \, a^{3} b + 26 \, a^{2} b^{2} + 17 \, a b^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(7 \, a^{2} b^{2} + 22 \, a b^{3} + 15 \, b^{4}\right)} \cos\left(f x + e\right)\right)}}{a^{7} \cos\left(f x + e\right)^{4} + 2 \, a^{6} b \cos\left(f x + e\right)^{2} + a^{5} b^{2}} - \frac{15 \, {\left(15 \, a^{2} b + 70 \, a b^{2} + 63 \, b^{3}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{5}} + \frac{8 \, {\left(3 \, a^{2} \cos\left(f x + e\right)^{5} - 5 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cos\left(f x + e\right)^{3} + 15 \, {\left(a^{2} + 6 \, a b + 6 \, b^{2}\right)} \cos\left(f x + e\right)\right)}}{a^{5}}}{120 \, f}"," ",0,"-1/120*(15*((9*a^3*b + 26*a^2*b^2 + 17*a*b^3)*cos(f*x + e)^3 + (7*a^2*b^2 + 22*a*b^3 + 15*b^4)*cos(f*x + e))/(a^7*cos(f*x + e)^4 + 2*a^6*b*cos(f*x + e)^2 + a^5*b^2) - 15*(15*a^2*b + 70*a*b^2 + 63*b^3)*arctan(a*cos(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^5) + 8*(3*a^2*cos(f*x + e)^5 - 5*(2*a^2 + 3*a*b)*cos(f*x + e)^3 + 15*(a^2 + 6*a*b + 6*b^2)*cos(f*x + e))/a^5)/f","A",0
55,1,149,0,0.445126," ","integrate(sin(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left({\left(9 \, a^{2} b + 13 \, a b^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(7 \, a b^{2} + 11 \, b^{3}\right)} \cos\left(f x + e\right)\right)}}{a^{6} \cos\left(f x + e\right)^{4} + 2 \, a^{5} b \cos\left(f x + e\right)^{2} + a^{4} b^{2}} - \frac{15 \, {\left(3 \, a b + 7 \, b^{2}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}} - \frac{8 \, {\left(a \cos\left(f x + e\right)^{3} - 3 \, {\left(a + 3 \, b\right)} \cos\left(f x + e\right)\right)}}{a^{4}}}{24 \, f}"," ",0,"-1/24*(3*((9*a^2*b + 13*a*b^2)*cos(f*x + e)^3 + (7*a*b^2 + 11*b^3)*cos(f*x + e))/(a^6*cos(f*x + e)^4 + 2*a^5*b*cos(f*x + e)^2 + a^4*b^2) - 15*(3*a*b + 7*b^2)*arctan(a*cos(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^4) - 8*(a*cos(f*x + e)^3 - 3*(a + 3*b)*cos(f*x + e))/a^4)/f","A",0
56,1,103,0,0.451426," ","integrate(sin(f*x+e)/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{9 \, a b \cos\left(f x + e\right)^{3} + 7 \, b^{2} \cos\left(f x + e\right)}{a^{5} \cos\left(f x + e\right)^{4} + 2 \, a^{4} b \cos\left(f x + e\right)^{2} + a^{3} b^{2}} - \frac{15 \, b \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} + \frac{8 \, \cos\left(f x + e\right)}{a^{3}}}{8 \, f}"," ",0,"-1/8*((9*a*b*cos(f*x + e)^3 + 7*b^2*cos(f*x + e))/(a^5*cos(f*x + e)^4 + 2*a^4*b*cos(f*x + e)^2 + a^3*b^2) - 15*b*arctan(a*cos(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^3) + 8*cos(f*x + e)/a^3)/f","A",0
57,1,261,0,0.432916," ","integrate(csc(f*x+e)/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(15 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{a b}} - \frac{{\left(9 \, a^{2} b + 5 \, a b^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(7 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(f x + e\right)}{a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \cos\left(f x + e\right)^{4} + 2 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cos\left(f x + e\right)^{2}} - \frac{4 \, \log\left(\cos\left(f x + e\right) + 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{4 \, \log\left(\cos\left(f x + e\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}}{8 \, f}"," ",0,"1/8*((15*a^2*b + 10*a*b^2 + 3*b^3)*arctan(a*cos(f*x + e)/sqrt(a*b))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sqrt(a*b)) - ((9*a^2*b + 5*a*b^2)*cos(f*x + e)^3 + (7*a*b^2 + 3*b^3)*cos(f*x + e))/(a^4*b^2 + 2*a^3*b^3 + a^2*b^4 + (a^6 + 2*a^5*b + a^4*b^2)*cos(f*x + e)^4 + 2*(a^5*b + 2*a^4*b^2 + a^3*b^3)*cos(f*x + e)^2) - 4*log(cos(f*x + e) + 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 4*log(cos(f*x + e) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))/f","A",0
58,1,399,0,0.437319," ","integrate(csc(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a - 5 \, b\right)} \log\left(\cos\left(f x + e\right) + 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{2 \, {\left(a - 5 \, b\right)} \log\left(\cos\left(f x + e\right) - 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{{\left(15 \, a^{2} b - 10 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \sqrt{a b}} - \frac{{\left(4 \, a^{3} - 9 \, a^{2} b - a b^{2}\right)} \cos\left(f x + e\right)^{5} + {\left(17 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(11 \, a b^{2} - b^{3}\right)} \cos\left(f x + e\right)}{{\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cos\left(f x + e\right)^{6} - a^{4} b^{2} - 3 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5} - {\left(a^{6} + a^{5} b - 3 \, a^{4} b^{2} - 5 \, a^{3} b^{3} - 2 \, a^{2} b^{4}\right)} \cos\left(f x + e\right)^{4} - {\left(2 \, a^{5} b + 5 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4} - a b^{5}\right)} \cos\left(f x + e\right)^{2}}}{8 \, f}"," ",0,"-1/8*(2*(a - 5*b)*log(cos(f*x + e) + 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 2*(a - 5*b)*log(cos(f*x + e) - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - (15*a^2*b - 10*a*b^2 - b^3)*arctan(a*cos(f*x + e)/sqrt(a*b))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*sqrt(a*b)) - ((4*a^3 - 9*a^2*b - a*b^2)*cos(f*x + e)^5 + (17*a^2*b - 6*a*b^2 + b^3)*cos(f*x + e)^3 + (11*a*b^2 - b^3)*cos(f*x + e))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cos(f*x + e)^6 - a^4*b^2 - 3*a^3*b^3 - 3*a^2*b^4 - a*b^5 - (a^6 + a^5*b - 3*a^4*b^2 - 5*a^3*b^3 - 2*a^2*b^4)*cos(f*x + e)^4 - (2*a^5*b + 5*a^4*b^2 + 3*a^3*b^3 - a^2*b^4 - a*b^5)*cos(f*x + e)^2))/f","B",0
59,1,528,0,0.443311," ","integrate(csc(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a^{2} - 10 \, a b + 5 \, b^{2}\right)} \log\left(\cos\left(f x + e\right) + 1\right)}{a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}} - \frac{3 \, {\left(a^{2} - 10 \, a b + 5 \, b^{2}\right)} \log\left(\cos\left(f x + e\right) - 1\right)}{a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}} - \frac{6 \, {\left(5 \, a^{2} b - 10 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{a \cos\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sqrt{a b}} - \frac{2 \, {\left(3 \, {\left(a^{3} - 6 \, a^{2} b + a b^{2}\right)} \cos\left(f x + e\right)^{7} - {\left(5 \, a^{3} - 31 \, a^{2} b + 31 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(f x + e\right)^{5} - {\left(19 \, a^{2} b - 34 \, a b^{2} + 19 \, b^{3}\right)} \cos\left(f x + e\right)^{3} - 12 \, {\left(a b^{2} - b^{3}\right)} \cos\left(f x + e\right)\right)}}{{\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(f x + e\right)^{8} - 2 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cos\left(f x + e\right)^{6} + a^{4} b^{2} + 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 4 \, a b^{5} + b^{6} + {\left(a^{6} - 9 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 9 \, a^{2} b^{4} + b^{6}\right)} \cos\left(f x + e\right)^{4} + 2 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cos\left(f x + e\right)^{2}}}{16 \, f}"," ",0,"-1/16*(3*(a^2 - 10*a*b + 5*b^2)*log(cos(f*x + e) + 1)/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) - 3*(a^2 - 10*a*b + 5*b^2)*log(cos(f*x + e) - 1)/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) - 6*(5*a^2*b - 10*a*b^2 + b^3)*arctan(a*cos(f*x + e)/sqrt(a*b))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sqrt(a*b)) - 2*(3*(a^3 - 6*a^2*b + a*b^2)*cos(f*x + e)^7 - (5*a^3 - 31*a^2*b + 31*a*b^2 - 5*b^3)*cos(f*x + e)^5 - (19*a^2*b - 34*a*b^2 + 19*b^3)*cos(f*x + e)^3 - 12*(a*b^2 - b^3)*cos(f*x + e))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cos(f*x + e)^8 - 2*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cos(f*x + e)^6 + a^4*b^2 + 4*a^3*b^3 + 6*a^2*b^4 + 4*a*b^5 + b^6 + (a^6 - 9*a^4*b^2 - 16*a^3*b^3 - 9*a^2*b^4 + b^6)*cos(f*x + e)^4 + 2*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cos(f*x + e)^2))/f","B",0
60,1,418,0,0.446334," ","integrate(sin(f*x+e)^6/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(5 \, a^{2} b^{2} + 20 \, a b^{3} + 16 \, b^{4}\right)} \tan\left(f x + e\right)^{9} + 40 \, {\left(3 \, a^{3} b + 19 \, a^{2} b^{2} + 39 \, a b^{3} + 24 \, b^{4}\right)} \tan\left(f x + e\right)^{7} + {\left(33 \, a^{4} + 470 \, a^{3} b + 1910 \, a^{2} b^{2} + 2880 \, a b^{3} + 1440 \, b^{4}\right)} \tan\left(f x + e\right)^{5} + 40 \, {\left(a^{4} + 14 \, a^{3} b + 46 \, a^{2} b^{2} + 57 \, a b^{3} + 24 \, b^{4}\right)} \tan\left(f x + e\right)^{3} + 15 \, {\left(a^{4} + 14 \, a^{3} b + 41 \, a^{2} b^{2} + 44 \, a b^{3} + 16 \, b^{4}\right)} \tan\left(f x + e\right)}{a^{5} b^{2} \tan\left(f x + e\right)^{10} + {\left(2 \, a^{6} b + 5 \, a^{5} b^{2}\right)} \tan\left(f x + e\right)^{8} + a^{7} + 2 \, a^{6} b + a^{5} b^{2} + {\left(a^{7} + 8 \, a^{6} b + 10 \, a^{5} b^{2}\right)} \tan\left(f x + e\right)^{6} + {\left(3 \, a^{7} + 12 \, a^{6} b + 10 \, a^{5} b^{2}\right)} \tan\left(f x + e\right)^{4} + {\left(3 \, a^{7} + 8 \, a^{6} b + 5 \, a^{5} b^{2}\right)} \tan\left(f x + e\right)^{2}} - \frac{15 \, {\left(a^{3} + 18 \, a^{2} b + 48 \, a b^{2} + 32 \, b^{3}\right)} {\left(f x + e\right)}}{a^{6}} + \frac{30 \, {\left(3 \, a^{3} b + 19 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{6}}}{48 \, f}"," ",0,"-1/48*((15*(5*a^2*b^2 + 20*a*b^3 + 16*b^4)*tan(f*x + e)^9 + 40*(3*a^3*b + 19*a^2*b^2 + 39*a*b^3 + 24*b^4)*tan(f*x + e)^7 + (33*a^4 + 470*a^3*b + 1910*a^2*b^2 + 2880*a*b^3 + 1440*b^4)*tan(f*x + e)^5 + 40*(a^4 + 14*a^3*b + 46*a^2*b^2 + 57*a*b^3 + 24*b^4)*tan(f*x + e)^3 + 15*(a^4 + 14*a^3*b + 41*a^2*b^2 + 44*a*b^3 + 16*b^4)*tan(f*x + e))/(a^5*b^2*tan(f*x + e)^10 + (2*a^6*b + 5*a^5*b^2)*tan(f*x + e)^8 + a^7 + 2*a^6*b + a^5*b^2 + (a^7 + 8*a^6*b + 10*a^5*b^2)*tan(f*x + e)^6 + (3*a^7 + 12*a^6*b + 10*a^5*b^2)*tan(f*x + e)^4 + (3*a^7 + 8*a^6*b + 5*a^5*b^2)*tan(f*x + e)^2) - 15*(a^3 + 18*a^2*b + 48*a*b^2 + 32*b^3)*(f*x + e)/a^6 + 30*(3*a^3*b + 19*a^2*b^2 + 32*a*b^3 + 16*b^4)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^6))/f","A",0
61,1,299,0,0.436908," ","integrate(sin(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{12 \, {\left(a b^{2} + 2 \, b^{3}\right)} \tan\left(f x + e\right)^{7} + {\left(19 \, a^{2} b + 72 \, a b^{2} + 72 \, b^{3}\right)} \tan\left(f x + e\right)^{5} + {\left(5 \, a^{3} + 46 \, a^{2} b + 108 \, a b^{2} + 72 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + 9 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \tan\left(f x + e\right)}{a^{4} b^{2} \tan\left(f x + e\right)^{8} + 2 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \tan\left(f x + e\right)^{6} + a^{6} + 2 \, a^{5} b + a^{4} b^{2} + {\left(a^{6} + 6 \, a^{5} b + 6 \, a^{4} b^{2}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \tan\left(f x + e\right)^{2}} - \frac{3 \, {\left(a^{2} + 12 \, a b + 16 \, b^{2}\right)} {\left(f x + e\right)}}{a^{5}} + \frac{3 \, {\left(5 \, a^{2} b + 20 \, a b^{2} + 16 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{5}}}{8 \, f}"," ",0,"-1/8*((12*(a*b^2 + 2*b^3)*tan(f*x + e)^7 + (19*a^2*b + 72*a*b^2 + 72*b^3)*tan(f*x + e)^5 + (5*a^3 + 46*a^2*b + 108*a*b^2 + 72*b^3)*tan(f*x + e)^3 + 3*(a^3 + 9*a^2*b + 16*a*b^2 + 8*b^3)*tan(f*x + e))/(a^4*b^2*tan(f*x + e)^8 + 2*(a^5*b + 2*a^4*b^2)*tan(f*x + e)^6 + a^6 + 2*a^5*b + a^4*b^2 + (a^6 + 6*a^5*b + 6*a^4*b^2)*tan(f*x + e)^4 + 2*(a^6 + 3*a^5*b + 2*a^4*b^2)*tan(f*x + e)^2) - 3*(a^2 + 12*a*b + 16*b^2)*(f*x + e)/a^5 + 3*(5*a^2*b + 20*a*b^2 + 16*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^5))/f","A",0
62,1,272,0,0.438511," ","integrate(sin(f*x+e)^2/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{2} b + 40 \, a b^{2} + 24 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{5} + a^{4} b\right)} \sqrt{{\left(a + b\right)} b}} + \frac{{\left(11 \, a b^{2} + 12 \, b^{3}\right)} \tan\left(f x + e\right)^{5} + {\left(17 \, a^{2} b + 40 \, a b^{2} + 24 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(4 \, a^{3} + 21 \, a^{2} b + 29 \, a b^{2} + 12 \, b^{3}\right)} \tan\left(f x + e\right)}{{\left(a^{4} b^{2} + a^{3} b^{3}\right)} \tan\left(f x + e\right)^{6} + a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3} + {\left(2 \, a^{5} b + 5 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} \tan\left(f x + e\right)^{4} + {\left(a^{6} + 5 \, a^{5} b + 7 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} \tan\left(f x + e\right)^{2}} - \frac{4 \, {\left(f x + e\right)} {\left(a + 6 \, b\right)}}{a^{4}}}{8 \, f}"," ",0,"-1/8*((15*a^2*b + 40*a*b^2 + 24*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^5 + a^4*b)*sqrt((a + b)*b)) + ((11*a*b^2 + 12*b^3)*tan(f*x + e)^5 + (17*a^2*b + 40*a*b^2 + 24*b^3)*tan(f*x + e)^3 + (4*a^3 + 21*a^2*b + 29*a*b^2 + 12*b^3)*tan(f*x + e))/((a^4*b^2 + a^3*b^3)*tan(f*x + e)^6 + a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3 + (2*a^5*b + 5*a^4*b^2 + 3*a^3*b^3)*tan(f*x + e)^4 + (a^6 + 5*a^5*b + 7*a^4*b^2 + 3*a^3*b^3)*tan(f*x + e)^2) - 4*(f*x + e)*(a + 6*b)/a^4)/f","A",0
63,1,231,0,0.430451," ","integrate(1/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{{\left(7 \, a b^{2} + 4 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(9 \, a^{2} b + 13 \, a b^{2} + 4 \, b^{3}\right)} \tan\left(f x + e\right)}{a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(f x + e\right)^{2}} - \frac{8 \, {\left(f x + e\right)}}{a^{3}}}{8 \, f}"," ",0,"-1/8*((15*a^2*b + 20*a*b^2 + 8*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*b)) + ((7*a*b^2 + 4*b^3)*tan(f*x + e)^3 + (9*a^2*b + 13*a*b^2 + 4*b^3)*tan(f*x + e))/(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4 + (a^4*b^2 + 2*a^3*b^3 + a^2*b^4)*tan(f*x + e)^4 + 2*(a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*tan(f*x + e)^2) - 8*(f*x + e)/a^3)/f","A",0
64,1,219,0,0.436533," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{15 \, b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{15 \, b^{2} \tan\left(f x + e\right)^{4} + 25 \, {\left(a b + b^{2}\right)} \tan\left(f x + e\right)^{2} + 8 \, a^{2} + 16 \, a b + 8 \, b^{2}}{{\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \tan\left(f x + e\right)^{5} + 2 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 4 \, a b^{4} + b^{5}\right)} \tan\left(f x + e\right)^{3} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \tan\left(f x + e\right)}}{8 \, f}"," ",0,"-1/8*(15*b*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*b)) + (15*b^2*tan(f*x + e)^4 + 25*(a*b + b^2)*tan(f*x + e)^2 + 8*a^2 + 16*a*b + 8*b^2)/((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*tan(f*x + e)^5 + 2*(a^4*b + 4*a^3*b^2 + 6*a^2*b^3 + 4*a*b^4 + b^5)*tan(f*x + e)^3 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*tan(f*x + e)))/f","B",0
65,1,323,0,0.443612," ","integrate(csc(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(3 \, a b - 4 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{15 \, {\left(3 \, a b^{2} - 4 \, b^{3}\right)} \tan\left(f x + e\right)^{6} + 25 \, {\left(3 \, a^{2} b - a b^{2} - 4 \, b^{3}\right)} \tan\left(f x + e\right)^{4} + 8 \, a^{3} + 24 \, a^{2} b + 24 \, a b^{2} + 8 \, b^{3} + 8 \, {\left(3 \, a^{3} + 2 \, a^{2} b - 5 \, a b^{2} - 4 \, b^{3}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{4} b^{2} + 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 4 \, a b^{5} + b^{6}\right)} \tan\left(f x + e\right)^{7} + 2 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \tan\left(f x + e\right)^{5} + {\left(a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}\right)} \tan\left(f x + e\right)^{3}}}{24 \, f}"," ",0,"-1/24*(15*(3*a*b - 4*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt((a + b)*b)) + (15*(3*a*b^2 - 4*b^3)*tan(f*x + e)^6 + 25*(3*a^2*b - a*b^2 - 4*b^3)*tan(f*x + e)^4 + 8*a^3 + 24*a^2*b + 24*a*b^2 + 8*b^3 + 8*(3*a^3 + 2*a^2*b - 5*a*b^2 - 4*b^3)*tan(f*x + e)^2)/((a^4*b^2 + 4*a^3*b^3 + 6*a^2*b^4 + 4*a*b^5 + b^6)*tan(f*x + e)^7 + 2*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*tan(f*x + e)^5 + (a^6 + 6*a^5*b + 15*a^4*b^2 + 20*a^3*b^3 + 15*a^2*b^4 + 6*a*b^5 + b^6)*tan(f*x + e)^3))/f","B",0
66,1,434,0,0.450201," ","integrate(csc(f*x+e)^6/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(15 \, a^{2} b - 40 \, a b^{2} + 8 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{15 \, {\left(15 \, a^{2} b^{2} - 40 \, a b^{3} + 8 \, b^{4}\right)} \tan\left(f x + e\right)^{8} + 25 \, {\left(15 \, a^{3} b - 25 \, a^{2} b^{2} - 32 \, a b^{3} + 8 \, b^{4}\right)} \tan\left(f x + e\right)^{6} + 8 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 57 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \tan\left(f x + e\right)^{4} + 24 \, a^{4} + 96 \, a^{3} b + 144 \, a^{2} b^{2} + 96 \, a b^{3} + 24 \, b^{4} + 8 \, {\left(10 \, a^{4} + 31 \, a^{3} b + 33 \, a^{2} b^{2} + 13 \, a b^{3} + b^{4}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \tan\left(f x + e\right)^{9} + 2 \, {\left(a^{6} b + 6 \, a^{5} b^{2} + 15 \, a^{4} b^{3} + 20 \, a^{3} b^{4} + 15 \, a^{2} b^{5} + 6 \, a b^{6} + b^{7}\right)} \tan\left(f x + e\right)^{7} + {\left(a^{7} + 7 \, a^{6} b + 21 \, a^{5} b^{2} + 35 \, a^{4} b^{3} + 35 \, a^{3} b^{4} + 21 \, a^{2} b^{5} + 7 \, a b^{6} + b^{7}\right)} \tan\left(f x + e\right)^{5}}}{120 \, f}"," ",0,"-1/120*(15*(15*a^2*b - 40*a*b^2 + 8*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sqrt((a + b)*b)) + (15*(15*a^2*b^2 - 40*a*b^3 + 8*b^4)*tan(f*x + e)^8 + 25*(15*a^3*b - 25*a^2*b^2 - 32*a*b^3 + 8*b^4)*tan(f*x + e)^6 + 8*(15*a^4 - 10*a^3*b - 57*a^2*b^2 - 24*a*b^3 + 8*b^4)*tan(f*x + e)^4 + 24*a^4 + 96*a^3*b + 144*a^2*b^2 + 96*a*b^3 + 24*b^4 + 8*(10*a^4 + 31*a^3*b + 33*a^2*b^2 + 13*a*b^3 + b^4)*tan(f*x + e)^2)/((a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*tan(f*x + e)^9 + 2*(a^6*b + 6*a^5*b^2 + 15*a^4*b^3 + 20*a^3*b^4 + 15*a^2*b^5 + 6*a*b^6 + b^7)*tan(f*x + e)^7 + (a^7 + 7*a^6*b + 21*a^5*b^2 + 35*a^4*b^3 + 35*a^3*b^4 + 21*a^2*b^5 + 7*a*b^6 + b^7)*tan(f*x + e)^5))/f","A",0
67,1,171,0,0.434321," ","integrate(sin(f*x+e)^5*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{20 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}}{a} - 30 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - 15 \, \sqrt{b} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right) - \frac{2 \, {\left(3 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{5} - 5 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} b \cos\left(f x + e\right)^{3}\right)}}{a^{2}}}{30 \, f}"," ",0,"1/30*(20*(a + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3/a - 30*sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) - 15*sqrt(b)*log((sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))) - 2*(3*(a + b/cos(f*x + e)^2)^(5/2)*cos(f*x + e)^5 - 5*(a + b/cos(f*x + e)^2)^(3/2)*b*cos(f*x + e)^3)/a^2)/f","A",0
68,1,116,0,0.420814," ","integrate(sin(f*x+e)^3*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}}{a} - 6 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - 3 \, \sqrt{b} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right)}{6 \, f}"," ",0,"1/6*(2*(a + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3/a - 6*sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) - 3*sqrt(b)*log((sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))))/f","A",0
69,1,88,0,0.422491," ","integrate(sin(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right)}{2 \, f}"," ",0,"-1/2*(2*sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b)*log((sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))))/f","A",0
70,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*csc(f*x + e), x)","F",0
71,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*csc(f*x + e)^3, x)","F",0
72,0,0,0,0.000000," ","integrate(csc(f*x+e)^5*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \csc\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*csc(f*x + e)^5, x)","F",0
73,0,0,0,0.000000," ","integrate(sin(f*x+e)^6*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \sin\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*sin(f*x + e)^6, x)","F",0
74,0,0,0,0.000000," ","integrate(sin(f*x+e)^4*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \sin\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*sin(f*x + e)^4, x)","F",0
75,0,0,0,0.000000," ","integrate(sin(f*x+e)^2*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*sin(f*x + e)^2, x)","F",0
76,-2,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(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
77,1,50,0,0.331214," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) - \frac{\sqrt{b \tan\left(f x + e\right)^{2} + a + b}}{\tan\left(f x + e\right)}}{f}"," ",0,"(sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) - sqrt(b*tan(f*x + e)^2 + a + b)/tan(f*x + e))/f","A",0
78,1,82,0,0.346041," ","integrate(csc(f*x+e)^4*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) - \frac{3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b}}{\tan\left(f x + e\right)} - \frac{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}}}{{\left(a + b\right)} \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(3*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) - 3*sqrt(b*tan(f*x + e)^2 + a + b)/tan(f*x + e) - (b*tan(f*x + e)^2 + a + b)^(3/2)/((a + b)*tan(f*x + e)^3))/f","A",0
79,1,143,0,0.336051," ","integrate(csc(f*x+e)^6*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{15 \, \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) - \frac{15 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b}}{\tan\left(f x + e\right)} - \frac{10 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}}}{{\left(a + b\right)} \tan\left(f x + e\right)^{3}} + \frac{2 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b}{{\left(a + b\right)}^{2} \tan\left(f x + e\right)^{3}} - \frac{3 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}}}{{\left(a + b\right)} \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"1/15*(15*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) - 15*sqrt(b*tan(f*x + e)^2 + a + b)/tan(f*x + e) - 10*(b*tan(f*x + e)^2 + a + b)^(3/2)/((a + b)*tan(f*x + e)^3) + 2*(b*tan(f*x + e)^2 + a + b)^(3/2)*b/((a + b)^2*tan(f*x + e)^3) - 3*(b*tan(f*x + e)^2 + a + b)^(3/2)/((a + b)*tan(f*x + e)^5))/f","A",0
80,1,277,0,0.431456," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e)^5,x, algorithm=""maxima"")","-\frac{\frac{12 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{5}}{a} - 40 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} + 60 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a \cos\left(f x + e\right) - 120 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right) - \frac{30 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a b \cos\left(f x + e\right)}{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} \cos\left(f x + e\right)^{2} - b} + 45 \, a \sqrt{b} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right) - 60 \, b^{\frac{3}{2}} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right)}{60 \, f}"," ",0,"-1/60*(12*(a + b/cos(f*x + e)^2)^(5/2)*cos(f*x + e)^5/a - 40*(a + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 + 60*sqrt(a + b/cos(f*x + e)^2)*a*cos(f*x + e) - 120*sqrt(a + b/cos(f*x + e)^2)*b*cos(f*x + e) - 30*sqrt(a + b/cos(f*x + e)^2)*a*b*cos(f*x + e)/((a + b/cos(f*x + e)^2)*cos(f*x + e)^2 - b) + 45*a*sqrt(b)*log((sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))) - 60*b^(3/2)*log((sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))))/f","A",0
81,1,250,0,0.435535," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 12 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a \cos\left(f x + e\right) + 12 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right) + \frac{6 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a b \cos\left(f x + e\right)}{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} \cos\left(f x + e\right)^{2} - b} - 9 \, a \sqrt{b} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right) + 6 \, b^{\frac{3}{2}} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right)}{12 \, f}"," ",0,"1/12*(4*(a + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 12*sqrt(a + b/cos(f*x + e)^2)*a*cos(f*x + e) + 12*sqrt(a + b/cos(f*x + e)^2)*b*cos(f*x + e) + 6*sqrt(a + b/cos(f*x + e)^2)*a*b*cos(f*x + e)/((a + b/cos(f*x + e)^2)*cos(f*x + e)^2 - b) - 9*a*sqrt(b)*log((sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))) + 6*b^(3/2)*log((sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))))/f","A",0
82,1,142,0,0.431840," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e),x, algorithm=""maxima"")","-\frac{4 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a \cos\left(f x + e\right) - \frac{2 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a b \cos\left(f x + e\right)}{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} \cos\left(f x + e\right)^{2} - b} + 3 \, a \sqrt{b} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right)}{4 \, f}"," ",0,"-1/4*(4*sqrt(a + b/cos(f*x + e)^2)*a*cos(f*x + e) - 2*sqrt(a + b/cos(f*x + e)^2)*a*b*cos(f*x + e)/((a + b/cos(f*x + e)^2)*cos(f*x + e)^2 - b) + 3*a*sqrt(b)*log((sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))))/f","A",0
83,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*csc(f*x + e), x)","F",0
84,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*csc(f*x + e)^3, x)","F",0
85,0,0,0,0.000000," ","integrate(csc(f*x+e)^5*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*csc(f*x + e)^5, x)","F",0
86,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e)^6,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*sin(f*x + e)^6, x)","F",0
87,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e)^4,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*sin(f*x + e)^4, x)","F",0
88,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*sin(f*x+e)^2,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*sin(f*x + e)^2, x)","F",0
89,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
90,1,98,0,0.337121," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{3 \, a \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + 3 \, b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + 3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} b \tan\left(f x + e\right) - \frac{2 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}}}{\tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(3*a*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) + 3*b^(3/2)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) + 3*sqrt(b*tan(f*x + e)^2 + a + b)*b*tan(f*x + e) - 2*(b*tan(f*x + e)^2 + a + b)^(3/2)/tan(f*x + e))/f","A",0
