1,1,95,0,0.325740," ","integrate((a+a*sin(d*x+c))*tan(d*x+c)^5,x, algorithm=""maxima"")","\frac{7 \, a \log\left(\sin\left(d x + c\right) + 1\right) - 23 \, a \log\left(\sin\left(d x + c\right) - 1\right) - 16 \, a \sin\left(d x + c\right) + \frac{2 \, {\left(9 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - 6 \, a\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} - \sin\left(d x + c\right) + 1}}{16 \, d}"," ",0,"1/16*(7*a*log(sin(d*x + c) + 1) - 23*a*log(sin(d*x + c) - 1) - 16*a*sin(d*x + c) + 2*(9*a*sin(d*x + c)^2 - a*sin(d*x + c) - 6*a)/(sin(d*x + c)^3 - sin(d*x + c)^2 - sin(d*x + c) + 1))/d","A",0
2,1,51,0,0.307005," ","integrate((a+a*sin(d*x+c))*tan(d*x+c)^3,x, algorithm=""maxima"")","-\frac{a \log\left(\sin\left(d x + c\right) + 1\right) - 5 \, a \log\left(\sin\left(d x + c\right) - 1\right) - 4 \, a \sin\left(d x + c\right) + \frac{2 \, a}{\sin\left(d x + c\right) - 1}}{4 \, d}"," ",0,"-1/4*(a*log(sin(d*x + c) + 1) - 5*a*log(sin(d*x + c) - 1) - 4*a*sin(d*x + c) + 2*a/(sin(d*x + c) - 1))/d","A",0
3,1,25,0,0.301152," ","integrate((a+a*sin(d*x+c))*tan(d*x+c),x, algorithm=""maxima"")","-\frac{a \log\left(\sin\left(d x + c\right) - 1\right) + a \sin\left(d x + c\right)}{d}"," ",0,"-(a*log(sin(d*x + c) - 1) + a*sin(d*x + c))/d","A",0
4,1,22,0,0.355492," ","integrate(cot(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\sin\left(d x + c\right)\right) + a \sin\left(d x + c\right)}{d}"," ",0,"(a*log(sin(d*x + c)) + a*sin(d*x + c))/d","A",0
5,1,45,0,0.302169," ","integrate(cot(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, a \log\left(\sin\left(d x + c\right)\right) + 2 \, a \sin\left(d x + c\right) + \frac{2 \, a \sin\left(d x + c\right) + a}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*a*log(sin(d*x + c)) + 2*a*sin(d*x + c) + (2*a*sin(d*x + c) + a)/sin(d*x + c)^2)/d","A",0
6,1,69,0,0.646814," ","integrate(cot(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, a \log\left(\sin\left(d x + c\right)\right) + 12 \, a \sin\left(d x + c\right) + \frac{24 \, a \sin\left(d x + c\right)^{3} + 12 \, a \sin\left(d x + c\right)^{2} - 4 \, a \sin\left(d x + c\right) - 3 \, a}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*a*log(sin(d*x + c)) + 12*a*sin(d*x + c) + (24*a*sin(d*x + c)^3 + 12*a*sin(d*x + c)^2 - 4*a*sin(d*x + c) - 3*a)/sin(d*x + c)^4)/d","A",0
7,1,91,0,0.304605," ","integrate(cot(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{60 \, a \log\left(\sin\left(d x + c\right)\right) + 60 \, a \sin\left(d x + c\right) + \frac{180 \, a \sin\left(d x + c\right)^{5} + 90 \, a \sin\left(d x + c\right)^{4} - 60 \, a \sin\left(d x + c\right)^{3} - 45 \, a \sin\left(d x + c\right)^{2} + 12 \, a \sin\left(d x + c\right) + 10 \, a}{\sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(60*a*log(sin(d*x + c)) + 60*a*sin(d*x + c) + (180*a*sin(d*x + c)^5 + 90*a*sin(d*x + c)^4 - 60*a*sin(d*x + c)^3 - 45*a*sin(d*x + c)^2 + 12*a*sin(d*x + c) + 10*a)/sin(d*x + c)^6)/d","A",0
8,1,87,0,0.405126," ","integrate((a+a*sin(d*x+c))*tan(d*x+c)^6,x, algorithm=""maxima"")","\frac{{\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a + 3 \, a {\left(\frac{15 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{2} + 1}{\cos\left(d x + c\right)^{5}} + 5 \, \cos\left(d x + c\right)\right)}}{15 \, d}"," ",0,"1/15*((3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a + 3*a*((15*cos(d*x + c)^4 - 5*cos(d*x + c)^2 + 1)/cos(d*x + c)^5 + 5*cos(d*x + c)))/d","A",0
9,1,65,0,0.417720," ","integrate((a+a*sin(d*x+c))*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a - a {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a - a*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
10,1,39,0,0.395795," ","integrate((a+a*sin(d*x+c))*tan(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(d x + c - \tan\left(d x + c\right)\right)} a - a {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{d}"," ",0,"-((d*x + c - tan(d*x + c))*a - a*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
11,1,54,0,0.420918," ","integrate(cot(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a - a {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c + 1/tan(d*x + c))*a - a*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
12,1,92,0,0.401916," ","integrate(cot(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a + 3 \, a {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(4*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a + 3*a*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
13,1,125,0,0.409941," ","integrate(cot(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{16 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a + 15 \, a {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"-1/240*(16*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a + 15*a*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
14,1,96,0,0.305509," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c)^5,x, algorithm=""maxima"")","-\frac{4 \, a^{2} \sin\left(d x + c\right)^{2} + a^{2} \log\left(\sin\left(d x + c\right) + 1\right) + 31 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) + 16 \, a^{2} \sin\left(d x + c\right) - \frac{2 \, {\left(9 \, a^{2} \sin\left(d x + c\right) - 8 \, a^{2}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{8 \, d}"," ",0,"-1/8*(4*a^2*sin(d*x + c)^2 + a^2*log(sin(d*x + c) + 1) + 31*a^2*log(sin(d*x + c) - 1) + 16*a^2*sin(d*x + c) - 2*(9*a^2*sin(d*x + c) - 8*a^2)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
15,1,58,0,0.303761," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{a^{2} \sin\left(d x + c\right)^{2} + 6 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) + 4 \, a^{2} \sin\left(d x + c\right) - \frac{2 \, a^{2}}{\sin\left(d x + c\right) - 1}}{2 \, d}"," ",0,"1/2*(a^2*sin(d*x + c)^2 + 6*a^2*log(sin(d*x + c) - 1) + 4*a^2*sin(d*x + c) - 2*a^2/(sin(d*x + c) - 1))/d","A",0
16,1,43,0,0.305321," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c),x, algorithm=""maxima"")","-\frac{a^{2} \sin\left(d x + c\right)^{2} + 4 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) + 4 \, a^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(a^2*sin(d*x + c)^2 + 4*a^2*log(sin(d*x + c) - 1) + 4*a^2*sin(d*x + c))/d","A",0
17,1,53,0,0.309392," ","integrate(cot(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} \sin\left(d x + c\right)^{2} + 4 \, a^{2} \sin\left(d x + c\right) + \frac{4 \, a^{2} \sin\left(d x + c\right) + a^{2}}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(a^2*sin(d*x + c)^2 + 4*a^2*sin(d*x + c) + (4*a^2*sin(d*x + c) + a^2)/sin(d*x + c)^2)/d","A",0
18,1,107,0,0.314649," ","integrate(cot(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{15 \, a^{2} \sin\left(d x + c\right)^{2} - 60 \, a^{2} \log\left(\sin\left(d x + c\right)\right) + 60 \, a^{2} \sin\left(d x + c\right) + \frac{180 \, a^{2} \sin\left(d x + c\right)^{5} - 60 \, a^{2} \sin\left(d x + c\right)^{3} - 15 \, a^{2} \sin\left(d x + c\right)^{2} + 12 \, a^{2} \sin\left(d x + c\right) + 5 \, a^{2}}{\sin\left(d x + c\right)^{6}}}{30 \, d}"," ",0,"-1/30*(15*a^2*sin(d*x + c)^2 - 60*a^2*log(sin(d*x + c)) + 60*a^2*sin(d*x + c) + (180*a^2*sin(d*x + c)^5 - 60*a^2*sin(d*x + c)^3 - 15*a^2*sin(d*x + c)^2 + 12*a^2*sin(d*x + c) + 5*a^2)/sin(d*x + c)^6)/d","A",0
19,1,152,0,0.421947," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c)^6,x, algorithm=""maxima"")","\frac{{\left(6 \, \tan\left(d x + c\right)^{5} - 20 \, \tan\left(d x + c\right)^{3} - 105 \, d x - 105 \, c + \frac{15 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} + 90 \, \tan\left(d x + c\right)\right)} a^{2} + 2 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a^{2} + 12 \, a^{2} {\left(\frac{15 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{2} + 1}{\cos\left(d x + c\right)^{5}} + 5 \, \cos\left(d x + c\right)\right)}}{30 \, d}"," ",0,"1/30*((6*tan(d*x + c)^5 - 20*tan(d*x + c)^3 - 105*d*x - 105*c + 15*tan(d*x + c)/(tan(d*x + c)^2 + 1) + 90*tan(d*x + c))*a^2 + 2*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a^2 + 12*a^2*((15*cos(d*x + c)^4 - 5*cos(d*x + c)^2 + 1)/cos(d*x + c)^5 + 5*cos(d*x + c)))/d","A",0
20,1,120,0,0.403388," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{{\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a^{2} + 2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{2} - 4 \, a^{2} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"1/6*((2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a^2 + 2*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^2 - 4*a^2*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
21,1,84,0,0.413718," ","integrate((a+a*sin(d*x+c))^2*tan(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{2} + 2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} - 4 \, a^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{2 \, d}"," ",0,"-1/2*((3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^2 + 2*(d*x + c - tan(d*x + c))*a^2 - 4*a^2*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
22,1,47,0,0.302463," ","integrate((a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{4 \, d} - \frac{2 \, a^{2} \cos\left(d x + c\right)}{d}"," ",0,"a^2*x + 1/4*(2*d*x + 2*c - sin(2*d*x + 2*c))*a^2/d - 2*a^2*cos(d*x + c)/d","A",0
23,1,79,0,0.648637," ","integrate(cot(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 4 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{2} + 4 \, a^{2} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a^2 - 4*(d*x + c + 1/tan(d*x + c))*a^2 + 4*a^2*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
24,1,139,0,0.456767," ","integrate(cot(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{2} - 2 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{2} - 3 \, a^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{6 \, d}"," ",0,"-1/6*(3*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^2 - 2*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^2 - 3*a^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
25,1,133,0,0.316495," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c)^7,x, algorithm=""maxima"")","\frac{16 \, a^{3} \sin\left(d x + c\right)^{3} + 72 \, a^{3} \sin\left(d x + c\right)^{2} - 3 \, a^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 627 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) + 336 \, a^{3} \sin\left(d x + c\right) - \frac{2 \, {\left(213 \, a^{3} \sin\left(d x + c\right)^{2} - 387 \, a^{3} \sin\left(d x + c\right) + 178 \, a^{3}\right)}}{\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 1}}{48 \, d}"," ",0,"1/48*(16*a^3*sin(d*x + c)^3 + 72*a^3*sin(d*x + c)^2 - 3*a^3*log(sin(d*x + c) + 1) + 627*a^3*log(sin(d*x + c) - 1) + 336*a^3*sin(d*x + c) - 2*(213*a^3*sin(d*x + c)^2 - 387*a^3*sin(d*x + c) + 178*a^3)/(sin(d*x + c)^3 - 3*sin(d*x + c)^2 + 3*sin(d*x + c) - 1))/d","A",0
26,1,72,0,0.303483," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{2 \, a^{3} \sin\left(d x + c\right)^{3} + 9 \, a^{3} \sin\left(d x + c\right)^{2} + 42 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) + 30 \, a^{3} \sin\left(d x + c\right) - \frac{12 \, a^{3}}{\sin\left(d x + c\right) - 1}}{6 \, d}"," ",0,"1/6*(2*a^3*sin(d*x + c)^3 + 9*a^3*sin(d*x + c)^2 + 42*a^3*log(sin(d*x + c) - 1) + 30*a^3*sin(d*x + c) - 12*a^3/(sin(d*x + c) - 1))/d","A",0
27,1,57,0,0.309699," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c),x, algorithm=""maxima"")","-\frac{2 \, a^{3} \sin\left(d x + c\right)^{3} + 9 \, a^{3} \sin\left(d x + c\right)^{2} + 24 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) + 24 \, a^{3} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*a^3*sin(d*x + c)^3 + 9*a^3*sin(d*x + c)^2 + 24*a^3*log(sin(d*x + c) - 1) + 24*a^3*sin(d*x + c))/d","A",0
