1,1,113,0,0.337479," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^9,x, algorithm=""maxima"")","-\frac{280 \, a \cos\left(d x + c\right)^{9} + 315 \, a \cos\left(d x + c\right)^{8} - 1440 \, a \cos\left(d x + c\right)^{7} - 1680 \, a \cos\left(d x + c\right)^{6} + 3024 \, a \cos\left(d x + c\right)^{5} + 3780 \, a \cos\left(d x + c\right)^{4} - 3360 \, a \cos\left(d x + c\right)^{3} - 5040 \, a \cos\left(d x + c\right)^{2} + 2520 \, a \cos\left(d x + c\right) + 2520 \, a \log\left(\cos\left(d x + c\right)\right)}{2520 \, d}"," ",0,"-1/2520*(280*a*cos(d*x + c)^9 + 315*a*cos(d*x + c)^8 - 1440*a*cos(d*x + c)^7 - 1680*a*cos(d*x + c)^6 + 3024*a*cos(d*x + c)^5 + 3780*a*cos(d*x + c)^4 - 3360*a*cos(d*x + c)^3 - 5040*a*cos(d*x + c)^2 + 2520*a*cos(d*x + c) + 2520*a*log(cos(d*x + c)))/d","A",0
2,1,91,0,0.617927," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^7,x, algorithm=""maxima"")","\frac{60 \, a \cos\left(d x + c\right)^{7} + 70 \, a \cos\left(d x + c\right)^{6} - 252 \, a \cos\left(d x + c\right)^{5} - 315 \, a \cos\left(d x + c\right)^{4} + 420 \, a \cos\left(d x + c\right)^{3} + 630 \, a \cos\left(d x + c\right)^{2} - 420 \, a \cos\left(d x + c\right) - 420 \, a \log\left(\cos\left(d x + c\right)\right)}{420 \, d}"," ",0,"1/420*(60*a*cos(d*x + c)^7 + 70*a*cos(d*x + c)^6 - 252*a*cos(d*x + c)^5 - 315*a*cos(d*x + c)^4 + 420*a*cos(d*x + c)^3 + 630*a*cos(d*x + c)^2 - 420*a*cos(d*x + c) - 420*a*log(cos(d*x + c)))/d","A",0
3,1,69,0,0.387905," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^5,x, algorithm=""maxima"")","-\frac{12 \, a \cos\left(d x + c\right)^{5} + 15 \, a \cos\left(d x + c\right)^{4} - 40 \, a \cos\left(d x + c\right)^{3} - 60 \, a \cos\left(d x + c\right)^{2} + 60 \, a \cos\left(d x + c\right) + 60 \, a \log\left(\cos\left(d x + c\right)\right)}{60 \, d}"," ",0,"-1/60*(12*a*cos(d*x + c)^5 + 15*a*cos(d*x + c)^4 - 40*a*cos(d*x + c)^3 - 60*a*cos(d*x + c)^2 + 60*a*cos(d*x + c) + 60*a*log(cos(d*x + c)))/d","A",0
4,1,47,0,0.619248," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^3,x, algorithm=""maxima"")","\frac{2 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)^{2} - 6 \, a \cos\left(d x + c\right) - 6 \, a \log\left(\cos\left(d x + c\right)\right)}{6 \, d}"," ",0,"1/6*(2*a*cos(d*x + c)^3 + 3*a*cos(d*x + c)^2 - 6*a*cos(d*x + c) - 6*a*log(cos(d*x + c)))/d","A",0
5,1,23,0,0.348896," ","integrate((a+a*sec(d*x+c))*sin(d*x+c),x, algorithm=""maxima"")","-\frac{a \cos\left(d x + c\right) + a \log\left(\cos\left(d x + c\right)\right)}{d}"," ",0,"-(a*cos(d*x + c) + a*log(cos(d*x + c)))/d","A",0
6,1,26,0,0.353478," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\cos\left(d x + c\right) - 1\right) - a \log\left(\cos\left(d x + c\right)\right)}{d}"," ",0,"(a*log(cos(d*x + c) - 1) - a*log(cos(d*x + c)))/d","A",0
7,1,52,0,0.354549," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, a \log\left(\cos\left(d x + c\right) - 1\right) - 4 \, a \log\left(\cos\left(d x + c\right)\right) + \frac{2 \, a}{\cos\left(d x + c\right) - 1}}{4 \, d}"," ",0,"1/4*(a*log(cos(d*x + c) + 1) + 3*a*log(cos(d*x + c) - 1) - 4*a*log(cos(d*x + c)) + 2*a/(cos(d*x + c) - 1))/d","A",0
8,1,95,0,0.517060," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{5 \, a \log\left(\cos\left(d x + c\right) + 1\right) + 11 \, a \log\left(\cos\left(d x + c\right) - 1\right) - 16 \, a \log\left(\cos\left(d x + c\right)\right) + \frac{2 \, {\left(3 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) - 6 \, a\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 1}}{16 \, d}"," ",0,"1/16*(5*a*log(cos(d*x + c) + 1) + 11*a*log(cos(d*x + c) - 1) - 16*a*log(cos(d*x + c)) + 2*(3*a*cos(d*x + c)^2 + a*cos(d*x + c) - 6*a)/(cos(d*x + c)^3 - cos(d*x + c)^2 - cos(d*x + c) + 1))/d","A",0
9,1,136,0,0.450289," ","integrate(csc(d*x+c)^7*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{33 \, a \log\left(\cos\left(d x + c\right) + 1\right) + 63 \, a \log\left(\cos\left(d x + c\right) - 1\right) - 96 \, a \log\left(\cos\left(d x + c\right)\right) + \frac{2 \, {\left(15 \, a \cos\left(d x + c\right)^{4} + 9 \, a \cos\left(d x + c\right)^{3} - 49 \, a \cos\left(d x + c\right)^{2} - 11 \, a \cos\left(d x + c\right) + 44 \, a\right)}}{\cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) - 1}}{96 \, d}"," ",0,"1/96*(33*a*log(cos(d*x + c) + 1) + 63*a*log(cos(d*x + c) - 1) - 96*a*log(cos(d*x + c)) + 2*(15*a*cos(d*x + c)^4 + 9*a*cos(d*x + c)^3 - 49*a*cos(d*x + c)^2 - 11*a*cos(d*x + c) + 44*a)/(cos(d*x + c)^5 - cos(d*x + c)^4 - 2*cos(d*x + c)^3 + 2*cos(d*x + c)^2 + cos(d*x + c) - 1))/d","A",0
10,1,127,0,0.346473," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^8,x, algorithm=""maxima"")","-\frac{512 \, {\left(30 \, \sin\left(d x + c\right)^{7} + 42 \, \sin\left(d x + c\right)^{5} + 70 \, \sin\left(d x + c\right)^{3} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right) + 210 \, \sin\left(d x + c\right)\right)} a - 35 \, {\left(128 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 840 \, d x + 840 \, c + 3 \, \sin\left(8 \, d x + 8 \, c\right) + 168 \, \sin\left(4 \, d x + 4 \, c\right) - 768 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{107520 \, d}"," ",0,"-1/107520*(512*(30*sin(d*x + c)^7 + 42*sin(d*x + c)^5 + 70*sin(d*x + c)^3 - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1) + 210*sin(d*x + c))*a - 35*(128*sin(2*d*x + 2*c)^3 + 840*d*x + 840*c + 3*sin(8*d*x + 8*c) + 168*sin(4*d*x + 4*c) - 768*sin(2*d*x + 2*c))*a)/d","A",0
11,1,106,0,0.473562," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^6,x, algorithm=""maxima"")","-\frac{32 \, {\left(6 \, \sin\left(d x + c\right)^{5} + 10 \, \sin\left(d x + c\right)^{3} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 30 \, \sin\left(d x + c\right)\right)} a - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{960 \, d}"," ",0,"-1/960*(32*(6*sin(d*x + c)^5 + 10*sin(d*x + c)^3 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 30*sin(d*x + c))*a - 5*(4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a)/d","A",0
12,1,81,0,0.611953," ","integrate((a+a*sec(d*x+c))*sin(d*x+c)^4,x, algorithm=""maxima"")","-\frac{16 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a - 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}{96 \, d}"," ",0,"-1/96*(16*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*a)/d","A",0
13,1,59,0,0.324868," ","integrate((a+a*sec(d*x+c))*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 \, a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c - sin(2*d*x + 2*c))*a + 2*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)))/d","A",0
14,1,50,0,0.365472," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{a {\left(\frac{2}{\sin\left(d x + c\right)} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{2 \, a}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(a*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*a/tan(d*x + c))/d","A",0
15,1,76,0,0.421462," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 1\right)}}{\sin\left(d x + c\right)^{3}} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{2 \, {\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} a}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(a*(2*(3*sin(d*x + c)^2 + 1)/sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 2*(3*tan(d*x + c)^2 + 1)*a/tan(d*x + c)^3)/d","A",0
16,1,96,0,0.374730," ","integrate(csc(d*x+c)^6*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{a {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} + 3\right)}}{\sin\left(d x + c\right)^{5}} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{2 \, {\left(15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} + 3\right)} a}{\tan\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"-1/30*(a*(2*(15*sin(d*x + c)^4 + 5*sin(d*x + c)^2 + 3)/sin(d*x + c)^5 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 2*(15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 + 3)*a/tan(d*x + c)^5)/d","A",0
17,1,116,0,0.451496," ","integrate(csc(d*x+c)^8*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{a {\left(\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{6} + 35 \, \sin\left(d x + c\right)^{4} + 21 \, \sin\left(d x + c\right)^{2} + 15\right)}}{\sin\left(d x + c\right)^{7}} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{6 \, {\left(35 \, \tan\left(d x + c\right)^{6} + 35 \, \tan\left(d x + c\right)^{4} + 21 \, \tan\left(d x + c\right)^{2} + 5\right)} a}{\tan\left(d x + c\right)^{7}}}{210 \, d}"," ",0,"-1/210*(a*(2*(105*sin(d*x + c)^6 + 35*sin(d*x + c)^4 + 21*sin(d*x + c)^2 + 15)/sin(d*x + c)^7 - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1)) + 6*(35*tan(d*x + c)^6 + 35*tan(d*x + c)^4 + 21*tan(d*x + c)^2 + 5)*a/tan(d*x + c)^7)/d","A",0
18,1,136,0,0.330853," ","integrate(csc(d*x+c)^10*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{a {\left(\frac{2 \, {\left(315 \, \sin\left(d x + c\right)^{8} + 105 \, \sin\left(d x + c\right)^{6} + 63 \, \sin\left(d x + c\right)^{4} + 45 \, \sin\left(d x + c\right)^{2} + 35\right)}}{\sin\left(d x + c\right)^{9}} - 315 \, \log\left(\sin\left(d x + c\right) + 1\right) + 315 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{2 \, {\left(315 \, \tan\left(d x + c\right)^{8} + 420 \, \tan\left(d x + c\right)^{6} + 378 \, \tan\left(d x + c\right)^{4} + 180 \, \tan\left(d x + c\right)^{2} + 35\right)} a}{\tan\left(d x + c\right)^{9}}}{630 \, d}"," ",0,"-1/630*(a*(2*(315*sin(d*x + c)^8 + 105*sin(d*x + c)^6 + 63*sin(d*x + c)^4 + 45*sin(d*x + c)^2 + 35)/sin(d*x + c)^9 - 315*log(sin(d*x + c) + 1) + 315*log(sin(d*x + c) - 1)) + 2*(315*tan(d*x + c)^8 + 420*tan(d*x + c)^6 + 378*tan(d*x + c)^4 + 180*tan(d*x + c)^2 + 35)*a/tan(d*x + c)^9)/d","A",0
19,1,146,0,0.332887," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^9,x, algorithm=""maxima"")","-\frac{140 \, a^{2} \cos\left(d x + c\right)^{9} + 315 \, a^{2} \cos\left(d x + c\right)^{8} - 540 \, a^{2} \cos\left(d x + c\right)^{7} - 1680 \, a^{2} \cos\left(d x + c\right)^{6} + 504 \, a^{2} \cos\left(d x + c\right)^{5} + 3780 \, a^{2} \cos\left(d x + c\right)^{4} + 840 \, a^{2} \cos\left(d x + c\right)^{3} - 5040 \, a^{2} \cos\left(d x + c\right)^{2} - 3780 \, a^{2} \cos\left(d x + c\right) + 2520 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{1260 \, a^{2}}{\cos\left(d x + c\right)}}{1260 \, d}"," ",0,"-1/1260*(140*a^2*cos(d*x + c)^9 + 315*a^2*cos(d*x + c)^8 - 540*a^2*cos(d*x + c)^7 - 1680*a^2*cos(d*x + c)^6 + 504*a^2*cos(d*x + c)^5 + 3780*a^2*cos(d*x + c)^4 + 840*a^2*cos(d*x + c)^3 - 5040*a^2*cos(d*x + c)^2 - 3780*a^2*cos(d*x + c) + 2520*a^2*log(cos(d*x + c)) - 1260*a^2/cos(d*x + c))/d","A",0
20,1,107,0,0.337093," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^7,x, algorithm=""maxima"")","\frac{30 \, a^{2} \cos\left(d x + c\right)^{7} + 70 \, a^{2} \cos\left(d x + c\right)^{6} - 84 \, a^{2} \cos\left(d x + c\right)^{5} - 315 \, a^{2} \cos\left(d x + c\right)^{4} + 630 \, a^{2} \cos\left(d x + c\right)^{2} + 420 \, a^{2} \cos\left(d x + c\right) - 420 \, a^{2} \log\left(\cos\left(d x + c\right)\right) + \frac{210 \, a^{2}}{\cos\left(d x + c\right)}}{210 \, d}"," ",0,"1/210*(30*a^2*cos(d*x + c)^7 + 70*a^2*cos(d*x + c)^6 - 84*a^2*cos(d*x + c)^5 - 315*a^2*cos(d*x + c)^4 + 630*a^2*cos(d*x + c)^2 + 420*a^2*cos(d*x + c) - 420*a^2*log(cos(d*x + c)) + 210*a^2/cos(d*x + c))/d","A",0
21,1,94,0,0.348563," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^5,x, algorithm=""maxima"")","-\frac{6 \, a^{2} \cos\left(d x + c\right)^{5} + 15 \, a^{2} \cos\left(d x + c\right)^{4} - 10 \, a^{2} \cos\left(d x + c\right)^{3} - 60 \, a^{2} \cos\left(d x + c\right)^{2} - 30 \, a^{2} \cos\left(d x + c\right) + 60 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{30 \, a^{2}}{\cos\left(d x + c\right)}}{30 \, d}"," ",0,"-1/30*(6*a^2*cos(d*x + c)^5 + 15*a^2*cos(d*x + c)^4 - 10*a^2*cos(d*x + c)^3 - 60*a^2*cos(d*x + c)^2 - 30*a^2*cos(d*x + c) + 60*a^2*log(cos(d*x + c)) - 30*a^2/cos(d*x + c))/d","A",0
22,1,56,0,0.324192," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^3,x, algorithm=""maxima"")","\frac{a^{2} \cos\left(d x + c\right)^{3} + 3 \, a^{2} \cos\left(d x + c\right)^{2} - 6 \, a^{2} \log\left(\cos\left(d x + c\right)\right) + \frac{3 \, a^{2}}{\cos\left(d x + c\right)}}{3 \, d}"," ",0,"1/3*(a^2*cos(d*x + c)^3 + 3*a^2*cos(d*x + c)^2 - 6*a^2*log(cos(d*x + c)) + 3*a^2/cos(d*x + c))/d","A",0
23,1,41,0,0.344921," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c),x, algorithm=""maxima"")","-\frac{a^{2} \cos\left(d x + c\right) + 2 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{a^{2}}{\cos\left(d x + c\right)}}{d}"," ",0,"-(a^2*cos(d*x + c) + 2*a^2*log(cos(d*x + c)) - a^2/cos(d*x + c))/d","A",0
24,1,43,0,0.327522," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, a^{2} \log\left(\cos\left(d x + c\right) - 1\right) - 2 \, a^{2} \log\left(\cos\left(d x + c\right)\right) + \frac{a^{2}}{\cos\left(d x + c\right)}}{d}"," ",0,"(2*a^2*log(cos(d*x + c) - 1) - 2*a^2*log(cos(d*x + c)) + a^2/cos(d*x + c))/d","A",0
25,1,68,0,0.323900," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, a^{2} \log\left(\cos\left(d x + c\right) - 1\right) - 2 \, a^{2} \log\left(\cos\left(d x + c\right)\right) + \frac{2 \, a^{2} \cos\left(d x + c\right) - a^{2}}{\cos\left(d x + c\right)^{2} - \cos\left(d x + c\right)}}{d}"," ",0,"(2*a^2*log(cos(d*x + c) - 1) - 2*a^2*log(cos(d*x + c)) + (2*a^2*cos(d*x + c) - a^2)/(cos(d*x + c)^2 - cos(d*x + c)))/d","A",0
26,1,104,0,0.318992," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\cos\left(d x + c\right) + 1\right) - 17 \, a^{2} \log\left(\cos\left(d x + c\right) - 1\right) + 16 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{2 \, {\left(9 \, a^{2} \cos\left(d x + c\right)^{2} - 14 \, a^{2} \cos\left(d x + c\right) + 4 \, a^{2}\right)}}{\cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)}}{8 \, d}"," ",0,"-1/8*(a^2*log(cos(d*x + c) + 1) - 17*a^2*log(cos(d*x + c) - 1) + 16*a^2*log(cos(d*x + c)) - 2*(9*a^2*cos(d*x + c)^2 - 14*a^2*cos(d*x + c) + 4*a^2)/(cos(d*x + c)^3 - 2*cos(d*x + c)^2 + cos(d*x + c)))/d","A",0
27,1,143,0,0.327008," ","integrate(csc(d*x+c)^7*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} \log\left(\cos\left(d x + c\right) + 1\right) - 27 \, a^{2} \log\left(\cos\left(d x + c\right) - 1\right) + 24 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{2 \, {\left(15 \, a^{2} \cos\left(d x + c\right)^{4} - 24 \, a^{2} \cos\left(d x + c\right)^{3} - 7 \, a^{2} \cos\left(d x + c\right)^{2} + 23 \, a^{2} \cos\left(d x + c\right) - 6 \, a^{2}\right)}}{\cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right)}}{12 \, d}"," ",0,"-1/12*(3*a^2*log(cos(d*x + c) + 1) - 27*a^2*log(cos(d*x + c) - 1) + 24*a^2*log(cos(d*x + c)) - 2*(15*a^2*cos(d*x + c)^4 - 24*a^2*cos(d*x + c)^3 - 7*a^2*cos(d*x + c)^2 + 23*a^2*cos(d*x + c) - 6*a^2)/(cos(d*x + c)^5 - 2*cos(d*x + c)^4 + 2*cos(d*x + c)^2 - cos(d*x + c)))/d","A",0
28,1,197,0,0.366222," ","integrate(csc(d*x+c)^9*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{141 \, a^{2} \log\left(\cos\left(d x + c\right) + 1\right) - 909 \, a^{2} \log\left(\cos\left(d x + c\right) - 1\right) + 768 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{2 \, {\left(525 \, a^{2} \cos\left(d x + c\right)^{6} - 858 \, a^{2} \cos\left(d x + c\right)^{5} - 734 \, a^{2} \cos\left(d x + c\right)^{4} + 1654 \, a^{2} \cos\left(d x + c\right)^{3} - 19 \, a^{2} \cos\left(d x + c\right)^{2} - 784 \, a^{2} \cos\left(d x + c\right) + 192 \, a^{2}\right)}}{\cos\left(d x + c\right)^{7} - 2 \, \cos\left(d x + c\right)^{6} - \cos\left(d x + c\right)^{5} + 4 \, \cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)}}{384 \, d}"," ",0,"-1/384*(141*a^2*log(cos(d*x + c) + 1) - 909*a^2*log(cos(d*x + c) - 1) + 768*a^2*log(cos(d*x + c)) - 2*(525*a^2*cos(d*x + c)^6 - 858*a^2*cos(d*x + c)^5 - 734*a^2*cos(d*x + c)^4 + 1654*a^2*cos(d*x + c)^3 - 19*a^2*cos(d*x + c)^2 - 784*a^2*cos(d*x + c) + 192*a^2)/(cos(d*x + c)^7 - 2*cos(d*x + c)^6 - cos(d*x + c)^5 + 4*cos(d*x + c)^4 - cos(d*x + c)^3 - 2*cos(d*x + c)^2 + cos(d*x + c)))/d","A",0