91,1,243,0,0.341993," ","integrate(csc(f*x+e)^4*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{9 \, a \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + \frac{6 \, a b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{a + b} + 9 \, b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + \frac{6 \, b^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{a + b} + 9 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} b \tan\left(f x + e\right) + \frac{6 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} b^{2} \tan\left(f x + e\right)}{a + b} - \frac{6 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}}}{\tan\left(f x + e\right)} - \frac{4 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b}{{\left(a + b\right)} \tan\left(f x + e\right)} - \frac{2 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{5}{2}}}{{\left(a + b\right)} \tan\left(f x + e\right)^{3}}}{6 \, f}"," ",0,"1/6*(9*a*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) + 6*a*b^(3/2)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/(a + b) + 9*b^(3/2)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) + 6*b^(5/2)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/(a + b) + 9*sqrt(b*tan(f*x + e)^2 + a + b)*b*tan(f*x + e) + 6*sqrt(b*tan(f*x + e)^2 + a + b)*b^2*tan(f*x + e)/(a + b) - 6*(b*tan(f*x + e)^2 + a + b)^(3/2)/tan(f*x + e) - 4*(b*tan(f*x + e)^2 + a + b)^(3/2)*b/((a + b)*tan(f*x + e)) - 2*(b*tan(f*x + e)^2 + a + b)^(5/2)/((a + b)*tan(f*x + e)^3))/f","A",0
92,1,273,0,0.348660," ","integrate(csc(f*x+e)^6*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{45 \, a \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + \frac{60 \, a b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{a + b} + 45 \, b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + \frac{60 \, b^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{a + b} + 45 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} b \tan\left(f x + e\right) + \frac{60 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} b^{2} \tan\left(f x + e\right)}{a + b} - \frac{30 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}}}{\tan\left(f x + e\right)} - \frac{40 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b}{{\left(a + b\right)} \tan\left(f x + e\right)} - \frac{20 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{5}{2}}}{{\left(a + b\right)} \tan\left(f x + e\right)^{3}} - \frac{6 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{5}{2}}}{{\left(a + b\right)} \tan\left(f x + e\right)^{5}}}{30 \, f}"," ",0,"1/30*(45*a*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) + 60*a*b^(3/2)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/(a + b) + 45*b^(3/2)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) + 60*b^(5/2)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/(a + b) + 45*sqrt(b*tan(f*x + e)^2 + a + b)*b*tan(f*x + e) + 60*sqrt(b*tan(f*x + e)^2 + a + b)*b^2*tan(f*x + e)/(a + b) - 30*(b*tan(f*x + e)^2 + a + b)^(3/2)/tan(f*x + e) - 40*(b*tan(f*x + e)^2 + a + b)^(3/2)*b/((a + b)*tan(f*x + e)) - 20*(b*tan(f*x + e)^2 + a + b)^(5/2)/((a + b)*tan(f*x + e)^3) - 6*(b*tan(f*x + e)^2 + a + b)^(5/2)/((a + b)*tan(f*x + e)^5))/f","A",0
93,1,162,0,0.350178," ","integrate(sin(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a} - \frac{10 \, {\left({\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 3 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)\right)}}{a^{2}} + \frac{3 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{5} - 10 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} b \cos\left(f x + e\right)^{3} + 15 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b^{2} \cos\left(f x + e\right)}{a^{3}}}{15 \, f}"," ",0,"-1/15*(15*sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e)/a - 10*((a + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 3*sqrt(a + b/cos(f*x + e)^2)*b*cos(f*x + e))/a^2 + (3*(a + b/cos(f*x + e)^2)^(5/2)*cos(f*x + e)^5 - 10*(a + b/cos(f*x + e)^2)^(3/2)*b*cos(f*x + e)^3 + 15*sqrt(a + b/cos(f*x + e)^2)*b^2*cos(f*x + e))/a^3)/f","A",0
94,1,83,0,0.343868," ","integrate(sin(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a} - \frac{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 3 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)}{a^{2}}}{3 \, f}"," ",0,"-1/3*(3*sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e)/a - ((a + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 3*sqrt(a + b/cos(f*x + e)^2)*b*cos(f*x + e))/a^2)/f","A",0
95,1,28,0,0.330051," ","integrate(sin(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a f}"," ",0,"-sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e)/(a*f)","A",0
96,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
97,0,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{3}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)^3/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
98,0,0,0,0.000000," ","integrate(csc(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{5}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)^5/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
99,0,0,0,0.000000," ","integrate(sin(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{6}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)^6/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
100,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
101,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
102,1,992,0,0.616994," ","integrate(1/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\arctan\left(2 \, a \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, a \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 2 \, a + 4 \, b\right) - \arctan\left(2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 4 \, a + 4 \, b\right)}{2 \, \sqrt{a} f}"," ",0,"1/2*(arctan2(2*a*sin(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*a*cos(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 2*a + 4*b) - arctan2(2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 4*a + 4*b))/(sqrt(a)*f)","B",0
103,1,33,0,0.362051," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{b \tan\left(f x + e\right)^{2} + a + b}}{{\left(a + b\right)} f \tan\left(f x + e\right)}"," ",0,"-sqrt(b*tan(f*x + e)^2 + a + b)/((a + b)*f*tan(f*x + e))","A",0
104,1,96,0,0.362595," ","integrate(csc(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b}}{{\left(a + b\right)} \tan\left(f x + e\right)} - \frac{2 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} b}{{\left(a + b\right)}^{2} \tan\left(f x + e\right)} + \frac{\sqrt{b \tan\left(f x + e\right)^{2} + a + b}}{{\left(a + b\right)} \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*sqrt(b*tan(f*x + e)^2 + a + b)/((a + b)*tan(f*x + e)) - 2*sqrt(b*tan(f*x + e)^2 + a + b)*b/((a + b)^2*tan(f*x + e)) + sqrt(b*tan(f*x + e)^2 + a + b)/((a + b)*tan(f*x + e)^3))/f","A",0
105,1,191,0,0.351153," ","integrate(csc(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b}}{{\left(a + b\right)} \tan\left(f x + e\right)} - \frac{20 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} b}{{\left(a + b\right)}^{2} \tan\left(f x + e\right)} + \frac{8 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} b^{2}}{{\left(a + b\right)}^{3} \tan\left(f x + e\right)} + \frac{10 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b}}{{\left(a + b\right)} \tan\left(f x + e\right)^{3}} - \frac{4 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} b}{{\left(a + b\right)}^{2} \tan\left(f x + e\right)^{3}} + \frac{3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b}}{{\left(a + b\right)} \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(15*sqrt(b*tan(f*x + e)^2 + a + b)/((a + b)*tan(f*x + e)) - 20*sqrt(b*tan(f*x + e)^2 + a + b)*b/((a + b)^2*tan(f*x + e)) + 8*sqrt(b*tan(f*x + e)^2 + a + b)*b^2/((a + b)^3*tan(f*x + e)) + 10*sqrt(b*tan(f*x + e)^2 + a + b)/((a + b)*tan(f*x + e)^3) - 4*sqrt(b*tan(f*x + e)^2 + a + b)*b/((a + b)^2*tan(f*x + e)^3) + 3*sqrt(b*tan(f*x + e)^2 + a + b)/((a + b)*tan(f*x + e)^5))/f","A",0
106,1,250,0,0.376776," ","integrate(sin(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{2}} - \frac{10 \, {\left({\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 6 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)\right)}}{a^{3}} + \frac{15 \, b}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a^{2} \cos\left(f x + e\right)} + \frac{30 \, b^{2}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a^{3} \cos\left(f x + e\right)} + \frac{15 \, b^{3}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a^{4} \cos\left(f x + e\right)} + \frac{3 \, {\left({\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{5} - 5 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} b \cos\left(f x + e\right)^{3} + 15 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b^{2} \cos\left(f x + e\right)\right)}}{a^{4}}}{15 \, f}"," ",0,"-1/15*(15*sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e)/a^2 - 10*((a + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 6*sqrt(a + b/cos(f*x + e)^2)*b*cos(f*x + e))/a^3 + 15*b/(sqrt(a + b/cos(f*x + e)^2)*a^2*cos(f*x + e)) + 30*b^2/(sqrt(a + b/cos(f*x + e)^2)*a^3*cos(f*x + e)) + 15*b^3/(sqrt(a + b/cos(f*x + e)^2)*a^4*cos(f*x + e)) + 3*((a + b/cos(f*x + e)^2)^(5/2)*cos(f*x + e)^5 - 5*(a + b/cos(f*x + e)^2)^(3/2)*b*cos(f*x + e)^3 + 15*sqrt(a + b/cos(f*x + e)^2)*b^2*cos(f*x + e))/a^4)/f","A",0
107,1,141,0,0.361951," ","integrate(sin(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{2}} - \frac{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 6 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)}{a^{3}} + \frac{3 \, b}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a^{2} \cos\left(f x + e\right)} + \frac{3 \, b^{2}}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a^{3} \cos\left(f x + e\right)}}{3 \, f}"," ",0,"-1/3*(3*sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e)/a^2 - ((a + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 6*sqrt(a + b/cos(f*x + e)^2)*b*cos(f*x + e))/a^3 + 3*b/(sqrt(a + b/cos(f*x + e)^2)*a^2*cos(f*x + e)) + 3*b^2/(sqrt(a + b/cos(f*x + e)^2)*a^3*cos(f*x + e)))/f","A",0
108,1,57,0,0.345621," ","integrate(sin(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{2}} + \frac{b}{\sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} a^{2} \cos\left(f x + e\right)}}{f}"," ",0,"-(sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e)/a^2 + b/(sqrt(a + b/cos(f*x + e)^2)*a^2*cos(f*x + e)))/f","A",0
109,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(f*x + e)/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
110,-1,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(csc(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,0,0,0,0.000000," ","integrate(sin(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{6}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^6/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
113,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
114,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
115,1,2055,0,0.920604," ","integrate(1/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, a b \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} + a b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{3} - 2 \, {\left(a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + a b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} - a^{2} - 2 \, a b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) - {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left({\left(a + b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + {\left(a + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} \arctan\left(2 \, a \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, a \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 2 \, a + 4 \, b\right) - {\left({\left(a + b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + {\left(a + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} \arctan\left(2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 4 \, a + 4 \, b\right)\right)} \sqrt{a}}{2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left(a^{3} + a^{2} b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + {\left(a^{3} + a^{2} b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} f}"," ",0,"-1/2*(2*a*b*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))*sin(2*f*x + 2*e) - 2*(a^2 + a*b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^3 - 2*(a*b*cos(2*f*x + 2*e) + (a^2 + a*b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 - a^2 - 2*a*b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) - (a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*(((a + b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + (a + b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*arctan2(2*a*sin(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*a*cos(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 2*a + 4*b) - ((a + b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + (a + b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*arctan2(2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 4*a + 4*b))*sqrt(a))/((a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*((a^3 + a^2*b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + (a^3 + a^2*b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*f)","B",0
116,1,64,0,0.365069," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2}} + \frac{1}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right)}}{f}"," ",0,"-(2*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2) + 1/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e)))/f","A",0
117,1,156,0,0.428795," ","integrate(csc(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{6 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2}} - \frac{8 \, b^{2} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{3}} + \frac{3}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right)} - \frac{4 \, b}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2} \tan\left(f x + e\right)} + \frac{1}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(6*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2) - 8*b^2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^3) + 3/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e)) - 4*b/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2*tan(f*x + e)) + 1/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e)^3))/f","A",0
118,1,282,0,0.457884," ","integrate(csc(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{30 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2}} - \frac{80 \, b^{2} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{3}} + \frac{48 \, b^{3} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{4}} + \frac{15}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right)} - \frac{40 \, b}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2} \tan\left(f x + e\right)} + \frac{24 \, b^{2}}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{3} \tan\left(f x + e\right)} + \frac{10}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right)^{3}} - \frac{6 \, b}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2} \tan\left(f x + e\right)^{3}} + \frac{3}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(30*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2) - 80*b^2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^3) + 48*b^3*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^4) + 15/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e)) - 40*b/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2*tan(f*x + e)) + 24*b^2/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^3*tan(f*x + e)) + 10/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e)^3) - 6*b/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2*tan(f*x + e)^3) + 3/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e)^5))/f","A",0
119,1,334,0,0.423722," ","integrate(sin(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{3}} - \frac{10 \, {\left({\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 9 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)\right)}}{a^{4}} + \frac{3 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{5} - 20 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} b \cos\left(f x + e\right)^{3} + 90 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b^{2} \cos\left(f x + e\right)}{a^{5}} + \frac{5 \, {\left(6 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b \cos\left(f x + e\right)^{2} - b^{2}\right)}}{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} a^{3} \cos\left(f x + e\right)^{3}} + \frac{10 \, {\left(9 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b^{2} \cos\left(f x + e\right)^{2} - b^{3}\right)}}{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} a^{4} \cos\left(f x + e\right)^{3}} + \frac{5 \, {\left(12 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b^{3} \cos\left(f x + e\right)^{2} - b^{4}\right)}}{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} a^{5} \cos\left(f x + e\right)^{3}}}{15 \, f}"," ",0,"-1/15*(15*sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e)/a^3 - 10*((a + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 9*sqrt(a + b/cos(f*x + e)^2)*b*cos(f*x + e))/a^4 + (3*(a + b/cos(f*x + e)^2)^(5/2)*cos(f*x + e)^5 - 20*(a + b/cos(f*x + e)^2)^(3/2)*b*cos(f*x + e)^3 + 90*sqrt(a + b/cos(f*x + e)^2)*b^2*cos(f*x + e))/a^5 + 5*(6*(a + b/cos(f*x + e)^2)*b*cos(f*x + e)^2 - b^2)/((a + b/cos(f*x + e)^2)^(3/2)*a^3*cos(f*x + e)^3) + 10*(9*(a + b/cos(f*x + e)^2)*b^2*cos(f*x + e)^2 - b^3)/((a + b/cos(f*x + e)^2)^(3/2)*a^4*cos(f*x + e)^3) + 5*(12*(a + b/cos(f*x + e)^2)*b^3*cos(f*x + e)^2 - b^4)/((a + b/cos(f*x + e)^2)^(3/2)*a^5*cos(f*x + e)^3))/f","A",0
120,1,195,0,0.408353," ","integrate(sin(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{3}} - \frac{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 9 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)}{a^{4}} + \frac{6 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b \cos\left(f x + e\right)^{2} - b^{2}}{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} a^{3} \cos\left(f x + e\right)^{3}} + \frac{9 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b^{2} \cos\left(f x + e\right)^{2} - b^{3}}{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} a^{4} \cos\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e)/a^3 - ((a + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 9*sqrt(a + b/cos(f*x + e)^2)*b*cos(f*x + e))/a^4 + (6*(a + b/cos(f*x + e)^2)*b*cos(f*x + e)^2 - b^2)/((a + b/cos(f*x + e)^2)^(3/2)*a^3*cos(f*x + e)^3) + (9*(a + b/cos(f*x + e)^2)*b^2*cos(f*x + e)^2 - b^3)/((a + b/cos(f*x + e)^2)^(3/2)*a^4*cos(f*x + e)^3))/f","A",0
121,1,86,0,0.391399," ","integrate(sin(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{a + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{3}} + \frac{6 \, {\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b \cos\left(f x + e\right)^{2} - b^{2}}{{\left(a + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} a^{3} \cos\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*sqrt(a + b/cos(f*x + e)^2)*cos(f*x + e)/a^3 + (6*(a + b/cos(f*x + e)^2)*b*cos(f*x + e)^2 - b^2)/((a + b/cos(f*x + e)^2)^(3/2)*a^3*cos(f*x + e)^3))/f","A",0
122,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(f*x + e)/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
123,-1,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate(csc(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,0,0,0,0.000000," ","integrate(sin(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{6}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^6/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
126,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
127,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
128,-1,0,0,0.000000," ","integrate(1/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,1,94,0,0.360118," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{3}} + \frac{4 \, b \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{2}} + \frac{3}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)} \tan\left(f x + e\right)}}{3 \, f}"," ",0,"-1/3*(8*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^3) + 4*b*tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^2) + 3/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)*tan(f*x + e)))/f","A",0
130,1,216,0,0.357540," ","integrate(csc(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{3}} + \frac{4 \, b \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{2}} - \frac{16 \, b^{2} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{4}} - \frac{8 \, b^{2} \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{3}} + \frac{3}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)} \tan\left(f x + e\right)} - \frac{6 \, b}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{2} \tan\left(f x + e\right)} + \frac{1}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)} \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(8*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^3) + 4*b*tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^2) - 16*b^2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^4) - 8*b^2*tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^3) + 3/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)*tan(f*x + e)) - 6*b/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^2*tan(f*x + e)) + 1/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)*tan(f*x + e)^3))/f","A",0
131,1,373,0,0.378078," ","integrate(csc(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{40 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{3}} + \frac{20 \, b \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{2}} - \frac{160 \, b^{2} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{4}} - \frac{80 \, b^{2} \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{3}} + \frac{128 \, b^{3} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{5}} + \frac{64 \, b^{3} \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{4}} + \frac{15}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)} \tan\left(f x + e\right)} - \frac{60 \, b}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{2} \tan\left(f x + e\right)} + \frac{48 \, b^{2}}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{3} \tan\left(f x + e\right)} + \frac{10}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)} \tan\left(f x + e\right)^{3}} - \frac{8 \, b}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{2} \tan\left(f x + e\right)^{3}} + \frac{3}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)} \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(40*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^3) + 20*b*tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^2) - 160*b^2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^4) - 80*b^2*tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^3) + 128*b^3*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^5) + 64*b^3*tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^4) + 15/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)*tan(f*x + e)) - 60*b/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^2*tan(f*x + e)) + 48*b^2/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^3*tan(f*x + e)) + 10/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)*tan(f*x + e)^3) - 8*b/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^2*tan(f*x + e)^3) + 3/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)*tan(f*x + e)^5))/f","A",0
132,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*(d*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*(d*sin(f*x + e))^m, x)","F",0
133,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^5,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*sin(f*x + e)^5, x)","F",0
134,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*sin(f*x + e)^3, x)","F",0
135,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*sin(f*x+e),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*sin(f*x + e), x)","F",0
136,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*csc(f*x + e), x)","F",0
137,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*csc(f*x + e)^3, x)","F",0
138,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^4,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*sin(f*x + e)^4, x)","F",0
139,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*sin(f*x+e)^2,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*sin(f*x + e)^2, x)","F",0
140,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p, x)","F",0
141,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*csc(f*x + e)^2, x)","F",0
142,0,0,0,0.000000," ","integrate(csc(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*csc(f*x + e)^4, x)","F",0
143,0,0,0,0.000000," ","integrate(csc(f*x+e)^6*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*csc(f*x + e)^6, x)","F",0
144,1,129,0,0.329395," ","integrate((a-a*sec(d*x+c)^2)^4,x, algorithm=""maxima"")","a^{4} x + \frac{{\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} a^{4}}{35 \, d} - \frac{4 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{4}}{15 \, d} + \frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{4}}{d} - \frac{4 \, a^{4} \tan\left(d x + c\right)}{d}"," ",0,"a^4*x + 1/35*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*a^4/d - 4/15*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^4/d + 2*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^4/d - 4*a^4*tan(d*x + c)/d","A",0
145,1,81,0,0.326285," ","integrate((a-a*sec(d*x+c)^2)^3,x, algorithm=""maxima"")","a^{3} x - \frac{{\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{3}}{15 \, d} + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3}}{d} - \frac{3 \, a^{3} \tan\left(d x + c\right)}{d}"," ",0,"a^3*x - 1/15*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^3/d + (tan(d*x + c)^3 + 3*tan(d*x + c))*a^3/d - 3*a^3*tan(d*x + c)/d","A",0