28,1,80,0,0.301400," ","integrate(cot(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, a^{3} \sin\left(d x + c\right)^{3} + 9 \, a^{3} \sin\left(d x + c\right)^{2} - 12 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + 12 \, a^{3} \sin\left(d x + c\right) + \frac{3 \, {\left(6 \, a^{3} \sin\left(d x + c\right) + a^{3}\right)}}{\sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"-1/6*(2*a^3*sin(d*x + c)^3 + 9*a^3*sin(d*x + c)^2 - 12*a^3*log(sin(d*x + c)) + 12*a^3*sin(d*x + c) + 3*(6*a^3*sin(d*x + c) + a^3)/sin(d*x + c)^2)/d","A",0
29,1,209,0,0.402289," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c)^6,x, algorithm=""maxima"")","\frac{3 \, {\left(6 \, \tan\left(d x + c\right)^{5} - 20 \, \tan\left(d x + c\right)^{3} - 105 \, d x - 105 \, c + \frac{15 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} + 90 \, \tan\left(d x + c\right)\right)} a^{3} + 2 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a^{3} - 2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - \frac{90 \, \cos\left(d x + c\right)^{4} - 20 \, \cos\left(d x + c\right)^{2} + 3}{\cos\left(d x + c\right)^{5}} - 60 \, \cos\left(d x + c\right)\right)} a^{3} + 18 \, a^{3} {\left(\frac{15 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{2} + 1}{\cos\left(d x + c\right)^{5}} + 5 \, \cos\left(d x + c\right)\right)}}{30 \, d}"," ",0,"1/30*(3*(6*tan(d*x + c)^5 - 20*tan(d*x + c)^3 - 105*d*x - 105*c + 15*tan(d*x + c)/(tan(d*x + c)^2 + 1) + 90*tan(d*x + c))*a^3 + 2*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a^3 - 2*(5*cos(d*x + c)^3 - (90*cos(d*x + c)^4 - 20*cos(d*x + c)^2 + 3)/cos(d*x + c)^5 - 60*cos(d*x + c))*a^3 + 18*a^3*((15*cos(d*x + c)^4 - 5*cos(d*x + c)^2 + 1)/cos(d*x + c)^5 + 5*cos(d*x + c)))/d","A",0
30,1,165,0,0.422095," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{9 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} - 9 \, \cos\left(d x + c\right)\right)} a^{3} + 3 \, {\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a^{3} + 2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{3} - 6 \, a^{3} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"1/6*(2*(cos(d*x + c)^3 - (9*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 - 9*cos(d*x + c))*a^3 + 3*(2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a^3 + 2*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^3 - 6*a^3*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
31,1,117,0,0.436979," ","integrate((a+a*sin(d*x+c))^3*tan(d*x+c)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a^{3} + 9 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{3} + 6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} - 18 \, a^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"-1/6*(2*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a^3 + 9*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^3 + 6*(d*x + c - tan(d*x + c))*a^3 - 18*a^3*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
32,1,72,0,0.292669," ","integrate((a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x + \frac{{\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{3}}{3 \, d} + \frac{3 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3}}{4 \, d} - \frac{3 \, a^{3} \cos\left(d x + c\right)}{d}"," ",0,"a^3*x + 1/3*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^3/d + 3/4*(2*d*x + 2*c - sin(2*d*x + 2*c))*a^3/d - 3*a^3*cos(d*x + c)/d","A",0
33,1,93,0,0.399407," ","integrate(cot(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{4 \, a^{3} \cos\left(d x + c\right)^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} + 12 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{3} - 18 \, a^{3} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"-1/12*(4*a^3*cos(d*x + c)^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 + 12*(d*x + c + 1/tan(d*x + c))*a^3 - 18*a^3*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
34,1,109,0,0.295317," ","integrate((a+a*sin(d*x+c))^4*tan(d*x+c)^5,x, algorithm=""maxima"")","-\frac{3 \, a^{4} \sin\left(d x + c\right)^{4} + 16 \, a^{4} \sin\left(d x + c\right)^{3} + 54 \, a^{4} \sin\left(d x + c\right)^{2} + 300 \, a^{4} \log\left(\sin\left(d x + c\right) - 1\right) + 192 \, a^{4} \sin\left(d x + c\right) - \frac{12 \, {\left(11 \, a^{4} \sin\left(d x + c\right) - 10 \, a^{4}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{12 \, d}"," ",0,"-1/12*(3*a^4*sin(d*x + c)^4 + 16*a^4*sin(d*x + c)^3 + 54*a^4*sin(d*x + c)^2 + 300*a^4*log(sin(d*x + c) - 1) + 192*a^4*sin(d*x + c) - 12*(11*a^4*sin(d*x + c) - 10*a^4)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
35,1,85,0,0.293634," ","integrate((a+a*sin(d*x+c))^4*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{3 \, a^{4} \sin\left(d x + c\right)^{4} + 16 \, a^{4} \sin\left(d x + c\right)^{3} + 48 \, a^{4} \sin\left(d x + c\right)^{2} + 192 \, a^{4} \log\left(\sin\left(d x + c\right) - 1\right) + 144 \, a^{4} \sin\left(d x + c\right) - \frac{48 \, a^{4}}{\sin\left(d x + c\right) - 1}}{12 \, d}"," ",0,"1/12*(3*a^4*sin(d*x + c)^4 + 16*a^4*sin(d*x + c)^3 + 48*a^4*sin(d*x + c)^2 + 192*a^4*log(sin(d*x + c) - 1) + 144*a^4*sin(d*x + c) - 48*a^4/(sin(d*x + c) - 1))/d","A",0
36,1,70,0,0.294561," ","integrate((a+a*sin(d*x+c))^4*tan(d*x+c),x, algorithm=""maxima"")","-\frac{3 \, a^{4} \sin\left(d x + c\right)^{4} + 16 \, a^{4} \sin\left(d x + c\right)^{3} + 42 \, a^{4} \sin\left(d x + c\right)^{2} + 96 \, a^{4} \log\left(\sin\left(d x + c\right) - 1\right) + 96 \, a^{4} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*a^4*sin(d*x + c)^4 + 16*a^4*sin(d*x + c)^3 + 42*a^4*sin(d*x + c)^2 + 96*a^4*log(sin(d*x + c) - 1) + 96*a^4*sin(d*x + c))/d","A",0
37,1,82,0,0.309135," ","integrate(cot(d*x+c)^3*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, a^{4} \sin\left(d x + c\right)^{4} + 16 \, a^{4} \sin\left(d x + c\right)^{3} + 30 \, a^{4} \sin\left(d x + c\right)^{2} - 60 \, a^{4} \log\left(\sin\left(d x + c\right)\right) + \frac{6 \, {\left(8 \, a^{4} \sin\left(d x + c\right) + a^{4}\right)}}{\sin\left(d x + c\right)^{2}}}{12 \, d}"," ",0,"-1/12*(3*a^4*sin(d*x + c)^4 + 16*a^4*sin(d*x + c)^3 + 30*a^4*sin(d*x + c)^2 - 60*a^4*log(sin(d*x + c)) + 6*(8*a^4*sin(d*x + c) + a^4)/sin(d*x + c)^2)/d","A",0
38,1,238,0,0.421531," ","integrate((a+a*sin(d*x+c))^4*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{32 \, {\left(\cos\left(d x + c\right)^{3} - \frac{9 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} - 9 \, \cos\left(d x + c\right)\right)} a^{4} + {\left(8 \, \tan\left(d x + c\right)^{3} + 105 \, d x + 105 \, c - \frac{3 \, {\left(13 \, \tan\left(d x + c\right)^{3} + 11 \, \tan\left(d x + c\right)\right)}}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1} - 72 \, \tan\left(d x + c\right)\right)} a^{4} + 24 \, {\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a^{4} + 8 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{4} - 32 \, a^{4} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{24 \, d}"," ",0,"1/24*(32*(cos(d*x + c)^3 - (9*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 - 9*cos(d*x + c))*a^4 + (8*tan(d*x + c)^3 + 105*d*x + 105*c - 3*(13*tan(d*x + c)^3 + 11*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1) - 72*tan(d*x + c))*a^4 + 24*(2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a^4 + 8*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^4 - 32*a^4*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
39,1,181,0,0.454016," ","integrate((a+a*sin(d*x+c))^4*tan(d*x+c)^2,x, algorithm=""maxima"")","-\frac{32 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a^{4} + 3 \, {\left(15 \, d x + 15 \, c - \frac{9 \, \tan\left(d x + c\right)^{3} + 7 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1} - 8 \, \tan\left(d x + c\right)\right)} a^{4} + 72 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{4} + 24 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{4} - 96 \, a^{4} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{24 \, d}"," ",0,"-1/24*(32*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a^4 + 3*(15*d*x + 15*c - (9*tan(d*x + c)^3 + 7*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1) - 8*tan(d*x + c))*a^4 + 72*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^4 + 24*(d*x + c - tan(d*x + c))*a^4 - 96*a^4*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
40,1,108,0,0.296085," ","integrate((a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","a^{4} x + \frac{4 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{4}}{3 \, d} + \frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{32 \, d} + \frac{3 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{2 \, d} - \frac{4 \, a^{4} \cos\left(d x + c\right)}{d}"," ",0,"a^4*x + 4/3*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^4/d + 1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*a^4/d + 3/2*(2*d*x + 2*c - sin(2*d*x + 2*c))*a^4/d - 4*a^4*cos(d*x + c)/d","A",0
41,1,117,0,0.400291," ","integrate(cot(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{128 \, a^{4} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4} - 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 96 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{4} - 192 \, a^{4} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{96 \, d}"," ",0,"-1/96*(128*a^4*cos(d*x + c)^3 - 3*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^4 - 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 + 96*(d*x + c + 1/tan(d*x + c))*a^4 - 192*a^4*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
42,1,218,0,0.400087," ","integrate(cot(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{64 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{4} + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 288 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{4} + 32 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{4} + 96 \, a^{4} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{96 \, d}"," ",0,"1/96*(64*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^4 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4 - 288*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^4 + 32*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^4 + 96*a^4*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
43,1,313,0,0.405248," ","integrate(cot(d*x+c)^6*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{40 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{4} + 15 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{4} - 120 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a^{4} + 8 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{4} + 30 \, a^{4} {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{120 \, d}"," ",0,"-1/120*(40*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^4 + 15*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a^4 - 120*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a^4 + 8*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^4 + 30*a^4*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
44,1,175,0,0.312299," ","integrate(tan(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(279 \, \sin\left(d x + c\right)^{6} + 87 \, \sin\left(d x + c\right)^{5} - 424 \, \sin\left(d x + c\right)^{4} - 136 \, \sin\left(d x + c\right)^{3} + 249 \, \sin\left(d x + c\right)^{2} + 57 \, \sin\left(d x + c\right) - 48\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} + \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"-1/768*(2*(279*sin(d*x + c)^6 + 87*sin(d*x + c)^5 - 424*sin(d*x + c)^4 - 136*sin(d*x + c)^3 + 249*sin(d*x + c)^2 + 57*sin(d*x + c) - 48)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) + 105*log(sin(d*x + c) + 1)/a - 105*log(sin(d*x + c) - 1)/a)/d","A",0