29,1,215,0,0.437950," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^8,x, algorithm=""maxima"")","-\frac{1024 \, {\left(30 \, \sin\left(d x + c\right)^{7} + 42 \, \sin\left(d x + c\right)^{5} + 70 \, \sin\left(d x + c\right)^{3} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right) + 210 \, \sin\left(d x + c\right)\right)} a^{2} - 35 \, {\left(128 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 840 \, d x + 840 \, c + 3 \, \sin\left(8 \, d x + 8 \, c\right) + 168 \, \sin\left(4 \, d x + 4 \, c\right) - 768 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} + 2240 \, {\left(105 \, d x + 105 \, c - \frac{87 \, \tan\left(d x + c\right)^{5} + 136 \, \tan\left(d x + c\right)^{3} + 57 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{6} + 3 \, \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{2} + 1} - 48 \, \tan\left(d x + c\right)\right)} a^{2}}{107520 \, d}"," ",0,"-1/107520*(1024*(30*sin(d*x + c)^7 + 42*sin(d*x + c)^5 + 70*sin(d*x + c)^3 - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1) + 210*sin(d*x + c))*a^2 - 35*(128*sin(2*d*x + 2*c)^3 + 840*d*x + 840*c + 3*sin(8*d*x + 8*c) + 168*sin(4*d*x + 4*c) - 768*sin(2*d*x + 2*c))*a^2 + 2240*(105*d*x + 105*c - (87*tan(d*x + c)^5 + 136*tan(d*x + c)^3 + 57*tan(d*x + c))/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1) - 48*tan(d*x + c))*a^2)/d","A",0
30,1,174,0,0.537982," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^6,x, algorithm=""maxima"")","-\frac{64 \, {\left(6 \, \sin\left(d x + c\right)^{5} + 10 \, \sin\left(d x + c\right)^{3} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 30 \, \sin\left(d x + c\right)\right)} a^{2} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} + 120 \, {\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^{2}}{960 \, d}"," ",0,"-1/960*(64*(6*sin(d*x + c)^5 + 10*sin(d*x + c)^3 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 30*sin(d*x + c))*a^2 - 5*(4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^2 + 120*(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^2)/d","A",0
31,1,126,0,0.473942," ","integrate((a+a*sec(d*x+c))^2*sin(d*x+c)^4,x, algorithm=""maxima"")","-\frac{32 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a^{2} - 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^{2} + 48 \, {\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}}{96 \, d}"," ",0,"-1/96*(32*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a^2 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*a^2 + 48*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^2)/d","A",0
32,1,81,0,0.431110," ","integrate((a+a*sec(d*x+c))^2*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 - \tan\left(d x + c\right)\right)} a^{2} + 4 \, a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c - sin(2*d*x + 2*c))*a^2 - 4*(d*x + c - tan(d*x + c))*a^2 + 4*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)))/d","A",0
33,1,74,0,0.333293," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2}{\sin\left(d x + c\right)} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + a^{2} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} + \frac{a^{2}}{\tan\left(d x + c\right)}}{d}"," ",0,"-(a^2*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + a^2*(1/tan(d*x + c) - tan(d*x + c)) + a^2/tan(d*x + c))/d","A",0
34,1,113,0,0.344129," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 1\right)}}{\sin\left(d x + c\right)^{3}} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + a^{2} {\left(\frac{6 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{3}} - 3 \, \tan\left(d x + c\right)\right)} + \frac{{\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} a^{2}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"-1/3*(a^2*(2*(3*sin(d*x + c)^2 + 1)/sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + a^2*((6*tan(d*x + c)^2 + 1)/tan(d*x + c)^3 - 3*tan(d*x + c)) + (3*tan(d*x + c)^2 + 1)*a^2/tan(d*x + c)^3)/d","A",0
35,1,144,0,0.352123," ","integrate(csc(d*x+c)^6*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} + 3\right)}}{\sin\left(d x + c\right)^{5}} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 3 \, a^{2} {\left(\frac{15 \, \tan\left(d x + c\right)^{4} + 5 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{5}} - 5 \, \tan\left(d x + c\right)\right)} + \frac{{\left(15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{2}}{\tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*(a^2*(2*(15*sin(d*x + c)^4 + 5*sin(d*x + c)^2 + 3)/sin(d*x + c)^5 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 3*a^2*((15*tan(d*x + c)^4 + 5*tan(d*x + c)^2 + 1)/tan(d*x + c)^5 - 5*tan(d*x + c)) + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 + 3)*a^2/tan(d*x + c)^5)/d","A",0
36,1,175,0,0.355725," ","integrate(csc(d*x+c)^8*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{6} + 35 \, \sin\left(d x + c\right)^{4} + 21 \, \sin\left(d x + c\right)^{2} + 15\right)}}{\sin\left(d x + c\right)^{7}} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 3 \, a^{2} {\left(\frac{140 \, \tan\left(d x + c\right)^{6} + 70 \, \tan\left(d x + c\right)^{4} + 28 \, \tan\left(d x + c\right)^{2} + 5}{\tan\left(d x + c\right)^{7}} - 35 \, \tan\left(d x + c\right)\right)} + \frac{3 \, {\left(35 \, \tan\left(d x + c\right)^{6} + 35 \, \tan\left(d x + c\right)^{4} + 21 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{2}}{\tan\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"-1/105*(a^2*(2*(105*sin(d*x + c)^6 + 35*sin(d*x + c)^4 + 21*sin(d*x + c)^2 + 15)/sin(d*x + c)^7 - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1)) + 3*a^2*((140*tan(d*x + c)^6 + 70*tan(d*x + c)^4 + 28*tan(d*x + c)^2 + 5)/tan(d*x + c)^7 - 35*tan(d*x + c)) + 3*(35*tan(d*x + c)^6 + 35*tan(d*x + c)^4 + 21*tan(d*x + c)^2 + 5)*a^2/tan(d*x + c)^7)/d","A",0
37,1,204,0,0.347101," ","integrate(csc(d*x+c)^10*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2 \, {\left(315 \, \sin\left(d x + c\right)^{8} + 105 \, \sin\left(d x + c\right)^{6} + 63 \, \sin\left(d x + c\right)^{4} + 45 \, \sin\left(d x + c\right)^{2} + 35\right)}}{\sin\left(d x + c\right)^{9}} - 315 \, \log\left(\sin\left(d x + c\right) + 1\right) + 315 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 5 \, a^{2} {\left(\frac{315 \, \tan\left(d x + c\right)^{8} + 210 \, \tan\left(d x + c\right)^{6} + 126 \, \tan\left(d x + c\right)^{4} + 45 \, \tan\left(d x + c\right)^{2} + 7}{\tan\left(d x + c\right)^{9}} - 63 \, \tan\left(d x + c\right)\right)} + \frac{{\left(315 \, \tan\left(d x + c\right)^{8} + 420 \, \tan\left(d x + c\right)^{6} + 378 \, \tan\left(d x + c\right)^{4} + 180 \, \tan\left(d x + c\right)^{2} + 35\right)} a^{2}}{\tan\left(d x + c\right)^{9}}}{315 \, d}"," ",0,"-1/315*(a^2*(2*(315*sin(d*x + c)^8 + 105*sin(d*x + c)^6 + 63*sin(d*x + c)^4 + 45*sin(d*x + c)^2 + 35)/sin(d*x + c)^9 - 315*log(sin(d*x + c) + 1) + 315*log(sin(d*x + c) - 1)) + 5*a^2*((315*tan(d*x + c)^8 + 210*tan(d*x + c)^6 + 126*tan(d*x + c)^4 + 45*tan(d*x + c)^2 + 7)/tan(d*x + c)^9 - 63*tan(d*x + c)) + (315*tan(d*x + c)^8 + 420*tan(d*x + c)^6 + 378*tan(d*x + c)^4 + 180*tan(d*x + c)^2 + 35)*a^2/tan(d*x + c)^9)/d","A",0
38,1,158,0,0.328547," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^9,x, algorithm=""maxima"")","-\frac{280 \, a^{3} \cos\left(d x + c\right)^{9} + 945 \, a^{3} \cos\left(d x + c\right)^{8} - 360 \, a^{3} \cos\left(d x + c\right)^{7} - 4620 \, a^{3} \cos\left(d x + c\right)^{6} - 3024 \, a^{3} \cos\left(d x + c\right)^{5} + 8820 \, a^{3} \cos\left(d x + c\right)^{4} + 11760 \, a^{3} \cos\left(d x + c\right)^{3} - 7560 \, a^{3} \cos\left(d x + c\right)^{2} - 27720 \, a^{3} \cos\left(d x + c\right) - 2520 \, a^{3} \log\left(\cos\left(d x + c\right)\right) - \frac{1260 \, {\left(6 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)}}{\cos\left(d x + c\right)^{2}}}{2520 \, d}"," ",0,"-1/2520*(280*a^3*cos(d*x + c)^9 + 945*a^3*cos(d*x + c)^8 - 360*a^3*cos(d*x + c)^7 - 4620*a^3*cos(d*x + c)^6 - 3024*a^3*cos(d*x + c)^5 + 8820*a^3*cos(d*x + c)^4 + 11760*a^3*cos(d*x + c)^3 - 7560*a^3*cos(d*x + c)^2 - 27720*a^3*cos(d*x + c) - 2520*a^3*log(cos(d*x + c)) - 1260*(6*a^3*cos(d*x + c) + a^3)/cos(d*x + c)^2)/d","A",0
39,1,107,0,0.321559," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^7,x, algorithm=""maxima"")","\frac{2 \, a^{3} \cos\left(d x + c\right)^{7} + 7 \, a^{3} \cos\left(d x + c\right)^{6} - 28 \, a^{3} \cos\left(d x + c\right)^{4} - 28 \, a^{3} \cos\left(d x + c\right)^{3} + 42 \, a^{3} \cos\left(d x + c\right)^{2} + 112 \, a^{3} \cos\left(d x + c\right) + \frac{7 \, {\left(6 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)}}{\cos\left(d x + c\right)^{2}}}{14 \, d}"," ",0,"1/14*(2*a^3*cos(d*x + c)^7 + 7*a^3*cos(d*x + c)^6 - 28*a^3*cos(d*x + c)^4 - 28*a^3*cos(d*x + c)^3 + 42*a^3*cos(d*x + c)^2 + 112*a^3*cos(d*x + c) + 7*(6*a^3*cos(d*x + c) + a^3)/cos(d*x + c)^2)/d","A",0
40,1,106,0,0.326173," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^5,x, algorithm=""maxima"")","-\frac{12 \, a^{3} \cos\left(d x + c\right)^{5} + 45 \, a^{3} \cos\left(d x + c\right)^{4} + 20 \, a^{3} \cos\left(d x + c\right)^{3} - 150 \, a^{3} \cos\left(d x + c\right)^{2} - 300 \, a^{3} \cos\left(d x + c\right) + 60 \, a^{3} \log\left(\cos\left(d x + c\right)\right) - \frac{30 \, {\left(6 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)}}{\cos\left(d x + c\right)^{2}}}{60 \, d}"," ",0,"-1/60*(12*a^3*cos(d*x + c)^5 + 45*a^3*cos(d*x + c)^4 + 20*a^3*cos(d*x + c)^3 - 150*a^3*cos(d*x + c)^2 - 300*a^3*cos(d*x + c) + 60*a^3*log(cos(d*x + c)) - 30*(6*a^3*cos(d*x + c) + a^3)/cos(d*x + c)^2)/d","A",0
41,1,80,0,0.359204," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^3,x, algorithm=""maxima"")","\frac{2 \, a^{3} \cos\left(d x + c\right)^{3} + 9 \, a^{3} \cos\left(d x + c\right)^{2} + 12 \, a^{3} \cos\left(d x + c\right) - 12 \, a^{3} \log\left(\cos\left(d x + c\right)\right) + \frac{3 \, {\left(6 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)}}{\cos\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"1/6*(2*a^3*cos(d*x + c)^3 + 9*a^3*cos(d*x + c)^2 + 12*a^3*cos(d*x + c) - 12*a^3*log(cos(d*x + c)) + 3*(6*a^3*cos(d*x + c) + a^3)/cos(d*x + c)^2)/d","A",0
42,1,55,0,0.408159," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c),x, algorithm=""maxima"")","-\frac{2 \, a^{3} \cos\left(d x + c\right) + 6 \, a^{3} \log\left(\cos\left(d x + c\right)\right) - \frac{6 \, a^{3}}{\cos\left(d x + c\right)} - \frac{a^{3}}{\cos\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*a^3*cos(d*x + c) + 6*a^3*log(cos(d*x + c)) - 6*a^3/cos(d*x + c) - a^3/cos(d*x + c)^2)/d","A",0
43,1,56,0,0.561056," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{8 \, a^{3} \log\left(\cos\left(d x + c\right) - 1\right) - 8 \, a^{3} \log\left(\cos\left(d x + c\right)\right) + \frac{6 \, a^{3} \cos\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(8*a^3*log(cos(d*x + c) - 1) - 8*a^3*log(cos(d*x + c)) + (6*a^3*cos(d*x + c) + a^3)/cos(d*x + c)^2)/d","A",0
44,1,84,0,0.501181," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{10 \, a^{3} \log\left(\cos\left(d x + c\right) - 1\right) - 10 \, a^{3} \log\left(\cos\left(d x + c\right)\right) + \frac{10 \, a^{3} \cos\left(d x + c\right)^{2} - 5 \, a^{3} \cos\left(d x + c\right) - a^{3}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(10*a^3*log(cos(d*x + c) - 1) - 10*a^3*log(cos(d*x + c)) + (10*a^3*cos(d*x + c)^2 - 5*a^3*cos(d*x + c) - a^3)/(cos(d*x + c)^3 - cos(d*x + c)^2))/d","A",0
45,1,103,0,0.659234," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{12 \, a^{3} \log\left(\cos\left(d x + c\right) - 1\right) - 12 \, a^{3} \log\left(\cos\left(d x + c\right)\right) + \frac{12 \, a^{3} \cos\left(d x + c\right)^{3} - 18 \, a^{3} \cos\left(d x + c\right)^{2} + 4 \, a^{3} \cos\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(12*a^3*log(cos(d*x + c) - 1) - 12*a^3*log(cos(d*x + c)) + (12*a^3*cos(d*x + c)^3 - 18*a^3*cos(d*x + c)^2 + 4*a^3*cos(d*x + c) + a^3)/(cos(d*x + c)^4 - 2*cos(d*x + c)^3 + cos(d*x + c)^2))/d","A",0
46,1,145,0,0.425313," ","integrate(csc(d*x+c)^7*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, a^{3} \log\left(\cos\left(d x + c\right) + 1\right) + 333 \, a^{3} \log\left(\cos\left(d x + c\right) - 1\right) - 336 \, a^{3} \log\left(\cos\left(d x + c\right)\right) + \frac{2 \, {\left(165 \, a^{3} \cos\left(d x + c\right)^{4} - 411 \, a^{3} \cos\left(d x + c\right)^{3} + 298 \, a^{3} \cos\left(d x + c\right)^{2} - 36 \, a^{3} \cos\left(d x + c\right) - 12 \, a^{3}\right)}}{\cos\left(d x + c\right)^{5} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2}}}{48 \, d}"," ",0,"1/48*(3*a^3*log(cos(d*x + c) + 1) + 333*a^3*log(cos(d*x + c) - 1) - 336*a^3*log(cos(d*x + c)) + 2*(165*a^3*cos(d*x + c)^4 - 411*a^3*cos(d*x + c)^3 + 298*a^3*cos(d*x + c)^2 - 36*a^3*cos(d*x + c) - 12*a^3)/(cos(d*x + c)^5 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^3 - cos(d*x + c)^2))/d","A",0
47,1,189,0,0.505028," ","integrate(csc(d*x+c)^9*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{33 \, a^{3} \log\left(\cos\left(d x + c\right) + 1\right) + 1503 \, a^{3} \log\left(\cos\left(d x + c\right) - 1\right) - 1536 \, a^{3} \log\left(\cos\left(d x + c\right)\right) + \frac{2 \, {\left(735 \, a^{3} \cos\left(d x + c\right)^{6} - 1821 \, a^{3} \cos\left(d x + c\right)^{5} + 563 \, a^{3} \cos\left(d x + c\right)^{4} + 1695 \, a^{3} \cos\left(d x + c\right)^{3} - 1376 \, a^{3} \cos\left(d x + c\right)^{2} + 144 \, a^{3} \cos\left(d x + c\right) + 48 \, a^{3}\right)}}{\cos\left(d x + c\right)^{7} - 3 \, \cos\left(d x + c\right)^{6} + 2 \, \cos\left(d x + c\right)^{5} + 2 \, \cos\left(d x + c\right)^{4} - 3 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}}{192 \, d}"," ",0,"1/192*(33*a^3*log(cos(d*x + c) + 1) + 1503*a^3*log(cos(d*x + c) - 1) - 1536*a^3*log(cos(d*x + c)) + 2*(735*a^3*cos(d*x + c)^6 - 1821*a^3*cos(d*x + c)^5 + 563*a^3*cos(d*x + c)^4 + 1695*a^3*cos(d*x + c)^3 - 1376*a^3*cos(d*x + c)^2 + 144*a^3*cos(d*x + c) + 48*a^3)/(cos(d*x + c)^7 - 3*cos(d*x + c)^6 + 2*cos(d*x + c)^5 + 2*cos(d*x + c)^4 - 3*cos(d*x + c)^3 + cos(d*x + c)^2))/d","A",0
48,1,291,0,0.468944," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^8,x, algorithm=""maxima"")","-\frac{1536 \, {\left(30 \, \sin\left(d x + c\right)^{7} + 42 \, \sin\left(d x + c\right)^{5} + 70 \, \sin\left(d x + c\right)^{3} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right) + 210 \, \sin\left(d x + c\right)\right)} a^{3} - 1792 \, {\left(12 \, \sin\left(d x + c\right)^{5} + 40 \, \sin\left(d x + c\right)^{3} - \frac{30 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right) + 180 \, \sin\left(d x + c\right)\right)} a^{3} - 35 \, {\left(128 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 840 \, d x + 840 \, c + 3 \, \sin\left(8 \, d x + 8 \, c\right) + 168 \, \sin\left(4 \, d x + 4 \, c\right) - 768 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} + 6720 \, {\left(105 \, d x + 105 \, c - \frac{87 \, \tan\left(d x + c\right)^{5} + 136 \, \tan\left(d x + c\right)^{3} + 57 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{6} + 3 \, \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{2} + 1} - 48 \, \tan\left(d x + c\right)\right)} a^{3}}{107520 \, d}"," ",0,"-1/107520*(1536*(30*sin(d*x + c)^7 + 42*sin(d*x + c)^5 + 70*sin(d*x + c)^3 - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1) + 210*sin(d*x + c))*a^3 - 1792*(12*sin(d*x + c)^5 + 40*sin(d*x + c)^3 - 30*sin(d*x + c)/(sin(d*x + c)^2 - 1) - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1) + 180*sin(d*x + c))*a^3 - 35*(128*sin(2*d*x + 2*c)^3 + 840*d*x + 840*c + 3*sin(8*d*x + 8*c) + 168*sin(4*d*x + 4*c) - 768*sin(2*d*x + 2*c))*a^3 + 6720*(105*d*x + 105*c - (87*tan(d*x + c)^5 + 136*tan(d*x + c)^3 + 57*tan(d*x + c))/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1) - 48*tan(d*x + c))*a^3)/d","A",0