146,1,45,0,0.324802," ","integrate((a-a*sec(d*x+c)^2)^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2}}{3 \, d} - \frac{2 \, a^{2} \tan\left(d x + c\right)}{d}"," ",0,"a^2*x + 1/3*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2/d - 2*a^2*tan(d*x + c)/d","A",0
147,1,16,0,0.335823," ","integrate(a-a*sec(d*x+c)^2,x, algorithm=""maxima"")","a x - \frac{a \tan\left(d x + c\right)}{d}"," ",0,"a*x - a*tan(d*x + c)/d","A",0
148,1,26,0,0.415663," ","integrate(1/(a-a*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{d x + c}{a} + \frac{1}{a \tan\left(d x + c\right)}}{d}"," ",0,"((d*x + c)/a + 1/(a*tan(d*x + c)))/d","A",0
149,1,40,0,0.422340," ","integrate(1/(a-a*sec(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(d x + c\right)}}{a^{2}} + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{a^{2} \tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)/a^2 + (3*tan(d*x + c)^2 - 1)/(a^2*tan(d*x + c)^3))/d","A",0
150,1,50,0,0.422427," ","integrate(1/(a-a*sec(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(d x + c\right)}}{a^{3}} + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{a^{3} \tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*(15*(d*x + c)/a^3 + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/(a^3*tan(d*x + c)^5))/d","A",0
151,1,60,0,0.427587," ","integrate(1/(a-a*sec(d*x+c)^2)^4,x, algorithm=""maxima"")","\frac{\frac{105 \, {\left(d x + c\right)}}{a^{4}} + \frac{105 \, \tan\left(d x + c\right)^{6} - 35 \, \tan\left(d x + c\right)^{4} + 21 \, \tan\left(d x + c\right)^{2} - 15}{a^{4} \tan\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*(105*(d*x + c)/a^4 + (105*tan(d*x + c)^6 - 35*tan(d*x + c)^4 + 21*tan(d*x + c)^2 - 15)/(a^4*tan(d*x + c)^7))/d","A",0
152,1,126,0,0.339839," ","integrate(sec(f*x+e)^5*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(6 \, a + 5 \, b\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(6 \, a + 5 \, b\right)} \log\left(\sin\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(6 \, a + 5 \, b\right)} \sin\left(f x + e\right)^{5} - 8 \, {\left(6 \, a + 5 \, b\right)} \sin\left(f x + e\right)^{3} + 3 \, {\left(10 \, a + 11 \, b\right)} \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}}{96 \, f}"," ",0,"1/96*(3*(6*a + 5*b)*log(sin(f*x + e) + 1) - 3*(6*a + 5*b)*log(sin(f*x + e) - 1) - 2*(3*(6*a + 5*b)*sin(f*x + e)^5 - 8*(6*a + 5*b)*sin(f*x + e)^3 + 3*(10*a + 11*b)*sin(f*x + e))/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1))/f","A",0
153,1,97,0,0.340609," ","integrate(sec(f*x+e)^3*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{{\left(4 \, a + 3 \, b\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(4 \, a + 3 \, b\right)} \log\left(\sin\left(f x + e\right) - 1\right) - \frac{2 \, {\left({\left(4 \, a + 3 \, b\right)} \sin\left(f x + e\right)^{3} - {\left(4 \, a + 5 \, b\right)} \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1}}{16 \, f}"," ",0,"1/16*((4*a + 3*b)*log(sin(f*x + e) + 1) - (4*a + 3*b)*log(sin(f*x + e) - 1) - 2*((4*a + 3*b)*sin(f*x + e)^3 - (4*a + 5*b)*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1))/f","A",0
154,1,58,0,0.338941," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, a + b\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(2 \, a + b\right)} \log\left(\sin\left(f x + e\right) - 1\right) - \frac{2 \, b \sin\left(f x + e\right)}{\sin\left(f x + e\right)^{2} - 1}}{4 \, f}"," ",0,"1/4*((2*a + b)*log(sin(f*x + e) + 1) - (2*a + b)*log(sin(f*x + e) - 1) - 2*b*sin(f*x + e)/(sin(f*x + e)^2 - 1))/f","A",0
155,1,38,0,0.335721," ","integrate(cos(f*x+e)*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{b {\left(\log\left(\sin\left(f x + e\right) + 1\right) - \log\left(\sin\left(f x + e\right) - 1\right)\right)} + 2 \, a \sin\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(b*(log(sin(f*x + e) + 1) - log(sin(f*x + e) - 1)) + 2*a*sin(f*x + e))/f","A",0
156,1,27,0,0.337198," ","integrate(cos(f*x+e)^3*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{a \sin\left(f x + e\right)^{3} - 3 \, {\left(a + b\right)} \sin\left(f x + e\right)}{3 \, f}"," ",0,"-1/3*(a*sin(f*x + e)^3 - 3*(a + b)*sin(f*x + e))/f","A",0
157,1,43,0,0.324270," ","integrate(cos(f*x+e)^5*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, a \sin\left(f x + e\right)^{5} - 5 \, {\left(2 \, a + b\right)} \sin\left(f x + e\right)^{3} + 15 \, {\left(a + b\right)} \sin\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*a*sin(f*x + e)^5 - 5*(2*a + b)*sin(f*x + e)^3 + 15*(a + b)*sin(f*x + e))/f","A",0
158,1,60,0,0.345810," ","integrate(sec(f*x+e)^6*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{15 \, b \tan\left(f x + e\right)^{7} + 21 \, {\left(a + 3 \, b\right)} \tan\left(f x + e\right)^{5} + 35 \, {\left(2 \, a + 3 \, b\right)} \tan\left(f x + e\right)^{3} + 105 \, {\left(a + b\right)} \tan\left(f x + e\right)}{105 \, f}"," ",0,"1/105*(15*b*tan(f*x + e)^7 + 21*(a + 3*b)*tan(f*x + e)^5 + 35*(2*a + 3*b)*tan(f*x + e)^3 + 105*(a + b)*tan(f*x + e))/f","A",0
159,1,43,0,0.340368," ","integrate(sec(f*x+e)^4*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, b \tan\left(f x + e\right)^{5} + 5 \, {\left(a + 2 \, b\right)} \tan\left(f x + e\right)^{3} + 15 \, {\left(a + b\right)} \tan\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*b*tan(f*x + e)^5 + 5*(a + 2*b)*tan(f*x + e)^3 + 15*(a + b)*tan(f*x + e))/f","A",0
160,1,34,0,0.337668," ","integrate(sec(f*x+e)^2*(a+b*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)} b + 3 \, a \tan\left(f x + e\right)}{3 \, f}"," ",0,"1/3*((tan(f*x + e)^3 + 3*tan(f*x + e))*b + 3*a*tan(f*x + e))/f","A",0
161,1,15,0,0.336993," ","integrate(a+b*sec(f*x+e)^2,x, algorithm=""maxima"")","a x + \frac{b \tan\left(f x + e\right)}{f}"," ",0,"a*x + b*tan(f*x + e)/f","A",0
162,1,37,0,0.439239," ","integrate(cos(f*x+e)^2*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{{\left(f x + e\right)} {\left(a + 2 \, b\right)} + \frac{a \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}}{2 \, f}"," ",0,"1/2*((f*x + e)*(a + 2*b) + a*tan(f*x + e)/(tan(f*x + e)^2 + 1))/f","A",0
163,1,73,0,0.437925," ","integrate(cos(f*x+e)^4*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{{\left(f x + e\right)} {\left(3 \, a + 4 \, b\right)} + \frac{{\left(3 \, a + 4 \, b\right)} \tan\left(f x + e\right)^{3} + {\left(5 \, a + 4 \, b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{2} + 1}}{8 \, f}"," ",0,"1/8*((f*x + e)*(3*a + 4*b) + ((3*a + 4*b)*tan(f*x + e)^3 + (5*a + 4*b)*tan(f*x + e))/(tan(f*x + e)^4 + 2*tan(f*x + e)^2 + 1))/f","A",0
164,1,103,0,0.439141," ","integrate(cos(f*x+e)^6*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} {\left(5 \, a + 6 \, b\right)} + \frac{3 \, {\left(5 \, a + 6 \, b\right)} \tan\left(f x + e\right)^{5} + 8 \, {\left(5 \, a + 6 \, b\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(11 \, a + 10 \, b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{6} + 3 \, \tan\left(f x + e\right)^{4} + 3 \, \tan\left(f x + e\right)^{2} + 1}}{48 \, f}"," ",0,"1/48*(3*(f*x + e)*(5*a + 6*b) + (3*(5*a + 6*b)*tan(f*x + e)^5 + 8*(5*a + 6*b)*tan(f*x + e)^3 + 3*(11*a + 10*b)*tan(f*x + e))/(tan(f*x + e)^6 + 3*tan(f*x + e)^4 + 3*tan(f*x + e)^2 + 1))/f","A",0
165,1,200,0,0.341940," ","integrate(sec(f*x+e)^5*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(48 \, a^{2} + 80 \, a b + 35 \, b^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(48 \, a^{2} + 80 \, a b + 35 \, b^{2}\right)} \log\left(\sin\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(48 \, a^{2} + 80 \, a b + 35 \, b^{2}\right)} \sin\left(f x + e\right)^{7} - 11 \, {\left(48 \, a^{2} + 80 \, a b + 35 \, b^{2}\right)} \sin\left(f x + e\right)^{5} + {\left(624 \, a^{2} + 1168 \, a b + 511 \, b^{2}\right)} \sin\left(f x + e\right)^{3} - 3 \, {\left(80 \, a^{2} + 176 \, a b + 93 \, b^{2}\right)} \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{8} - 4 \, \sin\left(f x + e\right)^{6} + 6 \, \sin\left(f x + e\right)^{4} - 4 \, \sin\left(f x + e\right)^{2} + 1}}{768 \, f}"," ",0,"1/768*(3*(48*a^2 + 80*a*b + 35*b^2)*log(sin(f*x + e) + 1) - 3*(48*a^2 + 80*a*b + 35*b^2)*log(sin(f*x + e) - 1) - 2*(3*(48*a^2 + 80*a*b + 35*b^2)*sin(f*x + e)^7 - 11*(48*a^2 + 80*a*b + 35*b^2)*sin(f*x + e)^5 + (624*a^2 + 1168*a*b + 511*b^2)*sin(f*x + e)^3 - 3*(80*a^2 + 176*a*b + 93*b^2)*sin(f*x + e))/(sin(f*x + e)^8 - 4*sin(f*x + e)^6 + 6*sin(f*x + e)^4 - 4*sin(f*x + e)^2 + 1))/f","A",0
166,1,166,0,0.333999," ","integrate(sec(f*x+e)^3*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \log\left(\sin\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \sin\left(f x + e\right)^{5} - 8 \, {\left(6 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \sin\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} + 20 \, a b + 11 \, b^{2}\right)} \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}}{96 \, f}"," ",0,"1/96*(3*(8*a^2 + 12*a*b + 5*b^2)*log(sin(f*x + e) + 1) - 3*(8*a^2 + 12*a*b + 5*b^2)*log(sin(f*x + e) - 1) - 2*(3*(8*a^2 + 12*a*b + 5*b^2)*sin(f*x + e)^5 - 8*(6*a^2 + 12*a*b + 5*b^2)*sin(f*x + e)^3 + 3*(8*a^2 + 20*a*b + 11*b^2)*sin(f*x + e))/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1))/f","A",0
167,1,119,0,0.326500," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{{\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(f x + e\right) - 1\right) - \frac{2 \, {\left({\left(8 \, a b + 3 \, b^{2}\right)} \sin\left(f x + e\right)^{3} - {\left(8 \, a b + 5 \, b^{2}\right)} \sin\left(f x + e\right)\right)}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1}}{16 \, f}"," ",0,"1/16*((8*a^2 + 8*a*b + 3*b^2)*log(sin(f*x + e) + 1) - (8*a^2 + 8*a*b + 3*b^2)*log(sin(f*x + e) - 1) - 2*((8*a*b + 3*b^2)*sin(f*x + e)^3 - (8*a*b + 5*b^2)*sin(f*x + e))/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1))/f","A",0
168,1,87,0,0.324842," ","integrate(cos(f*x+e)*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{b^{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)} - 4 \, a b {\left(\log\left(\sin\left(f x + e\right) + 1\right) - \log\left(\sin\left(f x + e\right) - 1\right)\right)} - 4 \, a^{2} \sin\left(f x + e\right)}{4 \, f}"," ",0,"-1/4*(b^2*(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*b*(log(sin(f*x + e) + 1) - log(sin(f*x + e) - 1)) - 4*a^2*sin(f*x + e))/f","A",0
169,1,63,0,0.320791," ","integrate(cos(f*x+e)^3*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{2 \, a^{2} \sin\left(f x + e\right)^{3} - 3 \, b^{2} \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, b^{2} \log\left(\sin\left(f x + e\right) - 1\right) - 6 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(f x + e\right)}{6 \, f}"," ",0,"-1/6*(2*a^2*sin(f*x + e)^3 - 3*b^2*log(sin(f*x + e) + 1) + 3*b^2*log(sin(f*x + e) - 1) - 6*(a^2 + 2*a*b)*sin(f*x + e))/f","A",0
170,1,55,0,0.323274," ","integrate(cos(f*x+e)^5*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{3 \, a^{2} \sin\left(f x + e\right)^{5} - 10 \, {\left(a^{2} + a b\right)} \sin\left(f x + e\right)^{3} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sin\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*a^2*sin(f*x + e)^5 - 10*(a^2 + a*b)*sin(f*x + e)^3 + 15*(a^2 + 2*a*b + b^2)*sin(f*x + e))/f","A",0
171,1,103,0,0.340926," ","integrate(sec(f*x+e)^6*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{35 \, b^{2} \tan\left(f x + e\right)^{9} + 90 \, {\left(a b + 2 \, b^{2}\right)} \tan\left(f x + e\right)^{7} + 63 \, {\left(a^{2} + 6 \, a b + 6 \, b^{2}\right)} \tan\left(f x + e\right)^{5} + 210 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + 315 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)}{315 \, f}"," ",0,"1/315*(35*b^2*tan(f*x + e)^9 + 90*(a*b + 2*b^2)*tan(f*x + e)^7 + 63*(a^2 + 6*a*b + 6*b^2)*tan(f*x + e)^5 + 210*(a^2 + 3*a*b + 2*b^2)*tan(f*x + e)^3 + 315*(a^2 + 2*a*b + b^2)*tan(f*x + e))/f","A",0
172,1,81,0,0.341137," ","integrate(sec(f*x+e)^4*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{15 \, b^{2} \tan\left(f x + e\right)^{7} + 21 \, {\left(2 \, a b + 3 \, b^{2}\right)} \tan\left(f x + e\right)^{5} + 35 \, {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + 105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)}{105 \, f}"," ",0,"1/105*(15*b^2*tan(f*x + e)^7 + 21*(2*a*b + 3*b^2)*tan(f*x + e)^5 + 35*(a^2 + 4*a*b + 3*b^2)*tan(f*x + e)^3 + 105*(a^2 + 2*a*b + b^2)*tan(f*x + e))/f","A",0
173,1,71,0,0.344690," ","integrate(sec(f*x+e)^2*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{10 \, {\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} a b + {\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} b^{2} + 15 \, a^{2} \tan\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(10*(tan(f*x + e)^3 + 3*tan(f*x + e))*a*b + (3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*b^2 + 15*a^2*tan(f*x + e))/f","A",0
174,1,44,0,0.348629," ","integrate((a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} b^{2}}{3 \, f} + \frac{2 \, a b \tan\left(f x + e\right)}{f}"," ",0,"a^2*x + 1/3*(tan(f*x + e)^3 + 3*tan(f*x + e))*b^2/f + 2*a*b*tan(f*x + e)/f","A",0
175,1,53,0,0.430801," ","integrate(cos(f*x+e)^2*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{2 \, b^{2} \tan\left(f x + e\right) + {\left(a^{2} + 4 \, a b\right)} {\left(f x + e\right)} + \frac{a^{2} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}}{2 \, f}"," ",0,"1/2*(2*b^2*tan(f*x + e) + (a^2 + 4*a*b)*(f*x + e) + a^2*tan(f*x + e)/(tan(f*x + e)^2 + 1))/f","A",0
176,1,87,0,0.460085," ","integrate(cos(f*x+e)^4*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} {\left(f x + e\right)} + \frac{{\left(3 \, a^{2} + 8 \, a b\right)} \tan\left(f x + e\right)^{3} + {\left(5 \, a^{2} + 8 \, a b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{2} + 1}}{8 \, f}"," ",0,"1/8*((3*a^2 + 8*a*b + 8*b^2)*(f*x + e) + ((3*a^2 + 8*a*b)*tan(f*x + e)^3 + (5*a^2 + 8*a*b)*tan(f*x + e))/(tan(f*x + e)^4 + 2*tan(f*x + e)^2 + 1))/f","A",0
177,1,135,0,0.430196," ","integrate(cos(f*x+e)^6*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, a^{2} + 12 \, a b + 8 \, b^{2}\right)} {\left(f x + e\right)} + \frac{3 \, {\left(5 \, a^{2} + 12 \, a b + 8 \, b^{2}\right)} \tan\left(f x + e\right)^{5} + 8 \, {\left(5 \, a^{2} + 12 \, a b + 6 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(11 \, a^{2} + 20 \, a b + 8 \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{6} + 3 \, \tan\left(f x + e\right)^{4} + 3 \, \tan\left(f x + e\right)^{2} + 1}}{48 \, f}"," ",0,"1/48*(3*(5*a^2 + 12*a*b + 8*b^2)*(f*x + e) + (3*(5*a^2 + 12*a*b + 8*b^2)*tan(f*x + e)^5 + 8*(5*a^2 + 12*a*b + 6*b^2)*tan(f*x + e)^3 + 3*(11*a^2 + 20*a*b + 8*b^2)*tan(f*x + e))/(tan(f*x + e)^6 + 3*tan(f*x + e)^4 + 3*tan(f*x + e)^2 + 1))/f","A",0
178,1,83,0,0.352238," ","integrate((a+b*sec(d*x+c)^2)^3,x, algorithm=""maxima"")","a^{3} x + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a b^{2}}{d} + \frac{{\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} b^{3}}{15 \, d} + \frac{3 \, a^{2} b \tan\left(d x + c\right)}{d}"," ",0,"a^3*x + (tan(d*x + c)^3 + 3*tan(d*x + c))*a*b^2/d + 1/15*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*b^3/d + 3*a^2*b*tan(d*x + c)/d","A",0
179,1,134,0,0.363167," ","integrate((a+b*sec(d*x+c)^2)^4,x, algorithm=""maxima"")","a^{4} x + \frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} b^{2}}{d} + \frac{4 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a b^{3}}{15 \, d} + \frac{{\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} b^{4}}{35 \, d} + \frac{4 \, a^{3} b \tan\left(d x + c\right)}{d}"," ",0,"a^4*x + 2*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2*b^2/d + 4/15*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a*b^3/d + 1/35*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*b^4/d + 4*a^3*b*tan(d*x + c)/d","A",0
180,1,124,0,0.453113," ","integrate(sec(f*x+e)^5/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{2 \, a^{2} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b^{2}} + \frac{{\left(2 \, a - b\right)} \log\left(\sin\left(f x + e\right) + 1\right)}{b^{2}} - \frac{{\left(2 \, a - b\right)} \log\left(\sin\left(f x + e\right) - 1\right)}{b^{2}} + \frac{2 \, \sin\left(f x + e\right)}{b \sin\left(f x + e\right)^{2} - b}}{4 \, f}"," ",0,"-1/4*(2*a^2*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/(sqrt((a + b)*a)*b^2) + (2*a - b)*log(sin(f*x + e) + 1)/b^2 - (2*a - b)*log(sin(f*x + e) - 1)/b^2 + 2*sin(f*x + e)/(b*sin(f*x + e)^2 - b))/f","A",0
181,1,83,0,0.439683," ","integrate(sec(f*x+e)^3/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{a \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b} + \frac{\log\left(\sin\left(f x + e\right) + 1\right)}{b} - \frac{\log\left(\sin\left(f x + e\right) - 1\right)}{b}}{2 \, f}"," ",0,"1/2*(a*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/(sqrt((a + b)*a)*b) + log(sin(f*x + e) + 1)/b - log(sin(f*x + e) - 1)/b)/f","A",0
182,1,50,0,0.447604," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{2 \, \sqrt{{\left(a + b\right)} a} f}"," ",0,"-1/2*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/(sqrt((a + b)*a)*f)","A",0
183,1,67,0,0.444103," ","integrate(cos(f*x+e)/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{b \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a} + \frac{2 \, \sin\left(f x + e\right)}{a}}{2 \, f}"," ",0,"1/2*(b*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/(sqrt((a + b)*a)*a) + 2*sin(f*x + e)/a)/f","A",0
184,1,88,0,0.435825," ","integrate(cos(f*x+e)^3/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{3 \, b^{2} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a^{2}} + \frac{2 \, {\left(a \sin\left(f x + e\right)^{3} - 3 \, {\left(a - b\right)} \sin\left(f x + e\right)\right)}}{a^{2}}}{6 \, f}"," ",0,"-1/6*(3*b^2*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/(sqrt((a + b)*a)*a^2) + 2*(a*sin(f*x + e)^3 - 3*(a - b)*sin(f*x + e))/a^2)/f","A",0
185,1,117,0,0.456230," ","integrate(cos(f*x+e)^5/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{15 \, b^{3} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a^{3}} + \frac{2 \, {\left(3 \, a^{2} \sin\left(f x + e\right)^{5} - 5 \, {\left(2 \, a^{2} - a b\right)} \sin\left(f x + e\right)^{3} + 15 \, {\left(a^{2} - a b + b^{2}\right)} \sin\left(f x + e\right)\right)}}{a^{3}}}{30 \, f}"," ",0,"1/30*(15*b^3*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/(sqrt((a + b)*a)*a^3) + 2*(3*a^2*sin(f*x + e)^5 - 5*(2*a^2 - a*b)*sin(f*x + e)^3 + 15*(a^2 - a*b + b^2)*sin(f*x + e))/a^3)/f","A",0
186,1,65,0,0.454090," ","integrate(sec(f*x+e)^6/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, a^{2} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} b^{2}} + \frac{b \tan\left(f x + e\right)^{3} - 3 \, {\left(a - b\right)} \tan\left(f x + e\right)}{b^{2}}}{3 \, f}"," ",0,"1/3*(3*a^2*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*b^2) + (b*tan(f*x + e)^3 - 3*(a - b)*tan(f*x + e))/b^2)/f","A",0
187,1,45,0,0.450501," ","integrate(sec(f*x+e)^4/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{a \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} b} - \frac{\tan\left(f x + e\right)}{b}}{f}"," ",0,"-(a*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*b) - tan(f*x + e)/b)/f","A",0
188,1,27,0,0.433283," ","integrate(sec(f*x+e)^2/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} f}"," ",0,"arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*f)","A",0
189,1,44,0,0.430597," ","integrate(1/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a} - \frac{f x + e}{a}}{f}"," ",0,"-(b*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a) - (f*x + e)/a)/f","A",0
190,1,72,0,0.439166," ","integrate(cos(f*x+e)^2/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{2} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{2}} + \frac{{\left(f x + e\right)} {\left(a - 2 \, b\right)}}{a^{2}} + \frac{\tan\left(f x + e\right)}{a \tan\left(f x + e\right)^{2} + a}}{2 \, f}"," ",0,"1/2*(2*b^2*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^2) + (f*x + e)*(a - 2*b)/a^2 + tan(f*x + e)/(a*tan(f*x + e)^2 + a))/f","A",0
191,1,126,0,0.434785," ","integrate(cos(f*x+e)^4/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{8 \, b^{3} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{3}} - \frac{{\left(3 \, a - 4 \, b\right)} \tan\left(f x + e\right)^{3} + {\left(5 \, a - 4 \, b\right)} \tan\left(f x + e\right)}{a^{2} \tan\left(f x + e\right)^{4} + 2 \, a^{2} \tan\left(f x + e\right)^{2} + a^{2}} - \frac{{\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} {\left(f x + e\right)}}{a^{3}}}{8 \, f}"," ",0,"-1/8*(8*b^3*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^3) - ((3*a - 4*b)*tan(f*x + e)^3 + (5*a - 4*b)*tan(f*x + e))/(a^2*tan(f*x + e)^4 + 2*a^2*tan(f*x + e)^2 + a^2) - (3*a^2 - 4*a*b + 8*b^2)*(f*x + e)/a^3)/f","A",0
192,1,189,0,0.450459," ","integrate(cos(f*x+e)^6/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{48 \, b^{4} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{4}} + \frac{3 \, {\left(5 \, a^{2} - 6 \, a b + 8 \, b^{2}\right)} \tan\left(f x + e\right)^{5} + 8 \, {\left(5 \, a^{2} - 6 \, a b + 6 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(11 \, a^{2} - 10 \, a b + 8 \, b^{2}\right)} \tan\left(f x + e\right)}{a^{3} \tan\left(f x + e\right)^{6} + 3 \, a^{3} \tan\left(f x + e\right)^{4} + 3 \, a^{3} \tan\left(f x + e\right)^{2} + a^{3}} + \frac{3 \, {\left(5 \, a^{3} - 6 \, a^{2} b + 8 \, a b^{2} - 16 \, b^{3}\right)} {\left(f x + e\right)}}{a^{4}}}{48 \, f}"," ",0,"1/48*(48*b^4*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^4) + (3*(5*a^2 - 6*a*b + 8*b^2)*tan(f*x + e)^5 + 8*(5*a^2 - 6*a*b + 6*b^2)*tan(f*x + e)^3 + 3*(11*a^2 - 10*a*b + 8*b^2)*tan(f*x + e))/(a^3*tan(f*x + e)^6 + 3*a^3*tan(f*x + e)^4 + 3*a^3*tan(f*x + e)^2 + a^3) + 3*(5*a^3 - 6*a^2*b + 8*a*b^2 - 16*b^3)*(f*x + e)/a^4)/f","A",0
193,1,146,0,0.451906," ","integrate(sec(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(2 \, a + 3 \, b\right)} a \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{{\left(a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{2 \, a \sin\left(f x + e\right)}{a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{2} b + a b^{2}\right)} \sin\left(f x + e\right)^{2}} + \frac{2 \, \log\left(\sin\left(f x + e\right) + 1\right)}{b^{2}} - \frac{2 \, \log\left(\sin\left(f x + e\right) - 1\right)}{b^{2}}}{4 \, f}"," ",0,"1/4*((2*a + 3*b)*a*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/((a*b^2 + b^3)*sqrt((a + b)*a)) - 2*a*sin(f*x + e)/(a^2*b + 2*a*b^2 + b^3 - (a^2*b + a*b^2)*sin(f*x + e)^2) + 2*log(sin(f*x + e) + 1)/b^2 - 2*log(sin(f*x + e) - 1)/b^2)/f","A",0
194,1,98,0,0.437643," ","integrate(sec(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, \sin\left(f x + e\right)}{{\left(a^{2} + a b\right)} \sin\left(f x + e\right)^{2} - a^{2} - 2 \, a b - b^{2}} + \frac{\log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a + b\right)}}}{4 \, f}"," ",0,"-1/4*(2*sin(f*x + e)/((a^2 + a*b)*sin(f*x + e)^2 - a^2 - 2*a*b - b^2) + log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/(sqrt((a + b)*a)*(a + b)))/f","A",0
195,1,111,0,0.430733," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, b \sin\left(f x + e\right)}{a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + a^{2} b\right)} \sin\left(f x + e\right)^{2}} + \frac{{\left(2 \, a + b\right)} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a^{2} + a b\right)}}}{4 \, f}"," ",0,"-1/4*(2*b*sin(f*x + e)/(a^3 + 2*a^2*b + a*b^2 - (a^3 + a^2*b)*sin(f*x + e)^2) + (2*a + b)*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/(sqrt((a + b)*a)*(a^2 + a*b)))/f","A",0
196,1,133,0,0.427842," ","integrate(cos(f*x+e)/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{2 \, b^{2} \sin\left(f x + e\right)}{a^{4} + 2 \, a^{3} b + a^{2} b^{2} - {\left(a^{4} + a^{3} b\right)} \sin\left(f x + e\right)^{2}} + \frac{{\left(4 \, a b + 3 \, b^{2}\right)} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} a}} + \frac{4 \, \sin\left(f x + e\right)}{a^{2}}}{4 \, f}"," ",0,"1/4*(2*b^2*sin(f*x + e)/(a^4 + 2*a^3*b + a^2*b^2 - (a^4 + a^3*b)*sin(f*x + e)^2) + (4*a*b + 3*b^2)*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/((a^3 + a^2*b)*sqrt((a + b)*a)) + 4*sin(f*x + e)/a^2)/f","A",0
197,1,154,0,0.440343," ","integrate(cos(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{6 \, b^{3} \sin\left(f x + e\right)}{a^{5} + 2 \, a^{4} b + a^{3} b^{2} - {\left(a^{5} + a^{4} b\right)} \sin\left(f x + e\right)^{2}} + \frac{3 \, {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} a}} + \frac{4 \, {\left(a \sin\left(f x + e\right)^{3} - 3 \, {\left(a - 2 \, b\right)} \sin\left(f x + e\right)\right)}}{a^{3}}}{12 \, f}"," ",0,"-1/12*(6*b^3*sin(f*x + e)/(a^5 + 2*a^4*b + a^3*b^2 - (a^5 + a^4*b)*sin(f*x + e)^2) + 3*(6*a*b^2 + 5*b^3)*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/((a^4 + a^3*b)*sqrt((a + b)*a)) + 4*(a*sin(f*x + e)^3 - 3*(a - 2*b)*sin(f*x + e))/a^3)/f","A",0
198,1,183,0,0.447758," ","integrate(cos(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{30 \, b^{4} \sin\left(f x + e\right)}{a^{6} + 2 \, a^{5} b + a^{4} b^{2} - {\left(a^{6} + a^{5} b\right)} \sin\left(f x + e\right)^{2}} + \frac{15 \, {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{5} + a^{4} b\right)} \sqrt{{\left(a + b\right)} a}} + \frac{4 \, {\left(3 \, a^{2} \sin\left(f x + e\right)^{5} - 10 \, {\left(a^{2} - a b\right)} \sin\left(f x + e\right)^{3} + 15 \, {\left(a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sin\left(f x + e\right)\right)}}{a^{4}}}{60 \, f}"," ",0,"1/60*(30*b^4*sin(f*x + e)/(a^6 + 2*a^5*b + a^4*b^2 - (a^6 + a^5*b)*sin(f*x + e)^2) + 15*(8*a*b^3 + 7*b^4)*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/((a^5 + a^4*b)*sqrt((a + b)*a)) + 4*(3*a^2*sin(f*x + e)^5 - 10*(a^2 - a*b)*sin(f*x + e)^3 + 15*(a^2 - 2*a*b + 3*b^2)*sin(f*x + e))/a^4)/f","A",0