45,1,130,0,0.309477," ","integrate(tan(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(33 \, \sin\left(d x + c\right)^{4} + 9 \, \sin\left(d x + c\right)^{3} - 31 \, \sin\left(d x + c\right)^{2} - 7 \, \sin\left(d x + c\right) + 8\right)}}{a \sin\left(d x + c\right)^{5} + a \sin\left(d x + c\right)^{4} - 2 \, a \sin\left(d x + c\right)^{3} - 2 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} + \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{96 \, d}"," ",0,"1/96*(2*(33*sin(d*x + c)^4 + 9*sin(d*x + c)^3 - 31*sin(d*x + c)^2 - 7*sin(d*x + c) + 8)/(a*sin(d*x + c)^5 + a*sin(d*x + c)^4 - 2*a*sin(d*x + c)^3 - 2*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) + 15*log(sin(d*x + c) + 1)/a - 15*log(sin(d*x + c) - 1)/a)/d","A",0
46,1,89,0,0.312248," ","integrate(tan(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(5 \, \sin\left(d x + c\right)^{2} + \sin\left(d x + c\right) - 2\right)}}{a \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} + \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{16 \, d}"," ",0,"-1/16*(2*(5*sin(d*x + c)^2 + sin(d*x + c) - 2)/(a*sin(d*x + c)^3 + a*sin(d*x + c)^2 - a*sin(d*x + c) - a) + 3*log(sin(d*x + c) + 1)/a - 3*log(sin(d*x + c) - 1)/a)/d","A",0
47,1,47,0,0.353027," ","integrate(tan(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a} + \frac{2}{a \sin\left(d x + c\right) + a}}{4 \, d}"," ",0,"1/4*(log(sin(d*x + c) + 1)/a - log(sin(d*x + c) - 1)/a + 2/(a*sin(d*x + c) + a))/d","A",0
48,1,31,0,0.302039," ","integrate(cot(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\sin\left(d x + c\right)\right)}{a}}{d}"," ",0,"-(log(sin(d*x + c) + 1)/a - log(sin(d*x + c))/a)/d","A",0
49,1,26,0,0.301516," ","integrate(cot(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, \sin\left(d x + c\right) - 1}{2 \, a d \sin\left(d x + c\right)^{2}}"," ",0,"1/2*(2*sin(d*x + c) - 1)/(a*d*sin(d*x + c)^2)","A",0
50,1,46,0,0.306561," ","integrate(cot(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{12 \, \sin\left(d x + c\right)^{3} - 6 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) + 3}{12 \, a d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(12*sin(d*x + c)^3 - 6*sin(d*x + c)^2 - 4*sin(d*x + c) + 3)/(a*d*sin(d*x + c)^4)","A",0
51,1,66,0,0.301963," ","integrate(cot(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{30 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} - 20 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)^{2} + 6 \, \sin\left(d x + c\right) - 5}{30 \, a d \sin\left(d x + c\right)^{6}}"," ",0,"1/30*(30*sin(d*x + c)^5 - 15*sin(d*x + c)^4 - 20*sin(d*x + c)^3 + 15*sin(d*x + c)^2 + 6*sin(d*x + c) - 5)/(a*d*sin(d*x + c)^6)","A",0
52,1,86,0,0.305068," ","integrate(cot(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{280 \, \sin\left(d x + c\right)^{7} - 140 \, \sin\left(d x + c\right)^{6} - 280 \, \sin\left(d x + c\right)^{5} + 210 \, \sin\left(d x + c\right)^{4} + 168 \, \sin\left(d x + c\right)^{3} - 140 \, \sin\left(d x + c\right)^{2} - 40 \, \sin\left(d x + c\right) + 35}{280 \, a d \sin\left(d x + c\right)^{8}}"," ",0,"-1/280*(280*sin(d*x + c)^7 - 140*sin(d*x + c)^6 - 280*sin(d*x + c)^5 + 210*sin(d*x + c)^4 + 168*sin(d*x + c)^3 - 140*sin(d*x + c)^2 - 40*sin(d*x + c) + 35)/(a*d*sin(d*x + c)^8)","A",0
53,1,338,0,0.383459," ","integrate(tan(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{32 \, {\left(\frac{2 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 1\right)}}{35 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{10 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{20 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{5 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{10 \, a \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{4 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{2 \, a \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d}"," ",0,"32/35*(2*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 10*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 20*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 5*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 10*a*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 4*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 2*a*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d)","B",0
54,1,214,0,0.319030," ","integrate(tan(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{16 \, {\left(\frac{2 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 1\right)}}{15 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"-16/15*(2*sin(d*x + c)/(cos(d*x + c) + 1) - 2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
55,1,90,0,0.302622," ","integrate(tan(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{2 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}}{3 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d}"," ",0,"4/3*(2*sin(d*x + c)/(cos(d*x + c) + 1) + 1)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d)","A",0
56,1,27,0,0.331151," ","integrate(1/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2}{{\left(a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)} d}"," ",0,"-2/((a + a*sin(d*x + c)/(cos(d*x + c) + 1))*d)","A",0
57,1,70,0,0.296813," ","integrate(cot(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\cos\left(d x + c\right) + 1}{a \sin\left(d x + c\right)} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"-1/2*(2*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (cos(d*x + c) + 1)/(a*sin(d*x + c)) - sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
58,1,155,0,0.297605," ","integrate(cot(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{a \sin\left(d x + c\right)^{3}}}{24 \, d}"," ",0,"-1/24*((3*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a - 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (3*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)^3/(a*sin(d*x + c)^3))/d","B",0
59,1,234,0,0.497801," ","integrate(cot(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{20 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a} - \frac{120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{{\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{20 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 2\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a \sin\left(d x + c\right)^{5}}}{320 \, d}"," ",0,"1/320*((20*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a - 120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (5*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 20*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2)*(cos(d*x + c) + 1)^5/(a*sin(d*x + c)^5))/d","B",0
60,1,315,0,0.326603," ","integrate(cot(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{315 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{63 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{63 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{7 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a} - \frac{840 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{21 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{63 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{63 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{105 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{7}}{a \sin\left(d x + c\right)^{7}}}{2688 \, d}"," ",0,"-1/2688*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 315*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 63*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 63*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 7*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a - 840*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (7*sin(d*x + c)/(cos(d*x + c) + 1) + 21*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 63*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 63*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 315*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 105*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 3)*(cos(d*x + c) + 1)^7/(a*sin(d*x + c)^7))/d","B",0
61,1,202,0,0.314908," ","integrate(tan(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{7} - 750 \, \sin\left(d x + c\right)^{6} - 815 \, \sin\left(d x + c\right)^{5} + 560 \, \sin\left(d x + c\right)^{4} + 1039 \, \sin\left(d x + c\right)^{3} + 78 \, \sin\left(d x + c\right)^{2} - 393 \, \sin\left(d x + c\right) - 144\right)}}{a^{2} \sin\left(d x + c\right)^{8} + 2 \, a^{2} \sin\left(d x + c\right)^{7} - 2 \, a^{2} \sin\left(d x + c\right)^{6} - 6 \, a^{2} \sin\left(d x + c\right)^{5} + 6 \, a^{2} \sin\left(d x + c\right)^{3} + 2 \, a^{2} \sin\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - a^{2}} - \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{3840 \, d}"," ",0,"1/3840*(2*(105*sin(d*x + c)^7 - 750*sin(d*x + c)^6 - 815*sin(d*x + c)^5 + 560*sin(d*x + c)^4 + 1039*sin(d*x + c)^3 + 78*sin(d*x + c)^2 - 393*sin(d*x + c) - 144)/(a^2*sin(d*x + c)^8 + 2*a^2*sin(d*x + c)^7 - 2*a^2*sin(d*x + c)^6 - 6*a^2*sin(d*x + c)^5 + 6*a^2*sin(d*x + c)^3 + 2*a^2*sin(d*x + c)^2 - 2*a^2*sin(d*x + c) - a^2) - 105*log(sin(d*x + c) + 1)/a^2 + 105*log(sin(d*x + c) - 1)/a^2)/d","A",0
62,1,167,0,0.315813," ","integrate(tan(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 66 \, \sin\left(d x + c\right)^{4} - 74 \, \sin\left(d x + c\right)^{3} + 14 \, \sin\left(d x + c\right)^{2} + 47 \, \sin\left(d x + c\right) + 16\right)}}{a^{2} \sin\left(d x + c\right)^{6} + 2 \, a^{2} \sin\left(d x + c\right)^{5} - a^{2} \sin\left(d x + c\right)^{4} - 4 \, a^{2} \sin\left(d x + c\right)^{3} - a^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) + a^{2}} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{384 \, d}"," ",0,"-1/384*(2*(15*sin(d*x + c)^5 - 66*sin(d*x + c)^4 - 74*sin(d*x + c)^3 + 14*sin(d*x + c)^2 + 47*sin(d*x + c) + 16)/(a^2*sin(d*x + c)^6 + 2*a^2*sin(d*x + c)^5 - a^2*sin(d*x + c)^4 - 4*a^2*sin(d*x + c)^3 - a^2*sin(d*x + c)^2 + 2*a^2*sin(d*x + c) + a^2) - 15*log(sin(d*x + c) + 1)/a^2 + 15*log(sin(d*x + c) - 1)/a^2)/d","A",0
63,1,110,0,0.299331," ","integrate(tan(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 6 \, \sin\left(d x + c\right)^{2} - 7 \, \sin\left(d x + c\right) - 2\right)}}{a^{2} \sin\left(d x + c\right)^{4} + 2 \, a^{2} \sin\left(d x + c\right)^{3} - 2 \, a^{2} \sin\left(d x + c\right) - a^{2}} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{48 \, d}"," ",0,"1/48*(2*(3*sin(d*x + c)^3 - 6*sin(d*x + c)^2 - 7*sin(d*x + c) - 2)/(a^2*sin(d*x + c)^4 + 2*a^2*sin(d*x + c)^3 - 2*a^2*sin(d*x + c) - a^2) - 3*log(sin(d*x + c) + 1)/a^2 + 3*log(sin(d*x + c) - 1)/a^2)/d","A",0
64,1,70,0,0.295708," ","integrate(tan(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, \sin\left(d x + c\right)}{a^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) + a^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{8 \, d}"," ",0,"-1/8*(2*sin(d*x + c)/(a^2*sin(d*x + c)^2 + 2*a^2*sin(d*x + c) + a^2) - log(sin(d*x + c) + 1)/a^2 + log(sin(d*x + c) - 1)/a^2)/d","A",0
65,1,46,0,0.297207," ","integrate(cot(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{1}{a^{2} \sin\left(d x + c\right) + a^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{\log\left(\sin\left(d x + c\right)\right)}{a^{2}}}{d}"," ",0,"(1/(a^2*sin(d*x + c) + a^2) - log(sin(d*x + c) + 1)/a^2 + log(sin(d*x + c))/a^2)/d","A",0
66,1,55,0,0.299675," ","integrate(cot(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} - \frac{4 \, \log\left(\sin\left(d x + c\right)\right)}{a^{2}} - \frac{4 \, \sin\left(d x + c\right) - 1}{a^{2} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(4*log(sin(d*x + c) + 1)/a^2 - 4*log(sin(d*x + c))/a^2 - (4*sin(d*x + c) - 1)/(a^2*sin(d*x + c)^2))/d","A",0
67,1,36,0,0.297805," ","integrate(cot(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, \sin\left(d x + c\right)^{2} - 8 \, \sin\left(d x + c\right) + 3}{12 \, a^{2} d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(6*sin(d*x + c)^2 - 8*sin(d*x + c) + 3)/(a^2*d*sin(d*x + c)^4)","A",0