49,1,240,0,0.438905," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^6,x, algorithm=""maxima"")","-\frac{96 \, {\left(6 \, \sin\left(d x + c\right)^{5} + 10 \, \sin\left(d x + c\right)^{3} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 30 \, \sin\left(d x + c\right)\right)} a^{3} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 80 \, {\left(4 \, \sin\left(d x + c\right)^{3} - \frac{6 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 24 \, \sin\left(d x + c\right)\right)} a^{3} + 360 \, {\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^{3}}{960 \, d}"," ",0,"-1/960*(96*(6*sin(d*x + c)^5 + 10*sin(d*x + c)^3 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 30*sin(d*x + c))*a^3 - 5*(4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^3 - 80*(4*sin(d*x + c)^3 - 6*sin(d*x + c)/(sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 24*sin(d*x + c))*a^3 + 360*(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^3)/d","A",0
50,1,182,0,0.784006," ","integrate((a+a*sec(d*x+c))^3*sin(d*x+c)^4,x, algorithm=""maxima"")","-\frac{16 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a^{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^{3} + 48 \, {\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} + 8 \, a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + 3 \, \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \log\left(\sin\left(d x + c\right) - 1\right) - 4 \, \sin\left(d x + c\right)\right)}}{32 \, d}"," ",0,"-1/32*(16*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a^3 - (12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*a^3 + 48*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^3 + 8*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1) - 4*sin(d*x + c)))/d","A",0
51,1,127,0,0.510472," ","integrate((a+a*sec(d*x+c))^3*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^{3} - 12 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} - a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c - sin(2*d*x + 2*c))*a^3 - 12*(d*x + c - tan(d*x + c))*a^3 - a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)))/d","A",0
52,1,137,0,0.595729," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 2\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{3} {\left(\frac{2}{\sin\left(d x + c\right)} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a^{3} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} + \frac{4 \, a^{3}}{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(a^3*(2*(3*sin(d*x + c)^2 - 2)/(sin(d*x + c)^3 - sin(d*x + c)) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 6*a^3*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*a^3*(1/tan(d*x + c) - tan(d*x + c)) + 4*a^3/tan(d*x + c))/d","A",0
53,1,188,0,0.352498," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} - 10 \, \sin\left(d x + c\right)^{2} - 2\right)}}{\sin\left(d x + c\right)^{5} - \sin\left(d x + c\right)^{3}} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 1\right)}}{\sin\left(d x + c\right)^{3}} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a^{3} {\left(\frac{6 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{3}} - 3 \, \tan\left(d x + c\right)\right)} + \frac{4 \, {\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} a^{3}}{\tan\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(a^3*(2*(15*sin(d*x + c)^4 - 10*sin(d*x + c)^2 - 2)/(sin(d*x + c)^5 - sin(d*x + c)^3) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 6*a^3*(2*(3*sin(d*x + c)^2 + 1)/sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 12*a^3*((6*tan(d*x + c)^2 + 1)/tan(d*x + c)^3 - 3*tan(d*x + c)) + 4*(3*tan(d*x + c)^2 + 1)*a^3/tan(d*x + c)^3)/d","A",0
54,1,228,0,0.487374," ","integrate(csc(d*x+c)^6*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{a^{3} {\left(\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{6} - 70 \, \sin\left(d x + c\right)^{4} - 14 \, \sin\left(d x + c\right)^{2} - 6\right)}}{\sin\left(d x + c\right)^{7} - \sin\left(d x + c\right)^{5}} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} + 3\right)}}{\sin\left(d x + c\right)^{5}} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, a^{3} {\left(\frac{15 \, \tan\left(d x + c\right)^{4} + 5 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{5}} - 5 \, \tan\left(d x + c\right)\right)} + \frac{4 \, {\left(15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{3}}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(a^3*(2*(105*sin(d*x + c)^6 - 70*sin(d*x + c)^4 - 14*sin(d*x + c)^2 - 6)/(sin(d*x + c)^7 - sin(d*x + c)^5) - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1)) + 6*a^3*(2*(15*sin(d*x + c)^4 + 5*sin(d*x + c)^2 + 3)/sin(d*x + c)^5 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 36*a^3*((15*tan(d*x + c)^4 + 5*tan(d*x + c)^2 + 1)/tan(d*x + c)^5 - 5*tan(d*x + c)) + 4*(15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 + 3)*a^3/tan(d*x + c)^5)/d","A",0
55,1,268,0,0.370936," ","integrate(csc(d*x+c)^8*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{a^{3} {\left(\frac{2 \, {\left(315 \, \sin\left(d x + c\right)^{8} - 210 \, \sin\left(d x + c\right)^{6} - 42 \, \sin\left(d x + c\right)^{4} - 18 \, \sin\left(d x + c\right)^{2} - 10\right)}}{\sin\left(d x + c\right)^{9} - \sin\left(d x + c\right)^{7}} - 315 \, \log\left(\sin\left(d x + c\right) + 1\right) + 315 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, a^{3} {\left(\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{6} + 35 \, \sin\left(d x + c\right)^{4} + 21 \, \sin\left(d x + c\right)^{2} + 15\right)}}{\sin\left(d x + c\right)^{7}} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a^{3} {\left(\frac{140 \, \tan\left(d x + c\right)^{6} + 70 \, \tan\left(d x + c\right)^{4} + 28 \, \tan\left(d x + c\right)^{2} + 5}{\tan\left(d x + c\right)^{7}} - 35 \, \tan\left(d x + c\right)\right)} + \frac{4 \, {\left(35 \, \tan\left(d x + c\right)^{6} + 35 \, \tan\left(d x + c\right)^{4} + 21 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{3}}{\tan\left(d x + c\right)^{7}}}{140 \, d}"," ",0,"-1/140*(a^3*(2*(315*sin(d*x + c)^8 - 210*sin(d*x + c)^6 - 42*sin(d*x + c)^4 - 18*sin(d*x + c)^2 - 10)/(sin(d*x + c)^9 - sin(d*x + c)^7) - 315*log(sin(d*x + c) + 1) + 315*log(sin(d*x + c) - 1)) + 2*a^3*(2*(105*sin(d*x + c)^6 + 35*sin(d*x + c)^4 + 21*sin(d*x + c)^2 + 15)/sin(d*x + c)^7 - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1)) + 12*a^3*((140*tan(d*x + c)^6 + 70*tan(d*x + c)^4 + 28*tan(d*x + c)^2 + 5)/tan(d*x + c)^7 - 35*tan(d*x + c)) + 4*(35*tan(d*x + c)^6 + 35*tan(d*x + c)^4 + 21*tan(d*x + c)^2 + 5)*a^3/tan(d*x + c)^7)/d","A",0
56,1,308,0,0.365595," ","integrate(csc(d*x+c)^10*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{a^{3} {\left(\frac{2 \, {\left(3465 \, \sin\left(d x + c\right)^{10} - 2310 \, \sin\left(d x + c\right)^{8} - 462 \, \sin\left(d x + c\right)^{6} - 198 \, \sin\left(d x + c\right)^{4} - 110 \, \sin\left(d x + c\right)^{2} - 70\right)}}{\sin\left(d x + c\right)^{11} - \sin\left(d x + c\right)^{9}} - 3465 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3465 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{3} {\left(\frac{2 \, {\left(315 \, \sin\left(d x + c\right)^{8} + 105 \, \sin\left(d x + c\right)^{6} + 63 \, \sin\left(d x + c\right)^{4} + 45 \, \sin\left(d x + c\right)^{2} + 35\right)}}{\sin\left(d x + c\right)^{9}} - 315 \, \log\left(\sin\left(d x + c\right) + 1\right) + 315 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 60 \, a^{3} {\left(\frac{315 \, \tan\left(d x + c\right)^{8} + 210 \, \tan\left(d x + c\right)^{6} + 126 \, \tan\left(d x + c\right)^{4} + 45 \, \tan\left(d x + c\right)^{2} + 7}{\tan\left(d x + c\right)^{9}} - 63 \, \tan\left(d x + c\right)\right)} + \frac{4 \, {\left(315 \, \tan\left(d x + c\right)^{8} + 420 \, \tan\left(d x + c\right)^{6} + 378 \, \tan\left(d x + c\right)^{4} + 180 \, \tan\left(d x + c\right)^{2} + 35\right)} a^{3}}{\tan\left(d x + c\right)^{9}}}{1260 \, d}"," ",0,"-1/1260*(a^3*(2*(3465*sin(d*x + c)^10 - 2310*sin(d*x + c)^8 - 462*sin(d*x + c)^6 - 198*sin(d*x + c)^4 - 110*sin(d*x + c)^2 - 70)/(sin(d*x + c)^11 - sin(d*x + c)^9) - 3465*log(sin(d*x + c) + 1) + 3465*log(sin(d*x + c) - 1)) + 6*a^3*(2*(315*sin(d*x + c)^8 + 105*sin(d*x + c)^6 + 63*sin(d*x + c)^4 + 45*sin(d*x + c)^2 + 35)/sin(d*x + c)^9 - 315*log(sin(d*x + c) + 1) + 315*log(sin(d*x + c) - 1)) + 60*a^3*((315*tan(d*x + c)^8 + 210*tan(d*x + c)^6 + 126*tan(d*x + c)^4 + 45*tan(d*x + c)^2 + 7)/tan(d*x + c)^9 - 63*tan(d*x + c)) + 4*(315*tan(d*x + c)^8 + 420*tan(d*x + c)^6 + 378*tan(d*x + c)^4 + 180*tan(d*x + c)^2 + 35)*a^3/tan(d*x + c)^9)/d","A",0
57,1,89,0,0.330571," ","integrate(sin(d*x+c)^9/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{280 \, \cos\left(d x + c\right)^{9} - 315 \, \cos\left(d x + c\right)^{8} - 1080 \, \cos\left(d x + c\right)^{7} + 1260 \, \cos\left(d x + c\right)^{6} + 1512 \, \cos\left(d x + c\right)^{5} - 1890 \, \cos\left(d x + c\right)^{4} - 840 \, \cos\left(d x + c\right)^{3} + 1260 \, \cos\left(d x + c\right)^{2}}{2520 \, a d}"," ",0,"-1/2520*(280*cos(d*x + c)^9 - 315*cos(d*x + c)^8 - 1080*cos(d*x + c)^7 + 1260*cos(d*x + c)^6 + 1512*cos(d*x + c)^5 - 1890*cos(d*x + c)^4 - 840*cos(d*x + c)^3 + 1260*cos(d*x + c)^2)/(a*d)","A",0
58,1,69,0,0.339959," ","integrate(sin(d*x+c)^7/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{30 \, \cos\left(d x + c\right)^{7} - 35 \, \cos\left(d x + c\right)^{6} - 84 \, \cos\left(d x + c\right)^{5} + 105 \, \cos\left(d x + c\right)^{4} + 70 \, \cos\left(d x + c\right)^{3} - 105 \, \cos\left(d x + c\right)^{2}}{210 \, a d}"," ",0,"1/210*(30*cos(d*x + c)^7 - 35*cos(d*x + c)^6 - 84*cos(d*x + c)^5 + 105*cos(d*x + c)^4 + 70*cos(d*x + c)^3 - 105*cos(d*x + c)^2)/(a*d)","A",0
59,1,49,0,0.323456," ","integrate(sin(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{12 \, \cos\left(d x + c\right)^{5} - 15 \, \cos\left(d x + c\right)^{4} - 20 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right)^{2}}{60 \, a d}"," ",0,"-1/60*(12*cos(d*x + c)^5 - 15*cos(d*x + c)^4 - 20*cos(d*x + c)^3 + 30*cos(d*x + c)^2)/(a*d)","A",0
60,1,29,0,0.320046," ","integrate(sin(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2}}{6 \, a d}"," ",0,"1/6*(2*cos(d*x + c)^3 - 3*cos(d*x + c)^2)/(a*d)","A",0
61,1,30,0,0.323313," ","integrate(sin(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\cos\left(d x + c\right)}{a} - \frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a}}{d}"," ",0,"-(cos(d*x + c)/a - log(cos(d*x + c) + 1)/a)/d","A",0
62,1,47,0,0.317416," ","integrate(csc(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\cos\left(d x + c\right) - 1\right)}{a} + \frac{2}{a \cos\left(d x + c\right) + a}}{4 \, d}"," ",0,"-1/4*(log(cos(d*x + c) + 1)/a - log(cos(d*x + c) - 1)/a + 2/(a*cos(d*x + c) + a))/d","A",0
63,1,86,0,0.363874," ","integrate(csc(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) + 2\right)}}{a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - a} - \frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a} + \frac{\log\left(\cos\left(d x + c\right) - 1\right)}{a}}{16 \, d}"," ",0,"1/16*(2*(cos(d*x + c)^2 + cos(d*x + c) + 2)/(a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) - a) - log(cos(d*x + c) + 1)/a + log(cos(d*x + c) - 1)/a)/d","A",0
64,1,130,0,0.352670," ","integrate(csc(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)^{2} - 5 \, \cos\left(d x + c\right) - 8\right)}}{a \cos\left(d x + c\right)^{5} + a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{3} - 2 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) + a} - \frac{3 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a} + \frac{3 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a}}{96 \, d}"," ",0,"1/96*(2*(3*cos(d*x + c)^4 + 3*cos(d*x + c)^3 - 5*cos(d*x + c)^2 - 5*cos(d*x + c) - 8)/(a*cos(d*x + c)^5 + a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^3 - 2*a*cos(d*x + c)^2 + a*cos(d*x + c) + a) - 3*log(cos(d*x + c) + 1)/a + 3*log(cos(d*x + c) - 1)/a)/d","A",0
65,1,360,0,0.484740," ","integrate(sin(d*x+c)^8/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2681 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5053 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{44099 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{2681 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{805 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{105 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}}{a + \frac{8 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{56 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{56 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{8 \, a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}} - \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{1344 \, d}"," ",0,"1/1344*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2681*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5053*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 44099*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 2681*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 805*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 105*sin(d*x + c)^15/(cos(d*x + c) + 1)^15)/(a + 8*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 56*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 56*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 8*a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a*sin(d*x + c)^16/(cos(d*x + c) + 1)^16) - 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
66,1,278,0,0.438629," ","integrate(sin(d*x+c)^6/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{85 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{198 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1338 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{85 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{15 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{a + \frac{6 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, 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)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} - \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{120 \, d}"," ",0,"1/120*((15*sin(d*x + c)/(cos(d*x + c) + 1) + 85*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 198*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1338*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 85*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 15*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/(a + 6*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) - 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
67,1,196,0,0.427039," ","integrate(sin(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{11 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{53 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a + \frac{4 \, 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)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{12 \, d}"," ",0,"1/12*((3*sin(d*x + c)/(cos(d*x + c) + 1) + 11*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 53*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a + 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
68,1,112,0,0.446423," ","integrate(sin(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{d}"," ",0,"((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
69,1,49,0,0.336071," ","integrate(csc(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(\cos\left(d x + c\right) + 1\right)}}{a \sin\left(d x + c\right)} + \frac{\sin\left(d x + c\right)^{3}}{a {\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{12 \, d}"," ",0,"-1/12*(3*(cos(d*x + c) + 1)/(a*sin(d*x + c)) + sin(d*x + c)^3/(a*(cos(d*x + c) + 1)^3))/d","A",0
70,1,96,0,0.328113," ","integrate(csc(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a} + \frac{5 \, {\left(\frac{6 \, \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}}}{240 \, d}"," ",0,"-1/240*((10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a + 5*(6*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","A",0
71,1,136,0,0.336520," ","integrate(csc(d*x+c)^6/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{175 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{84 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a} + \frac{7 \, {\left(\frac{20 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a \sin\left(d x + c\right)^{5}}}{6720 \, d}"," ",0,"-1/6720*((175*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 84*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a + 7*(20*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 75*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3)*(cos(d*x + c) + 1)^5/(a*sin(d*x + c)^5))/d","B",0