199,1,110,0,0.449472," ","integrate(sec(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{a^{2} \tan\left(f x + e\right)}{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + {\left(a b^{3} + b^{4}\right)} \tan\left(f x + e\right)^{2}} - \frac{{\left(3 \, a^{2} + 4 \, a b\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{2 \, \tan\left(f x + e\right)}{b^{2}}}{2 \, f}"," ",0,"1/2*(a^2*tan(f*x + e)/(a^2*b^2 + 2*a*b^3 + b^4 + (a*b^3 + b^4)*tan(f*x + e)^2) - (3*a^2 + 4*a*b)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a*b^2 + b^3)*sqrt((a + b)*b)) + 2*tan(f*x + e)/b^2)/f","A",0
200,1,88,0,0.456913," ","integrate(sec(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{a \tan\left(f x + e\right)}{a^{2} b + 2 \, a b^{2} + b^{3} + {\left(a b^{2} + b^{3}\right)} \tan\left(f x + e\right)^{2}} - \frac{{\left(a + 2 \, b\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} {\left(a b + b^{2}\right)}}}{2 \, f}"," ",0,"-1/2*(a*tan(f*x + e)/(a^2*b + 2*a*b^2 + b^3 + (a*b^2 + b^3)*tan(f*x + e)^2) - (a + 2*b)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*(a*b + b^2)))/f","A",0
201,1,71,0,0.432575," ","integrate(sec(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{\tan\left(f x + e\right)}{{\left(a b + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} + 2 \, a b + b^{2}} + \frac{\arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} {\left(a + b\right)}}}{2 \, f}"," ",0,"1/2*(tan(f*x + e)/((a*b + b^2)*tan(f*x + e)^2 + a^2 + 2*a*b + b^2) + arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*(a + b)))/f","A",0
202,1,106,0,0.436871," ","integrate(1/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{b \tan\left(f x + e\right)}{a^{3} + 2 \, a^{2} b + a b^{2} + {\left(a^{2} b + a b^{2}\right)} \tan\left(f x + e\right)^{2}} + \frac{{\left(3 \, a b + 2 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b}} - \frac{2 \, {\left(f x + e\right)}}{a^{2}}}{2 \, f}"," ",0,"-1/2*(b*tan(f*x + e)/(a^3 + 2*a^2*b + a*b^2 + (a^2*b + a*b^2)*tan(f*x + e)^2) + (3*a*b + 2*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^3 + a^2*b)*sqrt((a + b)*b)) - 2*(f*x + e)/a^2)/f","A",0
203,1,175,0,0.452789," ","integrate(cos(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(5 \, a b^{2} + 4 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} b}} + \frac{{\left(a b + 2 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + {\left(a^{2} + 2 \, a b + 2 \, b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{3} b + a^{2} b^{2}\right)} \tan\left(f x + e\right)^{4} + a^{4} + 2 \, a^{3} b + a^{2} b^{2} + {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \tan\left(f x + e\right)^{2}} + \frac{{\left(f x + e\right)} {\left(a - 4 \, b\right)}}{a^{3}}}{2 \, f}"," ",0,"1/2*((5*a*b^2 + 4*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^4 + a^3*b)*sqrt((a + b)*b)) + ((a*b + 2*b^2)*tan(f*x + e)^3 + (a^2 + 2*a*b + 2*b^2)*tan(f*x + e))/((a^3*b + a^2*b^2)*tan(f*x + e)^4 + a^4 + 2*a^3*b + a^2*b^2 + (a^4 + 3*a^3*b + 2*a^2*b^2)*tan(f*x + e)^2) + (f*x + e)*(a - 4*b)/a^3)/f","A",0
204,1,268,0,0.457221," ","integrate(cos(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(7 \, a b^{3} + 6 \, b^{4}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{5} + a^{4} b\right)} \sqrt{{\left(a + b\right)} b}} - \frac{{\left(3 \, a^{2} b - 5 \, a b^{2} - 12 \, b^{3}\right)} \tan\left(f x + e\right)^{5} + {\left(3 \, a^{3} + 3 \, a^{2} b - 16 \, a b^{2} - 24 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(5 \, a^{3} + 2 \, a^{2} b - 11 \, a b^{2} - 12 \, b^{3}\right)} \tan\left(f x + e\right)}{{\left(a^{4} b + a^{3} b^{2}\right)} \tan\left(f x + e\right)^{6} + a^{5} + 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{5} + 4 \, a^{4} b + 3 \, a^{3} b^{2}\right)} \tan\left(f x + e\right)^{4} + {\left(2 \, a^{5} + 5 \, a^{4} b + 3 \, a^{3} b^{2}\right)} \tan\left(f x + e\right)^{2}} - \frac{{\left(3 \, a^{2} - 8 \, a b + 24 \, b^{2}\right)} {\left(f x + e\right)}}{a^{4}}}{8 \, f}"," ",0,"-1/8*(4*(7*a*b^3 + 6*b^4)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^5 + a^4*b)*sqrt((a + b)*b)) - ((3*a^2*b - 5*a*b^2 - 12*b^3)*tan(f*x + e)^5 + (3*a^3 + 3*a^2*b - 16*a*b^2 - 24*b^3)*tan(f*x + e)^3 + (5*a^3 + 2*a^2*b - 11*a*b^2 - 12*b^3)*tan(f*x + e))/((a^4*b + a^3*b^2)*tan(f*x + e)^6 + a^5 + 2*a^4*b + a^3*b^2 + (a^5 + 4*a^4*b + 3*a^3*b^2)*tan(f*x + e)^4 + (2*a^5 + 5*a^4*b + 3*a^3*b^2)*tan(f*x + e)^2) - (3*a^2 - 8*a*b + 24*b^2)*(f*x + e)/a^4)/f","A",0
205,1,369,0,0.462466," ","integrate(cos(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{24 \, {\left(9 \, a b^{4} + 8 \, b^{5}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{6} + a^{5} b\right)} \sqrt{{\left(a + b\right)} b}} + \frac{3 \, {\left(5 \, a^{3} b - 7 \, a^{2} b^{2} + 12 \, a b^{3} + 32 \, b^{4}\right)} \tan\left(f x + e\right)^{7} + {\left(15 \, a^{4} + 34 \, a^{3} b - 41 \, a^{2} b^{2} + 156 \, a b^{3} + 288 \, b^{4}\right)} \tan\left(f x + e\right)^{5} + {\left(40 \, a^{4} + 17 \, a^{3} b - 35 \, a^{2} b^{2} + 204 \, a b^{3} + 288 \, b^{4}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(11 \, a^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 28 \, a b^{3} + 32 \, b^{4}\right)} \tan\left(f x + e\right)}{{\left(a^{5} b + a^{4} b^{2}\right)} \tan\left(f x + e\right)^{8} + {\left(a^{6} + 5 \, a^{5} b + 4 \, a^{4} b^{2}\right)} \tan\left(f x + e\right)^{6} + a^{6} + 2 \, a^{5} b + a^{4} b^{2} + 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \tan\left(f x + e\right)^{4} + {\left(3 \, a^{6} + 7 \, a^{5} b + 4 \, a^{4} b^{2}\right)} \tan\left(f x + e\right)^{2}} + \frac{3 \, {\left(5 \, a^{3} - 12 \, a^{2} b + 24 \, a b^{2} - 64 \, b^{3}\right)} {\left(f x + e\right)}}{a^{5}}}{48 \, f}"," ",0,"1/48*(24*(9*a*b^4 + 8*b^5)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^6 + a^5*b)*sqrt((a + b)*b)) + (3*(5*a^3*b - 7*a^2*b^2 + 12*a*b^3 + 32*b^4)*tan(f*x + e)^7 + (15*a^4 + 34*a^3*b - 41*a^2*b^2 + 156*a*b^3 + 288*b^4)*tan(f*x + e)^5 + (40*a^4 + 17*a^3*b - 35*a^2*b^2 + 204*a*b^3 + 288*b^4)*tan(f*x + e)^3 + 3*(11*a^4 + 2*a^3*b - 5*a^2*b^2 + 28*a*b^3 + 32*b^4)*tan(f*x + e))/((a^5*b + a^4*b^2)*tan(f*x + e)^8 + (a^6 + 5*a^5*b + 4*a^4*b^2)*tan(f*x + e)^6 + a^6 + 2*a^5*b + a^4*b^2 + 3*(a^6 + 3*a^5*b + 2*a^4*b^2)*tan(f*x + e)^4 + (3*a^6 + 7*a^5*b + 4*a^4*b^2)*tan(f*x + e)^2) + 3*(5*a^3 - 12*a^2*b + 24*a*b^2 - 64*b^3)*(f*x + e)/a^5)/f","A",0
206,1,179,0,0.434083," ","integrate(sec(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, a \sin\left(f x + e\right)^{3} - 5 \, {\left(a + b\right)} \sin\left(f x + e\right)\right)}}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sin\left(f x + e\right)^{4} + a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} - 2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sin\left(f x + e\right)^{2}} + \frac{3 \, \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a^{2} + 2 \, a b + b^{2}\right)}}}{16 \, f}"," ",0,"-1/16*(2*(3*a*sin(f*x + e)^3 - 5*(a + b)*sin(f*x + e))/((a^4 + 2*a^3*b + a^2*b^2)*sin(f*x + e)^4 + a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 - 2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sin(f*x + e)^2) + 3*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/(sqrt((a + b)*a)*(a^2 + 2*a*b + b^2)))/f","A",0
207,1,212,0,0.446041," ","integrate(sec(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(4 \, a + b\right)} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{{\left(a + b\right)} a}} + \frac{2 \, {\left({\left(4 \, a^{2} + a b\right)} \sin\left(f x + e\right)^{3} - {\left(4 \, a^{2} + 3 \, a b - b^{2}\right)} \sin\left(f x + e\right)\right)}}{a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sin\left(f x + e\right)^{4} - 2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sin\left(f x + e\right)^{2}}}{16 \, f}"," ",0,"-1/16*((4*a + b)*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/((a^3 + 2*a^2*b + a*b^2)*sqrt((a + b)*a)) + 2*((4*a^2 + a*b)*sin(f*x + e)^3 - (4*a^2 + 3*a*b - b^2)*sin(f*x + e))/(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + (a^5 + 2*a^4*b + a^3*b^2)*sin(f*x + e)^4 - 2*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sin(f*x + e)^2))/f","A",0
208,1,233,0,0.450954," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{2 \, {\left({\left(8 \, a^{2} b + 5 \, a b^{2}\right)} \sin\left(f x + e\right)^{3} - {\left(8 \, a^{2} b + 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(f x + e\right)\right)}}{a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \sin\left(f x + e\right)^{4} - 2 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sin\left(f x + e\right)^{2}}}{16 \, f}"," ",0,"-1/16*((8*a^2 + 8*a*b + 3*b^2)*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/((a^4 + 2*a^3*b + a^2*b^2)*sqrt((a + b)*a)) - 2*((8*a^2*b + 5*a*b^2)*sin(f*x + e)^3 - (8*a^2*b + 11*a*b^2 + 3*b^3)*sin(f*x + e))/(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4 + (a^6 + 2*a^5*b + a^4*b^2)*sin(f*x + e)^4 - 2*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sin(f*x + e)^2))/f","A",0
209,1,253,0,0.439197," ","integrate(cos(f*x+e)/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{2 \, {\left(3 \, {\left(4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sin\left(f x + e\right)^{3} - {\left(12 \, a^{2} b^{2} + 19 \, a b^{3} + 7 \, b^{4}\right)} \sin\left(f x + e\right)\right)}}{a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \sin\left(f x + e\right)^{4} - 2 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sin\left(f x + e\right)^{2}} + \frac{16 \, \sin\left(f x + e\right)}{a^{3}}}{16 \, f}"," ",0,"1/16*(3*(8*a^2*b + 12*a*b^2 + 5*b^3)*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*a)) - 2*(3*(4*a^2*b^2 + 3*a*b^3)*sin(f*x + e)^3 - (12*a^2*b^2 + 19*a*b^3 + 7*b^4)*sin(f*x + e))/(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4 + (a^7 + 2*a^6*b + a^5*b^2)*sin(f*x + e)^4 - 2*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sin(f*x + e)^2) + 16*sin(f*x + e)/a^3)/f","A",0
210,1,272,0,0.444266," ","integrate(cos(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(48 \, a^{2} b^{2} + 80 \, a b^{3} + 35 \, b^{4}\right)} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{6 \, {\left({\left(16 \, a^{2} b^{3} + 13 \, a b^{4}\right)} \sin\left(f x + e\right)^{3} - {\left(16 \, a^{2} b^{3} + 27 \, a b^{4} + 11 \, b^{5}\right)} \sin\left(f x + e\right)\right)}}{a^{8} + 4 \, a^{7} b + 6 \, a^{6} b^{2} + 4 \, a^{5} b^{3} + a^{4} b^{4} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} \sin\left(f x + e\right)^{4} - 2 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \sin\left(f x + e\right)^{2}} + \frac{16 \, {\left(a \sin\left(f x + e\right)^{3} - 3 \, {\left(a - 3 \, b\right)} \sin\left(f x + e\right)\right)}}{a^{4}}}{48 \, f}"," ",0,"-1/48*(3*(48*a^2*b^2 + 80*a*b^3 + 35*b^4)*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/((a^6 + 2*a^5*b + a^4*b^2)*sqrt((a + b)*a)) - 6*((16*a^2*b^3 + 13*a*b^4)*sin(f*x + e)^3 - (16*a^2*b^3 + 27*a*b^4 + 11*b^5)*sin(f*x + e))/(a^8 + 4*a^7*b + 6*a^6*b^2 + 4*a^5*b^3 + a^4*b^4 + (a^8 + 2*a^7*b + a^6*b^2)*sin(f*x + e)^4 - 2*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*sin(f*x + e)^2) + 16*(a*sin(f*x + e)^3 - 3*(a - 3*b)*sin(f*x + e))/a^4)/f","A",0
211,1,303,0,0.456497," ","integrate(cos(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(80 \, a^{2} b^{3} + 140 \, a b^{4} + 63 \, b^{5}\right)} \log\left(\frac{a \sin\left(f x + e\right) - \sqrt{{\left(a + b\right)} a}}{a \sin\left(f x + e\right) + \sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{30 \, {\left({\left(20 \, a^{2} b^{4} + 17 \, a b^{5}\right)} \sin\left(f x + e\right)^{3} - 5 \, {\left(4 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \sin\left(f x + e\right)\right)}}{a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4} + {\left(a^{9} + 2 \, a^{8} b + a^{7} b^{2}\right)} \sin\left(f x + e\right)^{4} - 2 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} \sin\left(f x + e\right)^{2}} + \frac{16 \, {\left(3 \, a^{2} \sin\left(f x + e\right)^{5} - 5 \, {\left(2 \, a^{2} - 3 \, a b\right)} \sin\left(f x + e\right)^{3} + 15 \, {\left(a^{2} - 3 \, a b + 6 \, b^{2}\right)} \sin\left(f x + e\right)\right)}}{a^{5}}}{240 \, f}"," ",0,"1/240*(15*(80*a^2*b^3 + 140*a*b^4 + 63*b^5)*log((a*sin(f*x + e) - sqrt((a + b)*a))/(a*sin(f*x + e) + sqrt((a + b)*a)))/((a^7 + 2*a^6*b + a^5*b^2)*sqrt((a + b)*a)) - 30*((20*a^2*b^4 + 17*a*b^5)*sin(f*x + e)^3 - 5*(4*a^2*b^4 + 7*a*b^5 + 3*b^6)*sin(f*x + e))/(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4 + (a^9 + 2*a^8*b + a^7*b^2)*sin(f*x + e)^4 - 2*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*sin(f*x + e)^2) + 16*(3*a^2*sin(f*x + e)^5 - 5*(2*a^2 - 3*a*b)*sin(f*x + e)^3 + 15*(a^2 - 3*a*b + 6*b^2)*sin(f*x + e))/a^5)/f","A",0
212,1,210,0,0.448666," ","integrate(sec(f*x+e)^6/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{{\left(5 \, a^{2} b + 8 \, a b^{2}\right)} \tan\left(f x + e\right)^{3} + {\left(3 \, a^{3} + 11 \, a^{2} b + 8 \, a b^{2}\right)} \tan\left(f x + e\right)}{a^{4} b^{2} + 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 4 \, a b^{5} + b^{6} + {\left(a^{2} b^{4} + 2 \, a b^{5} + b^{6}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{3} b^{3} + 3 \, a^{2} b^{4} + 3 \, a b^{5} + b^{6}\right)} \tan\left(f x + e\right)^{2}}}{8 \, f}"," ",0,"1/8*((3*a^2 + 8*a*b + 8*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^2*b^2 + 2*a*b^3 + b^4)*sqrt((a + b)*b)) - ((5*a^2*b + 8*a*b^2)*tan(f*x + e)^3 + (3*a^3 + 11*a^2*b + 8*a*b^2)*tan(f*x + e))/(a^4*b^2 + 4*a^3*b^3 + 6*a^2*b^4 + 4*a*b^5 + b^6 + (a^2*b^4 + 2*a*b^5 + b^6)*tan(f*x + e)^4 + 2*(a^3*b^3 + 3*a^2*b^4 + 3*a*b^5 + b^6)*tan(f*x + e)^2))/f","A",0
213,1,187,0,0.457786," ","integrate(sec(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(a + 4 \, b\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{{\left(a b + 4 \, b^{2}\right)} \tan\left(f x + e\right)^{3} - {\left(a^{2} - 3 \, a b - 4 \, b^{2}\right)} \tan\left(f x + e\right)}{a^{4} b + 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 4 \, a b^{4} + b^{5} + {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \tan\left(f x + e\right)^{2}}}{8 \, f}"," ",0,"1/8*((a + 4*b)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^2*b + 2*a*b^2 + b^3)*sqrt((a + b)*b)) + ((a*b + 4*b^2)*tan(f*x + e)^3 - (a^2 - 3*a*b - 4*b^2)*tan(f*x + e))/(a^4*b + 4*a^3*b^2 + 6*a^2*b^3 + 4*a*b^4 + b^5 + (a^2*b^3 + 2*a*b^4 + b^5)*tan(f*x + e)^4 + 2*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*tan(f*x + e)^2))/f","A",0
214,1,156,0,0.457400," ","integrate(sec(f*x+e)^2/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{3 \, b \tan\left(f x + e\right)^{3} + 5 \, {\left(a + b\right)} \tan\left(f x + e\right)}{{\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \tan\left(f x + e\right)^{4} + a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \tan\left(f x + e\right)^{2}} + \frac{3 \, \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b}}}{8 \, f}"," ",0,"1/8*((3*b*tan(f*x + e)^3 + 5*(a + b)*tan(f*x + e))/((a^2*b^2 + 2*a*b^3 + b^4)*tan(f*x + e)^4 + a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*tan(f*x + e)^2) + 3*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)))/f","A",0
215,1,231,0,0.463636," ","integrate(1/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{{\left(7 \, a b^{2} + 4 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(9 \, a^{2} b + 13 \, a b^{2} + 4 \, b^{3}\right)} \tan\left(f x + e\right)}{a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(f x + e\right)^{2}} - \frac{8 \, {\left(f x + e\right)}}{a^{3}}}{8 \, f}"," ",0,"-1/8*((15*a^2*b + 20*a*b^2 + 8*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*b)) + ((7*a*b^2 + 4*b^3)*tan(f*x + e)^3 + (9*a^2*b + 13*a*b^2 + 4*b^3)*tan(f*x + e))/(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4 + (a^4*b^2 + 2*a^3*b^3 + a^2*b^4)*tan(f*x + e)^4 + 2*(a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*tan(f*x + e)^2) - 8*(f*x + e)/a^3)/f","A",0
216,1,338,0,0.460741," ","integrate(cos(f*x+e)^2/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(35 \, a^{2} b^{2} + 56 \, a b^{3} + 24 \, b^{4}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{{\left(4 \, a^{2} b^{2} + 19 \, a b^{3} + 12 \, b^{4}\right)} \tan\left(f x + e\right)^{5} + {\left(8 \, a^{3} b + 37 \, a^{2} b^{2} + 56 \, a b^{3} + 24 \, b^{4}\right)} \tan\left(f x + e\right)^{3} + {\left(4 \, a^{4} + 16 \, a^{3} b + 37 \, a^{2} b^{2} + 37 \, a b^{3} + 12 \, b^{4}\right)} \tan\left(f x + e\right)}{a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} \tan\left(f x + e\right)^{6} + {\left(2 \, a^{6} b + 7 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} \tan\left(f x + e\right)^{4} + {\left(a^{7} + 6 \, a^{6} b + 12 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} \tan\left(f x + e\right)^{2}} + \frac{4 \, {\left(f x + e\right)} {\left(a - 6 \, b\right)}}{a^{4}}}{8 \, f}"," ",0,"1/8*((35*a^2*b^2 + 56*a*b^3 + 24*b^4)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^6 + 2*a^5*b + a^4*b^2)*sqrt((a + b)*b)) + ((4*a^2*b^2 + 19*a*b^3 + 12*b^4)*tan(f*x + e)^5 + (8*a^3*b + 37*a^2*b^2 + 56*a*b^3 + 24*b^4)*tan(f*x + e)^3 + (4*a^4 + 16*a^3*b + 37*a^2*b^2 + 37*a*b^3 + 12*b^4)*tan(f*x + e))/(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4 + (a^5*b^2 + 2*a^4*b^3 + a^3*b^4)*tan(f*x + e)^6 + (2*a^6*b + 7*a^5*b^2 + 8*a^4*b^3 + 3*a^3*b^4)*tan(f*x + e)^4 + (a^7 + 6*a^6*b + 12*a^5*b^2 + 10*a^4*b^3 + 3*a^3*b^4)*tan(f*x + e)^2) + 4*(f*x + e)*(a - 6*b)/a^4)/f","A",0
217,1,464,0,0.473265," ","integrate(cos(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(21 \, a^{2} b^{3} + 36 \, a b^{4} + 16 \, b^{5}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{3 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} - 12 \, a b^{4} - 8 \, b^{5}\right)} \tan\left(f x + e\right)^{7} + {\left(6 \, a^{4} b - a^{3} b^{2} - 73 \, a^{2} b^{3} - 144 \, a b^{4} - 72 \, b^{5}\right)} \tan\left(f x + e\right)^{5} + {\left(3 \, a^{5} + 10 \, a^{4} b - 24 \, a^{3} b^{2} - 136 \, a^{2} b^{3} - 180 \, a b^{4} - 72 \, b^{5}\right)} \tan\left(f x + e\right)^{3} + {\left(5 \, a^{5} + 8 \, a^{4} b - 18 \, a^{3} b^{2} - 69 \, a^{2} b^{3} - 72 \, a b^{4} - 24 \, b^{5}\right)} \tan\left(f x + e\right)}{{\left(a^{6} b^{2} + 2 \, a^{5} b^{3} + a^{4} b^{4}\right)} \tan\left(f x + e\right)^{8} + a^{8} + 4 \, a^{7} b + 6 \, a^{6} b^{2} + 4 \, a^{5} b^{3} + a^{4} b^{4} + 2 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} \tan\left(f x + e\right)^{6} + {\left(a^{8} + 8 \, a^{7} b + 19 \, a^{6} b^{2} + 18 \, a^{5} b^{3} + 6 \, a^{4} b^{4}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} \tan\left(f x + e\right)^{2}} - \frac{3 \, {\left(a^{2} - 4 \, a b + 16 \, b^{2}\right)} {\left(f x + e\right)}}{a^{5}}}{8 \, f}"," ",0,"-1/8*(3*(21*a^2*b^3 + 36*a*b^4 + 16*b^5)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^7 + 2*a^6*b + a^5*b^2)*sqrt((a + b)*b)) - (3*(a^3*b^2 - 2*a^2*b^3 - 12*a*b^4 - 8*b^5)*tan(f*x + e)^7 + (6*a^4*b - a^3*b^2 - 73*a^2*b^3 - 144*a*b^4 - 72*b^5)*tan(f*x + e)^5 + (3*a^5 + 10*a^4*b - 24*a^3*b^2 - 136*a^2*b^3 - 180*a*b^4 - 72*b^5)*tan(f*x + e)^3 + (5*a^5 + 8*a^4*b - 18*a^3*b^2 - 69*a^2*b^3 - 72*a*b^4 - 24*b^5)*tan(f*x + e))/((a^6*b^2 + 2*a^5*b^3 + a^4*b^4)*tan(f*x + e)^8 + a^8 + 4*a^7*b + 6*a^6*b^2 + 4*a^5*b^3 + a^4*b^4 + 2*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*tan(f*x + e)^6 + (a^8 + 8*a^7*b + 19*a^6*b^2 + 18*a^5*b^3 + 6*a^4*b^4)*tan(f*x + e)^4 + 2*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*tan(f*x + e)^2) - 3*(a^2 - 4*a*b + 16*b^2)*(f*x + e)/a^5)/f","A",0
218,1,611,0,0.477237," ","integrate(cos(f*x+e)^6/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(99 \, a^{2} b^{4} + 176 \, a b^{5} + 80 \, b^{6}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{3 \, {\left(5 \, a^{4} b^{2} - 8 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 116 \, a b^{5} + 80 \, b^{6}\right)} \tan\left(f x + e\right)^{9} + 2 \, {\left(15 \, a^{5} b + 11 \, a^{4} b^{2} - 5 \, a^{3} b^{3} + 368 \, a^{2} b^{4} + 876 \, a b^{5} + 480 \, b^{6}\right)} \tan\left(f x + e\right)^{7} + {\left(15 \, a^{6} + 86 \, a^{5} b + 3 \, a^{4} b^{2} + 240 \, a^{3} b^{3} + 1982 \, a^{2} b^{4} + 3168 \, a b^{5} + 1440 \, b^{6}\right)} \tan\left(f x + e\right)^{5} + 2 \, {\left(20 \, a^{6} + 41 \, a^{5} b - 15 \, a^{4} b^{2} + 197 \, a^{3} b^{3} + 980 \, a^{2} b^{4} + 1236 \, a b^{5} + 480 \, b^{6}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(11 \, a^{6} + 14 \, a^{5} b - 6 \, a^{4} b^{2} + 56 \, a^{3} b^{3} + 221 \, a^{2} b^{4} + 236 \, a b^{5} + 80 \, b^{6}\right)} \tan\left(f x + e\right)}{{\left(a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4}\right)} \tan\left(f x + e\right)^{10} + a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4} + {\left(2 \, a^{8} b + 9 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 5 \, a^{5} b^{4}\right)} \tan\left(f x + e\right)^{8} + {\left(a^{9} + 10 \, a^{8} b + 27 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 10 \, a^{5} b^{4}\right)} \tan\left(f x + e\right)^{6} + {\left(3 \, a^{9} + 18 \, a^{8} b + 37 \, a^{7} b^{2} + 32 \, a^{6} b^{3} + 10 \, a^{5} b^{4}\right)} \tan\left(f x + e\right)^{4} + {\left(3 \, a^{9} + 14 \, a^{8} b + 24 \, a^{7} b^{2} + 18 \, a^{6} b^{3} + 5 \, a^{5} b^{4}\right)} \tan\left(f x + e\right)^{2}} + \frac{3 \, {\left(5 \, a^{3} - 18 \, a^{2} b + 48 \, a b^{2} - 160 \, b^{3}\right)} {\left(f x + e\right)}}{a^{6}}}{48 \, f}"," ",0,"1/48*(6*(99*a^2*b^4 + 176*a*b^5 + 80*b^6)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^8 + 2*a^7*b + a^6*b^2)*sqrt((a + b)*b)) + (3*(5*a^4*b^2 - 8*a^3*b^3 + 17*a^2*b^4 + 116*a*b^5 + 80*b^6)*tan(f*x + e)^9 + 2*(15*a^5*b + 11*a^4*b^2 - 5*a^3*b^3 + 368*a^2*b^4 + 876*a*b^5 + 480*b^6)*tan(f*x + e)^7 + (15*a^6 + 86*a^5*b + 3*a^4*b^2 + 240*a^3*b^3 + 1982*a^2*b^4 + 3168*a*b^5 + 1440*b^6)*tan(f*x + e)^5 + 2*(20*a^6 + 41*a^5*b - 15*a^4*b^2 + 197*a^3*b^3 + 980*a^2*b^4 + 1236*a*b^5 + 480*b^6)*tan(f*x + e)^3 + 3*(11*a^6 + 14*a^5*b - 6*a^4*b^2 + 56*a^3*b^3 + 221*a^2*b^4 + 236*a*b^5 + 80*b^6)*tan(f*x + e))/((a^7*b^2 + 2*a^6*b^3 + a^5*b^4)*tan(f*x + e)^10 + a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4 + (2*a^8*b + 9*a^7*b^2 + 12*a^6*b^3 + 5*a^5*b^4)*tan(f*x + e)^8 + (a^9 + 10*a^8*b + 27*a^7*b^2 + 28*a^6*b^3 + 10*a^5*b^4)*tan(f*x + e)^6 + (3*a^9 + 18*a^8*b + 37*a^7*b^2 + 32*a^6*b^3 + 10*a^5*b^4)*tan(f*x + e)^4 + (3*a^9 + 14*a^8*b + 24*a^7*b^2 + 18*a^6*b^3 + 5*a^5*b^4)*tan(f*x + e)^2) + 3*(5*a^3 - 18*a^2*b + 48*a*b^2 - 160*b^3)*(f*x + e)/a^6)/f","A",0
219,1,401,0,0.445558," ","integrate(1/(a+b*sec(d*x+c)^2)^4,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(35 \, a^{3} b + 70 \, a^{2} b^{2} + 56 \, a b^{3} + 16 \, b^{4}\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{3 \, {\left(19 \, a^{2} b^{3} + 22 \, a b^{4} + 8 \, b^{5}\right)} \tan\left(d x + c\right)^{5} + 8 \, {\left(17 \, a^{3} b^{2} + 35 \, a^{2} b^{3} + 24 \, a b^{4} + 6 \, b^{5}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(29 \, a^{4} b + 84 \, a^{3} b^{2} + 89 \, a^{2} b^{3} + 42 \, a b^{4} + 8 \, b^{5}\right)} \tan\left(d x + c\right)}{a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6} + {\left(a^{6} b^{3} + 3 \, a^{5} b^{4} + 3 \, a^{4} b^{5} + a^{3} b^{6}\right)} \tan\left(d x + c\right)^{6} + 3 \, {\left(a^{7} b^{2} + 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{8} b + 5 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 10 \, a^{5} b^{4} + 5 \, a^{4} b^{5} + a^{3} b^{6}\right)} \tan\left(d x + c\right)^{2}} - \frac{48 \, {\left(d x + c\right)}}{a^{4}}}{48 \, d}"," ",0,"-1/48*(3*(35*a^3*b + 70*a^2*b^2 + 56*a*b^3 + 16*b^4)*arctan(b*tan(d*x + c)/sqrt((a + b)*b))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sqrt((a + b)*b)) + (3*(19*a^2*b^3 + 22*a*b^4 + 8*b^5)*tan(d*x + c)^5 + 8*(17*a^3*b^2 + 35*a^2*b^3 + 24*a*b^4 + 6*b^5)*tan(d*x + c)^3 + 3*(29*a^4*b + 84*a^3*b^2 + 89*a^2*b^3 + 42*a*b^4 + 8*b^5)*tan(d*x + c))/(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6 + (a^6*b^3 + 3*a^5*b^4 + 3*a^4*b^5 + a^3*b^6)*tan(d*x + c)^6 + 3*(a^7*b^2 + 4*a^6*b^3 + 6*a^5*b^4 + 4*a^4*b^5 + a^3*b^6)*tan(d*x + c)^4 + 3*(a^8*b + 5*a^7*b^2 + 10*a^6*b^3 + 10*a^5*b^4 + 5*a^4*b^5 + a^3*b^6)*tan(d*x + c)^2) - 48*(d*x + c)/a^4)/d","B",0
220,1,81,0,0.450301," ","integrate((a-a*sec(d*x+c)^2)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a} a^{3} \tan\left(d x + c\right)^{6} - 3 \, \sqrt{-a} a^{3} \tan\left(d x + c\right)^{4} + 6 \, \sqrt{-a} a^{3} \tan\left(d x + c\right)^{2} - 6 \, \sqrt{-a} a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{12 \, d}"," ",0,"-1/12*(2*sqrt(-a)*a^3*tan(d*x + c)^6 - 3*sqrt(-a)*a^3*tan(d*x + c)^4 + 6*sqrt(-a)*a^3*tan(d*x + c)^2 - 6*sqrt(-a)*a^3*log(tan(d*x + c)^2 + 1))/d","A",0
221,1,62,0,0.454251," ","integrate((a-a*sec(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{-a} a^{2} \tan\left(d x + c\right)^{4} - 2 \, \sqrt{-a} a^{2} \tan\left(d x + c\right)^{2} + 2 \, \sqrt{-a} a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{4 \, d}"," ",0,"1/4*(sqrt(-a)*a^2*tan(d*x + c)^4 - 2*sqrt(-a)*a^2*tan(d*x + c)^2 + 2*sqrt(-a)*a^2*log(tan(d*x + c)^2 + 1))/d","A",0
222,1,40,0,0.429965," ","integrate((a-a*sec(d*x+c)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{-a} a \tan\left(d x + c\right)^{2} - \sqrt{-a} a \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"-1/2*(sqrt(-a)*a*tan(d*x + c)^2 - sqrt(-a)*a*log(tan(d*x + c)^2 + 1))/d","A",0
223,1,21,0,0.439021," ","integrate((a-a*sec(d*x+c)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{-a} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*sqrt(-a)*log(tan(d*x + c)^2 + 1)/d","A",0
224,1,37,0,0.434872," ","integrate(1/(a-a*sec(d*x+c)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\tan\left(d x + c\right)^{2} + 1\right)}{\sqrt{-a}} - \frac{2 \, \log\left(\tan\left(d x + c\right)\right)}{\sqrt{-a}}}{2 \, d}"," ",0,"-1/2*(log(tan(d*x + c)^2 + 1)/sqrt(-a) - 2*log(tan(d*x + c))/sqrt(-a))/d","A",0
225,1,60,0,0.434318," ","integrate(1/(a-a*sec(d*x+c)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\tan\left(d x + c\right)^{2} + 1\right)}{\sqrt{-a} a} - \frac{2 \, \log\left(\tan\left(d x + c\right)\right)}{\sqrt{-a} a} + \frac{\sqrt{-a}}{a^{2} \tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(log(tan(d*x + c)^2 + 1)/(sqrt(-a)*a) - 2*log(tan(d*x + c))/(sqrt(-a)*a) + sqrt(-a)/(a^2*tan(d*x + c)^2))/d","A",0