68,1,46,0,0.307552," ","integrate(cot(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{15 \, \sin\left(d x + c\right)^{4} - 20 \, \sin\left(d x + c\right)^{3} + 12 \, \sin\left(d x + c\right) - 5}{30 \, a^{2} d \sin\left(d x + c\right)^{6}}"," ",0,"1/30*(15*sin(d*x + c)^4 - 20*sin(d*x + c)^3 + 12*sin(d*x + c) - 5)/(a^2*d*sin(d*x + c)^6)","A",0
69,1,76,0,0.327183," ","integrate(cot(d*x+c)^9/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{420 \, \sin\left(d x + c\right)^{6} - 560 \, \sin\left(d x + c\right)^{5} - 210 \, \sin\left(d x + c\right)^{4} + 672 \, \sin\left(d x + c\right)^{3} - 140 \, \sin\left(d x + c\right)^{2} - 240 \, \sin\left(d x + c\right) + 105}{840 \, a^{2} d \sin\left(d x + c\right)^{8}}"," ",0,"-1/840*(420*sin(d*x + c)^6 - 560*sin(d*x + c)^5 - 210*sin(d*x + c)^4 + 672*sin(d*x + c)^3 - 140*sin(d*x + c)^2 - 240*sin(d*x + c) + 105)/(a^2*d*sin(d*x + c)^8)","A",0
70,1,86,0,0.309457," ","integrate(cot(d*x+c)^11/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{630 \, \sin\left(d x + c\right)^{8} - 840 \, \sin\left(d x + c\right)^{7} - 630 \, \sin\left(d x + c\right)^{6} + 1512 \, \sin\left(d x + c\right)^{5} - 1080 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)^{2} + 280 \, \sin\left(d x + c\right) - 126}{1260 \, a^{2} d \sin\left(d x + c\right)^{10}}"," ",0,"1/1260*(630*sin(d*x + c)^8 - 840*sin(d*x + c)^7 - 630*sin(d*x + c)^6 + 1512*sin(d*x + c)^5 - 1080*sin(d*x + c)^3 + 315*sin(d*x + c)^2 + 280*sin(d*x + c) - 126)/(a^2*d*sin(d*x + c)^10)","A",0
71,1,116,0,0.304421," ","integrate(cot(d*x+c)^13/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6930 \, \sin\left(d x + c\right)^{10} - 9240 \, \sin\left(d x + c\right)^{9} - 10395 \, \sin\left(d x + c\right)^{8} + 22176 \, \sin\left(d x + c\right)^{7} + 4620 \, \sin\left(d x + c\right)^{6} - 23760 \, \sin\left(d x + c\right)^{5} + 3465 \, \sin\left(d x + c\right)^{4} + 12320 \, \sin\left(d x + c\right)^{3} - 4158 \, \sin\left(d x + c\right)^{2} - 2520 \, \sin\left(d x + c\right) + 1155}{13860 \, a^{2} d \sin\left(d x + c\right)^{12}}"," ",0,"-1/13860*(6930*sin(d*x + c)^10 - 9240*sin(d*x + c)^9 - 10395*sin(d*x + c)^8 + 22176*sin(d*x + c)^7 + 4620*sin(d*x + c)^6 - 23760*sin(d*x + c)^5 + 3465*sin(d*x + c)^4 + 12320*sin(d*x + c)^3 - 4158*sin(d*x + c)^2 - 2520*sin(d*x + c) + 1155)/(a^2*d*sin(d*x + c)^12)","A",0
72,1,188,0,0.321272," ","integrate(tan(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{6} + 45 \, \sin\left(d x + c\right)^{5} - 620 \, \sin\left(d x + c\right)^{4} - 540 \, \sin\left(d x + c\right)^{3} + 157 \, \sin\left(d x + c\right)^{2} + 351 \, \sin\left(d x + c\right) + 112\right)}}{a^{3} \sin\left(d x + c\right)^{7} + 3 \, a^{3} \sin\left(d x + c\right)^{6} + a^{3} \sin\left(d x + c\right)^{5} - 5 \, a^{3} \sin\left(d x + c\right)^{4} - 5 \, a^{3} \sin\left(d x + c\right)^{3} + a^{3} \sin\left(d x + c\right)^{2} + 3 \, a^{3} \sin\left(d x + c\right) + a^{3}} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3}}}{3840 \, d}"," ",0,"-1/3840*(2*(15*sin(d*x + c)^6 + 45*sin(d*x + c)^5 - 620*sin(d*x + c)^4 - 540*sin(d*x + c)^3 + 157*sin(d*x + c)^2 + 351*sin(d*x + c) + 112)/(a^3*sin(d*x + c)^7 + 3*a^3*sin(d*x + c)^6 + a^3*sin(d*x + c)^5 - 5*a^3*sin(d*x + c)^4 - 5*a^3*sin(d*x + c)^3 + a^3*sin(d*x + c)^2 + 3*a^3*sin(d*x + c) + a^3) - 15*log(sin(d*x + c) + 1)/a^3 + 15*log(sin(d*x + c) - 1)/a^3)/d","A",0
73,1,146,0,0.299306," ","integrate(tan(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{4} + 9 \, \sin\left(d x + c\right)^{3} - 25 \, \sin\left(d x + c\right)^{2} - 27 \, \sin\left(d x + c\right) - 8\right)}}{a^{3} \sin\left(d x + c\right)^{5} + 3 \, a^{3} \sin\left(d x + c\right)^{4} + 2 \, a^{3} \sin\left(d x + c\right)^{3} - 2 \, a^{3} \sin\left(d x + c\right)^{2} - 3 \, a^{3} \sin\left(d x + c\right) - a^{3}} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3}}}{192 \, d}"," ",0,"1/192*(2*(3*sin(d*x + c)^4 + 9*sin(d*x + c)^3 - 25*sin(d*x + c)^2 - 27*sin(d*x + c) - 8)/(a^3*sin(d*x + c)^5 + 3*a^3*sin(d*x + c)^4 + 2*a^3*sin(d*x + c)^3 - 2*a^3*sin(d*x + c)^2 - 3*a^3*sin(d*x + c) - a^3) - 3*log(sin(d*x + c) + 1)/a^3 + 3*log(sin(d*x + c) - 1)/a^3)/d","A",0
74,1,98,0,0.296815," ","integrate(tan(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 9 \, \sin\left(d x + c\right) + 2\right)}}{a^{3} \sin\left(d x + c\right)^{3} + 3 \, a^{3} \sin\left(d x + c\right)^{2} + 3 \, a^{3} \sin\left(d x + c\right) + a^{3}} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3}}}{48 \, d}"," ",0,"-1/48*(2*(3*sin(d*x + c)^2 + 9*sin(d*x + c) + 2)/(a^3*sin(d*x + c)^3 + 3*a^3*sin(d*x + c)^2 + 3*a^3*sin(d*x + c) + a^3) - 3*log(sin(d*x + c) + 1)/a^3 + 3*log(sin(d*x + c) - 1)/a^3)/d","A",0
75,1,72,0,0.300130," ","integrate(cot(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, \sin\left(d x + c\right) + 3}{a^{3} \sin\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) + a^{3}} - \frac{2 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*((2*sin(d*x + c) + 3)/(a^3*sin(d*x + c)^2 + 2*a^3*sin(d*x + c) + a^3) - 2*log(sin(d*x + c) + 1)/a^3 + 2*log(sin(d*x + c))/a^3)/d","A",0
76,1,80,0,0.338118," ","integrate(cot(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{10 \, \sin\left(d x + c\right)^{2} + 5 \, \sin\left(d x + c\right) - 1}{a^{3} \sin\left(d x + c\right)^{3} + a^{3} \sin\left(d x + c\right)^{2}} - \frac{10 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{10 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*((10*sin(d*x + c)^2 + 5*sin(d*x + c) - 1)/(a^3*sin(d*x + c)^3 + a^3*sin(d*x + c)^2) - 10*log(sin(d*x + c) + 1)/a^3 + 10*log(sin(d*x + c))/a^3)/d","A",0
77,1,75,0,0.372638," ","integrate(cot(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{16 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} - \frac{16 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}} - \frac{16 \, \sin\left(d x + c\right)^{3} - 8 \, \sin\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right) - 1}{a^{3} \sin\left(d x + c\right)^{4}}}{4 \, d}"," ",0,"-1/4*(16*log(sin(d*x + c) + 1)/a^3 - 16*log(sin(d*x + c))/a^3 - (16*sin(d*x + c)^3 - 8*sin(d*x + c)^2 + 4*sin(d*x + c) - 1)/(a^3*sin(d*x + c)^4))/d","A",0
78,1,46,0,0.303049," ","integrate(cot(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{20 \, \sin\left(d x + c\right)^{3} - 45 \, \sin\left(d x + c\right)^{2} + 36 \, \sin\left(d x + c\right) - 10}{60 \, a^{3} d \sin\left(d x + c\right)^{6}}"," ",0,"1/60*(20*sin(d*x + c)^3 - 45*sin(d*x + c)^2 + 36*sin(d*x + c) - 10)/(a^3*d*sin(d*x + c)^6)","A",0
79,1,66,0,0.331229," ","integrate(cot(d*x+c)^9/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{280 \, \sin\left(d x + c\right)^{5} - 630 \, \sin\left(d x + c\right)^{4} + 336 \, \sin\left(d x + c\right)^{3} + 280 \, \sin\left(d x + c\right)^{2} - 360 \, \sin\left(d x + c\right) + 105}{840 \, a^{3} d \sin\left(d x + c\right)^{8}}"," ",0,"-1/840*(280*sin(d*x + c)^5 - 630*sin(d*x + c)^4 + 336*sin(d*x + c)^3 + 280*sin(d*x + c)^2 - 360*sin(d*x + c) + 105)/(a^3*d*sin(d*x + c)^8)","A",0
80,1,86,0,0.305776," ","integrate(cot(d*x+c)^11/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{280 \, \sin\left(d x + c\right)^{7} - 630 \, \sin\left(d x + c\right)^{6} + 168 \, \sin\left(d x + c\right)^{5} + 700 \, \sin\left(d x + c\right)^{4} - 600 \, \sin\left(d x + c\right)^{3} - 105 \, \sin\left(d x + c\right)^{2} + 280 \, \sin\left(d x + c\right) - 84}{840 \, a^{3} d \sin\left(d x + c\right)^{10}}"," ",0,"1/840*(280*sin(d*x + c)^7 - 630*sin(d*x + c)^6 + 168*sin(d*x + c)^5 + 700*sin(d*x + c)^4 - 600*sin(d*x + c)^3 - 105*sin(d*x + c)^2 + 280*sin(d*x + c) - 84)/(a^3*d*sin(d*x + c)^10)","A",0
81,1,86,0,0.304646," ","integrate(cot(d*x+c)^13/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{924 \, \sin\left(d x + c\right)^{9} - 2079 \, \sin\left(d x + c\right)^{8} + 3696 \, \sin\left(d x + c\right)^{6} - 2376 \, \sin\left(d x + c\right)^{5} - 2079 \, \sin\left(d x + c\right)^{4} + 2464 \, \sin\left(d x + c\right)^{3} - 756 \, \sin\left(d x + c\right) + 231}{2772 \, a^{3} d \sin\left(d x + c\right)^{12}}"," ",0,"-1/2772*(924*sin(d*x + c)^9 - 2079*sin(d*x + c)^8 + 3696*sin(d*x + c)^6 - 2376*sin(d*x + c)^5 - 2079*sin(d*x + c)^4 + 2464*sin(d*x + c)^3 - 756*sin(d*x + c) + 231)/(a^3*d*sin(d*x + c)^12)","A",0
82,1,213,0,0.533916," ","integrate(tan(d*x+c)^5/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{7} + 60 \, \sin\left(d x + c\right)^{6} + 65 \, \sin\left(d x + c\right)^{5} + 440 \, \sin\left(d x + c\right)^{4} + 257 \, \sin\left(d x + c\right)^{3} - 132 \, \sin\left(d x + c\right)^{2} - 177 \, \sin\left(d x + c\right) - 48\right)}}{a^{4} \sin\left(d x + c\right)^{8} + 4 \, a^{4} \sin\left(d x + c\right)^{7} + 4 \, a^{4} \sin\left(d x + c\right)^{6} - 4 \, a^{4} \sin\left(d x + c\right)^{5} - 10 \, a^{4} \sin\left(d x + c\right)^{4} - 4 \, a^{4} \sin\left(d x + c\right)^{3} + 4 \, a^{4} \sin\left(d x + c\right)^{2} + 4 \, a^{4} \sin\left(d x + c\right) + a^{4}} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{4}}}{3840 \, d}"," ",0,"1/3840*(2*(15*sin(d*x + c)^7 + 60*sin(d*x + c)^6 + 65*sin(d*x + c)^5 + 440*sin(d*x + c)^4 + 257*sin(d*x + c)^3 - 132*sin(d*x + c)^2 - 177*sin(d*x + c) - 48)/(a^4*sin(d*x + c)^8 + 4*a^4*sin(d*x + c)^7 + 4*a^4*sin(d*x + c)^6 - 4*a^4*sin(d*x + c)^5 - 10*a^4*sin(d*x + c)^4 - 4*a^4*sin(d*x + c)^3 + 4*a^4*sin(d*x + c)^2 + 4*a^4*sin(d*x + c) + a^4) - 15*log(sin(d*x + c) + 1)/a^4 + 15*log(sin(d*x + c) - 1)/a^4)/d","A",0
83,1,95,0,0.368776," ","integrate(tan(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, \sin\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right) + 1}{20 \, {\left(a^{4} \sin\left(d x + c\right)^{6} + 4 \, a^{4} \sin\left(d x + c\right)^{5} + 5 \, a^{4} \sin\left(d x + c\right)^{4} - 5 \, a^{4} \sin\left(d x + c\right)^{2} - 4 \, a^{4} \sin\left(d x + c\right) - a^{4}\right)} d}"," ",0,"-1/20*(5*sin(d*x + c)^2 + 4*sin(d*x + c) + 1)/((a^4*sin(d*x + c)^6 + 4*a^4*sin(d*x + c)^5 + 5*a^4*sin(d*x + c)^4 - 5*a^4*sin(d*x + c)^2 - 4*a^4*sin(d*x + c) - a^4)*d)","A",0
84,1,121,0,0.330952," ","integrate(tan(d*x+c)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} + 12 \, \sin\left(d x + c\right)^{2} + 19 \, \sin\left(d x + c\right) + 4\right)}}{a^{4} \sin\left(d x + c\right)^{4} + 4 \, a^{4} \sin\left(d x + c\right)^{3} + 6 \, a^{4} \sin\left(d x + c\right)^{2} + 4 \, a^{4} \sin\left(d x + c\right) + a^{4}} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{4}}}{96 \, d}"," ",0,"-1/96*(2*(3*sin(d*x + c)^3 + 12*sin(d*x + c)^2 + 19*sin(d*x + c) + 4)/(a^4*sin(d*x + c)^4 + 4*a^4*sin(d*x + c)^3 + 6*a^4*sin(d*x + c)^2 + 4*a^4*sin(d*x + c) + a^4) - 3*log(sin(d*x + c) + 1)/a^4 + 3*log(sin(d*x + c) - 1)/a^4)/d","A",0
85,1,103,0,0.327252," ","integrate(cot(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{18 \, \sin\left(d x + c\right)^{3} + 27 \, \sin\left(d x + c\right)^{2} + 6 \, \sin\left(d x + c\right) - 1}{a^{4} \sin\left(d x + c\right)^{4} + 2 \, a^{4} \sin\left(d x + c\right)^{3} + a^{4} \sin\left(d x + c\right)^{2}} - \frac{18 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}} + \frac{18 \, \log\left(\sin\left(d x + c\right)\right)}{a^{4}}}{2 \, d}"," ",0,"1/2*((18*sin(d*x + c)^3 + 27*sin(d*x + c)^2 + 6*sin(d*x + c) - 1)/(a^4*sin(d*x + c)^4 + 2*a^4*sin(d*x + c)^3 + a^4*sin(d*x + c)^2) - 18*log(sin(d*x + c) + 1)/a^4 + 18*log(sin(d*x + c))/a^4)/d","A",0
86,1,95,0,0.316154," ","integrate(cot(d*x+c)^7/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{480 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}} - \frac{480 \, \log\left(\sin\left(d x + c\right)\right)}{a^{4}} - \frac{480 \, \sin\left(d x + c\right)^{5} - 240 \, \sin\left(d x + c\right)^{4} + 160 \, \sin\left(d x + c\right)^{3} - 105 \, \sin\left(d x + c\right)^{2} + 48 \, \sin\left(d x + c\right) - 10}{a^{4} \sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(480*log(sin(d*x + c) + 1)/a^4 - 480*log(sin(d*x + c))/a^4 - (480*sin(d*x + c)^5 - 240*sin(d*x + c)^4 + 160*sin(d*x + c)^3 - 105*sin(d*x + c)^2 + 48*sin(d*x + c) - 10)/(a^4*sin(d*x + c)^6))/d","A",0