72,1,176,0,0.403398," ","integrate(csc(d*x+c)^8/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{1470 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{882 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{270 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a} + \frac{3 \, {\left(\frac{126 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{490 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1470 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 15\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{7}}{a \sin\left(d x + c\right)^{7}}}{80640 \, d}"," ",0,"-1/80640*((1470*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 882*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 270*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a + 3*(126*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 490*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1470*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15)*(cos(d*x + c) + 1)^7/(a*sin(d*x + c)^7))/d","B",0
73,1,216,0,0.339762," ","integrate(csc(d*x+c)^10/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{48510 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{33264 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{13365 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3080 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{315 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{a} + \frac{11 \, {\left(\frac{360 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1701 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{5040 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{13230 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 35\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{9}}{a \sin\left(d x + c\right)^{9}}}{3548160 \, d}"," ",0,"-1/3548160*((48510*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 33264*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 13365*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3080*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 315*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/a + 11*(360*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1701*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 5040*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 13230*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 35)*(cos(d*x + c) + 1)^9/(a*sin(d*x + c)^9))/d","B",0
74,1,89,0,0.327029," ","integrate(sin(d*x+c)^11/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{180 \, \cos\left(d x + c\right)^{11} - 396 \, \cos\left(d x + c\right)^{10} - 440 \, \cos\left(d x + c\right)^{9} + 1485 \, \cos\left(d x + c\right)^{8} - 1980 \, \cos\left(d x + c\right)^{6} + 792 \, \cos\left(d x + c\right)^{5} + 990 \, \cos\left(d x + c\right)^{4} - 660 \, \cos\left(d x + c\right)^{3}}{1980 \, a^{2} d}"," ",0,"1/1980*(180*cos(d*x + c)^11 - 396*cos(d*x + c)^10 - 440*cos(d*x + c)^9 + 1485*cos(d*x + c)^8 - 1980*cos(d*x + c)^6 + 792*cos(d*x + c)^5 + 990*cos(d*x + c)^4 - 660*cos(d*x + c)^3)/(a^2*d)","A",0
75,1,79,0,0.325102," ","integrate(sin(d*x+c)^9/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{140 \, \cos\left(d x + c\right)^{9} - 315 \, \cos\left(d x + c\right)^{8} - 180 \, \cos\left(d x + c\right)^{7} + 840 \, \cos\left(d x + c\right)^{6} - 252 \, \cos\left(d x + c\right)^{5} - 630 \, \cos\left(d x + c\right)^{4} + 420 \, \cos\left(d x + c\right)^{3}}{1260 \, a^{2} d}"," ",0,"-1/1260*(140*cos(d*x + c)^9 - 315*cos(d*x + c)^8 - 180*cos(d*x + c)^7 + 840*cos(d*x + c)^6 - 252*cos(d*x + c)^5 - 630*cos(d*x + c)^4 + 420*cos(d*x + c)^3)/(a^2*d)","A",0
76,1,49,0,0.323571," ","integrate(sin(d*x+c)^7/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, \cos\left(d x + c\right)^{7} - 14 \, \cos\left(d x + c\right)^{6} + 21 \, \cos\left(d x + c\right)^{4} - 14 \, \cos\left(d x + c\right)^{3}}{42 \, a^{2} d}"," ",0,"1/42*(6*cos(d*x + c)^7 - 14*cos(d*x + c)^6 + 21*cos(d*x + c)^4 - 14*cos(d*x + c)^3)/(a^2*d)","A",0
77,1,39,0,0.324822," ","integrate(sin(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, \cos\left(d x + c\right)^{5} - 15 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3}}{30 \, a^{2} d}"," ",0,"-1/30*(6*cos(d*x + c)^5 - 15*cos(d*x + c)^4 + 10*cos(d*x + c)^3)/(a^2*d)","A",0
78,1,51,0,0.332079," ","integrate(sin(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} + 6 \, \cos\left(d x + c\right)}{a^{2}} - \frac{6 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}}}{3 \, d}"," ",0,"1/3*((cos(d*x + c)^3 - 3*cos(d*x + c)^2 + 6*cos(d*x + c))/a^2 - 6*log(cos(d*x + c) + 1)/a^2)/d","A",0
79,1,46,0,0.374599," ","integrate(sin(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{1}{a^{2} \cos\left(d x + c\right) + a^{2}} - \frac{\cos\left(d x + c\right)}{a^{2}} + \frac{2 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}}}{d}"," ",0,"(1/(a^2*cos(d*x + c) + a^2) - cos(d*x + c)/a^2 + 2*log(cos(d*x + c) + 1)/a^2)/d","A",0
80,1,74,0,0.395307," ","integrate(csc(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, \cos\left(d x + c\right) + 2\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}} + \frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}} - \frac{\log\left(\cos\left(d x + c\right) - 1\right)}{a^{2}}}{8 \, d}"," ",0,"-1/8*(2*(3*cos(d*x + c) + 2)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2) + log(cos(d*x + c) + 1)/a^2 - log(cos(d*x + c) - 1)/a^2)/d","A",0
81,1,59,0,0.575144," ","integrate(csc(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, \cos\left(d x + c\right) + 1}{6 \, {\left(a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} \cos\left(d x + c\right) - a^{2}\right)} d}"," ",0,"1/6*(2*cos(d*x + c) + 1)/((a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c) - a^2)*d)","A",0
82,1,167,0,0.372412," ","integrate(csc(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{5} + 6 \, \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 10 \, \cos\left(d x + c\right)^{2} + 35 \, \cos\left(d x + c\right) + 16\right)}}{a^{2} \cos\left(d x + c\right)^{6} + 2 \, a^{2} \cos\left(d x + c\right)^{5} - a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{3} - a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}} - \frac{3 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}} + \frac{3 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{2}}}{384 \, d}"," ",0,"-1/384*(2*(3*cos(d*x + c)^5 + 6*cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 10*cos(d*x + c)^2 + 35*cos(d*x + c) + 16)/(a^2*cos(d*x + c)^6 + 2*a^2*cos(d*x + c)^5 - a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^3 - a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2) - 3*log(cos(d*x + c) + 1)/a^2 + 3*log(cos(d*x + c) - 1)/a^2)/d","A",0
83,1,378,0,0.444216," ","integrate(sin(d*x+c)^8/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{1155 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{8855 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{29491 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{55583 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{31007 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{142541 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{8855 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{1155 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}}{a^{2} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{56 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{56 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a^{2} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}} - \frac{1155 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{6720 \, d}"," ",0,"-1/6720*((1155*sin(d*x + c)/(cos(d*x + c) + 1) + 8855*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 29491*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 55583*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 31007*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 142541*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 8855*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 1155*sin(d*x + c)^15/(cos(d*x + c) + 1)^15)/(a^2 + 8*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 56*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 56*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 8*a^2*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a^2*sin(d*x + c)^16/(cos(d*x + c) + 1)^16) - 1155*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
84,1,292,0,0.545420," ","integrate(sin(d*x+c)^6/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{45 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{255 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{594 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{174 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{1025 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{45 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{a^{2} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} - \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{120 \, d}"," ",0,"-1/120*((45*sin(d*x + c)/(cos(d*x + c) + 1) + 255*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 594*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 174*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 1025*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 45*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/(a^2 + 6*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) - 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
85,1,206,0,0.560100," ","integrate(sin(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{83 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{75 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{21 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{12 \, d}"," ",0,"-1/12*((21*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 83*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 75*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^2 + 4*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 21*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
86,1,140,0,0.508394," ","integrate(sin(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{5 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{2 \, \sin\left(d x + c\right)}{a^{2} {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"((3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 5*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 2*sin(d*x + c)/(a^2*(cos(d*x + c) + 1)))/d","B",0
87,1,90,0,0.521841," ","integrate(csc(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{2}} + \frac{15 \, {\left(\cos\left(d x + c\right) + 1\right)}}{a^{2} \sin\left(d x + c\right)}}{120 \, d}"," ",0,"-1/120*((15*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^2 + 15*(cos(d*x + c) + 1)/(a^2*sin(d*x + c)))/d","A",0
88,1,134,0,0.480243," ","integrate(csc(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{210 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{70 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{2}} + \frac{35 \, {\left(\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^{2} \sin\left(d x + c\right)^{3}}}{3360 \, d}"," ",0,"-1/3360*((210*sin(d*x + c)/(cos(d*x + c) + 1) + 70*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^2 + 35*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)*(cos(d*x + c) + 1)^3/(a^2*sin(d*x + c)^3))/d","A",0
89,1,174,0,0.474541," ","integrate(csc(d*x+c)^6/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{1575 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{525 \, \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)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{135 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{2}} + \frac{63 \, {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a^{2} \sin\left(d x + c\right)^{5}}}{40320 \, d}"," ",0,"-1/40320*((1575*sin(d*x + c)/(cos(d*x + c) + 1) + 525*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 135*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^2 + 63*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)*(cos(d*x + c) + 1)^5/(a^2*sin(d*x + c)^5))/d","A",0
90,1,174,0,0.432400," ","integrate(csc(d*x+c)^8/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{9702 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3234 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{792 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{385 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{63 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{a^{2}} + \frac{33 \, {\left(\frac{21 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{56 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{7}}{a^{2} \sin\left(d x + c\right)^{7}}}{354816 \, d}"," ",0,"-1/354816*((9702*sin(d*x + c)/(cos(d*x + c) + 1) + 3234*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 792*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 385*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 63*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/a^2 + 33*(21*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 56*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3)*(cos(d*x + c) + 1)^7/(a^2*sin(d*x + c)^7))/d","A",0
91,1,89,0,0.533755," ","integrate(sin(d*x+c)^11/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{2520 \, \cos\left(d x + c\right)^{11} - 8316 \, \cos\left(d x + c\right)^{10} + 3080 \, \cos\left(d x + c\right)^{9} + 17325 \, \cos\left(d x + c\right)^{8} - 19800 \, \cos\left(d x + c\right)^{7} - 4620 \, \cos\left(d x + c\right)^{6} + 16632 \, \cos\left(d x + c\right)^{5} - 6930 \, \cos\left(d x + c\right)^{4}}{27720 \, a^{3} d}"," ",0,"1/27720*(2520*cos(d*x + c)^11 - 8316*cos(d*x + c)^10 + 3080*cos(d*x + c)^9 + 17325*cos(d*x + c)^8 - 19800*cos(d*x + c)^7 - 4620*cos(d*x + c)^6 + 16632*cos(d*x + c)^5 - 6930*cos(d*x + c)^4)/(a^3*d)","A",0
92,1,69,0,0.513006," ","integrate(sin(d*x+c)^9/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{280 \, \cos\left(d x + c\right)^{9} - 945 \, \cos\left(d x + c\right)^{8} + 720 \, \cos\left(d x + c\right)^{7} + 840 \, \cos\left(d x + c\right)^{6} - 1512 \, \cos\left(d x + c\right)^{5} + 630 \, \cos\left(d x + c\right)^{4}}{2520 \, a^{3} d}"," ",0,"-1/2520*(280*cos(d*x + c)^9 - 945*cos(d*x + c)^8 + 720*cos(d*x + c)^7 + 840*cos(d*x + c)^6 - 1512*cos(d*x + c)^5 + 630*cos(d*x + c)^4)/(a^3*d)","A",0
93,1,49,0,0.322030," ","integrate(sin(d*x+c)^7/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{20 \, \cos\left(d x + c\right)^{7} - 70 \, \cos\left(d x + c\right)^{6} + 84 \, \cos\left(d x + c\right)^{5} - 35 \, \cos\left(d x + c\right)^{4}}{140 \, a^{3} d}"," ",0,"1/140*(20*cos(d*x + c)^7 - 70*cos(d*x + c)^6 + 84*cos(d*x + c)^5 - 35*cos(d*x + c)^4)/(a^3*d)","A",0
94,1,73,0,0.331208," ","integrate(sin(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{12 \, \cos\left(d x + c\right)^{5} - 45 \, \cos\left(d x + c\right)^{4} + 80 \, \cos\left(d x + c\right)^{3} - 120 \, \cos\left(d x + c\right)^{2} + 240 \, \cos\left(d x + c\right)}{a^{3}} - \frac{240 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}}}{60 \, d}"," ",0,"-1/60*((12*cos(d*x + c)^5 - 45*cos(d*x + c)^4 + 80*cos(d*x + c)^3 - 120*cos(d*x + c)^2 + 240*cos(d*x + c))/a^3 - 240*log(cos(d*x + c) + 1)/a^3)/d","A",0
95,1,72,0,0.338763," ","integrate(sin(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{12}{a^{3} \cos\left(d x + c\right) + a^{3}} - \frac{2 \, \cos\left(d x + c\right)^{3} - 9 \, \cos\left(d x + c\right)^{2} + 30 \, \cos\left(d x + c\right)}{a^{3}} + \frac{42 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}}}{6 \, d}"," ",0,"-1/6*(12/(a^3*cos(d*x + c) + a^3) - (2*cos(d*x + c)^3 - 9*cos(d*x + c)^2 + 30*cos(d*x + c))/a^3 + 42*log(cos(d*x + c) + 1)/a^3)/d","A",0
96,1,71,0,0.510617," ","integrate(sin(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{6 \, \cos\left(d x + c\right) + 5}{a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} \cos\left(d x + c\right) + a^{3}} - \frac{2 \, \cos\left(d x + c\right)}{a^{3}} + \frac{6 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*((6*cos(d*x + c) + 5)/(a^3*cos(d*x + c)^2 + 2*a^3*cos(d*x + c) + a^3) - 2*cos(d*x + c)/a^3 + 6*log(cos(d*x + c) + 1)/a^3)/d","A",0