226,1,79,0,0.450239," ","integrate(1/(a-a*sec(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{\sqrt{-a} a^{2}} - \frac{4 \, \log\left(\tan\left(d x + c\right)\right)}{\sqrt{-a} a^{2}} + \frac{2 \, \sqrt{-a} \tan\left(d x + c\right)^{2} - \sqrt{-a}}{a^{3} \tan\left(d x + c\right)^{4}}}{4 \, d}"," ",0,"-1/4*(2*log(tan(d*x + c)^2 + 1)/(sqrt(-a)*a^2) - 4*log(tan(d*x + c))/(sqrt(-a)*a^2) + (2*sqrt(-a)*tan(d*x + c)^2 - sqrt(-a))/(a^3*tan(d*x + c)^4))/d","A",0
227,1,94,0,0.454045," ","integrate(1/(a-a*sec(d*x+c)^2)^(7/2),x, algorithm=""maxima"")","-\frac{\frac{6 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{\sqrt{-a} a^{3}} - \frac{12 \, \log\left(\tan\left(d x + c\right)\right)}{\sqrt{-a} a^{3}} + \frac{6 \, \sqrt{-a} \tan\left(d x + c\right)^{4} - 3 \, \sqrt{-a} \tan\left(d x + c\right)^{2} + 2 \, \sqrt{-a}}{a^{4} \tan\left(d x + c\right)^{6}}}{12 \, d}"," ",0,"-1/12*(6*log(tan(d*x + c)^2 + 1)/(sqrt(-a)*a^3) - 12*log(tan(d*x + c))/(sqrt(-a)*a^3) + (6*sqrt(-a)*tan(d*x + c)^4 - 3*sqrt(-a)*tan(d*x + c)^2 + 2*sqrt(-a))/(a^4*tan(d*x + c)^6))/d","A",0
228,0,0,0,0.000000," ","integrate(sec(f*x+e)^5*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \sec\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*sec(f*x + e)^5, x)","F",0
229,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*sec(f*x + e)^3, x)","F",0
230,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*sec(f*x + e), x)","F",0
231,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cos(f*x + e), x)","F",0
232,0,0,0,0.000000," ","integrate(cos(f*x+e)^3*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cos\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cos(f*x + e)^3, x)","F",0
233,0,0,0,0.000000," ","integrate(cos(f*x+e)^5*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cos\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cos(f*x + e)^5, x)","F",0
234,1,317,0,0.357300," ","integrate(sec(f*x+e)^6*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{3}}{b} + \frac{3 \, {\left(a + b\right)}^{2} a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{5}{2}}} + \frac{3 \, {\left(a + b\right)}^{2} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} - \frac{12 \, {\left(a + b\right)} a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} - \frac{12 \, {\left(a + b\right)} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} + \frac{24 \, a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} + 24 \, \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + 24 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} \tan\left(f x + e\right) - \frac{6 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)} \tan\left(f x + e\right)}{b^{2}} + \frac{3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2} \tan\left(f x + e\right)}{b^{2}} + \frac{24 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} \tan\left(f x + e\right)}{b} - \frac{12 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right)}{b}}{48 \, f}"," ",0,"1/48*(8*(b*tan(f*x + e)^2 + a + b)^(3/2)*tan(f*x + e)^3/b + 3*(a + b)^2*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(5/2) + 3*(a + b)^2*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) - 12*(a + b)*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) - 12*(a + b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) + 24*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) + 24*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) + 24*sqrt(b*tan(f*x + e)^2 + a + b)*tan(f*x + e) - 6*(b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)*tan(f*x + e)/b^2 + 3*sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2*tan(f*x + e)/b^2 + 24*(b*tan(f*x + e)^2 + a + b)^(3/2)*tan(f*x + e)/b - 12*sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e)/b)/f","A",0
235,1,173,0,0.357707," ","integrate(sec(f*x+e)^4*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(a + b\right)} a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} + \frac{{\left(a + b\right)} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} - \frac{4 \, a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} - 4 \, \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) - 4 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} \tan\left(f x + e\right) - \frac{2 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} \tan\left(f x + e\right)}{b} + \frac{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right)}{b}}{8 \, f}"," ",0,"-1/8*((a + b)*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) + (a + b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) - 4*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) - 4*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) - 4*sqrt(b*tan(f*x + e)^2 + a + b)*tan(f*x + e) - 2*(b*tan(f*x + e)^2 + a + b)^(3/2)*tan(f*x + e)/b + sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e)/b)/f","A",0
236,1,69,0,0.338689," ","integrate(sec(f*x+e)^2*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} + \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + \sqrt{b \tan\left(f x + e\right)^{2} + a + b} \tan\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) + sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) + sqrt(b*tan(f*x + e)^2 + a + b)*tan(f*x + e))/f","A",0
237,-2,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(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
238,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cos(f*x + e)^2, x)","F",0
239,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cos(f*x + e)^4, x)","F",0
240,0,0,0,0.000000," ","integrate(cos(f*x+e)^6*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cos\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cos(f*x + e)^6, x)","F",0
241,0,0,0,0.000000," ","integrate(sec(f*x+e)^5*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*sec(f*x + e)^5, x)","F",0
242,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*sec(f*x + e)^3, x)","F",0
243,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*sec(f*x + e), x)","F",0
244,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cos(f*x + e), x)","F",0
245,0,0,0,0.000000," ","integrate(cos(f*x+e)^3*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cos(f*x + e)^3, x)","F",0
246,0,0,0,0.000000," ","integrate(cos(f*x+e)^5*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cos(f*x + e)^5, x)","F",0
247,1,415,0,0.355483," ","integrate(sec(f*x+e)^6*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{48 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{5}{2}} \tan\left(f x + e\right)^{3}}{b} + \frac{9 \, {\left(a + b\right)}^{3} a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{5}{2}}} + \frac{9 \, {\left(a + b\right)}^{3} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} - \frac{48 \, {\left(a + b\right)}^{2} a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} - \frac{48 \, {\left(a + b\right)}^{2} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} + \frac{144 \, {\left(a + b\right)} a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} + 144 \, {\left(a + b\right)} \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + 96 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} \tan\left(f x + e\right) + 144 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right) - \frac{24 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{5}{2}} {\left(a + b\right)} \tan\left(f x + e\right)}{b^{2}} + \frac{6 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}^{2} \tan\left(f x + e\right)}{b^{2}} + \frac{9 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{3} \tan\left(f x + e\right)}{b^{2}} + \frac{128 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{5}{2}} \tan\left(f x + e\right)}{b} - \frac{32 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)} \tan\left(f x + e\right)}{b} - \frac{48 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2} \tan\left(f x + e\right)}{b}}{384 \, f}"," ",0,"1/384*(48*(b*tan(f*x + e)^2 + a + b)^(5/2)*tan(f*x + e)^3/b + 9*(a + b)^3*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(5/2) + 9*(a + b)^3*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) - 48*(a + b)^2*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) - 48*(a + b)^2*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) + 144*(a + b)*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) + 144*(a + b)*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) + 96*(b*tan(f*x + e)^2 + a + b)^(3/2)*tan(f*x + e) + 144*sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e) - 24*(b*tan(f*x + e)^2 + a + b)^(5/2)*(a + b)*tan(f*x + e)/b^2 + 6*(b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)^2*tan(f*x + e)/b^2 + 9*sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^3*tan(f*x + e)/b^2 + 128*(b*tan(f*x + e)^2 + a + b)^(5/2)*tan(f*x + e)/b - 32*(b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)*tan(f*x + e)/b - 48*sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2*tan(f*x + e)/b)/f","A",0
248,1,243,0,0.363943," ","integrate(sec(f*x+e)^4*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a + b\right)}^{2} a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} + \frac{3 \, {\left(a + b\right)}^{2} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} - \frac{18 \, {\left(a + b\right)} a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} - 18 \, {\left(a + b\right)} \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) - 12 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} \tan\left(f x + e\right) - 18 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right) - \frac{8 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{5}{2}} \tan\left(f x + e\right)}{b} + \frac{2 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)} \tan\left(f x + e\right)}{b} + \frac{3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2} \tan\left(f x + e\right)}{b}}{48 \, f}"," ",0,"-1/48*(3*(a + b)^2*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) + 3*(a + b)^2*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) - 18*(a + b)*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) - 18*(a + b)*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) - 12*(b*tan(f*x + e)^2 + a + b)^(3/2)*tan(f*x + e) - 18*sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e) - 8*(b*tan(f*x + e)^2 + a + b)^(5/2)*tan(f*x + e)/b + 2*(b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)*tan(f*x + e)/b + 3*sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2*tan(f*x + e)/b)/f","A",0
249,1,104,0,0.341111," ","integrate(sec(f*x+e)^2*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a + b\right)} a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} + 3 \, {\left(a + b\right)} \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + 2 \, {\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} \tan\left(f x + e\right) + 3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right)}{8 \, f}"," ",0,"1/8*(3*(a + b)*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) + 3*(a + b)*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b)) + 2*(b*tan(f*x + e)^2 + a + b)^(3/2)*tan(f*x + e) + 3*sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e))/f","A",0
250,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
251,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cos(f*x + e)^2, x)","F",0
252,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cos(f*x + e)^4, x)","F",0
253,0,0,0,0.000000," ","integrate(cos(f*x+e)^6*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cos(f*x + e)^6, x)","F",0
254,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right)^{2} + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c)^2 + a)^(5/2), x)","F",0
255,0,0,0,0.000000," ","integrate((1+sec(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(\sec\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((sec(x)^2 + 1)^(3/2), x)","F",0
256,-2,0,0,0.000000," ","integrate((1+sec(x)^2)^(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
257,0,0,0,0.000000," ","integrate(sec(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{5}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sec(f*x + e)^5/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
258,0,0,0,0.000000," ","integrate(sec(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{3}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sec(f*x + e)^3/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
259,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sec(f*x + e)/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
260,0,0,0,0.000000," ","integrate(cos(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cos(f*x + e)/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
261,0,0,0,0.000000," ","integrate(cos(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{3}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cos(f*x + e)^3/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
262,0,0,0,0.000000," ","integrate(cos(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{5}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cos(f*x + e)^5/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
263,1,160,0,0.359885," ","integrate(sec(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} \tan\left(f x + e\right)^{3}}{b} + \frac{3 \, {\left(a + b\right)} a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{5}{2}}} + \frac{3 \, {\left(a + b\right)} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} - \frac{8 \, a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} - \frac{3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \tan\left(f x + e\right)}{b^{2}} + \frac{8 \, \sqrt{b \tan\left(f x + e\right)^{2} + a + b} \tan\left(f x + e\right)}{b}}{8 \, f}"," ",0,"1/8*(2*sqrt(b*tan(f*x + e)^2 + a + b)*tan(f*x + e)^3/b + 3*(a + b)*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(5/2) + 3*(a + b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) - 8*a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) - 3*sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*tan(f*x + e)/b^2 + 8*sqrt(b*tan(f*x + e)^2 + a + b)*tan(f*x + e)/b)/f","A",0
264,1,74,0,0.330025," ","integrate(sec(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{a \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} - \frac{\operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} - \frac{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} \tan\left(f x + e\right)}{b}}{2 \, f}"," ",0,"-1/2*(a*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) - arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/sqrt(b) - sqrt(b*tan(f*x + e)^2 + a + b)*tan(f*x + e)/b)/f","A",0
265,1,23,0,0.330312," ","integrate(sec(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b} f}"," ",0,"arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt(b)*f)","A",0
266,1,992,0,0.625670," ","integrate(1/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\arctan\left(2 \, a \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, a \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 2 \, a + 4 \, b\right) - \arctan\left(2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 4 \, a + 4 \, b\right)}{2 \, \sqrt{a} f}"," ",0,"1/2*(arctan2(2*a*sin(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*a*cos(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 2*a + 4*b) - arctan2(2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 4*a + 4*b))/(sqrt(a)*f)","B",0
267,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
268,0,0,0,0.000000," ","integrate(cos(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{4}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cos(f*x + e)^4/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
269,0,0,0,0.000000," ","integrate(cos(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{6}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cos(f*x + e)^6/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
270,0,0,0,0.000000," ","integrate(sec(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{5}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^5/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
271,0,0,0,0.000000," ","integrate(sec(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{3}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^3/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
272,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
273,0,0,0,0.000000," ","integrate(cos(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
274,0,0,0,0.000000," ","integrate(cos(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{3}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^3/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
275,0,0,0,0.000000," ","integrate(cos(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{5}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^5/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
276,1,161,0,0.358372," ","integrate(sec(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{\tan\left(f x + e\right)^{3}}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} b} - \frac{3 \, {\left(a + b\right)} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{5}{2}}} + \frac{4 \, \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} + \frac{2 \, \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}} + \frac{3 \, {\left(a + b\right)} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} b^{2}} - \frac{4 \, \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} b}}{2 \, f}"," ",0,"1/2*(tan(f*x + e)^3/(sqrt(b*tan(f*x + e)^2 + a + b)*b) - 3*(a + b)*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(5/2) + 4*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) + 2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)) + 3*(a + b)*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*b^2) - 4*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*b))/f","A",0
277,1,78,0,0.350843," ","integrate(sec(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{\operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} + \frac{\tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}} - \frac{\tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} b}}{f}"," ",0,"(arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(3/2) + tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)) - tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*b))/f","A",0
278,1,30,0,0.330311," ","integrate(sec(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} f}"," ",0,"tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*f)","A",0
279,1,2055,0,0.840761," ","integrate(1/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, a b \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} + a b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{3} - 2 \, {\left(a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + a b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} - a^{2} - 2 \, a b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) - {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left({\left(a + b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + {\left(a + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} \arctan\left(2 \, a \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, a \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 2 \, a + 4 \, b\right) - {\left({\left(a + b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + {\left(a + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} \arctan\left(2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 4 \, a + 4 \, b\right)\right)} \sqrt{a}}{2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left(a^{3} + a^{2} b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + {\left(a^{3} + a^{2} b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} f}"," ",0,"-1/2*(2*a*b*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))*sin(2*f*x + 2*e) - 2*(a^2 + a*b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^3 - 2*(a*b*cos(2*f*x + 2*e) + (a^2 + a*b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 - a^2 - 2*a*b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) - (a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*(((a + b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + (a + b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*arctan2(2*a*sin(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*a*cos(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 2*a + 4*b) - ((a + b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + (a + b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*arctan2(2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 4*a + 4*b))*sqrt(a))/((a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*((a^3 + a^2*b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + (a^3 + a^2*b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*f)","B",0
280,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
281,0,0,0,0.000000," ","integrate(cos(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{4}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^4/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
282,0,0,0,0.000000," ","integrate(cos(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{6}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^6/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
283,0,0,0,0.000000," ","integrate(sec(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{5}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^5/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
284,0,0,0,0.000000," ","integrate(sec(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{3}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^3/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
285,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
286,0,0,0,0.000000," ","integrate(cos(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
287,0,0,0,0.000000," ","integrate(cos(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{3}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^3/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
288,0,0,0,0.000000," ","integrate(cos(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{5}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^5/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
289,1,275,0,0.385768," ","integrate(sec(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{{\left(\frac{3 \, \tan\left(f x + e\right)^{2}}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b^{2}} + \frac{2}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b}\right)} \tan\left(f x + e\right) - \frac{3 \, \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{5}{2}}} - \frac{2 \, \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2}} - \frac{\tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}} + \frac{3 \, \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} b^{2}} - \frac{2 \, a \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} b^{2}} + \frac{2 \, \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b} - \frac{4 \, \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} b}}{3 \, f}"," ",0,"-1/3*((3*tan(f*x + e)^2/((b*tan(f*x + e)^2 + a + b)^(3/2)*b) + 2*a/((b*tan(f*x + e)^2 + a + b)^(3/2)*b^2) + 2/((b*tan(f*x + e)^2 + a + b)^(3/2)*b))*tan(f*x + e) - 3*arcsinh(b*tan(f*x + e)/sqrt((a + b)*b))/b^(5/2) - 2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2) - tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)) + 3*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*b^2) - 2*a*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*b^2) + 2*tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*b) - 4*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*b))/f","B",0
290,1,117,0,0.362969," ","integrate(sec(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2}} + \frac{\tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}} - \frac{\tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b} + \frac{\tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} b}}{3 \, f}"," ",0,"1/3*(2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2) + tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)) - tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*b) + tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)*b))/f","A",0
291,1,61,0,0.370221," ","integrate(sec(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2}} + \frac{\tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}}}{3 \, f}"," ",0,"1/3*(2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a + b)*(a + b)^2) + tan(f*x + e)/((b*tan(f*x + e)^2 + a + b)^(3/2)*(a + b)))/f","A",0
292,-1,0,0,0.000000," ","integrate(1/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
294,0,0,0,0.000000," ","integrate(cos(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{4}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^4/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
295,0,0,0,0.000000," ","integrate(cos(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{6}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^6/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