87,1,356,0,0.377894," ","integrate(tan(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{16 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{54 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{201 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{294 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{378 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{210 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{105 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 2\right)}}{315 \, {\left(a^{4} + \frac{8 \, a^{4} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{27 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{48 \, a^{4} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{42 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{42 \, a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{48 \, a^{4} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{27 \, a^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{8 \, a^{4} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{4} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} d}"," ",0,"8/315*(16*sin(d*x + c)/(cos(d*x + c) + 1) + 54*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 201*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 294*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 378*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 210*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 105*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 2)/((a^4 + 8*a^4*sin(d*x + c)/(cos(d*x + c) + 1) + 27*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 48*a^4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 42*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 42*a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 48*a^4*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 27*a^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 8*a^4*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^4*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*d)","B",0
88,1,288,0,0.328019," ","integrate(cot(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{\frac{491 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{1690 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2570 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1815 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{555 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 15}{\frac{a^{4} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{4} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{10 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{5 \, a^{4} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}} - \frac{15 \, \sin\left(d x + c\right)}{a^{4} {\left(\cos\left(d x + c\right) + 1\right)}}}{30 \, d}"," ",0,"-1/30*((491*sin(d*x + c)/(cos(d*x + c) + 1) + 1690*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2570*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1815*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 555*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15)/(a^4*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 10*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 5*a^4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^4 - 15*sin(d*x + c)/(a^4*(cos(d*x + c) + 1)))/d","B",0
89,1,285,0,0.331071," ","integrate(cot(d*x+c)^4/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{72 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{984 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1647 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{873 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 1}{\frac{a^{4} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3 \, a^{4} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{12 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{4}} - \frac{336 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}}{24 \, d}"," ",0,"1/24*((9*sin(d*x + c)/(cos(d*x + c) + 1) - 72*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 984*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1647*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 873*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1)/(a^4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3*a^4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (105*sin(d*x + c)/(cos(d*x + c) + 1) - 12*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^4 - 336*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^4)/d","B",0
90,1,279,0,0.322619," ","integrate(cot(d*x+c)^6/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{45 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{185 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{870 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3670 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 1}{\frac{a^{4} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{1110 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{240 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{55 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{4}} - \frac{2160 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}}{160 \, d}"," ",0,"1/160*((9*sin(d*x + c)/(cos(d*x + c) + 1) - 45*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 185*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 870*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3670*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1)/(a^4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (1110*sin(d*x + c)/(cos(d*x + c) + 1) - 240*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 55*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^4 - 2160*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^4)/d","B",0
91,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*tan(f*x+e)^4,x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*tan(f*x + e)^4, x)","F",0
92,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*tan(f*x+e)^2,x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*tan(f*x + e)^2, x)","F",0
93,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*cot(f*x + e)^2, x)","F",0
94,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*cot(f*x + e)^4, x)","F",0
95,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*tan(f*x+e)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,1,145,0,0.584057," ","integrate((a+a*sin(f*x+e))^(3/2)*tan(f*x+e)^2,x, algorithm=""maxima"")","-\frac{8 \, {\left(2 \, a^{\frac{3}{2}} - \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)}}{3 \, f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}"," ",0,"-8/3*(2*a^(3/2) - 2*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 2*a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)/(f*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2))","A",0
97,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*cot(f*x + e)^2, x)","F",0
98,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*cot(f*x + e)^4, x)","F",0
99,1,277,0,1.291082," ","integrate((a+a*sin(f*x+e))^(5/2)*tan(f*x+e)^4,x, algorithm=""maxima"")","\frac{32 \, {\left(8 \, a^{\frac{5}{2}} - \frac{24 \, a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{44 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{68 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{75 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{68 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{44 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{24 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{8 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)}}{15 \, f {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}"," ",0,"32/15*(8*a^(5/2) - 24*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 44*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 68*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 75*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 68*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 44*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 24*a^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 8*a^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)/(f*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2))","B",0
100,1,191,0,0.481508," ","integrate((a+a*sin(f*x+e))^(5/2)*tan(f*x+e)^2,x, algorithm=""maxima"")","-\frac{8 \, {\left(22 \, a^{\frac{5}{2}} - \frac{22 \, a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{50 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{55 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{22 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{22 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)}}{15 \, f {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}"," ",0,"-8/15*(22*a^(5/2) - 22*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 55*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 50*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 55*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 22*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 22*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)/(f*(sin(f*x + e)/(cos(f*x + e) + 1) - 1)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2))","A",0
101,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*cot(f*x + e)^2, x)","F",0
102,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*cot(f*x + e)^4, x)","F",0
103,0,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{4}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)^4/sqrt(a*sin(f*x + e) + a), x)","F",0
104,0,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{2}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)^2/sqrt(a*sin(f*x + e) + a), x)","F",0
105,0,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{2}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(cot(f*x + e)^2/sqrt(a*sin(f*x + e) + a), x)","F",0
106,0,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{4}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(cot(f*x + e)^4/sqrt(a*sin(f*x + e) + a), x)","F",0
107,-1,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,0,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(f*x + e)^2/(a*sin(f*x + e) + a)^(3/2), x)","F",0
110,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/3)*tan(f*x+e)^4,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(1/3)*tan(f*x + e)^4, x)","F",0
116,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/3)*tan(f*x+e)^2,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(1/3)*tan(f*x + e)^2, x)","F",0
117,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+a*sin(f*x+e))^(1/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(1/3)*cot(f*x + e)^2, x)","F",0
118,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+a*sin(f*x+e))^(1/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(1/3)*cot(f*x + e)^4, x)","F",0
119,0,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+a*sin(f*x+e))^(1/3),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(f*x + e)^4/(a*sin(f*x + e) + a)^(1/3), x)","F",0
120,0,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+a*sin(f*x+e))^(1/3),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(f*x + e)^2/(a*sin(f*x + e) + a)^(1/3), x)","F",0
121,0,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+a*sin(f*x+e))^(1/3),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cot(f*x + e)^2/(a*sin(f*x + e) + a)^(1/3), x)","F",0
122,0,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+a*sin(f*x+e))^(1/3),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cot(f*x + e)^4/(a*sin(f*x + e) + a)^(1/3), x)","F",0
123,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(g*tan(f*x+e))^p,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(g*tan(f*x + e))^p, x)","F",0