97,1,98,0,0.323589," ","integrate(csc(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(21 \, \cos\left(d x + c\right)^{2} + 27 \, \cos\left(d x + c\right) + 10\right)}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}} + \frac{3 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}} - \frac{3 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{3}}}{48 \, d}"," ",0,"-1/48*(2*(21*cos(d*x + c)^2 + 27*cos(d*x + c) + 10)/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3) + 3*log(cos(d*x + c) + 1)/a^3 - 3*log(cos(d*x + c) - 1)/a^3)/d","A",0
98,1,146,0,0.398899," ","integrate(csc(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{4} + 9 \, \cos\left(d x + c\right)^{3} - 25 \, \cos\left(d x + c\right)^{2} - 27 \, \cos\left(d x + c\right) - 8\right)}}{a^{3} \cos\left(d x + c\right)^{5} + 3 \, a^{3} \cos\left(d x + c\right)^{4} + 2 \, a^{3} \cos\left(d x + c\right)^{3} - 2 \, a^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{3} \cos\left(d x + c\right) - a^{3}} - \frac{3 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}} + \frac{3 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{3}}}{192 \, d}"," ",0,"-1/192*(2*(3*cos(d*x + c)^4 + 9*cos(d*x + c)^3 - 25*cos(d*x + c)^2 - 27*cos(d*x + c) - 8)/(a^3*cos(d*x + c)^5 + 3*a^3*cos(d*x + c)^4 + 2*a^3*cos(d*x + c)^3 - 2*a^3*cos(d*x + c)^2 - 3*a^3*cos(d*x + c) - a^3) - 3*log(cos(d*x + c) + 1)/a^3 + 3*log(cos(d*x + c) - 1)/a^3)/d","A",0
99,1,188,0,0.379559," ","integrate(csc(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{6} + 45 \, \cos\left(d x + c\right)^{5} + 20 \, \cos\left(d x + c\right)^{4} - 60 \, \cos\left(d x + c\right)^{3} + 61 \, \cos\left(d x + c\right)^{2} + 63 \, \cos\left(d x + c\right) + 16\right)}}{a^{3} \cos\left(d x + c\right)^{7} + 3 \, a^{3} \cos\left(d x + c\right)^{6} + a^{3} \cos\left(d x + c\right)^{5} - 5 \, a^{3} \cos\left(d x + c\right)^{4} - 5 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}} - \frac{15 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}} + \frac{15 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{3}}}{1280 \, d}"," ",0,"-1/1280*(2*(15*cos(d*x + c)^6 + 45*cos(d*x + c)^5 + 20*cos(d*x + c)^4 - 60*cos(d*x + c)^3 + 61*cos(d*x + c)^2 + 63*cos(d*x + c) + 16)/(a^3*cos(d*x + c)^7 + 3*a^3*cos(d*x + c)^6 + a^3*cos(d*x + c)^5 - 5*a^3*cos(d*x + c)^4 - 5*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3) - 15*log(cos(d*x + c) + 1)/a^3 + 15*log(cos(d*x + c) - 1)/a^3)/d","A",0
100,1,378,0,0.450120," ","integrate(sin(d*x+c)^8/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{3045 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{23345 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{77749 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{146537 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{218007 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{36939 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{120015 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{3045 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}}{a^{3} + \frac{8 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{56 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{56 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{8 \, a^{3} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a^{3} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}} - \frac{3045 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{6720 \, d}"," ",0,"1/6720*((3045*sin(d*x + c)/(cos(d*x + c) + 1) + 23345*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 77749*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 146537*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 218007*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 36939*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 120015*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 3045*sin(d*x + c)^15/(cos(d*x + c) + 1)^15)/(a^3 + 8*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 56*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 56*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 8*a^3*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a^3*sin(d*x + c)^16/(cos(d*x + c) + 1)^16) - 3045*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
101,1,292,0,0.499606," ","integrate(sin(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{345 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{1955 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4554 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5814 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3165 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{1575 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} - \frac{345 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{120 \, d}"," ",0,"1/120*((345*sin(d*x + c)/(cos(d*x + c) + 1) + 1955*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4554*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5814*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3165*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 1575*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/(a^3 + 6*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) - 345*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
102,1,227,0,0.504344," ","integrate(sin(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{123 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{149 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{77 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{3} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{51 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{16 \, \sin\left(d x + c\right)}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}}{4 \, d}"," ",0,"-1/4*((35*sin(d*x + c)/(cos(d*x + c) + 1) + 123*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 149*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 77*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^3 + 4*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 51*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + 16*sin(d*x + c)/(a^3*(cos(d*x + c) + 1)))/d","B",0
103,1,164,0,0.587401," ","integrate(sin(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{18 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{3}} - \frac{33 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{3 \, d}"," ",0,"1/3*(3*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (18*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^3 - 33*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","A",0
104,1,90,0,0.399672," ","integrate(csc(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{70 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{14 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{3}} + \frac{35 \, {\left(\cos\left(d x + c\right) + 1\right)}}{a^{3} \sin\left(d x + c\right)}}{560 \, d}"," ",0,"-1/560*((70*sin(d*x + c)/(cos(d*x + c) + 1) - 14*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^3 + 35*(cos(d*x + c) + 1)/(a^3*sin(d*x + c)))/d","A",0
105,1,92,0,0.396346," ","integrate(csc(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{135 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{27 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{3}} + \frac{15 \, {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{a^{3} \sin\left(d x + c\right)^{3}}}{2880 \, d}"," ",0,"-1/2880*((135*sin(d*x + c)/(cos(d*x + c) + 1) - 27*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^3 + 15*(cos(d*x + c) + 1)^3/(a^3*sin(d*x + c)^3))/d","A",0
106,1,174,0,0.564439," ","integrate(csc(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{20790 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4158 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{990 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{770 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{315 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{a^{3}} + \frac{231 \, {\left(\frac{10 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{30 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a^{3} \sin\left(d x + c\right)^{5}}}{887040 \, d}"," ",0,"-1/887040*((20790*sin(d*x + c)/(cos(d*x + c) + 1) - 4158*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 990*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 770*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 315*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/a^3 + 231*(10*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 30*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3)*(cos(d*x + c) + 1)^5/(a^3*sin(d*x + c)^5))/d","A",0
107,1,214,0,0.589819," ","integrate(csc(d*x+c)^8/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{210210 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{42042 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{17160 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{5005 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{5460 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{1155 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}}{a^{3}} + \frac{429 \, {\left(\frac{28 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{280 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 5\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{7}}{a^{3} \sin\left(d x + c\right)^{7}}}{15375360 \, d}"," ",0,"-1/15375360*((210210*sin(d*x + c)/(cos(d*x + c) + 1) - 42042*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 17160*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 5005*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 5460*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 1155*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)/a^3 + 429*(28*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 35*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 280*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5)*(cos(d*x + c) + 1)^7/(a^3*sin(d*x + c)^7))/d","A",0
108,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*(e*sin(d*x + c))^(5/2), x)","F",0
109,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*(e*sin(d*x + c))^(3/2), x)","F",0
110,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sqrt(e*sin(d*x + c)), x)","F",0
111,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sqrt(e*sin(d*x + c)), x)","F",0
112,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*(e*sin(d*x + c))^(3/2), x)","F",0
116,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{e \sin\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sqrt(e*sin(d*x + c)), x)","F",0
117,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(7/2)/(a*sec(d*x + c) + a), x)","F",0
121,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(5/2)/(a*sec(d*x + c) + a), x)","F",0
122,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(3/2)/(a*sec(d*x + c) + a), x)","F",0
123,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
124,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sqrt(e*sin(d*x + c))), x)","F",0
125,-1,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
130,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
131,-1,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*(e*sin(d*x + c))^m, x)","F",0
135,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*(e*sin(d*x + c))^m, x)","F",0
136,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
137,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(a*sec(d*x + c) + a), x)","F",0
138,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(a*sec(d*x + c) + a)^2, x)","F",0
139,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(a*sec(d*x + c) + a)^3, x)","F",0
140,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*(e*sin(d*x + c))^m, x)","F",0
141,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
142,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/sqrt(a*sec(d*x + c) + a), x)","F",0
143,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(a*sec(d*x + c) + a)^(3/2), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*(e*sin(d*x + c))^m, x)","F",0
145,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^7,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^7, x)","F",0
146,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^5, x)","F",0
147,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^3, x)","F",0
148,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
149,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sec(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*csc(d*x + c), x)","F",0
150,0,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+a*sec(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*csc(d*x + c)^3, x)","F",0
151,0,0,0,0.000000," ","integrate(csc(d*x+c)^5*(a+a*sec(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*csc(d*x + c)^5, x)","F",0
152,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^4, x)","F",0
153,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^2, x)","F",0
154,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sec(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
155,0,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+a*sec(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*csc(d*x + c)^4, x)","F",0
156,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sin(d*x + c)^(3/2), x)","F",0
157,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*sin(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\sin\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sqrt(sin(d*x + c)), x)","F",0
158,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n/sin(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{n}}{\sqrt{\sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n/sqrt(sin(d*x + c)), x)","F",0
159,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n/sin(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{n}}{\sin\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n/sin(d*x + c)^(3/2), x)","F",0
160,1,91,0,0.338131," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^7,x, algorithm=""maxima"")","\frac{60 \, a \cos\left(d x + c\right)^{7} + 70 \, b \cos\left(d x + c\right)^{6} - 252 \, a \cos\left(d x + c\right)^{5} - 315 \, b \cos\left(d x + c\right)^{4} + 420 \, a \cos\left(d x + c\right)^{3} + 630 \, b \cos\left(d x + c\right)^{2} - 420 \, a \cos\left(d x + c\right) - 420 \, b \log\left(\cos\left(d x + c\right)\right)}{420 \, d}"," ",0,"1/420*(60*a*cos(d*x + c)^7 + 70*b*cos(d*x + c)^6 - 252*a*cos(d*x + c)^5 - 315*b*cos(d*x + c)^4 + 420*a*cos(d*x + c)^3 + 630*b*cos(d*x + c)^2 - 420*a*cos(d*x + c) - 420*b*log(cos(d*x + c)))/d","A",0
161,1,69,0,0.451396," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^5,x, algorithm=""maxima"")","-\frac{12 \, a \cos\left(d x + c\right)^{5} + 15 \, b \cos\left(d x + c\right)^{4} - 40 \, a \cos\left(d x + c\right)^{3} - 60 \, b \cos\left(d x + c\right)^{2} + 60 \, a \cos\left(d x + c\right) + 60 \, b \log\left(\cos\left(d x + c\right)\right)}{60 \, d}"," ",0,"-1/60*(12*a*cos(d*x + c)^5 + 15*b*cos(d*x + c)^4 - 40*a*cos(d*x + c)^3 - 60*b*cos(d*x + c)^2 + 60*a*cos(d*x + c) + 60*b*log(cos(d*x + c)))/d","A",0
162,1,47,0,0.510676," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^3,x, algorithm=""maxima"")","\frac{2 \, a \cos\left(d x + c\right)^{3} + 3 \, b \cos\left(d x + c\right)^{2} - 6 \, a \cos\left(d x + c\right) - 6 \, b \log\left(\cos\left(d x + c\right)\right)}{6 \, d}"," ",0,"1/6*(2*a*cos(d*x + c)^3 + 3*b*cos(d*x + c)^2 - 6*a*cos(d*x + c) - 6*b*log(cos(d*x + c)))/d","A",0
163,1,23,0,0.437872," ","integrate((a+b*sec(d*x+c))*sin(d*x+c),x, algorithm=""maxima"")","-\frac{a \cos\left(d x + c\right) + b \log\left(\cos\left(d x + c\right)\right)}{d}"," ",0,"-(a*cos(d*x + c) + b*log(cos(d*x + c)))/d","A",0
164,1,45,0,0.548419," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(a - b\right)} \log\left(\cos\left(d x + c\right) + 1\right) - {\left(a + b\right)} \log\left(\cos\left(d x + c\right) - 1\right) + 2 \, b \log\left(\cos\left(d x + c\right)\right)}{2 \, d}"," ",0,"-1/2*((a - b)*log(cos(d*x + c) + 1) - (a + b)*log(cos(d*x + c) - 1) + 2*b*log(cos(d*x + c)))/d","A",0