296,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c)^2)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,1,388,0,0.577192," ","integrate(1/(1+sec(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \arctan\left(2 \, {\left(2 \, {\left(6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 36 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 12 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, \sin\left(2 \, x\right)^{2} + 12 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right), \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) + 1\right)\right), 2 \, {\left(2 \, {\left(6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 36 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 12 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, \sin\left(2 \, x\right)^{2} + 12 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right), \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) + 1\right)\right) + 8\right) + \frac{1}{2} \, \arctan\left(2 \, {\left(2 \, {\left(6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 36 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 12 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, \sin\left(2 \, x\right)^{2} + 12 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right), \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) + 1\right)\right) + 2 \, \sin\left(2 \, x\right), 2 \, {\left(2 \, {\left(6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 36 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 12 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, \sin\left(2 \, x\right)^{2} + 12 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right), \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) + 1\right)\right) + 2 \, \cos\left(2 \, x\right) + 6\right)"," ",0,"-1/2*arctan2(2*(2*(6*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 36*cos(2*x)^2 + sin(4*x)^2 + 12*sin(4*x)*sin(2*x) + 36*sin(2*x)^2 + 12*cos(2*x) + 1)^(1/4)*sin(1/2*arctan2(sin(4*x) + 6*sin(2*x), cos(4*x) + 6*cos(2*x) + 1)), 2*(2*(6*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 36*cos(2*x)^2 + sin(4*x)^2 + 12*sin(4*x)*sin(2*x) + 36*sin(2*x)^2 + 12*cos(2*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x) + 6*sin(2*x), cos(4*x) + 6*cos(2*x) + 1)) + 8) + 1/2*arctan2(2*(2*(6*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 36*cos(2*x)^2 + sin(4*x)^2 + 12*sin(4*x)*sin(2*x) + 36*sin(2*x)^2 + 12*cos(2*x) + 1)^(1/4)*sin(1/2*arctan2(sin(4*x) + 6*sin(2*x), cos(4*x) + 6*cos(2*x) + 1)) + 2*sin(2*x), 2*(2*(6*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 36*cos(2*x)^2 + sin(4*x)^2 + 12*sin(4*x)*sin(2*x) + 36*sin(2*x)^2 + 12*cos(2*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x) + 6*sin(2*x), cos(4*x) + 6*cos(2*x) + 1)) + 2*cos(2*x) + 6)","B",0
298,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*(d*sec(f*x + e))^m, x)","F",0
299,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*sec(f*x + e)^3, x)","F",0
300,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*sec(f*x + e), x)","F",0
301,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*cos(f*x + e), x)","F",0
302,0,0,0,0.000000," ","integrate(cos(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*cos(f*x + e)^3, x)","F",0
303,0,0,0,0.000000," ","integrate(cos(f*x+e)^5*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*cos(f*x + e)^5, x)","F",0
304,0,0,0,0.000000," ","integrate(sec(f*x+e)^6*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \sec\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*sec(f*x + e)^6, x)","F",0
305,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*sec(f*x + e)^4, x)","F",0
306,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*sec(f*x + e)^2, x)","F",0
307,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p, x)","F",0
308,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*cos(f*x + e)^2, x)","F",0
309,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*cos(f*x + e)^4, x)","F",0
310,0,0,0,0.000000," ","integrate(cos(f*x+e)^6*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*cos(f*x + e)^6, x)","F",0
311,1,95,0,0.325852," ","integrate((a+b*sec(f*x+e)^2)*tan(f*x+e)^5,x, algorithm=""maxima"")","-\frac{6 \, a \log\left(\sin\left(f x + e\right)^{2} - 1\right) - \frac{6 \, {\left(2 \, a - b\right)} \sin\left(f x + e\right)^{4} - 3 \, {\left(7 \, a - 2 \, b\right)} \sin\left(f x + e\right)^{2} + 9 \, a - 2 \, b}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1}}{12 \, f}"," ",0,"-1/12*(6*a*log(sin(f*x + e)^2 - 1) - (6*(2*a - b)*sin(f*x + e)^4 - 3*(7*a - 2*b)*sin(f*x + e)^2 + 9*a - 2*b)/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1))/f","A",0
312,1,64,0,0.326544," ","integrate((a+b*sec(f*x+e)^2)*tan(f*x+e)^3,x, algorithm=""maxima"")","\frac{2 \, a \log\left(\sin\left(f x + e\right)^{2} - 1\right) - \frac{2 \, {\left(a - b\right)} \sin\left(f x + e\right)^{2} - 2 \, a + b}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1}}{4 \, f}"," ",0,"1/4*(2*a*log(sin(f*x + e)^2 - 1) - (2*(a - b)*sin(f*x + e)^2 - 2*a + b)/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1))/f","A",0
313,1,33,0,0.319789," ","integrate((a+b*sec(f*x+e)^2)*tan(f*x+e),x, algorithm=""maxima"")","-\frac{a \log\left(\sin\left(f x + e\right)^{2} - 1\right) + \frac{b}{\sin\left(f x + e\right)^{2} - 1}}{2 \, f}"," ",0,"-1/2*(a*log(sin(f*x + e)^2 - 1) + b/(sin(f*x + e)^2 - 1))/f","A",0
314,1,33,0,0.338298," ","integrate(cot(f*x+e)*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{b \log\left(\sin\left(f x + e\right)^{2} - 1\right) - {\left(a + b\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{2 \, f}"," ",0,"-1/2*(b*log(sin(f*x + e)^2 - 1) - (a + b)*log(sin(f*x + e)^2))/f","A",0
315,1,29,0,0.321999," ","integrate(cot(f*x+e)^3*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{a \log\left(\sin\left(f x + e\right)^{2}\right) + \frac{a + b}{\sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"-1/2*(a*log(sin(f*x + e)^2) + (a + b)/sin(f*x + e)^2)/f","A",0
316,1,49,0,0.323790," ","integrate(cot(f*x+e)^5*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{2 \, a \log\left(\sin\left(f x + e\right)^{2}\right) + \frac{2 \, {\left(2 \, a + b\right)} \sin\left(f x + e\right)^{2} - a - b}{\sin\left(f x + e\right)^{4}}}{4 \, f}"," ",0,"1/4*(2*a*log(sin(f*x + e)^2) + (2*(2*a + b)*sin(f*x + e)^2 - a - b)/sin(f*x + e)^4)/f","A",0
317,1,56,0,0.415379," ","integrate((a+b*sec(f*x+e)^2)*tan(f*x+e)^6,x, algorithm=""maxima"")","\frac{15 \, b \tan\left(f x + e\right)^{7} + 21 \, a \tan\left(f x + e\right)^{5} - 35 \, a \tan\left(f x + e\right)^{3} - 105 \, {\left(f x + e\right)} a + 105 \, a \tan\left(f x + e\right)}{105 \, f}"," ",0,"1/105*(15*b*tan(f*x + e)^7 + 21*a*tan(f*x + e)^5 - 35*a*tan(f*x + e)^3 - 105*(f*x + e)*a + 105*a*tan(f*x + e))/f","A",0
318,1,45,0,0.411472," ","integrate((a+b*sec(f*x+e)^2)*tan(f*x+e)^4,x, algorithm=""maxima"")","\frac{3 \, b \tan\left(f x + e\right)^{5} + 5 \, a \tan\left(f x + e\right)^{3} + 15 \, {\left(f x + e\right)} a - 15 \, a \tan\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*b*tan(f*x + e)^5 + 5*a*tan(f*x + e)^3 + 15*(f*x + e)*a - 15*a*tan(f*x + e))/f","A",0
319,1,33,0,0.418809," ","integrate((a+b*sec(f*x+e)^2)*tan(f*x+e)^2,x, algorithm=""maxima"")","\frac{b \tan\left(f x + e\right)^{3} - 3 \, {\left(f x + e\right)} a + 3 \, a \tan\left(f x + e\right)}{3 \, f}"," ",0,"1/3*(b*tan(f*x + e)^3 - 3*(f*x + e)*a + 3*a*tan(f*x + e))/f","A",0
320,1,15,0,0.331455," ","integrate(a+b*sec(f*x+e)^2,x, algorithm=""maxima"")","a x + \frac{b \tan\left(f x + e\right)}{f}"," ",0,"a*x + b*tan(f*x + e)/f","A",0
321,1,25,0,0.430719," ","integrate(cot(f*x+e)^2*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{{\left(f x + e\right)} a + \frac{a + b}{\tan\left(f x + e\right)}}{f}"," ",0,"-((f*x + e)*a + (a + b)/tan(f*x + e))/f","A",0
322,1,41,0,0.419327," ","integrate(cot(f*x+e)^4*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} a + \frac{3 \, a \tan\left(f x + e\right)^{2} - a - b}{\tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*a + (3*a*tan(f*x + e)^2 - a - b)/tan(f*x + e)^3)/f","A",0
323,1,52,0,0.420118," ","integrate(cot(f*x+e)^6*(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{15 \, {\left(f x + e\right)} a + \frac{15 \, a \tan\left(f x + e\right)^{4} - 5 \, a \tan\left(f x + e\right)^{2} + 3 \, a + 3 \, b}{\tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(15*(f*x + e)*a + (15*a*tan(f*x + e)^4 - 5*a*tan(f*x + e)^2 + 3*a + 3*b)/tan(f*x + e)^5)/f","A",0
324,1,147,0,0.344155," ","integrate((a+b*sec(f*x+e)^2)^2*tan(f*x+e)^5,x, algorithm=""maxima"")","-\frac{12 \, a^{2} \log\left(\sin\left(f x + e\right)^{2} - 1\right) - \frac{24 \, {\left(a^{2} - a b\right)} \sin\left(f x + e\right)^{6} - 6 \, {\left(11 \, a^{2} - 8 \, a b - b^{2}\right)} \sin\left(f x + e\right)^{4} + 4 \, {\left(15 \, a^{2} - 8 \, a b - b^{2}\right)} \sin\left(f x + e\right)^{2} - 18 \, a^{2} + 8 \, a b + b^{2}}{\sin\left(f x + e\right)^{8} - 4 \, \sin\left(f x + e\right)^{6} + 6 \, \sin\left(f x + e\right)^{4} - 4 \, \sin\left(f x + e\right)^{2} + 1}}{24 \, f}"," ",0,"-1/24*(12*a^2*log(sin(f*x + e)^2 - 1) - (24*(a^2 - a*b)*sin(f*x + e)^6 - 6*(11*a^2 - 8*a*b - b^2)*sin(f*x + e)^4 + 4*(15*a^2 - 8*a*b - b^2)*sin(f*x + e)^2 - 18*a^2 + 8*a*b + b^2)/(sin(f*x + e)^8 - 4*sin(f*x + e)^6 + 6*sin(f*x + e)^4 - 4*sin(f*x + e)^2 + 1))/f","A",0
325,1,114,0,0.325135," ","integrate((a+b*sec(f*x+e)^2)^2*tan(f*x+e)^3,x, algorithm=""maxima"")","\frac{6 \, a^{2} \log\left(\sin\left(f x + e\right)^{2} - 1\right) - \frac{6 \, {\left(a^{2} - 2 \, a b\right)} \sin\left(f x + e\right)^{4} - 3 \, {\left(4 \, a^{2} - 6 \, a b - b^{2}\right)} \sin\left(f x + e\right)^{2} + 6 \, a^{2} - 6 \, a b - b^{2}}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1}}{12 \, f}"," ",0,"1/12*(6*a^2*log(sin(f*x + e)^2 - 1) - (6*(a^2 - 2*a*b)*sin(f*x + e)^4 - 3*(4*a^2 - 6*a*b - b^2)*sin(f*x + e)^2 + 6*a^2 - 6*a*b - b^2)/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1))/f","A",0
326,1,67,0,0.330440," ","integrate((a+b*sec(f*x+e)^2)^2*tan(f*x+e),x, algorithm=""maxima"")","-\frac{2 \, a^{2} \log\left(\sin\left(f x + e\right)^{2} - 1\right) + \frac{4 \, a b \sin\left(f x + e\right)^{2} - 4 \, a b - b^{2}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1}}{4 \, f}"," ",0,"-1/4*(2*a^2*log(sin(f*x + e)^2 - 1) + (4*a*b*sin(f*x + e)^2 - 4*a*b - b^2)/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1))/f","A",0
327,1,64,0,0.342120," ","integrate(cot(f*x+e)*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, a b + b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2} - 1\right) - {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2}\right) + \frac{b^{2}}{\sin\left(f x + e\right)^{2} - 1}}{2 \, f}"," ",0,"-1/2*((2*a*b + b^2)*log(sin(f*x + e)^2 - 1) - (a^2 + 2*a*b + b^2)*log(sin(f*x + e)^2) + b^2/(sin(f*x + e)^2 - 1))/f","A",0
328,1,60,0,0.332772," ","integrate(cot(f*x+e)^3*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(\sin\left(f x + e\right)^{2} - 1\right) + {\left(a^{2} - b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2}\right) + \frac{a^{2} + 2 \, a b + b^{2}}{\sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"-1/2*(b^2*log(sin(f*x + e)^2 - 1) + (a^2 - b^2)*log(sin(f*x + e)^2) + (a^2 + 2*a*b + b^2)/sin(f*x + e)^2)/f","A",0
329,1,61,0,0.337960," ","integrate(cot(f*x+e)^5*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{2 \, a^{2} \log\left(\sin\left(f x + e\right)^{2}\right) + \frac{4 \, {\left(a^{2} + a b\right)} \sin\left(f x + e\right)^{2} - a^{2} - 2 \, a b - b^{2}}{\sin\left(f x + e\right)^{4}}}{4 \, f}"," ",0,"1/4*(2*a^2*log(sin(f*x + e)^2) + (4*(a^2 + a*b)*sin(f*x + e)^2 - a^2 - 2*a*b - b^2)/sin(f*x + e)^4)/f","A",0
330,1,84,0,0.436849," ","integrate((a+b*sec(f*x+e)^2)^2*tan(f*x+e)^6,x, algorithm=""maxima"")","\frac{35 \, b^{2} \tan\left(f x + e\right)^{9} + 45 \, {\left(2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{7} + 63 \, a^{2} \tan\left(f x + e\right)^{5} - 105 \, a^{2} \tan\left(f x + e\right)^{3} - 315 \, {\left(f x + e\right)} a^{2} + 315 \, a^{2} \tan\left(f x + e\right)}{315 \, f}"," ",0,"1/315*(35*b^2*tan(f*x + e)^9 + 45*(2*a*b + b^2)*tan(f*x + e)^7 + 63*a^2*tan(f*x + e)^5 - 105*a^2*tan(f*x + e)^3 - 315*(f*x + e)*a^2 + 315*a^2*tan(f*x + e))/f","A",0
331,1,71,0,0.433753," ","integrate((a+b*sec(f*x+e)^2)^2*tan(f*x+e)^4,x, algorithm=""maxima"")","\frac{15 \, b^{2} \tan\left(f x + e\right)^{7} + 21 \, {\left(2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{5} + 35 \, a^{2} \tan\left(f x + e\right)^{3} + 105 \, {\left(f x + e\right)} a^{2} - 105 \, a^{2} \tan\left(f x + e\right)}{105 \, f}"," ",0,"1/105*(15*b^2*tan(f*x + e)^7 + 21*(2*a*b + b^2)*tan(f*x + e)^5 + 35*a^2*tan(f*x + e)^3 + 105*(f*x + e)*a^2 - 105*a^2*tan(f*x + e))/f","A",0
332,1,58,0,0.435915," ","integrate((a+b*sec(f*x+e)^2)^2*tan(f*x+e)^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} \tan\left(f x + e\right)^{5} + 5 \, {\left(2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{3} - 15 \, {\left(f x + e\right)} a^{2} + 15 \, a^{2} \tan\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*b^2*tan(f*x + e)^5 + 5*(2*a*b + b^2)*tan(f*x + e)^3 - 15*(f*x + e)*a^2 + 15*a^2*tan(f*x + e))/f","A",0
333,1,44,0,0.340473," ","integrate((a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} b^{2}}{3 \, f} + \frac{2 \, a b \tan\left(f x + e\right)}{f}"," ",0,"a^2*x + 1/3*(tan(f*x + e)^3 + 3*tan(f*x + e))*b^2/f + 2*a*b*tan(f*x + e)/f","A",0
334,1,46,0,0.448664," ","integrate(cot(f*x+e)^2*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{{\left(f x + e\right)} a^{2} - b^{2} \tan\left(f x + e\right) + \frac{a^{2} + 2 \, a b + b^{2}}{\tan\left(f x + e\right)}}{f}"," ",0,"-((f*x + e)*a^2 - b^2*tan(f*x + e) + (a^2 + 2*a*b + b^2)/tan(f*x + e))/f","A",0
335,1,59,0,0.455476," ","integrate(cot(f*x+e)^4*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} a^{2} + \frac{3 \, {\left(a^{2} - b^{2}\right)} \tan\left(f x + e\right)^{2} - a^{2} - 2 \, a b - b^{2}}{\tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*a^2 + (3*(a^2 - b^2)*tan(f*x + e)^2 - a^2 - 2*a*b - b^2)/tan(f*x + e)^3)/f","A",0
336,1,72,0,0.434270," ","integrate(cot(f*x+e)^6*(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{15 \, {\left(f x + e\right)} a^{2} + \frac{15 \, a^{2} \tan\left(f x + e\right)^{4} - 5 \, {\left(a^{2} - b^{2}\right)} \tan\left(f x + e\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}}{\tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(15*(f*x + e)*a^2 + (15*a^2*tan(f*x + e)^4 - 5*(a^2 - b^2)*tan(f*x + e)^2 + 3*a^2 + 6*a*b + 3*b^2)/tan(f*x + e)^5)/f","A",0
337,1,81,0,0.341129," ","integrate(tan(f*x+e)^5/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{{\left(a + 2 \, b\right)} \log\left(\sin\left(f x + e\right)^{2} - 1\right)}{b^{2}} - \frac{1}{b \sin\left(f x + e\right)^{2} - b} - \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a b^{2}}}{2 \, f}"," ",0,"1/2*((a + 2*b)*log(sin(f*x + e)^2 - 1)/b^2 - 1/(b*sin(f*x + e)^2 - b) - (a^2 + 2*a*b + b^2)*log(a*sin(f*x + e)^2 - a - b)/(a*b^2))/f","A",0
338,1,50,0,0.357278," ","integrate(tan(f*x+e)^3/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{{\left(a + b\right)} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a b} - \frac{\log\left(\sin\left(f x + e\right)^{2} - 1\right)}{b}}{2 \, f}"," ",0,"1/2*((a + b)*log(a*sin(f*x + e)^2 - a - b)/(a*b) - log(sin(f*x + e)^2 - 1)/b)/f","A",0
339,1,26,0,0.341771," ","integrate(tan(f*x+e)/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{2 \, a f}"," ",0,"-1/2*log(a*sin(f*x + e)^2 - a - b)/(a*f)","A",0
340,1,50,0,0.344869," ","integrate(cot(f*x+e)/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{b \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{2} + a b} + \frac{\log\left(\sin\left(f x + e\right)^{2}\right)}{a + b}}{2 \, f}"," ",0,"1/2*(b*log(a*sin(f*x + e)^2 - a - b)/(a^2 + a*b) + log(sin(f*x + e)^2)/(a + b))/f","A",0
341,1,87,0,0.343350," ","integrate(cot(f*x+e)^3/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{b^{2} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{3} + 2 \, a^{2} b + a b^{2}} + \frac{{\left(a + 2 \, b\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{1}{{\left(a + b\right)} \sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"-1/2*(b^2*log(a*sin(f*x + e)^2 - a - b)/(a^3 + 2*a^2*b + a*b^2) + (a + 2*b)*log(sin(f*x + e)^2)/(a^2 + 2*a*b + b^2) + 1/((a + b)*sin(f*x + e)^2))/f","A",0
342,1,145,0,0.349404," ","integrate(cot(f*x+e)^5/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{3} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}} + \frac{2 \, {\left(a^{2} + 3 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(2 \, a + 3 \, b\right)} \sin\left(f x + e\right)^{2} - a - b}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sin\left(f x + e\right)^{4}}}{4 \, f}"," ",0,"1/4*(2*b^3*log(a*sin(f*x + e)^2 - a - b)/(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3) + 2*(a^2 + 3*a*b + 3*b^2)*log(sin(f*x + e)^2)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + (2*(2*a + 3*b)*sin(f*x + e)^2 - a - b)/((a^2 + 2*a*b + b^2)*sin(f*x + e)^4))/f","A",0
343,1,95,0,0.442324," ","integrate(tan(f*x+e)^6/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(f x + e\right)}}{a} - \frac{b \tan\left(f x + e\right)^{3} - 3 \, {\left(a + 2 \, b\right)} \tan\left(f x + e\right)}{b^{2}} - \frac{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a b^{2}}}{3 \, f}"," ",0,"-1/3*(3*(f*x + e)/a - (b*tan(f*x + e)^3 - 3*(a + 2*b)*tan(f*x + e))/b^2 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a*b^2))/f","A",0
344,1,66,0,0.441004," ","integrate(tan(f*x+e)^4/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{f x + e}{a} + \frac{\tan\left(f x + e\right)}{b} - \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a b}}{f}"," ",0,"((f*x + e)/a + tan(f*x + e)/b - (a^2 + 2*a*b + b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a*b))/f","A",0
345,1,45,0,0.437189," ","integrate(tan(f*x+e)^2/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{{\left(a + b\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a} - \frac{f x + e}{a}}{f}"," ",0,"((a + b)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a) - (f*x + e)/a)/f","A",0
346,1,44,0,0.454333," ","integrate(1/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a} - \frac{f x + e}{a}}{f}"," ",0,"-(b*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a) - (f*x + e)/a)/f","A",0
347,1,66,0,0.454152," ","integrate(cot(f*x+e)^2/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{b^{2} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{2} + a b\right)} \sqrt{{\left(a + b\right)} b}} - \frac{f x + e}{a} - \frac{1}{{\left(a + b\right)} \tan\left(f x + e\right)}}{f}"," ",0,"(b^2*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^2 + a*b)*sqrt((a + b)*b)) - (f*x + e)/a - 1/((a + b)*tan(f*x + e)))/f","A",0
348,1,106,0,0.458915," ","integrate(cot(f*x+e)^4/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{3 \, b^{3} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{3 \, {\left(f x + e\right)}}{a} - \frac{3 \, {\left(a + 2 \, b\right)} \tan\left(f x + e\right)^{2} - a - b}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*b^3*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^3 + 2*a^2*b + a*b^2)*sqrt((a + b)*b)) - 3*(f*x + e)/a - (3*(a + 2*b)*tan(f*x + e)^2 - a - b)/((a^2 + 2*a*b + b^2)*tan(f*x + e)^3))/f","A",0
349,1,161,0,0.437304," ","integrate(cot(f*x+e)^6/(a+b*sec(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{15 \, b^{4} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{15 \, {\left(f x + e\right)}}{a} - \frac{15 \, {\left(a^{2} + 3 \, a b + 3 \, b^{2}\right)} \tan\left(f x + e\right)^{4} - 5 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \tan\left(f x + e\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"1/15*(15*b^4*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt((a + b)*b)) - 15*(f*x + e)/a - (15*(a^2 + 3*a*b + 3*b^2)*tan(f*x + e)^4 - 5*(a^2 + 3*a*b + 2*b^2)*tan(f*x + e)^2 + 3*a^2 + 6*a*b + 3*b^2)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*tan(f*x + e)^5))/f","A",0
350,1,98,0,0.345577," ","integrate(tan(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{a^{2} + 2 \, a b + b^{2}}{a^{3} b \sin\left(f x + e\right)^{2} - a^{3} b - a^{2} b^{2}} - \frac{\log\left(\sin\left(f x + e\right)^{2} - 1\right)}{b^{2}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{2} b^{2}}}{2 \, f}"," ",0,"1/2*((a^2 + 2*a*b + b^2)/(a^3*b*sin(f*x + e)^2 - a^3*b - a^2*b^2) - log(sin(f*x + e)^2 - 1)/b^2 + (a^2 - b^2)*log(a*sin(f*x + e)^2 - a - b)/(a^2*b^2))/f","A",0
351,1,59,0,0.357426," ","integrate(tan(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{a + b}{a^{3} \sin\left(f x + e\right)^{2} - a^{3} - a^{2} b} - \frac{\log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{2}}}{2 \, f}"," ",0,"-1/2*((a + b)/(a^3*sin(f*x + e)^2 - a^3 - a^2*b) - log(a*sin(f*x + e)^2 - a - b)/a^2)/f","A",0
352,1,57,0,0.356578," ","integrate(tan(f*x+e)/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{b}{a^{3} \sin\left(f x + e\right)^{2} - a^{3} - a^{2} b} - \frac{\log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{2}}}{2 \, f}"," ",0,"1/2*(b/(a^3*sin(f*x + e)^2 - a^3 - a^2*b) - log(a*sin(f*x + e)^2 - a - b)/a^2)/f","A",0
353,1,117,0,0.349072," ","integrate(cot(f*x+e)/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{b^{2}}{a^{4} + 2 \, a^{3} b + a^{2} b^{2} - {\left(a^{4} + a^{3} b\right)} \sin\left(f x + e\right)^{2}} + \frac{{\left(2 \, a b + b^{2}\right)} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{4} + 2 \, a^{3} b + a^{2} b^{2}} + \frac{\log\left(\sin\left(f x + e\right)^{2}\right)}{a^{2} + 2 \, a b + b^{2}}}{2 \, f}"," ",0,"1/2*(b^2/(a^4 + 2*a^3*b + a^2*b^2 - (a^4 + a^3*b)*sin(f*x + e)^2) + (2*a*b + b^2)*log(a*sin(f*x + e)^2 - a - b)/(a^4 + 2*a^3*b + a^2*b^2) + log(sin(f*x + e)^2)/(a^2 + 2*a*b + b^2))/f","A",0
354,1,192,0,0.357408," ","integrate(cot(f*x+e)^3/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{{\left(3 \, a b^{2} + b^{3}\right)} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}} + \frac{{\left(a + 3 \, b\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{a^{3} + a^{2} b - {\left(a^{3} - b^{3}\right)} \sin\left(f x + e\right)^{2}}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sin\left(f x + e\right)^{4} - {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"-1/2*((3*a*b^2 + b^3)*log(a*sin(f*x + e)^2 - a - b)/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3) + (a + 3*b)*log(sin(f*x + e)^2)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (a^3 + a^2*b - (a^3 - b^3)*sin(f*x + e)^2)/((a^5 + 2*a^4*b + a^3*b^2)*sin(f*x + e)^4 - (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sin(f*x + e)^2))/f","A",0
355,1,279,0,0.342852," ","integrate(cot(f*x+e)^5/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(4 \, a b^{3} + b^{4}\right)} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}} + \frac{2 \, {\left(a^{2} + 4 \, a b + 6 \, b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{2 \, {\left(2 \, a^{4} + 4 \, a^{3} b - b^{4}\right)} \sin\left(f x + e\right)^{4} + a^{4} + 2 \, a^{3} b + a^{2} b^{2} - {\left(5 \, a^{4} + 13 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sin\left(f x + e\right)^{2}}{{\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sin\left(f x + e\right)^{6} - {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(f x + e\right)^{4}}}{4 \, f}"," ",0,"1/4*(2*(4*a*b^3 + b^4)*log(a*sin(f*x + e)^2 - a - b)/(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4) + 2*(a^2 + 4*a*b + 6*b^2)*log(sin(f*x + e)^2)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + (2*(2*a^4 + 4*a^3*b - b^4)*sin(f*x + e)^4 + a^4 + 2*a^3*b + a^2*b^2 - (5*a^4 + 13*a^3*b + 8*a^2*b^2)*sin(f*x + e)^2)/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sin(f*x + e)^6 - (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*sin(f*x + e)^4))/f","B",0
356,1,127,0,0.433096," ","integrate(tan(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)}{a b^{3} \tan\left(f x + e\right)^{2} + a^{2} b^{2} + a b^{3}} - \frac{2 \, {\left(f x + e\right)}}{a^{2}} + \frac{2 \, \tan\left(f x + e\right)}{b^{2}} - \frac{{\left(3 \, a^{3} + 4 \, a^{2} b - a b^{2} - 2 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{2} b^{2}}}{2 \, f}"," ",0,"1/2*((a^2 + 2*a*b + b^2)*tan(f*x + e)/(a*b^3*tan(f*x + e)^2 + a^2*b^2 + a*b^3) - 2*(f*x + e)/a^2 + 2*tan(f*x + e)/b^2 - (3*a^3 + 4*a^2*b - a*b^2 - 2*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^2*b^2))/f","A",0
357,1,96,0,0.427237," ","integrate(tan(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{{\left(a + b\right)} \tan\left(f x + e\right)}{a b^{2} \tan\left(f x + e\right)^{2} + a^{2} b + a b^{2}} - \frac{2 \, {\left(f x + e\right)}}{a^{2}} - \frac{{\left(a^{2} - a b - 2 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{2} b}}{2 \, f}"," ",0,"-1/2*((a + b)*tan(f*x + e)/(a*b^2*tan(f*x + e)^2 + a^2*b + a*b^2) - 2*(f*x + e)/a^2 - (a^2 - a*b - 2*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^2*b))/f","A",0
358,1,75,0,0.423949," ","integrate(tan(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{\tan\left(f x + e\right)}{a b \tan\left(f x + e\right)^{2} + a^{2} + a b} + \frac{{\left(a + 2 \, b\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{2}} - \frac{2 \, {\left(f x + e\right)}}{a^{2}}}{2 \, f}"," ",0,"1/2*(tan(f*x + e)/(a*b*tan(f*x + e)^2 + a^2 + a*b) + (a + 2*b)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^2) - 2*(f*x + e)/a^2)/f","A",0
359,1,106,0,0.423729," ","integrate(1/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{b \tan\left(f x + e\right)}{a^{3} + 2 \, a^{2} b + a b^{2} + {\left(a^{2} b + a b^{2}\right)} \tan\left(f x + e\right)^{2}} + \frac{{\left(3 \, a b + 2 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b}} - \frac{2 \, {\left(f x + e\right)}}{a^{2}}}{2 \, f}"," ",0,"-1/2*(b*tan(f*x + e)/(a^3 + 2*a^2*b + a*b^2 + (a^2*b + a*b^2)*tan(f*x + e)^2) + (3*a*b + 2*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^3 + a^2*b)*sqrt((a + b)*b)) - 2*(f*x + e)/a^2)/f","A",0
360,1,163,0,0.442801," ","integrate(cot(f*x+e)^2/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(5 \, a b^{2} + 2 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{{\left(2 \, a b - b^{2}\right)} \tan\left(f x + e\right)^{2} + 2 \, a^{2} + 2 \, a b}{{\left(a^{3} b + 2 \, a^{2} b^{2} + a b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \tan\left(f x + e\right)} - \frac{2 \, {\left(f x + e\right)}}{a^{2}}}{2 \, f}"," ",0,"1/2*((5*a*b^2 + 2*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^4 + 2*a^3*b + a^2*b^2)*sqrt((a + b)*b)) - ((2*a*b - b^2)*tan(f*x + e)^2 + 2*a^2 + 2*a*b)/((a^3*b + 2*a^2*b^2 + a*b^3)*tan(f*x + e)^3 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*tan(f*x + e)) - 2*(f*x + e)/a^2)/f","A",0