124,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(g*tan(f*x+e))^p,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(g*tan(f*x + e))^p, x)","F",0
125,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(g*tan(f*x+e))^p,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(g*tan(f*x + e))^p, x)","F",0
126,0,0,0,0.000000," ","integrate((g*tan(f*x+e))^p/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \tan\left(f x + e\right)\right)^{p}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*tan(f*x + e))^p/(a*sin(f*x + e) + a), x)","F",0
127,0,0,0,0.000000," ","integrate((g*tan(f*x+e))^p/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(g \tan\left(f x + e\right)\right)^{p}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((g*tan(f*x + e))^p/(a*sin(f*x + e) + a)^2, x)","F",0
128,0,0,0,0.000000," ","integrate((g*tan(f*x+e))^p/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{\left(g \tan\left(f x + e\right)\right)^{p}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((g*tan(f*x + e))^p/(a*sin(f*x + e) + a)^3, x)","F",0
129,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(g*tan(f*x+e))^p,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(g*tan(f*x + e))^p, x)","F",0
130,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*tan(f*x+e)^3,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*tan(f*x + e)^3, x)","F",0
131,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*tan(f*x+e),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*tan(f*x + e), x)","F",0
132,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cot(f*x + e), x)","F",0
133,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cot(f*x + e)^3, x)","F",0
134,-1,0,0,0.000000," ","integrate(cot(f*x+e)^5*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*tan(f*x+e)^4,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*tan(f*x + e)^4, x)","F",0
136,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*tan(f*x+e)^2,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*tan(f*x + e)^2, x)","F",0
137,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m, x)","F",0
138,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cot(f*x + e)^2, x)","F",0
139,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cot(f*x + e)^4, x)","F",0
140,1,73,0,1.624552," ","integrate((a+b*sin(d*x+c))*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{{\left(2 \, a - 3 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(2 \, a + 3 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 4 \, b \sin\left(d x + c\right) - \frac{2 \, {\left(b \sin\left(d x + c\right) + a\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*((2*a - 3*b)*log(sin(d*x + c) + 1) + (2*a + 3*b)*log(sin(d*x + c) - 1) + 4*b*sin(d*x + c) - 2*(b*sin(d*x + c) + a)/(sin(d*x + c)^2 - 1))/d","A",0
141,1,43,0,1.152880," ","integrate((a+b*sin(d*x+c))*tan(d*x+c),x, algorithm=""maxima"")","-\frac{{\left(a - b\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a + b\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 2 \, b \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*((a - b)*log(sin(d*x + c) + 1) + (a + b)*log(sin(d*x + c) - 1) + 2*b*sin(d*x + c))/d","A",0
142,1,22,0,0.605786," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\sin\left(d x + c\right)\right) + b \sin\left(d x + c\right)}{d}"," ",0,"(a*log(sin(d*x + c)) + b*sin(d*x + c))/d","A",0
143,1,45,0,0.957043," ","integrate(cot(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, a \log\left(\sin\left(d x + c\right)\right) + 2 \, b \sin\left(d x + c\right) + \frac{2 \, b \sin\left(d x + c\right) + a}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*a*log(sin(d*x + c)) + 2*b*sin(d*x + c) + (2*b*sin(d*x + c) + a)/sin(d*x + c)^2)/d","A",0
144,1,69,0,1.402057," ","integrate(cot(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, a \log\left(\sin\left(d x + c\right)\right) + 12 \, b \sin\left(d x + c\right) + \frac{24 \, b \sin\left(d x + c\right)^{3} + 12 \, a \sin\left(d x + c\right)^{2} - 4 \, b \sin\left(d x + c\right) - 3 \, a}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*a*log(sin(d*x + c)) + 12*b*sin(d*x + c) + (24*b*sin(d*x + c)^3 + 12*a*sin(d*x + c)^2 - 4*b*sin(d*x + c) - 3*a)/sin(d*x + c)^4)/d","A",0
145,1,65,0,1.702718," ","integrate((a+b*sin(d*x+c))*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a - b {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a - b*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
146,1,39,0,1.367367," ","integrate((a+b*sin(d*x+c))*tan(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(d x + c - \tan\left(d x + c\right)\right)} a - b {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{d}"," ",0,"-((d*x + c - tan(d*x + c))*a - b*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
147,1,54,0,1.381328," ","integrate(cot(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a - b {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c + 1/tan(d*x + c))*a - b*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
148,1,92,0,1.818548," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a + 3 \, b {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(4*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a + 3*b*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
149,1,125,0,1.885169," ","integrate(cot(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{16 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a + 15 \, b {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"-1/240*(16*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a + 15*b*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
150,1,105,0,0.463591," ","integrate((a+b*sin(d*x+c))^2*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{b^{2} \sin\left(d x + c\right)^{2} + 4 \, a b \sin\left(d x + c\right) + {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, a b \sin\left(d x + c\right) + a^{2} + b^{2}}{\sin\left(d x + c\right)^{2} - 1}}{2 \, d}"," ",0,"1/2*(b^2*sin(d*x + c)^2 + 4*a*b*sin(d*x + c) + (a^2 - 3*a*b + 2*b^2)*log(sin(d*x + c) + 1) + (a^2 + 3*a*b + 2*b^2)*log(sin(d*x + c) - 1) - (2*a*b*sin(d*x + c) + a^2 + b^2)/(sin(d*x + c)^2 - 1))/d","A",0
151,1,70,0,0.371974," ","integrate((a+b*sin(d*x+c))^2*tan(d*x+c),x, algorithm=""maxima"")","-\frac{b^{2} \sin\left(d x + c\right)^{2} + 4 \, a b \sin\left(d x + c\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{2 \, d}"," ",0,"-1/2*(b^2*sin(d*x + c)^2 + 4*a*b*sin(d*x + c) + (a^2 - 2*a*b + b^2)*log(sin(d*x + c) + 1) + (a^2 + 2*a*b + b^2)*log(sin(d*x + c) - 1))/d","A",0
152,1,40,0,0.484569," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{b^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \log\left(\sin\left(d x + c\right)\right) + 4 \, a b \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b^2*sin(d*x + c)^2 + 2*a^2*log(sin(d*x + c)) + 4*a*b*sin(d*x + c))/d","A",0
153,1,69,0,0.769881," ","integrate(cot(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{b^{2} \sin\left(d x + c\right)^{2} + 4 \, a b \sin\left(d x + c\right) + 2 \, {\left(a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right)\right) + \frac{4 \, a b \sin\left(d x + c\right) + a^{2}}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(b^2*sin(d*x + c)^2 + 4*a*b*sin(d*x + c) + 2*(a^2 - b^2)*log(sin(d*x + c)) + (4*a*b*sin(d*x + c) + a^2)/sin(d*x + c)^2)/d","A",0
154,1,105,0,0.985489," ","integrate(cot(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, b^{2} \sin\left(d x + c\right)^{2} + 24 \, a b \sin\left(d x + c\right) + 12 \, {\left(a^{2} - 2 \, b^{2}\right)} \log\left(\sin\left(d x + c\right)\right) + \frac{48 \, a b \sin\left(d x + c\right)^{3} - 8 \, a b \sin\left(d x + c\right) + 6 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - 3 \, a^{2}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(6*b^2*sin(d*x + c)^2 + 24*a*b*sin(d*x + c) + 12*(a^2 - 2*b^2)*log(sin(d*x + c)) + (48*a*b*sin(d*x + c)^3 - 8*a*b*sin(d*x + c) + 6*(2*a^2 - b^2)*sin(d*x + c)^2 - 3*a^2)/sin(d*x + c)^4)/d","A",0
155,1,119,0,1.246385," ","integrate((a+b*sin(d*x+c))^2*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{2} + {\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} b^{2} - 4 \, a b {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"1/6*(2*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^2 + (2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*b^2 - 4*a*b*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
156,1,83,0,1.036803," ","integrate((a+b*sin(d*x+c))^2*tan(d*x+c)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} + {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} b^{2} - 4 \, a b {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c - tan(d*x + c))*a^2 + (3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*b^2 - 4*a*b*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
157,1,79,0,0.726828," ","integrate(cot(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{2} - {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} b^{2} - 4 \, a b {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"-1/4*(4*(d*x + c + 1/tan(d*x + c))*a^2 - (2*d*x + 2*c + sin(2*d*x + 2*c))*b^2 - 4*a*b*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
158,1,138,0,1.027226," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{2} - 3 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} b^{2} + 3 \, a b {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{6 \, d}"," ",0,"1/6*(2*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^2 - 3*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*b^2 + 3*a*b*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
159,1,183,0,2.124677," ","integrate(cot(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{8 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{2} - 20 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} b^{2} + 15 \, a b {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{120 \, d}"," ",0,"-1/120*(8*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^2 - 20*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*b^2 + 15*a*b*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
160,1,162,0,0.401427," ","integrate((a+b*sin(d*x+c))^3*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, b^{3} \sin\left(d x + c\right)^{3} + 18 \, a b^{2} \sin\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 12 \, a b^{2} - 5 \, b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, a^{3} + 9 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 12 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right) - \frac{6 \, {\left(a^{3} + 3 \, a b^{2} + {\left(3 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{2} - 1}}{12 \, d}"," ",0,"1/12*(4*b^3*sin(d*x + c)^3 + 18*a*b^2*sin(d*x + c)^2 + 3*(2*a^3 - 9*a^2*b + 12*a*b^2 - 5*b^3)*log(sin(d*x + c) + 1) + 3*(2*a^3 + 9*a^2*b + 12*a*b^2 + 5*b^3)*log(sin(d*x + c) - 1) + 12*(3*a^2*b + 2*b^3)*sin(d*x + c) - 6*(a^3 + 3*a*b^2 + (3*a^2*b + b^3)*sin(d*x + c))/(sin(d*x + c)^2 - 1))/d","A",0
161,1,113,0,0.302649," ","integrate((a+b*sin(d*x+c))^3*tan(d*x+c),x, algorithm=""maxima"")","-\frac{2 \, b^{3} \sin\left(d x + c\right)^{3} + 9 \, a b^{2} \sin\left(d x + c\right)^{2} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, {\left(3 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*b^3*sin(d*x + c)^3 + 9*a*b^2*sin(d*x + c)^2 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*log(sin(d*x + c) + 1) + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*log(sin(d*x + c) - 1) + 6*(3*a^2*b + b^3)*sin(d*x + c))/d","A",0
162,1,57,0,1.197551," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, b^{3} \sin\left(d x + c\right)^{3} + 9 \, a b^{2} \sin\left(d x + c\right)^{2} + 6 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + 18 \, a^{2} b \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*b^3*sin(d*x + c)^3 + 9*a*b^2*sin(d*x + c)^2 + 6*a^3*log(sin(d*x + c)) + 18*a^2*b*sin(d*x + c))/d","A",0