165,1,71,0,0.396601," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(a - 2 \, b\right)} \log\left(\cos\left(d x + c\right) + 1\right) - {\left(a + 2 \, b\right)} \log\left(\cos\left(d x + c\right) - 1\right) + 4 \, b \log\left(\cos\left(d x + c\right)\right) - \frac{2 \, {\left(a \cos\left(d x + c\right) + b\right)}}{\cos\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"-1/4*((a - 2*b)*log(cos(d*x + c) + 1) - (a + 2*b)*log(cos(d*x + c) - 1) + 4*b*log(cos(d*x + c)) - 2*(a*cos(d*x + c) + b)/(cos(d*x + c)^2 - 1))/d","A",0
166,1,110,0,0.673764," ","integrate(csc(d*x+c)^5*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(3 \, a - 8 \, b\right)} \log\left(\cos\left(d x + c\right) + 1\right) - {\left(3 \, a + 8 \, b\right)} \log\left(\cos\left(d x + c\right) - 1\right) + 16 \, b \log\left(\cos\left(d x + c\right)\right) - \frac{2 \, {\left(3 \, a \cos\left(d x + c\right)^{3} + 4 \, b \cos\left(d x + c\right)^{2} - 5 \, a \cos\left(d x + c\right) - 6 \, b\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*((3*a - 8*b)*log(cos(d*x + c) + 1) - (3*a + 8*b)*log(cos(d*x + c) - 1) + 16*b*log(cos(d*x + c)) - 2*(3*a*cos(d*x + c)^3 + 4*b*cos(d*x + c)^2 - 5*a*cos(d*x + c) - 6*b)/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1))/d","A",0
167,1,143,0,0.345639," ","integrate(csc(d*x+c)^7*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, {\left(5 \, a - 16 \, b\right)} \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, a + 16 \, b\right)} \log\left(\cos\left(d x + c\right) - 1\right) + 96 \, b \log\left(\cos\left(d x + c\right)\right) - \frac{2 \, {\left(15 \, a \cos\left(d x + c\right)^{5} + 24 \, b \cos\left(d x + c\right)^{4} - 40 \, a \cos\left(d x + c\right)^{3} - 60 \, b \cos\left(d x + c\right)^{2} + 33 \, a \cos\left(d x + c\right) + 44 \, b\right)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1}}{96 \, d}"," ",0,"-1/96*(3*(5*a - 16*b)*log(cos(d*x + c) + 1) - 3*(5*a + 16*b)*log(cos(d*x + c) - 1) + 96*b*log(cos(d*x + c)) - 2*(15*a*cos(d*x + c)^5 + 24*b*cos(d*x + c)^4 - 40*a*cos(d*x + c)^3 - 60*b*cos(d*x + c)^2 + 33*a*cos(d*x + c) + 44*b)/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1))/d","A",0
168,1,106,0,0.333294," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^6,x, algorithm=""maxima"")","\frac{5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a - 32 \, {\left(6 \, \sin\left(d x + c\right)^{5} + 10 \, \sin\left(d x + c\right)^{3} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 30 \, \sin\left(d x + c\right)\right)} b}{960 \, d}"," ",0,"1/960*(5*(4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a - 32*(6*sin(d*x + c)^5 + 10*sin(d*x + c)^3 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 30*sin(d*x + c))*b)/d","A",0
169,1,81,0,0.474569," ","integrate((a+b*sec(d*x+c))*sin(d*x+c)^4,x, algorithm=""maxima"")","\frac{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 - 16 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} b}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*a - 16*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*b)/d","A",0
170,1,59,0,0.686536," ","integrate((a+b*sec(d*x+c))*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 \, b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c - sin(2*d*x + 2*c))*a + 2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)))/d","A",0
171,1,50,0,0.536055," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{b {\left(\frac{2}{\sin\left(d x + c\right)} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{2 \, a}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(b*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*a/tan(d*x + c))/d","A",0
172,1,76,0,0.664869," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 1\right)}}{\sin\left(d x + c\right)^{3}} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{2 \, {\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} a}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(b*(2*(3*sin(d*x + c)^2 + 1)/sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 2*(3*tan(d*x + c)^2 + 1)*a/tan(d*x + c)^3)/d","A",0
173,1,96,0,0.324215," ","integrate(csc(d*x+c)^6*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{b {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} + 3\right)}}{\sin\left(d x + c\right)^{5}} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{2 \, {\left(15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} + 3\right)} a}{\tan\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"-1/30*(b*(2*(15*sin(d*x + c)^4 + 5*sin(d*x + c)^2 + 3)/sin(d*x + c)^5 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 2*(15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 + 3)*a/tan(d*x + c)^5)/d","A",0
174,1,105,0,0.419335," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^5,x, algorithm=""maxima"")","-\frac{6 \, a^{2} \cos\left(d x + c\right)^{5} + 15 \, a b \cos\left(d x + c\right)^{4} - 60 \, a b \cos\left(d x + c\right)^{2} - 10 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{3} + 60 \, a b \log\left(\cos\left(d x + c\right)\right) + 30 \, {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right) - \frac{30 \, b^{2}}{\cos\left(d x + c\right)}}{30 \, d}"," ",0,"-1/30*(6*a^2*cos(d*x + c)^5 + 15*a*b*cos(d*x + c)^4 - 60*a*b*cos(d*x + c)^2 - 10*(2*a^2 - b^2)*cos(d*x + c)^3 + 60*a*b*log(cos(d*x + c)) + 30*(a^2 - 2*b^2)*cos(d*x + c) - 30*b^2/cos(d*x + c))/d","A",0
175,1,71,0,0.349487," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^3,x, algorithm=""maxima"")","\frac{a^{2} \cos\left(d x + c\right)^{3} + 3 \, a b \cos\left(d x + c\right)^{2} - 6 \, a b \log\left(\cos\left(d x + c\right)\right) - 3 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right) + \frac{3 \, b^{2}}{\cos\left(d x + c\right)}}{3 \, d}"," ",0,"1/3*(a^2*cos(d*x + c)^3 + 3*a*b*cos(d*x + c)^2 - 6*a*b*log(cos(d*x + c)) - 3*(a^2 - b^2)*cos(d*x + c) + 3*b^2/cos(d*x + c))/d","A",0
176,1,40,0,0.627571," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c),x, algorithm=""maxima"")","-\frac{a^{2} \cos\left(d x + c\right) + 2 \, a b \log\left(\cos\left(d x + c\right)\right) - \frac{b^{2}}{\cos\left(d x + c\right)}}{d}"," ",0,"-(a^2*cos(d*x + c) + 2*a*b*log(cos(d*x + c)) - b^2/cos(d*x + c))/d","A",0
177,1,73,0,0.740125," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4 \, a b \log\left(\cos\left(d x + c\right)\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} \log\left(\cos\left(d x + c\right) + 1\right) - {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, b^{2}}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(4*a*b*log(cos(d*x + c)) + (a^2 - 2*a*b + b^2)*log(cos(d*x + c) + 1) - (a^2 + 2*a*b + b^2)*log(cos(d*x + c) - 1) - 2*b^2/cos(d*x + c))/d","A",0
178,1,119,0,0.672123," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{8 \, a b \log\left(\cos\left(d x + c\right)\right) + {\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} \log\left(\cos\left(d x + c\right) + 1\right) - {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, {\left(2 \, a b \cos\left(d x + c\right) + {\left(a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, b^{2}\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(8*a*b*log(cos(d*x + c)) + (a^2 - 4*a*b + 3*b^2)*log(cos(d*x + c) + 1) - (a^2 + 4*a*b + 3*b^2)*log(cos(d*x + c) - 1) - 2*(2*a*b*cos(d*x + c) + (a^2 + 3*b^2)*cos(d*x + c)^2 - 2*b^2)/(cos(d*x + c)^3 - cos(d*x + c)))/d","A",0
179,1,173,0,0.808345," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^6,x, algorithm=""maxima"")","\frac{5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 64 \, {\left(6 \, \sin\left(d x + c\right)^{5} + 10 \, \sin\left(d x + c\right)^{3} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 30 \, \sin\left(d x + c\right)\right)} a b - 120 \, {\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)} b^{2}}{960 \, d}"," ",0,"1/960*(5*(4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^2 - 64*(6*sin(d*x + c)^5 + 10*sin(d*x + c)^3 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 30*sin(d*x + c))*a*b - 120*(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))*b^2)/d","A",0
180,1,125,0,0.883091," ","integrate((a+b*sec(d*x+c))^2*sin(d*x+c)^4,x, algorithm=""maxima"")","\frac{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^{2} - 32 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a b - 48 \, {\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}}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*a^2 - 32*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a*b - 48*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*b^2)/d","A",0
181,1,80,0,0.910468," ","integrate((a+b*sec(d*x+c))^2*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 - \tan\left(d x + c\right)\right)} b^{2} + 4 \, a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c - sin(2*d*x + 2*c))*a^2 - 4*(d*x + c - tan(d*x + c))*b^2 + 4*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)))/d","A",0
182,1,73,0,0.540707," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a b {\left(\frac{2}{\sin\left(d x + c\right)} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + b^{2} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} + \frac{a^{2}}{\tan\left(d x + c\right)}}{d}"," ",0,"-(a*b*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + b^2*(1/tan(d*x + c) - tan(d*x + c)) + a^2/tan(d*x + c))/d","A",0
183,1,112,0,0.745501," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 1\right)}}{\sin\left(d x + c\right)^{3}} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + b^{2} {\left(\frac{6 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{3}} - 3 \, \tan\left(d x + c\right)\right)} + \frac{{\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} a^{2}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"-1/3*(a*b*(2*(3*sin(d*x + c)^2 + 1)/sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + b^2*((6*tan(d*x + c)^2 + 1)/tan(d*x + c)^3 - 3*tan(d*x + c)) + (3*tan(d*x + c)^2 + 1)*a^2/tan(d*x + c)^3)/d","A",0
184,1,143,0,0.713564," ","integrate(csc(d*x+c)^6*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a b {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} + 3\right)}}{\sin\left(d x + c\right)^{5}} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 3 \, b^{2} {\left(\frac{15 \, \tan\left(d x + c\right)^{4} + 5 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{5}} - 5 \, \tan\left(d x + c\right)\right)} + \frac{{\left(15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{2}}{\tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*(a*b*(2*(15*sin(d*x + c)^4 + 5*sin(d*x + c)^2 + 3)/sin(d*x + c)^5 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 3*b^2*((15*tan(d*x + c)^4 + 5*tan(d*x + c)^2 + 1)/tan(d*x + c)^5 - 5*tan(d*x + c)) + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 + 3)*a^2/tan(d*x + c)^5)/d","A",0
185,1,142,0,0.336216," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^5,x, algorithm=""maxima"")","-\frac{12 \, a^{3} \cos\left(d x + c\right)^{5} + 45 \, a^{2} b \cos\left(d x + c\right)^{4} - 20 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(6 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 60 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cos\left(d x + c\right) + 60 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \log\left(\cos\left(d x + c\right)\right) - \frac{30 \, {\left(6 \, a b^{2} \cos\left(d x + c\right) + b^{3}\right)}}{\cos\left(d x + c\right)^{2}}}{60 \, d}"," ",0,"-1/60*(12*a^3*cos(d*x + c)^5 + 45*a^2*b*cos(d*x + c)^4 - 20*(2*a^3 - 3*a*b^2)*cos(d*x + c)^3 - 30*(6*a^2*b - b^3)*cos(d*x + c)^2 + 60*(a^3 - 6*a*b^2)*cos(d*x + c) + 60*(3*a^2*b - 2*b^3)*log(cos(d*x + c)) - 30*(6*a*b^2*cos(d*x + c) + b^3)/cos(d*x + c)^2)/d","A",0
186,1,98,0,0.606808," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^3,x, algorithm=""maxima"")","\frac{2 \, a^{3} \cos\left(d x + c\right)^{3} + 9 \, a^{2} b \cos\left(d x + c\right)^{2} - 6 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right) - 6 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\cos\left(d x + c\right)\right) + \frac{3 \, {\left(6 \, a b^{2} \cos\left(d x + c\right) + b^{3}\right)}}{\cos\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"1/6*(2*a^3*cos(d*x + c)^3 + 9*a^2*b*cos(d*x + c)^2 - 6*(a^3 - 3*a*b^2)*cos(d*x + c) - 6*(3*a^2*b - b^3)*log(cos(d*x + c)) + 3*(6*a*b^2*cos(d*x + c) + b^3)/cos(d*x + c)^2)/d","A",0
187,1,57,0,1.184921," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c),x, algorithm=""maxima"")","-\frac{2 \, a^{3} \cos\left(d x + c\right) + 6 \, a^{2} b \log\left(\cos\left(d x + c\right)\right) - \frac{6 \, a b^{2}}{\cos\left(d x + c\right)} - \frac{b^{3}}{\cos\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*a^3*cos(d*x + c) + 6*a^2*b*log(cos(d*x + c)) - 6*a*b^2/cos(d*x + c) - b^3/cos(d*x + c)^2)/d","A",0
188,1,112,0,0.498658," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \log\left(\cos\left(d x + c\right) + 1\right) - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(\cos\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} \log\left(\cos\left(d x + c\right)\right) - \frac{6 \, a b^{2} \cos\left(d x + c\right) + b^{3}}{\cos\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*log(cos(d*x + c) + 1) - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*log(cos(d*x + c) - 1) + 2*(3*a^2*b + b^3)*log(cos(d*x + c)) - (6*a*b^2*cos(d*x + c) + b^3)/cos(d*x + c)^2)/d","A",0
189,1,171,0,0.707772," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(a^{3} - 6 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \log\left(\cos\left(d x + c\right) + 1\right) - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \log\left(\cos\left(d x + c\right) - 1\right) + 4 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \log\left(\cos\left(d x + c\right)\right) + \frac{2 \, {\left(6 \, a b^{2} \cos\left(d x + c\right) - {\left(a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + b^{3} - {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)}}{\cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{2}}}{4 \, d}"," ",0,"-1/4*((a^3 - 6*a^2*b + 9*a*b^2 - 4*b^3)*log(cos(d*x + c) + 1) - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*log(cos(d*x + c) - 1) + 4*(3*a^2*b + 2*b^3)*log(cos(d*x + c)) + 2*(6*a*b^2*cos(d*x + c) - (a^3 + 9*a*b^2)*cos(d*x + c)^3 + b^3 - (3*a^2*b + 2*b^3)*cos(d*x + c)^2)/(cos(d*x + c)^4 - cos(d*x + c)^2))/d","A",0
190,1,242,0,0.914258," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^6,x, algorithm=""maxima"")","\frac{5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 96 \, {\left(6 \, \sin\left(d x + c\right)^{5} + 10 \, \sin\left(d x + c\right)^{3} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 30 \, \sin\left(d x + c\right)\right)} a^{2} b - 360 \, {\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 b^{2} + 80 \, {\left(4 \, \sin\left(d x + c\right)^{3} - \frac{6 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 24 \, \sin\left(d x + c\right)\right)} b^{3}}{960 \, d}"," ",0,"1/960*(5*(4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^3 - 96*(6*sin(d*x + c)^5 + 10*sin(d*x + c)^3 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 30*sin(d*x + c))*a^2*b - 360*(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*b^2 + 80*(4*sin(d*x + c)^3 - 6*sin(d*x + c)/(sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 24*sin(d*x + c))*b^3)/d","A",0
191,1,183,0,0.726521," ","integrate((a+b*sec(d*x+c))^3*sin(d*x+c)^4,x, algorithm=""maxima"")","\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^{3} - 16 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a^{2} b - 48 \, {\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} - 8 \, b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + 3 \, \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \log\left(\sin\left(d x + c\right) - 1\right) - 4 \, \sin\left(d x + c\right)\right)}}{32 \, d}"," ",0,"1/32*((12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*a^3 - 16*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a^2*b - 48*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a*b^2 - 8*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1) - 4*sin(d*x + c)))/d","A",0