361,1,235,0,0.447431," ","integrate(cot(f*x+e)^4/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(7 \, a b^{3} + 2 \, b^{4}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{3 \, {\left(2 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \tan\left(f x + e\right)^{4} - 2 \, a^{3} - 4 \, a^{2} b - 2 \, a b^{2} + 2 \, {\left(3 \, a^{3} + 11 \, a^{2} b + 8 \, a b^{2}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{4} b + 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4}\right)} \tan\left(f x + e\right)^{5} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \tan\left(f x + e\right)^{3}} - \frac{6 \, {\left(f x + e\right)}}{a^{2}}}{6 \, f}"," ",0,"-1/6*(3*(7*a*b^3 + 2*b^4)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sqrt((a + b)*b)) - (3*(2*a^2*b + 6*a*b^2 - b^3)*tan(f*x + e)^4 - 2*a^3 - 4*a^2*b - 2*a*b^2 + 2*(3*a^3 + 11*a^2*b + 8*a*b^2)*tan(f*x + e)^2)/((a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*tan(f*x + e)^5 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*tan(f*x + e)^3) - 6*(f*x + e)/a^2)/f","A",0
362,1,319,0,0.471876," ","integrate(cot(f*x+e)^6/(a+b*sec(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(9 \, a b^{4} + 2 \, b^{5}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{15 \, {\left(2 \, a^{3} b + 8 \, a^{2} b^{2} + 12 \, a b^{3} - b^{4}\right)} \tan\left(f x + e\right)^{6} + 10 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 26 \, a^{2} b^{2} + 15 \, a b^{3}\right)} \tan\left(f x + e\right)^{4} + 6 \, a^{4} + 18 \, a^{3} b + 18 \, a^{2} b^{2} + 6 \, a b^{3} - 2 \, {\left(5 \, a^{4} + 22 \, a^{3} b + 29 \, a^{2} b^{2} + 12 \, a b^{3}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{5} b + 4 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 4 \, a^{2} b^{4} + a b^{5}\right)} \tan\left(f x + e\right)^{7} + {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \tan\left(f x + e\right)^{5}} - \frac{30 \, {\left(f x + e\right)}}{a^{2}}}{30 \, f}"," ",0,"1/30*(15*(9*a*b^4 + 2*b^5)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*sqrt((a + b)*b)) - (15*(2*a^3*b + 8*a^2*b^2 + 12*a*b^3 - b^4)*tan(f*x + e)^6 + 10*(3*a^4 + 14*a^3*b + 26*a^2*b^2 + 15*a*b^3)*tan(f*x + e)^4 + 6*a^4 + 18*a^3*b + 18*a^2*b^2 + 6*a*b^3 - 2*(5*a^4 + 22*a^3*b + 29*a^2*b^2 + 12*a*b^3)*tan(f*x + e)^2)/((a^5*b + 4*a^4*b^2 + 6*a^3*b^3 + 4*a^2*b^4 + a*b^5)*tan(f*x + e)^7 + (a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*tan(f*x + e)^5) - 30*(f*x + e)/a^2)/f","A",0
363,1,112,0,0.350404," ","integrate(tan(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(a^{2} + a b\right)} \sin\left(f x + e\right)^{2} - 3 \, a^{2} - 6 \, a b - 3 \, b^{2}}{a^{5} \sin\left(f x + e\right)^{4} + a^{5} + 2 \, a^{4} b + a^{3} b^{2} - 2 \, {\left(a^{5} + a^{4} b\right)} \sin\left(f x + e\right)^{2}} - \frac{2 \, \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{3}}}{4 \, f}"," ",0,"1/4*((4*(a^2 + a*b)*sin(f*x + e)^2 - 3*a^2 - 6*a*b - 3*b^2)/(a^5*sin(f*x + e)^4 + a^5 + 2*a^4*b + a^3*b^2 - 2*(a^5 + a^4*b)*sin(f*x + e)^2) - 2*log(a*sin(f*x + e)^2 - a - b)/a^3)/f","A",0
364,1,113,0,0.351346," ","integrate(tan(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(f x + e\right)^{2} - 2 \, a^{2} - 5 \, a b - 3 \, b^{2}}{a^{5} \sin\left(f x + e\right)^{4} + a^{5} + 2 \, a^{4} b + a^{3} b^{2} - 2 \, {\left(a^{5} + a^{4} b\right)} \sin\left(f x + e\right)^{2}} - \frac{2 \, \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{3}}}{4 \, f}"," ",0,"-1/4*((2*(a^2 + 2*a*b)*sin(f*x + e)^2 - 2*a^2 - 5*a*b - 3*b^2)/(a^5*sin(f*x + e)^4 + a^5 + 2*a^4*b + a^3*b^2 - 2*(a^5 + a^4*b)*sin(f*x + e)^2) - 2*log(a*sin(f*x + e)^2 - a - b)/a^3)/f","A",0
365,1,102,0,0.367205," ","integrate(tan(f*x+e)/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{4 \, a b \sin\left(f x + e\right)^{2} - 4 \, a b - 3 \, b^{2}}{a^{5} \sin\left(f x + e\right)^{4} + a^{5} + 2 \, a^{4} b + a^{3} b^{2} - 2 \, {\left(a^{5} + a^{4} b\right)} \sin\left(f x + e\right)^{2}} - \frac{2 \, \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{3}}}{4 \, f}"," ",0,"1/4*((4*a*b*sin(f*x + e)^2 - 4*a*b - 3*b^2)/(a^5*sin(f*x + e)^4 + a^5 + 2*a^4*b + a^3*b^2 - 2*(a^5 + a^4*b)*sin(f*x + e)^2) - 2*log(a*sin(f*x + e)^2 - a - b)/a^3)/f","A",0
366,1,243,0,0.371179," ","integrate(cot(f*x+e)/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}} + \frac{6 \, a^{2} b^{2} + 9 \, a b^{3} + 3 \, b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \sin\left(f x + e\right)^{2}}{a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \sin\left(f x + e\right)^{4} - 2 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sin\left(f x + e\right)^{2}} + \frac{2 \, \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}}{4 \, f}"," ",0,"1/4*(2*(3*a^2*b + 3*a*b^2 + b^3)*log(a*sin(f*x + e)^2 - a - b)/(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3) + (6*a^2*b^2 + 9*a*b^3 + 3*b^4 - 2*(3*a^2*b^2 + 2*a*b^3)*sin(f*x + e)^2)/(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4 + (a^7 + 2*a^6*b + a^5*b^2)*sin(f*x + e)^4 - 2*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sin(f*x + e)^2) + 2*log(sin(f*x + e)^2)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))/f","A",0
367,1,344,0,0.354235," ","integrate(cot(f*x+e)^3/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}} + \frac{2 \, {\left(a + 4 \, b\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{2 \, a^{5} + 4 \, a^{4} b + 2 \, a^{3} b^{2} + 2 \, {\left(a^{5} - 4 \, a^{2} b^{3} - 2 \, a b^{4}\right)} \sin\left(f x + e\right)^{4} - {\left(4 \, a^{5} + 4 \, a^{4} b - 8 \, a^{2} b^{3} - 11 \, a b^{4} - 3 \, b^{5}\right)} \sin\left(f x + e\right)^{2}}{{\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \sin\left(f x + e\right)^{6} - 2 \, {\left(a^{8} + 4 \, a^{7} b + 6 \, a^{6} b^{2} + 4 \, a^{5} b^{3} + a^{4} b^{4}\right)} \sin\left(f x + e\right)^{4} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \sin\left(f x + e\right)^{2}}}{4 \, f}"," ",0,"-1/4*(2*(6*a^2*b^2 + 4*a*b^3 + b^4)*log(a*sin(f*x + e)^2 - a - b)/(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4) + 2*(a + 4*b)*log(sin(f*x + e)^2)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + (2*a^5 + 4*a^4*b + 2*a^3*b^2 + 2*(a^5 - 4*a^2*b^3 - 2*a*b^4)*sin(f*x + e)^4 - (4*a^5 + 4*a^4*b - 8*a^2*b^3 - 11*a*b^4 - 3*b^5)*sin(f*x + e)^2)/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*sin(f*x + e)^6 - 2*(a^8 + 4*a^7*b + 6*a^6*b^2 + 4*a^5*b^3 + a^4*b^4)*sin(f*x + e)^4 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*sin(f*x + e)^2))/f","B",0
368,1,454,0,0.355155," ","integrate(cot(f*x+e)^5/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \log\left(a \sin\left(f x + e\right)^{2} - a - b\right)}{a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}} + \frac{2 \, {\left(a^{2} + 5 \, a b + 10 \, b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}} + \frac{2 \, {\left(2 \, a^{6} + 5 \, a^{5} b - 5 \, a^{2} b^{4} - 2 \, a b^{5}\right)} \sin\left(f x + e\right)^{6} - a^{6} - 3 \, a^{5} b - 3 \, a^{4} b^{2} - a^{3} b^{3} - {\left(9 \, a^{6} + 29 \, a^{5} b + 20 \, a^{4} b^{2} - 10 \, a^{2} b^{4} - 13 \, a b^{5} - 3 \, b^{6}\right)} \sin\left(f x + e\right)^{4} + 2 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 13 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} \sin\left(f x + e\right)^{2}}{{\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} \sin\left(f x + e\right)^{8} - 2 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} \sin\left(f x + e\right)^{6} + {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} \sin\left(f x + e\right)^{4}}}{4 \, f}"," ",0,"1/4*(2*(10*a^2*b^3 + 5*a*b^4 + b^5)*log(a*sin(f*x + e)^2 - a - b)/(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5) + 2*(a^2 + 5*a*b + 10*b^2)*log(sin(f*x + e)^2)/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) + (2*(2*a^6 + 5*a^5*b - 5*a^2*b^4 - 2*a*b^5)*sin(f*x + e)^6 - a^6 - 3*a^5*b - 3*a^4*b^2 - a^3*b^3 - (9*a^6 + 29*a^5*b + 20*a^4*b^2 - 10*a^2*b^4 - 13*a*b^5 - 3*b^6)*sin(f*x + e)^4 + 2*(3*a^6 + 11*a^5*b + 13*a^4*b^2 + 5*a^3*b^3)*sin(f*x + e)^2)/((a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*sin(f*x + e)^8 - 2*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*sin(f*x + e)^6 + (a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*sin(f*x + e)^4))/f","B",0
369,1,193,0,0.438425," ","integrate(tan(f*x+e)^6/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(5 \, a^{2} b + a b^{2} - 4 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(3 \, a^{3} + 2 \, a^{2} b - 5 \, a b^{2} - 4 \, b^{3}\right)} \tan\left(f x + e\right)}{a^{2} b^{4} \tan\left(f x + e\right)^{4} + a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4} + 2 \, {\left(a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(f x + e\right)^{2}} + \frac{8 \, {\left(f x + e\right)}}{a^{3}} - \frac{{\left(3 \, a^{3} - a^{2} b + 4 \, a b^{2} + 8 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{3} b^{2}}}{8 \, f}"," ",0,"-1/8*(((5*a^2*b + a*b^2 - 4*b^3)*tan(f*x + e)^3 + (3*a^3 + 2*a^2*b - 5*a*b^2 - 4*b^3)*tan(f*x + e))/(a^2*b^4*tan(f*x + e)^4 + a^4*b^2 + 2*a^3*b^3 + a^2*b^4 + 2*(a^3*b^3 + a^2*b^4)*tan(f*x + e)^2) + 8*(f*x + e)/a^3 - (3*a^3 - a^2*b + 4*a*b^2 + 8*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^3*b^2))/f","A",0
370,1,163,0,0.445643," ","integrate(tan(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(a b - 4 \, b^{2}\right)} \tan\left(f x + e\right)^{3} - {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \tan\left(f x + e\right)}{a^{2} b^{3} \tan\left(f x + e\right)^{4} + a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3} + 2 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} \tan\left(f x + e\right)^{2}} + \frac{8 \, {\left(f x + e\right)}}{a^{3}} + \frac{{\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{3} b}}{8 \, f}"," ",0,"1/8*(((a*b - 4*b^2)*tan(f*x + e)^3 - (a^2 + 5*a*b + 4*b^2)*tan(f*x + e))/(a^2*b^3*tan(f*x + e)^4 + a^4*b + 2*a^3*b^2 + a^2*b^3 + 2*(a^3*b^2 + a^2*b^3)*tan(f*x + e)^2) + 8*(f*x + e)/a^3 + (a^2 - 4*a*b - 8*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/(sqrt((a + b)*b)*a^3*b))/f","A",0
371,1,191,0,0.441141," ","integrate(tan(f*x+e)^2/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, a^{2} + 12 \, a b + 8 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} b}} + \frac{{\left(3 \, a b + 4 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + {\left(5 \, a^{2} + 9 \, a b + 4 \, b^{2}\right)} \tan\left(f x + e\right)}{a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{3} b^{2} + a^{2} b^{3}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \tan\left(f x + e\right)^{2}} - \frac{8 \, {\left(f x + e\right)}}{a^{3}}}{8 \, f}"," ",0,"1/8*((3*a^2 + 12*a*b + 8*b^2)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^4 + a^3*b)*sqrt((a + b)*b)) + ((3*a*b + 4*b^2)*tan(f*x + e)^3 + (5*a^2 + 9*a*b + 4*b^2)*tan(f*x + e))/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^3*b^2 + a^2*b^3)*tan(f*x + e)^4 + 2*(a^4*b + 2*a^3*b^2 + a^2*b^3)*tan(f*x + e)^2) - 8*(f*x + e)/a^3)/f","A",0
372,1,231,0,0.465173," ","integrate(1/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{{\left(7 \, a b^{2} + 4 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(9 \, a^{2} b + 13 \, a b^{2} + 4 \, b^{3}\right)} \tan\left(f x + e\right)}{a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(f x + e\right)^{2}} - \frac{8 \, {\left(f x + e\right)}}{a^{3}}}{8 \, f}"," ",0,"-1/8*((15*a^2*b + 20*a*b^2 + 8*b^3)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*b)) + ((7*a*b^2 + 4*b^3)*tan(f*x + e)^3 + (9*a^2*b + 13*a*b^2 + 4*b^3)*tan(f*x + e))/(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4 + (a^4*b^2 + 2*a^3*b^3 + a^2*b^4)*tan(f*x + e)^4 + 2*(a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*tan(f*x + e)^2) - 8*(f*x + e)/a^3)/f","A",0
373,1,311,0,0.463794," ","integrate(cot(f*x+e)^2/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(35 \, a^{2} b^{2} + 28 \, a b^{3} + 8 \, b^{4}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{{\left(8 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} \tan\left(f x + e\right)^{4} + 8 \, a^{4} + 16 \, a^{3} b + 8 \, a^{2} b^{2} + {\left(16 \, a^{3} b + 3 \, a^{2} b^{2} - 17 \, a b^{3} - 4 \, b^{4}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} + a^{2} b^{5}\right)} \tan\left(f x + e\right)^{5} + 2 \, {\left(a^{6} b + 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} \tan\left(f x + e\right)^{3} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \tan\left(f x + e\right)} - \frac{8 \, {\left(f x + e\right)}}{a^{3}}}{8 \, f}"," ",0,"1/8*((35*a^2*b^2 + 28*a*b^3 + 8*b^4)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sqrt((a + b)*b)) - ((8*a^2*b^2 - 11*a*b^3 - 4*b^4)*tan(f*x + e)^4 + 8*a^4 + 16*a^3*b + 8*a^2*b^2 + (16*a^3*b + 3*a^2*b^2 - 17*a*b^3 - 4*b^4)*tan(f*x + e)^2)/((a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 + a^2*b^5)*tan(f*x + e)^5 + 2*(a^6*b + 4*a^5*b^2 + 6*a^4*b^3 + 4*a^3*b^4 + a^2*b^5)*tan(f*x + e)^3 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*tan(f*x + e)) - 8*(f*x + e)/a^3)/f","A",0
374,1,409,0,0.460384," ","integrate(cot(f*x+e)^4/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(63 \, a^{2} b^{3} + 36 \, a b^{4} + 8 \, b^{5}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{3 \, {\left(8 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 15 \, a b^{4} - 4 \, b^{5}\right)} \tan\left(f x + e\right)^{6} - 8 \, a^{5} - 24 \, a^{4} b - 24 \, a^{3} b^{2} - 8 \, a^{2} b^{3} + {\left(48 \, a^{4} b + 232 \, a^{3} b^{2} + 133 \, a^{2} b^{3} - 63 \, a b^{4} - 12 \, b^{5}\right)} \tan\left(f x + e\right)^{4} + 8 \, {\left(3 \, a^{5} + 16 \, a^{4} b + 23 \, a^{3} b^{2} + 10 \, a^{2} b^{3}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + a^{2} b^{6}\right)} \tan\left(f x + e\right)^{7} + 2 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} \tan\left(f x + e\right)^{5} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} \tan\left(f x + e\right)^{3}} - \frac{24 \, {\left(f x + e\right)}}{a^{3}}}{24 \, f}"," ",0,"-1/24*(3*(63*a^2*b^3 + 36*a*b^4 + 8*b^5)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*sqrt((a + b)*b)) - (3*(8*a^3*b^2 + 32*a^2*b^3 - 15*a*b^4 - 4*b^5)*tan(f*x + e)^6 - 8*a^5 - 24*a^4*b - 24*a^3*b^2 - 8*a^2*b^3 + (48*a^4*b + 232*a^3*b^2 + 133*a^2*b^3 - 63*a*b^4 - 12*b^5)*tan(f*x + e)^4 + 8*(3*a^5 + 16*a^4*b + 23*a^3*b^2 + 10*a^2*b^3)*tan(f*x + e)^2)/((a^6*b^2 + 4*a^5*b^3 + 6*a^4*b^4 + 4*a^3*b^5 + a^2*b^6)*tan(f*x + e)^7 + 2*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*tan(f*x + e)^5 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*tan(f*x + e)^3) - 24*(f*x + e)/a^3)/f","A",0
375,1,520,0,0.466763," ","integrate(cot(f*x+e)^6/(a+b*sec(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(99 \, a^{2} b^{4} + 44 \, a b^{5} + 8 \, b^{6}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \sqrt{{\left(a + b\right)} b}} - \frac{15 \, {\left(8 \, a^{4} b^{2} + 40 \, a^{3} b^{3} + 80 \, a^{2} b^{4} - 19 \, a b^{5} - 4 \, b^{6}\right)} \tan\left(f x + e\right)^{8} + 5 \, {\left(48 \, a^{5} b + 280 \, a^{4} b^{2} + 680 \, a^{3} b^{3} + 385 \, a^{2} b^{4} - 75 \, a b^{5} - 12 \, b^{6}\right)} \tan\left(f x + e\right)^{6} + 24 \, a^{6} + 96 \, a^{5} b + 144 \, a^{4} b^{2} + 96 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 8 \, {\left(15 \, a^{6} + 95 \, a^{5} b + 258 \, a^{4} b^{2} + 291 \, a^{3} b^{3} + 113 \, a^{2} b^{4}\right)} \tan\left(f x + e\right)^{4} - 8 \, {\left(5 \, a^{6} + 29 \, a^{5} b + 57 \, a^{4} b^{2} + 47 \, a^{3} b^{3} + 14 \, a^{2} b^{4}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{7} b^{2} + 5 \, a^{6} b^{3} + 10 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 5 \, a^{3} b^{6} + a^{2} b^{7}\right)} \tan\left(f x + e\right)^{9} + 2 \, {\left(a^{8} b + 6 \, a^{7} b^{2} + 15 \, a^{6} b^{3} + 20 \, a^{5} b^{4} + 15 \, a^{4} b^{5} + 6 \, a^{3} b^{6} + a^{2} b^{7}\right)} \tan\left(f x + e\right)^{7} + {\left(a^{9} + 7 \, a^{8} b + 21 \, a^{7} b^{2} + 35 \, a^{6} b^{3} + 35 \, a^{5} b^{4} + 21 \, a^{4} b^{5} + 7 \, a^{3} b^{6} + a^{2} b^{7}\right)} \tan\left(f x + e\right)^{5}} - \frac{120 \, {\left(f x + e\right)}}{a^{3}}}{120 \, f}"," ",0,"1/120*(15*(99*a^2*b^4 + 44*a*b^5 + 8*b^6)*arctan(b*tan(f*x + e)/sqrt((a + b)*b))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*sqrt((a + b)*b)) - (15*(8*a^4*b^2 + 40*a^3*b^3 + 80*a^2*b^4 - 19*a*b^5 - 4*b^6)*tan(f*x + e)^8 + 5*(48*a^5*b + 280*a^4*b^2 + 680*a^3*b^3 + 385*a^2*b^4 - 75*a*b^5 - 12*b^6)*tan(f*x + e)^6 + 24*a^6 + 96*a^5*b + 144*a^4*b^2 + 96*a^3*b^3 + 24*a^2*b^4 + 8*(15*a^6 + 95*a^5*b + 258*a^4*b^2 + 291*a^3*b^3 + 113*a^2*b^4)*tan(f*x + e)^4 - 8*(5*a^6 + 29*a^5*b + 57*a^4*b^2 + 47*a^3*b^3 + 14*a^2*b^4)*tan(f*x + e)^2)/((a^7*b^2 + 5*a^6*b^3 + 10*a^5*b^4 + 10*a^4*b^5 + 5*a^3*b^6 + a^2*b^7)*tan(f*x + e)^9 + 2*(a^8*b + 6*a^7*b^2 + 15*a^6*b^3 + 20*a^5*b^4 + 15*a^4*b^5 + 6*a^3*b^6 + a^2*b^7)*tan(f*x + e)^7 + (a^9 + 7*a^8*b + 21*a^7*b^2 + 35*a^6*b^3 + 35*a^5*b^4 + 21*a^4*b^5 + 7*a^3*b^6 + a^2*b^7)*tan(f*x + e)^5) - 120*(f*x + e)/a^3)/f","A",0
376,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e)^5,x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*tan(f*x + e)^5, x)","F",0
377,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e)^3,x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*tan(f*x + e)^3, x)","F",0
378,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*tan(f*x + e), x)","F",0
379,1,3317,0,0.932187," ","integrate(cot(f*x+e)*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{a^{\frac{3}{2}} \log\left(4 \, \sqrt{a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)} a \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + 4 \, \sqrt{a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)} a \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + 16 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left(a + b\right)} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 16 \, a^{2} + 32 \, a b + 16 \, b^{2}\right) - 2 \, \sqrt{a + b} a \log\left(\frac{4 \, {\left(4 \, \sqrt{a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)} {\left(a + b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + 4 \, \sqrt{a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)} {\left(a + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left| 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} - 2 \right|}^{2} + 4 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left(a + b\right)} {\left| 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} - 2 \right|} + 4 \, a + 4 \, b\right)} \sqrt{a + b} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 16 \, a^{2} + 32 \, a b + 16 \, b^{2} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left| 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} - 2 \right|}\right)}}{{\left| 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} - 2 \right|}^{2}}\right) - {\left(a^{\frac{3}{2}} + 2 \, \sqrt{a} b\right)} \log\left(4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} + 16 \, a b + 16 \, b^{2} + 8 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right) + 8 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left(a \sin\left(2 \, f x + 2 \, e\right) \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + {\left(a \cos\left(2 \, f x + 2 \, e\right) + a + 2 \, b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)\right)} \sqrt{a} + 4 \, \sqrt{a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)} {\left(a \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + a \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)}\right) + 2 \, {\left(a^{\frac{3}{2}} + \sqrt{a} b\right)} \log\left(a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} a^{\frac{3}{2}} \sin\left(2 \, f x + 2 \, e\right) \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + \sqrt{a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)} a \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + \sqrt{a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)} a \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left(a^{\frac{3}{2}} \cos\left(2 \, f x + 2 \, e\right) + a^{\frac{3}{2}} + 2 \, \sqrt{a} b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + a^{2} + 4 \, a b + 4 \, b^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}{4 \, a f}"," ",0,"1/4*(a^(3/2)*log(4*sqrt(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*a*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + 4*sqrt(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*a*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + 16*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*(a + b)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 16*a^2 + 32*a*b + 16*b^2) - 2*sqrt(a + b)*a*log(4*(4*sqrt(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*(a + b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + 4*sqrt(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*(a + b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + (a^2 + 2*a*b + b^2)*abs(2*e^(2*I*f*x + 2*I*e) - 2)^2 + 4*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*((a + b)*abs(2*e^(2*I*f*x + 2*I*e) - 2) + 4*a + 4*b)*sqrt(a + b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 16*a^2 + 32*a*b + 16*b^2 + 8*(a^2 + 2*a*b + b^2)*abs(2*e^(2*I*f*x + 2*I*e) - 2))/abs(2*e^(2*I*f*x + 2*I*e) - 2)^2) - (a^(3/2) + 2*sqrt(a)*b)*log(4*a^2*cos(2*f*x + 2*e)^2 + 4*a^2*sin(2*f*x + 2*e)^2 + 4*a^2 + 16*a*b + 16*b^2 + 8*(a^2 + 2*a*b)*cos(2*f*x + 2*e) + 8*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*(a*sin(2*f*x + 2*e)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + (a*cos(2*f*x + 2*e) + a + 2*b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)))*sqrt(a) + 4*sqrt(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*(a*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + a*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)) + 2*(a^(3/2) + sqrt(a)*b)*log(a^2*cos(2*f*x + 2*e)^2 + a^2*sin(2*f*x + 2*e)^2 + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*a^(3/2)*sin(2*f*x + 2*e)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + sqrt(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*a*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + sqrt(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*a*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*(a^(3/2)*cos(2*f*x + 2*e) + a^(3/2) + 2*sqrt(a)*b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + a^2 + 4*a*b + 4*b^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e)))/(a*f)","C",0
380,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cot(f*x + e)^3, x)","F",0
381,0,0,0,0.000000," ","integrate(cot(f*x+e)^5*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cot(f*x + e)^5, x)","F",0
382,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e)^6,x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*tan(f*x + e)^6, x)","F",0
383,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e)^4,x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*tan(f*x + e)^4, x)","F",0
384,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(1/2)*tan(f*x+e)^2,x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*tan(f*x + e)^2, x)","F",0
385,-2,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(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
386,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cot(f*x + e)^2, x)","F",0
387,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cot(f*x + e)^4, x)","F",0
388,0,0,0,0.000000," ","integrate(cot(f*x+e)^6*(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e)^2 + a)*cot(f*x + e)^6, x)","F",0
389,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e)^5,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^5, x)","F",0
390,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e)^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^3, x)","F",0
391,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*tan(f*x + e), x)","F",0
392,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cot(f*x + e), x)","F",0
393,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^3, x)","F",0
394,0,0,0,0.000000," ","integrate(cot(f*x+e)^5*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^5, x)","F",0
395,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e)^6,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^6, x)","F",0
396,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e)^4,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^4, x)","F",0
397,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2)*tan(f*x+e)^2,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^2, x)","F",0
398,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
399,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^2, x)","F",0
400,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^4, x)","F",0
401,0,0,0,0.000000," ","integrate(cot(f*x+e)^6*(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^6, x)","F",0
402,0,0,0,0.000000," ","integrate(tan(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{5}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)^5/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
403,0,0,0,0.000000," ","integrate(tan(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{3}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)^3/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
404,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
405,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cot(f*x + e)/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
406,0,0,0,0.000000," ","integrate(cot(f*x+e)^3/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{3}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cot(f*x + e)^3/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
407,-1,0,0,0.000000," ","integrate(cot(f*x+e)^5/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
408,-1,0,0,0.000000," ","integrate(tan(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,0,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{4}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)^4/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
410,0,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{2}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)^2/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