163,1,98,0,1.141385," ","integrate(cot(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, b^{3} \sin\left(d x + c\right)^{3} + 9 \, a b^{2} \sin\left(d x + c\right)^{2} + 6 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\sin\left(d x + c\right)\right) + 6 \, {\left(3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right) + \frac{3 \, {\left(6 \, a^{2} b \sin\left(d x + c\right) + a^{3}\right)}}{\sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"-1/6*(2*b^3*sin(d*x + c)^3 + 9*a*b^2*sin(d*x + c)^2 + 6*(a^3 - 3*a*b^2)*log(sin(d*x + c)) + 6*(3*a^2*b - b^3)*sin(d*x + c) + 3*(6*a^2*b*sin(d*x + c) + a^3)/sin(d*x + c)^2)/d","A",0
164,1,142,0,0.639328," ","integrate(cot(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, b^{3} \sin\left(d x + c\right)^{3} + 18 \, a b^{2} \sin\left(d x + c\right)^{2} + 12 \, {\left(a^{3} - 6 \, a b^{2}\right)} \log\left(\sin\left(d x + c\right)\right) + 12 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right) - \frac{3 \, {\left(4 \, a^{2} b \sin\left(d x + c\right) - 4 \, {\left(6 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{3} + a^{3} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \sin\left(d x + c\right)^{2}\right)}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(4*b^3*sin(d*x + c)^3 + 18*a*b^2*sin(d*x + c)^2 + 12*(a^3 - 6*a*b^2)*log(sin(d*x + c)) + 12*(3*a^2*b - 2*b^3)*sin(d*x + c) - 3*(4*a^2*b*sin(d*x + c) - 4*(6*a^2*b - b^3)*sin(d*x + c)^3 + a^3 - 2*(2*a^3 - 3*a*b^2)*sin(d*x + c)^2)/sin(d*x + c)^4)/d","A",0
165,1,167,0,1.262540," ","integrate((a+b*sin(d*x+c))^3*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{3} + 3 \, {\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a b^{2} + 2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{9 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} - 9 \, \cos\left(d x + c\right)\right)} b^{3} - 6 \, a^{2} b {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"1/6*(2*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^3 + 3*(2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a*b^2 + 2*(cos(d*x + c)^3 - (9*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 - 9*cos(d*x + c))*b^3 - 6*a^2*b*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
166,1,119,0,2.154502," ","integrate((a+b*sin(d*x+c))^3*tan(d*x+c)^2,x, algorithm=""maxima"")","-\frac{6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} + 9 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a b^{2} + 2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} b^{3} - 18 \, a^{2} b {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c - tan(d*x + c))*a^3 + 9*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a*b^2 + 2*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*b^3 - 18*a^2*b*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
167,1,95,0,0.904953," ","integrate(cot(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{4 \, b^{3} \cos\left(d x + c\right)^{3} + 12 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{2} - 18 \, a^{2} b {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"-1/12*(4*b^3*cos(d*x + c)^3 + 12*(d*x + c + 1/tan(d*x + c))*a^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*a*b^2 - 18*a^2*b*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
168,1,187,0,1.840416," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{3} - 18 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a b^{2} + 2 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} b^{3} + 9 \, a^{2} b {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(4*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^3 - 18*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a*b^2 + 2*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*b^3 + 9*a^2*b*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
169,1,252,0,1.890092," ","integrate(cot(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{16 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{3} - 120 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a b^{2} + 20 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} b^{3} + 45 \, a^{2} b {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"-1/240*(16*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^3 - 120*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a*b^2 + 20*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*b^3 + 45*a^2*b*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
170,1,288,0,1.896459," ","integrate(tan(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, a^{5} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{{\left(8 \, a^{2} - 9 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(8 \, a^{2} + 9 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left({\left(9 \, a^{2} b - 5 \, b^{3}\right)} \sin\left(d x + c\right)^{3} + 6 \, a^{3} - 2 \, a b^{2} - 4 \, {\left(2 \, a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{2} - {\left(7 \, a^{2} b - 3 \, b^{3}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"1/16*(16*a^5*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (8*a^2 - 9*a*b + 3*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (8*a^2 + 9*a*b + 3*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*((9*a^2*b - 5*b^3)*sin(d*x + c)^3 + 6*a^3 - 2*a*b^2 - 4*(2*a^3 - a*b^2)*sin(d*x + c)^2 - (7*a^2*b - 3*b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2))/d","A",0
171,1,142,0,0.689879," ","integrate(tan(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{4 \, a^{3} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(2 \, a - b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(2 \, a + b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(b \sin\left(d x + c\right) - a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - a^{2} + b^{2}}}{4 \, d}"," ",0,"-1/4*(4*a^3*log(b*sin(d*x + c) + a)/(a^4 - 2*a^2*b^2 + b^4) - (2*a - b)*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) - (2*a + b)*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) - 2*(b*sin(d*x + c) - a)/((a^2 - b^2)*sin(d*x + c)^2 - a^2 + b^2))/d","A",0
172,1,65,0,0.448251," ","integrate(tan(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, a \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} - b^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a - b} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a + b}}{2 \, d}"," ",0,"1/2*(2*a*log(b*sin(d*x + c) + a)/(a^2 - b^2) - log(sin(d*x + c) + 1)/(a - b) - log(sin(d*x + c) - 1)/(a + b))/d","A",0
173,1,33,0,0.651774," ","integrate(cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\log\left(b \sin\left(d x + c\right) + a\right)}{a} - \frac{\log\left(\sin\left(d x + c\right)\right)}{a}}{d}"," ",0,"-(log(b*sin(d*x + c) + a)/a - log(sin(d*x + c))/a)/d","A",0
174,1,77,0,2.084105," ","integrate(cot(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{3}} - \frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{3}} + \frac{2 \, b \sin\left(d x + c\right) - a}{a^{2} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*(a^2 - b^2)*log(b*sin(d*x + c) + a)/a^3 - 2*(a^2 - b^2)*log(sin(d*x + c))/a^3 + (2*b*sin(d*x + c) - a)/(a^2*sin(d*x + c)^2))/d","A",0
175,1,139,0,0.607674," ","integrate(cot(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{5}} - \frac{12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{5}} - \frac{4 \, a^{2} b \sin\left(d x + c\right) - 12 \, {\left(2 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{3} - 3 \, a^{3} + 6 \, {\left(2 \, a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{2}}{a^{4} \sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"-1/12*(12*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)/a^5 - 12*(a^4 - 2*a^2*b^2 + b^4)*log(sin(d*x + c))/a^5 - (4*a^2*b*sin(d*x + c) - 12*(2*a^2*b - b^3)*sin(d*x + c)^3 - 3*a^3 + 6*(2*a^3 - a*b^2)*sin(d*x + c)^2)/(a^4*sin(d*x + c)^4))/d","A",0
176,-2,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
177,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
178,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
179,-2,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
180,-2,0,0,0.000000," ","integrate(cot(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
181,1,505,0,1.060831," ","integrate(tan(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(a^{6} + 5 \, a^{4} b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{{\left(4 \, a^{2} - a b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{{\left(4 \, a^{2} + a b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{2 \, {\left(7 \, a^{5} + 6 \, a^{3} b^{2} - a b^{4} + {\left(4 \, a^{5} + 9 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)^{4} + {\left(5 \, a^{4} b - 7 \, a^{2} b^{3} + 2 \, b^{5}\right)} \sin\left(d x + c\right)^{3} - {\left(12 \, a^{5} + 13 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)\right)}}{a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)^{5} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)^{3} - 2 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)^{2} + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)}}{8 \, d}"," ",0,"1/8*(8*(a^6 + 5*a^4*b^2)*log(b*sin(d*x + c) + a)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - (4*a^2 - a*b)*log(sin(d*x + c) + 1)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - (4*a^2 + a*b)*log(sin(d*x + c) - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 2*(7*a^5 + 6*a^3*b^2 - a*b^4 + (4*a^5 + 9*a^3*b^2 - a*b^4)*sin(d*x + c)^4 + (5*a^4*b - 7*a^2*b^3 + 2*b^5)*sin(d*x + c)^3 - (12*a^5 + 13*a^3*b^2 - a*b^4)*sin(d*x + c)^2 - (4*a^4*b - 5*a^2*b^3 + b^5)*sin(d*x + c))/(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*sin(d*x + c)^5 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sin(d*x + c)^4 - 2*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*sin(d*x + c)^3 - 2*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sin(d*x + c)^2 + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*sin(d*x + c)))/d","B",0
182,1,274,0,1.451663," ","integrate(tan(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a^{4} + 3 \, a^{2} b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{a \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{a \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{3 \, a^{3} + a b^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} \sin\left(d x + c\right)^{2} - {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{a^{5} - 2 \, a^{3} b^{2} + a b^{4} - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)^{3} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(a^4 + 3*a^2*b^2)*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - a*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - a*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (3*a^3 + a*b^2 - 2*(a^3 + a*b^2)*sin(d*x + c)^2 - (a^2*b - b^3)*sin(d*x + c))/(a^5 - 2*a^3*b^2 + a*b^4 - (a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c)^3 - (a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c)^2 + (a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c)))/d","A",0
183,1,124,0,0.923544," ","integrate(tan(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a^{2} + b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, a}{a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}}}{2 \, d}"," ",0,"1/2*(2*(a^2 + b^2)*log(b*sin(d*x + c) + a)/(a^4 - 2*a^2*b^2 + b^4) - 2*a/(a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x + c)) - log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) - log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2))/d","A",0