192,1,129,0,1.036363," ","integrate((a+b*sec(d*x+c))^3*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^{3} - 12 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a b^{2} - b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c - sin(2*d*x + 2*c))*a^3 - 12*(d*x + c - tan(d*x + c))*a*b^2 - b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)))/d","A",0
193,1,139,0,0.865244," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 2\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{2} b {\left(\frac{2}{\sin\left(d x + c\right)} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a b^{2} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} + \frac{4 \, a^{3}}{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(b^3*(2*(3*sin(d*x + c)^2 - 2)/(sin(d*x + c)^3 - sin(d*x + c)) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 6*a^2*b*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*a*b^2*(1/tan(d*x + c) - tan(d*x + c)) + 4*a^3/tan(d*x + c))/d","A",0
194,1,190,0,1.563728," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{b^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} - 10 \, \sin\left(d x + c\right)^{2} - 2\right)}}{\sin\left(d x + c\right)^{5} - \sin\left(d x + c\right)^{3}} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{2} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 1\right)}}{\sin\left(d x + c\right)^{3}} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a b^{2} {\left(\frac{6 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{3}} - 3 \, \tan\left(d x + c\right)\right)} + \frac{4 \, {\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} a^{3}}{\tan\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(b^3*(2*(15*sin(d*x + c)^4 - 10*sin(d*x + c)^2 - 2)/(sin(d*x + c)^5 - sin(d*x + c)^3) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 6*a^2*b*(2*(3*sin(d*x + c)^2 + 1)/sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 12*a*b^2*((6*tan(d*x + c)^2 + 1)/tan(d*x + c)^3 - 3*tan(d*x + c)) + 4*(3*tan(d*x + c)^2 + 1)*a^3/tan(d*x + c)^3)/d","A",0
195,1,230,0,0.802245," ","integrate(csc(d*x+c)^6*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{b^{3} {\left(\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{6} - 70 \, \sin\left(d x + c\right)^{4} - 14 \, \sin\left(d x + c\right)^{2} - 6\right)}}{\sin\left(d x + c\right)^{7} - \sin\left(d x + c\right)^{5}} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{2} b {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} + 3\right)}}{\sin\left(d x + c\right)^{5}} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, a b^{2} {\left(\frac{15 \, \tan\left(d x + c\right)^{4} + 5 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{5}} - 5 \, \tan\left(d x + c\right)\right)} + \frac{4 \, {\left(15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{3}}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(b^3*(2*(105*sin(d*x + c)^6 - 70*sin(d*x + c)^4 - 14*sin(d*x + c)^2 - 6)/(sin(d*x + c)^7 - sin(d*x + c)^5) - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1)) + 6*a^2*b*(2*(15*sin(d*x + c)^4 + 5*sin(d*x + c)^2 + 3)/sin(d*x + c)^5 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 36*a*b^2*((15*tan(d*x + c)^4 + 5*tan(d*x + c)^2 + 1)/tan(d*x + c)^5 - 5*tan(d*x + c)) + 4*(15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 + 3)*a^3/tan(d*x + c)^5)/d","A",0
196,1,224,0,0.584959," ","integrate(sin(d*x+c)^7/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{60 \, a^{6} \cos\left(d x + c\right)^{7} - 70 \, a^{5} b \cos\left(d x + c\right)^{6} - 84 \, {\left(3 \, a^{6} - a^{4} b^{2}\right)} \cos\left(d x + c\right)^{5} + 105 \, {\left(3 \, a^{5} b - a^{3} b^{3}\right)} \cos\left(d x + c\right)^{4} + 140 \, {\left(3 \, a^{6} - 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} - 210 \, {\left(3 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{2} - 420 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)}{a^{7}} + \frac{420 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{8}}}{420 \, d}"," ",0,"1/420*((60*a^6*cos(d*x + c)^7 - 70*a^5*b*cos(d*x + c)^6 - 84*(3*a^6 - a^4*b^2)*cos(d*x + c)^5 + 105*(3*a^5*b - a^3*b^3)*cos(d*x + c)^4 + 140*(3*a^6 - 3*a^4*b^2 + a^2*b^4)*cos(d*x + c)^3 - 210*(3*a^5*b - 3*a^3*b^3 + a*b^5)*cos(d*x + c)^2 - 420*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cos(d*x + c))/a^7 + 420*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*log(a*cos(d*x + c) + b)/a^8)/d","A",0
197,1,141,0,0.723701," ","integrate(sin(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{12 \, a^{4} \cos\left(d x + c\right)^{5} - 15 \, a^{3} b \cos\left(d x + c\right)^{4} - 20 \, {\left(2 \, a^{4} - a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + 30 \, {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{2} + 60 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)}{a^{5}} - \frac{60 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{6}}}{60 \, d}"," ",0,"-1/60*((12*a^4*cos(d*x + c)^5 - 15*a^3*b*cos(d*x + c)^4 - 20*(2*a^4 - a^2*b^2)*cos(d*x + c)^3 + 30*(2*a^3*b - a*b^3)*cos(d*x + c)^2 + 60*(a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c))/a^5 - 60*(a^4*b - 2*a^2*b^3 + b^5)*log(a*cos(d*x + c) + b)/a^6)/d","A",0
198,1,80,0,0.583736," ","integrate(sin(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, a^{2} \cos\left(d x + c\right)^{3} - 3 \, a b \cos\left(d x + c\right)^{2} - 6 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)}{a^{3}} + \frac{6 \, {\left(a^{2} b - b^{3}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{4}}}{6 \, d}"," ",0,"1/6*((2*a^2*cos(d*x + c)^3 - 3*a*b*cos(d*x + c)^2 - 6*(a^2 - b^2)*cos(d*x + c))/a^3 + 6*(a^2*b - b^3)*log(a*cos(d*x + c) + b)/a^4)/d","A",0
199,1,33,0,0.529438," ","integrate(sin(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\cos\left(d x + c\right)}{a} - \frac{b \log\left(a \cos\left(d x + c\right) + b\right)}{a^{2}}}{d}"," ",0,"-(cos(d*x + c)/a - b*log(a*cos(d*x + c) + b)/a^2)/d","A",0
200,1,64,0,0.749119," ","integrate(csc(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, b \log\left(a \cos\left(d x + c\right) + b\right)}{a^{2} - b^{2}} - \frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a - b} + \frac{\log\left(\cos\left(d x + c\right) - 1\right)}{a + b}}{2 \, d}"," ",0,"1/2*(2*b*log(a*cos(d*x + c) + b)/(a^2 - b^2) - log(cos(d*x + c) + 1)/(a - b) + log(cos(d*x + c) - 1)/(a + b))/d","A",0
201,1,132,0,0.733948," ","integrate(csc(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{4 \, a^{2} b \log\left(a \cos\left(d x + c\right) + b\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{a \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{a \log\left(\cos\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(a \cos\left(d x + c\right) - b\right)}}{{\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + b^{2}}}{4 \, d}"," ",0,"1/4*(4*a^2*b*log(a*cos(d*x + c) + b)/(a^4 - 2*a^2*b^2 + b^4) - a*log(cos(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + a*log(cos(d*x + c) - 1)/(a^2 + 2*a*b + b^2) + 2*(a*cos(d*x + c) - b)/((a^2 - b^2)*cos(d*x + c)^2 - a^2 + b^2))/d","A",0
202,1,268,0,0.817635," ","integrate(csc(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, a^{4} b \log\left(a \cos\left(d x + c\right) + b\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{{\left(3 \, a^{2} - a b\right)} \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(3 \, a^{2} + a b\right)} \log\left(\cos\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left(4 \, a^{2} b \cos\left(d x + c\right)^{2} - {\left(3 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{3} - 6 \, a^{2} b + 2 \, b^{3} + {\left(5 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\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)} \cos\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"1/16*(16*a^4*b*log(a*cos(d*x + c) + b)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (3*a^2 - a*b)*log(cos(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (3*a^2 + a*b)*log(cos(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*(4*a^2*b*cos(d*x + c)^2 - (3*a^3 + a*b^2)*cos(d*x + c)^3 - 6*a^2*b + 2*b^3 + (5*a^3 - a*b^2)*cos(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2))/d","A",0
203,-2,0,0,0.000000," ","integrate(sin(d*x+c)^6/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
204,-2,0,0,0.000000," ","integrate(sin(d*x+c)^4/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
205,-2,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
206,-2,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
207,-2,0,0,0.000000," ","integrate(csc(d*x+c)^4/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
208,-2,0,0,0.000000," ","integrate(csc(d*x+c)^6/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
209,1,271,0,0.785794," ","integrate(sin(d*x+c)^7/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{210 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)}}{a^{10} \cos\left(d x + c\right) + a^{9} b} + \frac{30 \, a^{6} \cos\left(d x + c\right)^{7} - 70 \, a^{5} b \cos\left(d x + c\right)^{6} - 126 \, {\left(a^{6} - a^{4} b^{2}\right)} \cos\left(d x + c\right)^{5} + 105 \, {\left(3 \, a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left(3 \, a^{6} - 9 \, a^{4} b^{2} + 5 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} - 630 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{2} - 210 \, {\left(a^{6} - 9 \, a^{4} b^{2} + 15 \, a^{2} b^{4} - 7 \, b^{6}\right)} \cos\left(d x + c\right)}{a^{8}} + \frac{420 \, {\left(a^{6} b - 6 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 4 \, b^{7}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{9}}}{210 \, d}"," ",0,"1/210*(210*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)/(a^10*cos(d*x + c) + a^9*b) + (30*a^6*cos(d*x + c)^7 - 70*a^5*b*cos(d*x + c)^6 - 126*(a^6 - a^4*b^2)*cos(d*x + c)^5 + 105*(3*a^5*b - 2*a^3*b^3)*cos(d*x + c)^4 + 70*(3*a^6 - 9*a^4*b^2 + 5*a^2*b^4)*cos(d*x + c)^3 - 630*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c)^2 - 210*(a^6 - 9*a^4*b^2 + 15*a^2*b^4 - 7*b^6)*cos(d*x + c))/a^8 + 420*(a^6*b - 6*a^4*b^3 + 9*a^2*b^5 - 4*b^7)*log(a*cos(d*x + c) + b)/a^9)/d","A",0
210,1,184,0,0.419420," ","integrate(sin(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{30 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)}}{a^{8} \cos\left(d x + c\right) + a^{7} b} - \frac{6 \, a^{4} \cos\left(d x + c\right)^{5} - 15 \, a^{3} b \cos\left(d x + c\right)^{4} - 10 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + 60 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 5 \, b^{4}\right)} \cos\left(d x + c\right)}{a^{6}} + \frac{60 \, {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{7}}}{30 \, d}"," ",0,"1/30*(30*(a^4*b^2 - 2*a^2*b^4 + b^6)/(a^8*cos(d*x + c) + a^7*b) - (6*a^4*cos(d*x + c)^5 - 15*a^3*b*cos(d*x + c)^4 - 10*(2*a^4 - 3*a^2*b^2)*cos(d*x + c)^3 + 60*(a^3*b - a*b^3)*cos(d*x + c)^2 + 30*(a^4 - 6*a^2*b^2 + 5*b^4)*cos(d*x + c))/a^6 + 60*(a^4*b - 4*a^2*b^3 + 3*b^5)*log(a*cos(d*x + c) + b)/a^7)/d","A",0
211,1,112,0,0.511487," ","integrate(sin(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a^{2} b^{2} - b^{4}\right)}}{a^{6} \cos\left(d x + c\right) + a^{5} b} + \frac{a^{2} \cos\left(d x + c\right)^{3} - 3 \, a b \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)}{a^{4}} + \frac{6 \, {\left(a^{2} b - 2 \, b^{3}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{5}}}{3 \, d}"," ",0,"1/3*(3*(a^2*b^2 - b^4)/(a^6*cos(d*x + c) + a^5*b) + (a^2*cos(d*x + c)^3 - 3*a*b*cos(d*x + c)^2 - 3*(a^2 - 3*b^2)*cos(d*x + c))/a^4 + 6*(a^2*b - 2*b^3)*log(a*cos(d*x + c) + b)/a^5)/d","A",0
212,1,55,0,0.714607," ","integrate(sin(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{b^{2}}{a^{4} \cos\left(d x + c\right) + a^{3} b} - \frac{\cos\left(d x + c\right)}{a^{2}} + \frac{2 \, b \log\left(a \cos\left(d x + c\right) + b\right)}{a^{3}}}{d}"," ",0,"(b^2/(a^4*cos(d*x + c) + a^3*b) - cos(d*x + c)/a^2 + 2*b*log(a*cos(d*x + c) + b)/a^3)/d","A",0
213,1,123,0,0.845197," ","integrate(csc(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, a b \log\left(a \cos\left(d x + c\right) + b\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, b^{2}}{a^{3} b - a b^{3} + {\left(a^{4} - a^{2} b^{2}\right)} \cos\left(d x + c\right)} - \frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{\log\left(\cos\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}}}{2 \, d}"," ",0,"1/2*(4*a*b*log(a*cos(d*x + c) + b)/(a^4 - 2*a^2*b^2 + b^4) + 2*b^2/(a^3*b - a*b^3 + (a^4 - a^2*b^2)*cos(d*x + c)) - log(cos(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + log(cos(d*x + c) - 1)/(a^2 + 2*a*b + b^2))/d","A",0
214,1,274,0,0.799359," ","integrate(csc(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(a^{3} b + a b^{3}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{{\left(a + b\right)} \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(a - b\right)} \log\left(\cos\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(4 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)\right)}}{a^{4} b - 2 \, a^{2} b^{3} + b^{5} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*(8*(a^3*b + a*b^3)*log(a*cos(d*x + c) + b)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (a + b)*log(cos(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (a - b)*log(cos(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(4*a*b^2 - (a^3 + 3*a*b^2)*cos(d*x + c)^2 + (a^2*b - b^3)*cos(d*x + c))/(a^4*b - 2*a^2*b^3 + b^5 - (a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c)^3 - (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^2 + (a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c)))/d","A",0
215,1,511,0,0.729395," ","integrate(csc(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{32 \, {\left(a^{5} b + 2 \, a^{3} b^{3}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{{\left(3 \, a^{2} + 4 \, a b - b^{2}\right)} \log\left(\cos\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(3 \, a^{2} - 4 \, a b - b^{2}\right)} \log\left(\cos\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(20 \, a^{3} b^{2} + 4 \, a b^{4} + {\left(3 \, a^{5} + 20 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{4} - {\left(5 \, a^{4} b - 4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} - {\left(5 \, a^{5} + 36 \, a^{3} b^{2} + 7 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)\right)}}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{5} + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)}}{16 \, d}"," ",0,"1/16*(32*(a^5*b + 2*a^3*b^3)*log(a*cos(d*x + c) + b)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - (3*a^2 + 4*a*b - b^2)*log(cos(d*x + c) + 1)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) + (3*a^2 - 4*a*b - b^2)*log(cos(d*x + c) - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 2*(20*a^3*b^2 + 4*a*b^4 + (3*a^5 + 20*a^3*b^2 + a*b^4)*cos(d*x + c)^4 - (5*a^4*b - 4*a^2*b^3 - b^5)*cos(d*x + c)^3 - (5*a^5 + 36*a^3*b^2 + 7*a*b^4)*cos(d*x + c)^2 + (7*a^4*b - 8*a^2*b^3 + b^5)*cos(d*x + c))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c)^5 + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)^4 - 2*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c)^3 - 2*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)^2 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c)))/d","B",0
216,-2,0,0,0.000000," ","integrate(sin(d*x+c)^6/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
217,-2,0,0,0.000000," ","integrate(sin(d*x+c)^4/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
218,-2,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
219,-2,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
220,-2,0,0,0.000000," ","integrate(csc(d*x+c)^4/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