411,1,992,0,0.626467," ","integrate(1/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\arctan\left(2 \, a \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, a \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 2 \, a + 4 \, b\right) - \arctan\left(2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 4 \, a + 4 \, b\right)}{2 \, \sqrt{a} f}"," ",0,"1/2*(arctan2(2*a*sin(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*a*cos(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 2*a + 4*b) - arctan2(2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 4*a + 4*b))/(sqrt(a)*f)","B",0
412,0,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{2}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cot(f*x + e)^2/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
413,0,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{4}}{\sqrt{b \sec\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cot(f*x + e)^4/sqrt(b*sec(f*x + e)^2 + a), x)","F",0
414,-1,0,0,0.000000," ","integrate(cot(f*x+e)^6/(a+b*sec(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,-1,0,0,0.000000," ","integrate(tan(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,1,2532,0,0.953690," ","integrate(tan(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{4 \, a b \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{3} + 4 \, a b \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} - 4 \, {\left(a^{2} + a b\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) - 4 \, {\left(a^{2} + 2 \, a b + {\left(a^{2} + a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left(b \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + b \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} \log\left(4 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a^{2} + 16 \, a b + 16 \, b^{2} + 8 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right) + 8 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left(a \sin\left(2 \, f x + 2 \, e\right) \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + {\left(a \cos\left(2 \, f x + 2 \, e\right) + a + 2 \, b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)\right)} \sqrt{a} + 4 \, \sqrt{a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)} {\left(a \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + a \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)}\right) + {\left(b \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + b \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} \log\left(4 \, \sqrt{a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)} a \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + 4 \, \sqrt{a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)} a \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + 16 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left(a + b\right)} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 16 \, a^{2} + 32 \, a b + 16 \, b^{2}\right)\right)} \sqrt{a}}{4 \, {\left(a^{2} b \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + a^{2} b \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} f}"," ",0,"1/4*(4*a*b*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^3 + 4*a*b*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 - 4*(a^2 + a*b)*sin(2*f*x + 2*e)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) - 4*(a^2 + 2*a*b + (a^2 + a*b)*cos(2*f*x + 2*e))*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + (a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*((b*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + b*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*log(4*a^2*cos(2*f*x + 2*e)^2 + 4*a^2*sin(2*f*x + 2*e)^2 + 4*a^2 + 16*a*b + 16*b^2 + 8*(a^2 + 2*a*b)*cos(2*f*x + 2*e) + 8*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*(a*sin(2*f*x + 2*e)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + (a*cos(2*f*x + 2*e) + a + 2*b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)))*sqrt(a) + 4*sqrt(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*(a*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + a*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)) + (b*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + b*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*log(4*sqrt(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*a*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + 4*sqrt(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*a*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + 16*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*(a + b)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 16*a^2 + 32*a*b + 16*b^2))*sqrt(a))/((a^2*b*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + a^2*b*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*f)","B",0
417,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(f*x + e)/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
418,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(f*x + e)/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
419,-1,0,0,0.000000," ","integrate(cot(f*x+e)^3/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,-1,0,0,0.000000," ","integrate(cot(f*x+e)^5/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,-1,0,0,0.000000," ","integrate(tan(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,0,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{4}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(f*x + e)^4/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
423,1,2005,0,0.800786," ","integrate(tan(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{2 \, a \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{3} + 2 \, a \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} - a \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) - {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} \arctan\left(2 \, a \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, a \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 2 \, a + 4 \, b\right) - {\left(\cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} \arctan\left(2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 4 \, a + 4 \, b\right)\right)} \sqrt{a}}{2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left(a^{2} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} f}"," ",0,"1/2*(2*a*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^3 + 2*a*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))*sin(2*f*x + 2*e) + 2*(a*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 - a*cos(2*f*x + 2*e))*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) - (a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*((cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*arctan2(2*a*sin(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*a*cos(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 2*a + 4*b) - (cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*arctan2(2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 4*a + 4*b))*sqrt(a))/((a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*(a^2*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + a^2*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*f)","B",0
424,1,2055,0,0.869840," ","integrate(1/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, a b \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} + a b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{3} - 2 \, {\left(a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + a b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} - a^{2} - 2 \, a b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) - {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left({\left(a + b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + {\left(a + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} \arctan\left(2 \, a \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, a \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 2 \, a + 4 \, b\right) - {\left({\left(a + b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + {\left(a + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} \arctan\left(2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right), 2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \sqrt{a} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right) + 4 \, a + 4 \, b\right)\right)} \sqrt{a}}{2 \, {\left(a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + 2 \, {\left(a^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left(a^{3} + a^{2} b\right)} \cos\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2} + {\left(a^{3} + a^{2} b\right)} \sin\left(\frac{1}{2} \, \arctan\left(a \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \sin\left(2 \, f x + 2 \, e\right), a \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(a + 2 \, b\right)} \cos\left(2 \, f x + 2 \, e\right) + a\right)\right)^{2}\right)} f}"," ",0,"-1/2*(2*a*b*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))*sin(2*f*x + 2*e) - 2*(a^2 + a*b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^3 - 2*(a*b*cos(2*f*x + 2*e) + (a^2 + a*b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 - a^2 - 2*a*b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) - (a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*(((a + b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + (a + b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*arctan2(2*a*sin(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*a*cos(2*f*x + 2*e) + 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 2*a + 4*b) - ((a + b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + (a + b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*arctan2(2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)), 2*(a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*sqrt(a)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a)) + 4*a + 4*b))*sqrt(a))/((a^2*cos(4*f*x + 4*e)^2 + a^2*sin(4*f*x + 4*e)^2 + 4*(a^2 + 4*a*b + 4*b^2)*cos(2*f*x + 2*e)^2 + 4*(a^2 + 2*a*b)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(a^2 + 4*a*b + 4*b^2)*sin(2*f*x + 2*e)^2 + a^2 + 2*(a^2 + 2*(a^2 + 2*a*b)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) + 4*(a^2 + 2*a*b)*cos(2*f*x + 2*e))^(1/4)*((a^3 + a^2*b)*cos(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2 + (a^3 + a^2*b)*sin(1/2*arctan2(a*sin(4*f*x + 4*e) + 2*(a + 2*b)*sin(2*f*x + 2*e), a*cos(4*f*x + 4*e) + 2*(a + 2*b)*cos(2*f*x + 2*e) + a))^2)*f)","B",0
425,0,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{2}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(f*x + e)^2/(b*sec(f*x + e)^2 + a)^(3/2), x)","F",0
426,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,-1,0,0,0.000000," ","integrate(cot(f*x+e)^6/(a+b*sec(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,-1,0,0,0.000000," ","integrate(tan(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate(tan(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(f*x + e)/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
431,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(f*x + e)/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
432,-1,0,0,0.000000," ","integrate(cot(f*x+e)^3/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate(cot(f*x+e)^5/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,0,0,0,0.000000," ","integrate(tan(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{6}}{{\left(b \sec\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(f*x + e)^6/(b*sec(f*x + e)^2 + a)^(5/2), x)","F",0
435,-1,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,-1,0,0,0.000000," ","integrate(1/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,-1,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,-1,0,0,0.000000," ","integrate(cot(f*x+e)^6/(a+b*sec(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*(d*tan(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \left(d \tan\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*(d*tan(f*x + e))^m, x)","F",0
442,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^5,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \tan\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*tan(f*x + e)^5, x)","F",0
443,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*tan(f*x + e)^3, x)","F",0
444,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*tan(f*x+e),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*tan(f*x + e), x)","F",0
445,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*cot(f*x + e), x)","F",0
446,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*cot(f*x + e)^3, x)","F",0
447,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^4,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*tan(f*x + e)^4, x)","F",0
448,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p*tan(f*x+e)^2,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*tan(f*x + e)^2, x)","F",0
449,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p, x)","F",0
450,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*cot(f*x + e)^2, x)","F",0
451,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+b*sec(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right)^{2} + a\right)}^{p} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sec(f*x + e)^2 + a)^p*cot(f*x + e)^4, x)","F",0
452,1,73,0,0.341244," ","integrate((a+b*sec(f*x+e)^3)*tan(f*x+e)^5,x, algorithm=""maxima"")","-\frac{420 \, a \log\left(\cos\left(f x + e\right)\right) + \frac{420 \, a \cos\left(f x + e\right)^{5} - 140 \, b \cos\left(f x + e\right)^{4} - 105 \, a \cos\left(f x + e\right)^{3} + 168 \, b \cos\left(f x + e\right)^{2} - 60 \, b}{\cos\left(f x + e\right)^{7}}}{420 \, f}"," ",0,"-1/420*(420*a*log(cos(f*x + e)) + (420*a*cos(f*x + e)^5 - 140*b*cos(f*x + e)^4 - 105*a*cos(f*x + e)^3 + 168*b*cos(f*x + e)^2 - 60*b)/cos(f*x + e)^7)/f","A",0
453,1,51,0,0.345079," ","integrate((a+b*sec(f*x+e)^3)*tan(f*x+e)^3,x, algorithm=""maxima"")","\frac{30 \, a \log\left(\cos\left(f x + e\right)\right) + \frac{15 \, a \cos\left(f x + e\right)^{3} - 10 \, b \cos\left(f x + e\right)^{2} + 6 \, b}{\cos\left(f x + e\right)^{5}}}{30 \, f}"," ",0,"1/30*(30*a*log(cos(f*x + e)) + (15*a*cos(f*x + e)^3 - 10*b*cos(f*x + e)^2 + 6*b)/cos(f*x + e)^5)/f","A",0
454,1,28,0,0.344119," ","integrate((a+b*sec(f*x+e)^3)*tan(f*x+e),x, algorithm=""maxima"")","-\frac{a \log\left(\cos\left(f x + e\right)^{3}\right) - \frac{b}{\cos\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(a*log(cos(f*x + e)^3) - b/cos(f*x + e)^3)/f","A",0
455,1,45,0,0.345619," ","integrate(cot(f*x+e)*(a+b*sec(f*x+e)^3),x, algorithm=""maxima"")","\frac{{\left(a - b\right)} \log\left(\cos\left(f x + e\right) + 1\right) + {\left(a + b\right)} \log\left(\cos\left(f x + e\right) - 1\right) + \frac{2 \, b}{\cos\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*((a - b)*log(cos(f*x + e) + 1) + (a + b)*log(cos(f*x + e) - 1) + 2*b/cos(f*x + e))/f","A",0
456,1,62,0,0.338841," ","integrate(cot(f*x+e)^3*(a+b*sec(f*x+e)^3),x, algorithm=""maxima"")","-\frac{{\left(2 \, a + b\right)} \log\left(\cos\left(f x + e\right) + 1\right) + {\left(2 \, a - b\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left(b \cos\left(f x + e\right) + a\right)}}{\cos\left(f x + e\right)^{2} - 1}}{4 \, f}"," ",0,"-1/4*((2*a + b)*log(cos(f*x + e) + 1) + (2*a - b)*log(cos(f*x + e) - 1) - 2*(b*cos(f*x + e) + a)/(cos(f*x + e)^2 - 1))/f","A",0
457,1,218,0,0.441394," ","integrate(tan(f*x+e)^5/(a+b*sec(f*x+e)^3),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{3} {\left(2 \, a b {\left(3 \, \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{b}{a}\right)} + 3 \, a^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 2 \, b^{2}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} - 2 \, \cos\left(f x + e\right)\right)}}{3 \, \left(\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{a b^{2}} - \frac{3 \, {\left(2 \, b {\left(\left(\frac{b}{a}\right)^{\frac{2}{3}} + 1\right)} - a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \log\left(\cos\left(f x + e\right)^{2} - \left(\frac{b}{a}\right)^{\frac{1}{3}} \cos\left(f x + e\right) + \left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{a b \left(\frac{b}{a}\right)^{\frac{2}{3}}} - \frac{6 \, {\left(b {\left(\left(\frac{b}{a}\right)^{\frac{2}{3}} - 2\right)} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \log\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} + \cos\left(f x + e\right)\right)}{a b \left(\frac{b}{a}\right)^{\frac{2}{3}}} + \frac{18}{b \cos\left(f x + e\right)}}{18 \, f}"," ",0,"1/18*(2*sqrt(3)*(2*a*b*(3*(b/a)^(1/3) - b/a) + 3*a^2*(b/a)^(2/3) + 2*b^2)*arctan(-1/3*sqrt(3)*((b/a)^(1/3) - 2*cos(f*x + e))/(b/a)^(1/3))/(a*b^2) - 3*(2*b*((b/a)^(2/3) + 1) - a*(b/a)^(1/3))*log(cos(f*x + e)^2 - (b/a)^(1/3)*cos(f*x + e) + (b/a)^(2/3))/(a*b*(b/a)^(2/3)) - 6*(b*((b/a)^(2/3) - 2) + a*(b/a)^(1/3))*log((b/a)^(1/3) + cos(f*x + e))/(a*b*(b/a)^(2/3)) + 18/(b*cos(f*x + e)))/f","A",0
458,1,159,0,0.443054," ","integrate(tan(f*x+e)^3/(a+b*sec(f*x+e)^3),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{3} {\left(a {\left(3 \, \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{2 \, b}{a}\right)} + 2 \, b\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} - 2 \, \cos\left(f x + e\right)\right)}}{3 \, \left(\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{a b} - \frac{3 \, {\left(2 \, \left(\frac{b}{a}\right)^{\frac{2}{3}} + 1\right)} \log\left(\cos\left(f x + e\right)^{2} - \left(\frac{b}{a}\right)^{\frac{1}{3}} \cos\left(f x + e\right) + \left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{a \left(\frac{b}{a}\right)^{\frac{2}{3}}} - \frac{6 \, {\left(\left(\frac{b}{a}\right)^{\frac{2}{3}} - 1\right)} \log\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} + \cos\left(f x + e\right)\right)}{a \left(\frac{b}{a}\right)^{\frac{2}{3}}}}{18 \, f}"," ",0,"-1/18*(2*sqrt(3)*(a*(3*(b/a)^(1/3) - 2*b/a) + 2*b)*arctan(-1/3*sqrt(3)*((b/a)^(1/3) - 2*cos(f*x + e))/(b/a)^(1/3))/(a*b) - 3*(2*(b/a)^(2/3) + 1)*log(cos(f*x + e)^2 - (b/a)^(1/3)*cos(f*x + e) + (b/a)^(2/3))/(a*(b/a)^(2/3)) - 6*((b/a)^(2/3) - 1)*log((b/a)^(1/3) + cos(f*x + e))/(a*(b/a)^(2/3)))/f","A",0
459,1,21,0,0.341517," ","integrate(tan(f*x+e)/(a+b*sec(f*x+e)^3),x, algorithm=""maxima"")","-\frac{\log\left(a \cos\left(f x + e\right)^{3} + b\right)}{3 \, a f}"," ",0,"-1/3*log(a*cos(f*x + e)^3 + b)/(a*f)","A",0
460,1,306,0,0.443235," ","integrate(cot(f*x+e)/(a+b*sec(f*x+e)^3),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{3} {\left(a b^{2} {\left(3 \, \left(\frac{b}{a}\right)^{\frac{1}{3}} + \frac{2 \, b}{a}\right)} - 3 \, a^{2} b \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, b^{3}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} - 2 \, \cos\left(f x + e\right)\right)}}{3 \, \left(\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{{\left(a^{4} \left(\frac{b}{a}\right)^{\frac{2}{3}} - a^{2} b^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}} + \frac{3 \, {\left(b^{2} {\left(2 \, \left(\frac{b}{a}\right)^{\frac{2}{3}} - 1\right)} - a b \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \log\left(\cos\left(f x + e\right)^{2} - \left(\frac{b}{a}\right)^{\frac{1}{3}} \cos\left(f x + e\right) + \left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{a^{3} \left(\frac{b}{a}\right)^{\frac{2}{3}} - a b^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}}} + \frac{6 \, {\left(b^{2} {\left(\left(\frac{b}{a}\right)^{\frac{2}{3}} + 1\right)} + a b \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \log\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} + \cos\left(f x + e\right)\right)}{a^{3} \left(\frac{b}{a}\right)^{\frac{2}{3}} - a b^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}}} - \frac{9 \, \log\left(\cos\left(f x + e\right) + 1\right)}{a - b} - \frac{9 \, \log\left(\cos\left(f x + e\right) - 1\right)}{a + b}}{18 \, f}"," ",0,"-1/18*(2*sqrt(3)*(a*b^2*(3*(b/a)^(1/3) + 2*b/a) - 3*a^2*b*(b/a)^(2/3) - 2*b^3)*arctan(-1/3*sqrt(3)*((b/a)^(1/3) - 2*cos(f*x + e))/(b/a)^(1/3))/((a^4*(b/a)^(2/3) - a^2*b^2*(b/a)^(2/3))*(b/a)^(1/3)) + 3*(b^2*(2*(b/a)^(2/3) - 1) - a*b*(b/a)^(1/3))*log(cos(f*x + e)^2 - (b/a)^(1/3)*cos(f*x + e) + (b/a)^(2/3))/(a^3*(b/a)^(2/3) - a*b^2*(b/a)^(2/3)) + 6*(b^2*((b/a)^(2/3) + 1) + a*b*(b/a)^(1/3))*log((b/a)^(1/3) + cos(f*x + e))/(a^3*(b/a)^(2/3) - a*b^2*(b/a)^(2/3)) - 9*log(cos(f*x + e) + 1)/(a - b) - 9*log(cos(f*x + e) - 1)/(a + b))/f","A",0
461,1,488,0,0.431797," ","integrate(cot(f*x+e)^3/(a+b*sec(f*x+e)^3),x, algorithm=""maxima"")","\frac{\frac{4 \, \sqrt{3} {\left(a^{2} b^{3} {\left(9 \, \left(\frac{b}{a}\right)^{\frac{2}{3}} + 4\right)} - a^{3} b^{2} {\left(3 \, \left(\frac{b}{a}\right)^{\frac{1}{3}} + \frac{4 \, b}{a}\right)} - 2 \, a b^{4} {\left(3 \, \left(\frac{b}{a}\right)^{\frac{1}{3}} + \frac{b}{a}\right)} + 2 \, b^{5}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} - 2 \, \cos\left(f x + e\right)\right)}}{3 \, \left(\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{{\left(a^{6} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, a^{4} b^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a^{2} b^{4} \left(\frac{b}{a}\right)^{\frac{2}{3}}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}} - \frac{6 \, {\left(a^{2} b^{2} {\left(4 \, \left(\frac{b}{a}\right)^{\frac{2}{3}} - 1\right)} + 2 \, b^{4} {\left(\left(\frac{b}{a}\right)^{\frac{2}{3}} - 1\right)} - 3 \, a b^{3} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \log\left(\cos\left(f x + e\right)^{2} - \left(\frac{b}{a}\right)^{\frac{1}{3}} \cos\left(f x + e\right) + \left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{a^{5} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, a^{3} b^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a b^{4} \left(\frac{b}{a}\right)^{\frac{2}{3}}} - \frac{12 \, {\left(a^{2} b^{2} {\left(2 \, \left(\frac{b}{a}\right)^{\frac{2}{3}} + 1\right)} + b^{4} {\left(\left(\frac{b}{a}\right)^{\frac{2}{3}} + 2\right)} + 3 \, a b^{3} \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)} \log\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} + \cos\left(f x + e\right)\right)}{a^{5} \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, a^{3} b^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a b^{4} \left(\frac{b}{a}\right)^{\frac{2}{3}}} - \frac{9 \, {\left(2 \, a - 5 \, b\right)} \log\left(\cos\left(f x + e\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{9 \, {\left(2 \, a + 5 \, b\right)} \log\left(\cos\left(f x + e\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{18 \, {\left(b \cos\left(f x + e\right) - a\right)}}{{\left(a^{2} - b^{2}\right)} \cos\left(f x + e\right)^{2} - a^{2} + b^{2}}}{36 \, f}"," ",0,"1/36*(4*sqrt(3)*(a^2*b^3*(9*(b/a)^(2/3) + 4) - a^3*b^2*(3*(b/a)^(1/3) + 4*b/a) - 2*a*b^4*(3*(b/a)^(1/3) + b/a) + 2*b^5)*arctan(-1/3*sqrt(3)*((b/a)^(1/3) - 2*cos(f*x + e))/(b/a)^(1/3))/((a^6*(b/a)^(2/3) - 2*a^4*b^2*(b/a)^(2/3) + a^2*b^4*(b/a)^(2/3))*(b/a)^(1/3)) - 6*(a^2*b^2*(4*(b/a)^(2/3) - 1) + 2*b^4*((b/a)^(2/3) - 1) - 3*a*b^3*(b/a)^(1/3))*log(cos(f*x + e)^2 - (b/a)^(1/3)*cos(f*x + e) + (b/a)^(2/3))/(a^5*(b/a)^(2/3) - 2*a^3*b^2*(b/a)^(2/3) + a*b^4*(b/a)^(2/3)) - 12*(a^2*b^2*(2*(b/a)^(2/3) + 1) + b^4*((b/a)^(2/3) + 2) + 3*a*b^3*(b/a)^(1/3))*log((b/a)^(1/3) + cos(f*x + e))/(a^5*(b/a)^(2/3) - 2*a^3*b^2*(b/a)^(2/3) + a*b^4*(b/a)^(2/3)) - 9*(2*a - 5*b)*log(cos(f*x + e) + 1)/(a^2 - 2*a*b + b^2) - 9*(2*a + 5*b)*log(cos(f*x + e) - 1)/(a^2 + 2*a*b + b^2) - 18*(b*cos(f*x + e) - a)/((a^2 - b^2)*cos(f*x + e)^2 - a^2 + b^2))/f","A",0
462,0,0,0,0.000000," ","integrate((a+b*(c*sec(f*x+e))^n)^p*(d*tan(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(\left(c \sec\left(f x + e\right)\right)^{n} b + a\right)}^{p} \left(d \tan\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*sec(f*x + e))^n*b + a)^p*(d*tan(f*x + e))^m, x)","F",0
463,0,0,0,0.000000," ","integrate((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e)^5,x, algorithm=""maxima"")","\int {\left(\left(c \sec\left(f x + e\right)\right)^{n} b + a\right)}^{p} \tan\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(((c*sec(f*x + e))^n*b + a)^p*tan(f*x + e)^5, x)","F",0
464,0,0,0,0.000000," ","integrate((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e)^3,x, algorithm=""maxima"")","\int {\left(\left(c \sec\left(f x + e\right)\right)^{n} b + a\right)}^{p} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(((c*sec(f*x + e))^n*b + a)^p*tan(f*x + e)^3, x)","F",0
465,0,0,0,0.000000," ","integrate((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e),x, algorithm=""maxima"")","\int {\left(\left(c \sec\left(f x + e\right)\right)^{n} b + a\right)}^{p} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate(((c*sec(f*x + e))^n*b + a)^p*tan(f*x + e), x)","F",0
466,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*(c*sec(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \sec\left(f x + e\right)\right)^{n} b + a\right)}^{p} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate(((c*sec(f*x + e))^n*b + a)^p*cot(f*x + e), x)","F",0
467,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(a+b*(c*sec(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \sec\left(f x + e\right)\right)^{n} b + a\right)}^{p} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(((c*sec(f*x + e))^n*b + a)^p*cot(f*x + e)^3, x)","F",0
468,0,0,0,0.000000," ","integrate((a+b*(c*sec(f*x+e))^n)^p*tan(f*x+e)^2,x, algorithm=""maxima"")","\int {\left(\left(c \sec\left(f x + e\right)\right)^{n} b + a\right)}^{p} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(((c*sec(f*x + e))^n*b + a)^p*tan(f*x + e)^2, x)","F",0
469,0,0,0,0.000000," ","integrate((a+b*(c*sec(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \sec\left(f x + e\right)\right)^{n} b + a\right)}^{p}\,{d x}"," ",0,"integrate(((c*sec(f*x + e))^n*b + a)^p, x)","F",0
470,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+b*(c*sec(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \sec\left(f x + e\right)\right)^{n} b + a\right)}^{p} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(((c*sec(f*x + e))^n*b + a)^p*cot(f*x + e)^2, x)","F",0