184,1,47,0,0.604457," ","integrate(cot(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{1}{a b \sin\left(d x + c\right) + a^{2}} - \frac{\log\left(b \sin\left(d x + c\right) + a\right)}{a^{2}} + \frac{\log\left(\sin\left(d x + c\right)\right)}{a^{2}}}{d}"," ",0,"(1/(a*b*sin(d*x + c) + a^2) - log(b*sin(d*x + c) + a)/a^2 + log(sin(d*x + c))/a^2)/d","A",0
185,1,116,0,0.303919," ","integrate(cot(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{3 \, a b \sin\left(d x + c\right) - 2 \, {\left(a^{2} - 3 \, b^{2}\right)} \sin\left(d x + c\right)^{2} - a^{2}}{a^{3} b \sin\left(d x + c\right)^{3} + a^{4} \sin\left(d x + c\right)^{2}} + \frac{2 \, {\left(a^{2} - 3 \, b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4}} - \frac{2 \, {\left(a^{2} - 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{4}}}{2 \, d}"," ",0,"1/2*((3*a*b*sin(d*x + c) - 2*(a^2 - 3*b^2)*sin(d*x + c)^2 - a^2)/(a^3*b*sin(d*x + c)^3 + a^4*sin(d*x + c)^2) + 2*(a^2 - 3*b^2)*log(b*sin(d*x + c) + a)/a^4 - 2*(a^2 - 3*b^2)*log(sin(d*x + c))/a^4)/d","A",0
186,1,189,0,0.806323," ","integrate(cot(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{5 \, a^{3} b \sin\left(d x + c\right) + 12 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 5 \, b^{4}\right)} \sin\left(d x + c\right)^{4} - 3 \, a^{4} - 6 \, {\left(6 \, a^{3} b - 5 \, a b^{3}\right)} \sin\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{4} - 5 \, a^{2} b^{2}\right)} \sin\left(d x + c\right)^{2}}{a^{5} b \sin\left(d x + c\right)^{5} + a^{6} \sin\left(d x + c\right)^{4}} - \frac{12 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 5 \, b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6}} + \frac{12 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 5 \, b^{4}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{6}}}{12 \, d}"," ",0,"1/12*((5*a^3*b*sin(d*x + c) + 12*(a^4 - 6*a^2*b^2 + 5*b^4)*sin(d*x + c)^4 - 3*a^4 - 6*(6*a^3*b - 5*a*b^3)*sin(d*x + c)^3 + 2*(6*a^4 - 5*a^2*b^2)*sin(d*x + c)^2)/(a^5*b*sin(d*x + c)^5 + a^6*sin(d*x + c)^4) - 12*(a^4 - 6*a^2*b^2 + 5*b^4)*log(b*sin(d*x + c) + a)/a^6 + 12*(a^4 - 6*a^2*b^2 + 5*b^4)*log(sin(d*x + c))/a^6)/d","A",0
187,-2,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
188,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
189,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
190,-2,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
191,-2,0,0,0.000000," ","integrate(cot(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
192,1,730,0,1.438348," ","integrate(tan(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{16 \, {\left(a^{7} + 13 \, a^{5} b^{2} + 10 \, a^{3} b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{10} - 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}} - \frac{{\left(8 \, a^{2} + 5 \, a b - b^{2}\right)} \log\left(\sin\left(d x + c\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{{\left(8 \, a^{2} - 5 \, a b - b^{2}\right)} \log\left(\sin\left(d x + c\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{2 \, {\left(18 \, a^{7} + 72 \, a^{5} b^{2} + 6 \, a^{3} b^{4} + {\left(8 \, a^{6} b + 67 \, a^{4} b^{3} + 22 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)^{5} + 2 \, {\left(6 \, a^{7} + 41 \, a^{5} b^{2} + 2 \, a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)^{4} - {\left(5 \, a^{6} b + 159 \, a^{4} b^{3} + 27 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)^{3} - 4 \, {\left(8 \, a^{7} + 37 \, a^{5} b^{2} + 4 \, a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)^{2} - {\left(a^{6} b - 86 \, a^{4} b^{3} - 11 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)\right)}}{a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8} + {\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} \sin\left(d x + c\right)^{6} + 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} \sin\left(d x + c\right)^{5} + {\left(a^{10} - 6 \, a^{8} b^{2} + 14 \, a^{6} b^{4} - 16 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - 2 \, b^{10}\right)} \sin\left(d x + c\right)^{4} - 4 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} \sin\left(d x + c\right)^{3} - {\left(2 \, a^{10} - 9 \, a^{8} b^{2} + 16 \, a^{6} b^{4} - 14 \, a^{4} b^{6} + 6 \, a^{2} b^{8} - b^{10}\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} \sin\left(d x + c\right)}}{16 \, d}"," ",0,"1/16*(16*(a^7 + 13*a^5*b^2 + 10*a^3*b^4)*log(b*sin(d*x + c) + a)/(a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10) - (8*a^2 + 5*a*b - b^2)*log(sin(d*x + c) + 1)/(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5) - (8*a^2 - 5*a*b - b^2)*log(sin(d*x + c) - 1)/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) - 2*(18*a^7 + 72*a^5*b^2 + 6*a^3*b^4 + (8*a^6*b + 67*a^4*b^3 + 22*a^2*b^5 - b^7)*sin(d*x + c)^5 + 2*(6*a^7 + 41*a^5*b^2 + 2*a^3*b^4 - a*b^6)*sin(d*x + c)^4 - (5*a^6*b + 159*a^4*b^3 + 27*a^2*b^5 + b^7)*sin(d*x + c)^3 - 4*(8*a^7 + 37*a^5*b^2 + 4*a^3*b^4 - a*b^6)*sin(d*x + c)^2 - (a^6*b - 86*a^4*b^3 - 11*a^2*b^5)*sin(d*x + c))/(a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8 + (a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*sin(d*x + c)^6 + 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*sin(d*x + c)^5 + (a^10 - 6*a^8*b^2 + 14*a^6*b^4 - 16*a^4*b^6 + 9*a^2*b^8 - 2*b^10)*sin(d*x + c)^4 - 4*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*sin(d*x + c)^3 - (2*a^10 - 9*a^8*b^2 + 16*a^6*b^4 - 14*a^4*b^6 + 6*a^2*b^8 - b^10)*sin(d*x + c)^2 + 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*sin(d*x + c)))/d","B",0
193,1,441,0,0.739967," ","integrate(tan(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(a^{5} + 8 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{{\left(2 \, a + b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{{\left(2 \, a - b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{2 \, {\left(4 \, a^{5} + 8 \, a^{3} b^{2} - {\left(2 \, a^{4} b + 9 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)^{3} - {\left(3 \, a^{5} + 10 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)^{2} + {\left(a^{4} b + 11 \, a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)}}{a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6} - {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \sin\left(d x + c\right)^{4} - 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} \sin\left(d x + c\right)^{3} - {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} \sin\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(4*(a^5 + 8*a^3*b^2 + 3*a*b^4)*log(b*sin(d*x + c) + a)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - (2*a + b)*log(sin(d*x + c) + 1)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - (2*a - b)*log(sin(d*x + c) - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 2*(4*a^5 + 8*a^3*b^2 - (2*a^4*b + 9*a^2*b^3 + b^5)*sin(d*x + c)^3 - (3*a^5 + 10*a^3*b^2 - a*b^4)*sin(d*x + c)^2 + (a^4*b + 11*a^2*b^3)*sin(d*x + c))/(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*sin(d*x + c)^4 - 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*sin(d*x + c)^3 - (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*sin(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*sin(d*x + c)))/d","A",0
194,1,228,0,0.659229," ","integrate(tan(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a^{3} + 3 \, a b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{3 \, a^{3} + a b^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}}{2 \, d}"," ",0,"1/2*(2*(a^3 + 3*a*b^2)*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (3*a^3 + a*b^2 + 2*(a^2*b + b^3)*sin(d*x + c))/(a^6 - 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 - 2*a^2*b^4 + b^6)*sin(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*sin(d*x + c)) - log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))/d","A",0
195,1,81,0,0.686632," ","integrate(cot(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, b \sin\left(d x + c\right) + 3 \, a}{a^{2} b^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{3} b \sin\left(d x + c\right) + a^{4}} - \frac{2 \, \log\left(b \sin\left(d x + c\right) + a\right)}{a^{3}} + \frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*((2*b*sin(d*x + c) + 3*a)/(a^2*b^2*sin(d*x + c)^2 + 2*a^3*b*sin(d*x + c) + a^4) - 2*log(b*sin(d*x + c) + a)/a^3 + 2*log(sin(d*x + c))/a^3)/d","A",0
196,1,156,0,0.734896," ","integrate(cot(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{4 \, a^{2} b \sin\left(d x + c\right) - 2 \, {\left(a^{2} b - 6 \, b^{3}\right)} \sin\left(d x + c\right)^{3} - a^{3} - 3 \, {\left(a^{3} - 6 \, a b^{2}\right)} \sin\left(d x + c\right)^{2}}{a^{4} b^{2} \sin\left(d x + c\right)^{4} + 2 \, a^{5} b \sin\left(d x + c\right)^{3} + a^{6} \sin\left(d x + c\right)^{2}} + \frac{2 \, {\left(a^{2} - 6 \, b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{5}} - \frac{2 \, {\left(a^{2} - 6 \, b^{2}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{5}}}{2 \, d}"," ",0,"1/2*((4*a^2*b*sin(d*x + c) - 2*(a^2*b - 6*b^3)*sin(d*x + c)^3 - a^3 - 3*(a^3 - 6*a*b^2)*sin(d*x + c)^2)/(a^4*b^2*sin(d*x + c)^4 + 2*a^5*b*sin(d*x + c)^3 + a^6*sin(d*x + c)^2) + 2*(a^2 - 6*b^2)*log(b*sin(d*x + c) + a)/a^5 - 2*(a^2 - 6*b^2)*log(sin(d*x + c))/a^5)/d","A",0
197,1,236,0,0.700007," ","integrate(cot(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, a^{4} b \sin\left(d x + c\right) + 4 \, {\left(a^{4} b - 12 \, a^{2} b^{3} + 15 \, b^{5}\right)} \sin\left(d x + c\right)^{5} - a^{5} + 6 \, {\left(a^{5} - 12 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \sin\left(d x + c\right)^{4} - 4 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \sin\left(d x + c\right)^{3} + {\left(4 \, a^{5} - 5 \, a^{3} b^{2}\right)} \sin\left(d x + c\right)^{2}}{a^{6} b^{2} \sin\left(d x + c\right)^{6} + 2 \, a^{7} b \sin\left(d x + c\right)^{5} + a^{8} \sin\left(d x + c\right)^{4}} - \frac{4 \, {\left(a^{4} - 12 \, a^{2} b^{2} + 15 \, b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{7}} + \frac{4 \, {\left(a^{4} - 12 \, a^{2} b^{2} + 15 \, b^{4}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{7}}}{4 \, d}"," ",0,"1/4*((2*a^4*b*sin(d*x + c) + 4*(a^4*b - 12*a^2*b^3 + 15*b^5)*sin(d*x + c)^5 - a^5 + 6*(a^5 - 12*a^3*b^2 + 15*a*b^4)*sin(d*x + c)^4 - 4*(4*a^4*b - 5*a^2*b^3)*sin(d*x + c)^3 + (4*a^5 - 5*a^3*b^2)*sin(d*x + c)^2)/(a^6*b^2*sin(d*x + c)^6 + 2*a^7*b*sin(d*x + c)^5 + a^8*sin(d*x + c)^4) - 4*(a^4 - 12*a^2*b^2 + 15*b^4)*log(b*sin(d*x + c) + a)/a^7 + 4*(a^4 - 12*a^2*b^2 + 15*b^4)*log(sin(d*x + c))/a^7)/d","A",0
198,-2,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
199,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
200,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
201,-2,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
202,-2,0,0,0.000000," ","integrate(cot(d*x+c)^6/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
203,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3*(g*tan(f*x+e))^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*(g*tan(f*x + e))^p, x)","F",0
204,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2*(g*tan(f*x+e))^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(g*tan(f*x + e))^p, x)","F",0
205,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(g*tan(f*x+e))^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(g*tan(f*x + e))^p, x)","F",0
206,0,0,0,0.000000," ","integrate((g*tan(f*x+e))^p/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \tan\left(f x + e\right)\right)^{p}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*tan(f*x + e))^p/(b*sin(f*x + e) + a), x)","F",0
207,0,0,0,0.000000," ","integrate((g*tan(f*x+e))^p/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(g \tan\left(f x + e\right)\right)^{p}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((g*tan(f*x + e))^p/(b*sin(f*x + e) + a)^2, x)","F",0
208,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(g*tan(f*x+e))^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{m} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m*(g*tan(f*x + e))^p, x)","F",0