221,1,326,0,0.920465," ","integrate(sin(d*x+c)^7/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{70 \, {\left(5 \, a^{6} b^{3} - 27 \, a^{4} b^{5} + 39 \, a^{2} b^{7} - 17 \, b^{9} + 6 \, {\left(a^{7} b^{2} - 5 \, a^{5} b^{4} + 7 \, a^{3} b^{6} - 3 \, a b^{8}\right)} \cos\left(d x + c\right)\right)}}{a^{12} \cos\left(d x + c\right)^{2} + 2 \, a^{11} b \cos\left(d x + c\right) + a^{10} b^{2}} + \frac{20 \, a^{6} \cos\left(d x + c\right)^{7} - 70 \, a^{5} b \cos\left(d x + c\right)^{6} - 84 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)^{5} + 35 \, {\left(9 \, a^{5} b - 10 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{4} + 140 \, {\left(a^{6} - 6 \, a^{4} b^{2} + 5 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} - 210 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} - 140 \, {\left(a^{6} - 18 \, a^{4} b^{2} + 45 \, a^{2} b^{4} - 28 \, b^{6}\right)} \cos\left(d x + c\right)}{a^{9}} + \frac{420 \, {\left(a^{6} b - 10 \, a^{4} b^{3} + 21 \, a^{2} b^{5} - 12 \, b^{7}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{10}}}{140 \, d}"," ",0,"1/140*(70*(5*a^6*b^3 - 27*a^4*b^5 + 39*a^2*b^7 - 17*b^9 + 6*(a^7*b^2 - 5*a^5*b^4 + 7*a^3*b^6 - 3*a*b^8)*cos(d*x + c))/(a^12*cos(d*x + c)^2 + 2*a^11*b*cos(d*x + c) + a^10*b^2) + (20*a^6*cos(d*x + c)^7 - 70*a^5*b*cos(d*x + c)^6 - 84*(a^6 - 2*a^4*b^2)*cos(d*x + c)^5 + 35*(9*a^5*b - 10*a^3*b^3)*cos(d*x + c)^4 + 140*(a^6 - 6*a^4*b^2 + 5*a^2*b^4)*cos(d*x + c)^3 - 210*(3*a^5*b - 10*a^3*b^3 + 7*a*b^5)*cos(d*x + c)^2 - 140*(a^6 - 18*a^4*b^2 + 45*a^2*b^4 - 28*b^6)*cos(d*x + c))/a^9 + 420*(a^6*b - 10*a^4*b^3 + 21*a^2*b^5 - 12*b^7)*log(a*cos(d*x + c) + b)/a^10)/d","A",0
222,1,234,0,0.660354," ","integrate(sin(d*x+c)^5/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{30 \, {\left(5 \, a^{4} b^{3} - 18 \, a^{2} b^{5} + 13 \, b^{7} + 2 \, {\left(3 \, a^{5} b^{2} - 10 \, a^{3} b^{4} + 7 \, a b^{6}\right)} \cos\left(d x + c\right)\right)}}{a^{10} \cos\left(d x + c\right)^{2} + 2 \, a^{9} b \cos\left(d x + c\right) + a^{8} b^{2}} - \frac{12 \, a^{4} \cos\left(d x + c\right)^{5} - 45 \, a^{3} b \cos\left(d x + c\right)^{4} - 40 \, {\left(a^{4} - 3 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + 60 \, {\left(3 \, a^{3} b - 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + 60 \, {\left(a^{4} - 12 \, a^{2} b^{2} + 15 \, b^{4}\right)} \cos\left(d x + c\right)}{a^{7}} + \frac{60 \, {\left(3 \, a^{4} b - 20 \, a^{2} b^{3} + 21 \, b^{5}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{8}}}{60 \, d}"," ",0,"1/60*(30*(5*a^4*b^3 - 18*a^2*b^5 + 13*b^7 + 2*(3*a^5*b^2 - 10*a^3*b^4 + 7*a*b^6)*cos(d*x + c))/(a^10*cos(d*x + c)^2 + 2*a^9*b*cos(d*x + c) + a^8*b^2) - (12*a^4*cos(d*x + c)^5 - 45*a^3*b*cos(d*x + c)^4 - 40*(a^4 - 3*a^2*b^2)*cos(d*x + c)^3 + 60*(3*a^3*b - 5*a*b^3)*cos(d*x + c)^2 + 60*(a^4 - 12*a^2*b^2 + 15*b^4)*cos(d*x + c))/a^7 + 60*(3*a^4*b - 20*a^2*b^3 + 21*b^5)*log(a*cos(d*x + c) + b)/a^8)/d","A",0
223,1,154,0,0.873452," ","integrate(sin(d*x+c)^3/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(5 \, a^{2} b^{3} - 9 \, b^{5} + 2 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \cos\left(d x + c\right)\right)}}{a^{8} \cos\left(d x + c\right)^{2} + 2 \, a^{7} b \cos\left(d x + c\right) + a^{6} b^{2}} + \frac{2 \, a^{2} \cos\left(d x + c\right)^{3} - 9 \, a b \cos\left(d x + c\right)^{2} - 6 \, {\left(a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right)}{a^{5}} + \frac{6 \, {\left(3 \, a^{2} b - 10 \, b^{3}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*(3*(5*a^2*b^3 - 9*b^5 + 2*(3*a^3*b^2 - 5*a*b^4)*cos(d*x + c))/(a^8*cos(d*x + c)^2 + 2*a^7*b*cos(d*x + c) + a^6*b^2) + (2*a^2*cos(d*x + c)^3 - 9*a*b*cos(d*x + c)^2 - 6*(a^2 - 6*b^2)*cos(d*x + c))/a^5 + 6*(3*a^2*b - 10*b^3)*log(a*cos(d*x + c) + b)/a^6)/d","A",0
224,1,87,0,0.840086," ","integrate(sin(d*x+c)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{6 \, a b^{2} \cos\left(d x + c\right) + 5 \, b^{3}}{a^{6} \cos\left(d x + c\right)^{2} + 2 \, a^{5} b \cos\left(d x + c\right) + a^{4} b^{2}} - \frac{2 \, \cos\left(d x + c\right)}{a^{3}} + \frac{6 \, b \log\left(a \cos\left(d x + c\right) + b\right)}{a^{4}}}{2 \, d}"," ",0,"1/2*((6*a*b^2*cos(d*x + c) + 5*b^3)/(a^6*cos(d*x + c)^2 + 2*a^5*b*cos(d*x + c) + a^4*b^2) - 2*cos(d*x + c)/a^3 + 6*b*log(a*cos(d*x + c) + b)/a^4)/d","A",0
225,1,241,0,0.825219," ","integrate(csc(d*x+c)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3 \, a^{2} b + b^{3}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} + \frac{5 \, a^{2} b^{3} - b^{5} + 2 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)}{a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)} - \frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{\log\left(\cos\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*(3*a^2*b + b^3)*log(a*cos(d*x + c) + b)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) + (5*a^2*b^3 - b^5 + 2*(3*a^3*b^2 - a*b^4)*cos(d*x + c))/(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + (a^8 - 2*a^6*b^2 + a^4*b^4)*cos(d*x + c)^2 + 2*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c)) - log(cos(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + log(cos(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))/d","A",0
226,1,435,0,0.793308," ","integrate(csc(d*x+c)^3/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(3 \, a^{4} b + 8 \, a^{2} b^{3} + b^{5}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{{\left(a + 2 \, b\right)} \log\left(\cos\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(a - 2 \, b\right)} \log\left(\cos\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(8 \, a^{2} b^{3} + 4 \, b^{5} - {\left(a^{5} + 9 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{4} b - 10 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(11 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)}}{a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8} - {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} \cos\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)} \cos\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)} \cos\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)} \cos\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*(4*(3*a^4*b + 8*a^2*b^3 + b^5)*log(a*cos(d*x + c) + b)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - (a + 2*b)*log(cos(d*x + c) + 1)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) + (a - 2*b)*log(cos(d*x + c) - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 2*(8*a^2*b^3 + 4*b^5 - (a^5 + 9*a^3*b^2 + 2*a*b^4)*cos(d*x + c)^3 + (a^4*b - 10*a^2*b^3 - 3*b^5)*cos(d*x + c)^2 + (11*a^3*b^2 + a*b^4)*cos(d*x + c))/(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 - (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*cos(d*x + c)^4 - 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c)^3 + (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c)))/d","A",0
227,1,707,0,0.627576," ","integrate(csc(d*x+c)^5/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{48 \, {\left(a^{6} b + 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \log\left(a \cos\left(d x + c\right) + b\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{3 \, {\left(a^{2} + 3 \, a b\right)} \log\left(\cos\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{3 \, {\left(a^{2} - 3 \, a b\right)} \log\left(\cos\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(38 \, a^{4} b^{3} + 56 \, a^{2} b^{5} + 2 \, b^{7} + 3 \, {\left(a^{7} + 18 \, a^{5} b^{2} + 13 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{5} - 6 \, {\left(a^{6} b - 8 \, a^{4} b^{3} - 9 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} - {\left(5 \, a^{7} + 103 \, a^{5} b^{2} + 91 \, a^{3} b^{4} - 7 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{6} b - 23 \, a^{4} b^{3} - 26 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(55 \, a^{5} b^{2} + 46 \, a^{3} b^{4} - 5 \, a b^{6}\right)} \cos\left(d x + c\right)\right)}}{a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10} + {\left(a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} \cos\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)} \cos\left(d x + c\right)^{5} - {\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)} \cos\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)} \cos\left(d x + c\right)^{3} + {\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)} \cos\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)} \cos\left(d x + c\right)}}{16 \, d}"," ",0,"1/16*(48*(a^6*b + 5*a^4*b^3 + 2*a^2*b^5)*log(a*cos(d*x + c) + b)/(a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10) - 3*(a^2 + 3*a*b)*log(cos(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) + 3*(a^2 - 3*a*b)*log(cos(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*(38*a^4*b^3 + 56*a^2*b^5 + 2*b^7 + 3*(a^7 + 18*a^5*b^2 + 13*a^3*b^4)*cos(d*x + c)^5 - 6*(a^6*b - 8*a^4*b^3 - 9*a^2*b^5)*cos(d*x + c)^4 - (5*a^7 + 103*a^5*b^2 + 91*a^3*b^4 - 7*a*b^6)*cos(d*x + c)^3 + 4*(2*a^6*b - 23*a^4*b^3 - 26*a^2*b^5 - b^7)*cos(d*x + c)^2 + (55*a^5*b^2 + 46*a^3*b^4 - 5*a*b^6)*cos(d*x + c))/(a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10 + (a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8)*cos(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)*cos(d*x + c)^5 - (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)*cos(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)*cos(d*x + c)^3 + (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)*cos(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)*cos(d*x + c)))/d","B",0
228,-2,0,0,0.000000," ","integrate(sin(d*x+c)^6/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
229,-2,0,0,0.000000," ","integrate(sin(d*x+c)^4/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
230,-2,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
231,-2,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
232,-2,0,0,0.000000," ","integrate(csc(d*x+c)^4/(a+b*sec(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
233,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(7/2)/(b*sec(d*x + c) + a), x)","F",0
234,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(5/2)/(b*sec(d*x + c) + a), x)","F",0
235,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(3/2)/(b*sec(d*x + c) + a), x)","F",0
236,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
237,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sqrt(e*sin(d*x + c))), x)","F",0
238,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(9/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
245,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
246,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a), x)","F",0
250,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right) + a} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*csc(f*x + e)^2, x)","F",0
251,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2), x)","F",0
252,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2)*csc(f*x + e)^2, x)","F",0
253,0,0,0,0.000000," ","integrate(1/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sec(f*x + e) + a), x)","F",0
254,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{2}}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/sqrt(b*sec(f*x + e) + a), x)","F",0
255,0,0,0,0.000000," ","integrate(1/(a+b*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(-3/2), x)","F",0
256,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{2}}{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/(b*sec(f*x + e) + a)^(3/2), x)","F",0
257,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*(e*sin(d*x + c))^m, x)","F",0
258,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*(e*sin(d*x + c))^m, x)","F",0
259,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
260,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(b*sec(d*x + c) + a), x)","F",0
261,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(b*sec(d*x + c) + a)^2, x)","F",0
262,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(b*sec(d*x + c) + a)^3, x)","F",0
263,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*(e*sin(d*x + c))^m, x)","F",0
264,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*(e*sin(d*x + c))^m, x)","F",0
265,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/sqrt(b*sec(d*x + c) + a), x)","F",0
266,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{m}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^m/(b*sec(d*x + c) + a)^(3/2), x)","F",0
267,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*(e*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \left(e \sin\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*(e*sin(d*x + c))^m, x)","F",0
268,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c)^5, x)","F",0
269,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c)^3, x)","F",0
270,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c), x)","F",0
271,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*csc(d*x + c), x)","F",0
272,0,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*csc(d*x + c)^3, x)","F",0
273,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c)^4, x)","F",0
274,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c)^2, x)","F",0
275,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
276,0,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+b*sec(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*csc(d*x + c)^4, x)","F",0
277,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sin(d*x + c)^(3/2), x)","F",0
278,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*sin(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\sin\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sqrt(sin(d*x + c)), x)","F",0
279,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n/sin(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{n}}{\sqrt{\sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n/sqrt(sin(d*x + c)), x)","F",0
280,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n/sin(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{n}}{\sin\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n/sin(d*x + c)^(3/2), x)","F",0
281,-1,0,0,0.000000," ","integrate((e*csc(d*x+c))^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate((e*csc(d*x+c))^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a), x)","F",0
284,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\sqrt{e \csc\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sqrt(e*csc(d*x + c)), x)","F",0
285,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*csc(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/(e*csc(d*x + c))^(3/2), x)","F",0
286,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/(e*csc(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\left(e \csc\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/(e*csc(d*x + c))^(5/2), x)","F",0
287,-1,0,0,0.000000," ","integrate((e*csc(d*x+c))^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-1,0,0,0.000000," ","integrate((e*csc(d*x+c))^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \csc\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sqrt(e*csc(d*x + c)), x)","F",0
291,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/(e*csc(d*x + c))^(3/2), x)","F",0
292,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate((e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,-1,0,0,0.000000," ","integrate((e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
295,0,0,0,0.000000," ","integrate((e*csc(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{e \csc\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*csc(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
296,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a)), x)","F",0
297,0,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*csc(d*x + c))^(3/2)*(a*sec(d*x + c) + a)), x)","F",0
298,0,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \csc\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*csc(d*x + c))^(5/2)*(a*sec(d*x + c) + a)), x)","F",0
299,0,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \csc\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*csc(d*x + c))^(7/2)*(a*sec(d*x + c) + a)), x)","F",0
300,-1,0,0,0.000000," ","integrate((e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate((e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate((e*csc(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e \csc\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(e*csc(d*x + c))*(a*sec(d*x + c) + a)^2), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(e \csc\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*csc(d*x + c))^(3/2)*(a*sec(d*x + c) + a)^2), x)","F",0
305,-1,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate(1/(e*csc(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
